Virtual NanoLab. Tutorial. Version

Transcription

1 Virtual NanoLab Tutorial Version

2 Virtual NanoLab: Tutorial Version Copyright 2008 QuantumWise A/S Virtual NanoLab License to Use Agreement Licensor QuantumWise A/S Gyvelvej 20 Solrød Strand DK-2680 Denmark Introduction Each complete package, including Atomistix Virtual NanoLab(R), Atomistix ToolKit(R) and related documentation, is referred to collectively as the Software. The term use refers to the loading of the Software into computer memory, or the running of the Software in a CPU. The term Install refers to the copying of the Software to a specific location on a machine's hard drive. License Features are defined as the features in the FLEXlm license file. Licensee is defined as the end user of the Software. BY INSTALLING THIS SOFTWARE LICENSEE AGREES TO THE TERMS OF THIS AGREEMENT WHICH WILL BIND LICENSEE AND ITS EMPLOYEES. IF LICENSEE DOES NOT AGREE TO THE TERMS OF THIS AGREEMENT, LICENSOR IS UNWILLING TO LICENSE THE SOFTWARE TO LICENSEE AND LICENSEE MUST DISCONTINUE INSTALLATION OF THE SOFTWARE NOW. IN THIS CASE LICENSEE MUST IMMDEDIATELY DISCONTINUE THE DOWNLOADING PROCESS OR (IF APPLICABLE) IMMEDIATELY RETURN THE MEDIUM ON WHICH THE SOFTWARE IS STORED AND ALL AC- COMPANYING DOCUMENTATION TO THE RETAILER WHERE IT WAS PURCHASED TOGETHER WITH PROOF OF PAYMENT. 1. Delivery Licensor distributes the Software in electronic form from its website. Upon request, Licensor will ship the Software to the Licensee on other media. The additional costs of such an arrangement will be covered by the Licensee alone. 2. Grant and scope of license Subject to Licensee's compliance with the terms of this Agreement Licensor hereby grants a non-exclusive, non-transferable license to the Licensee to install and use the Software on a network server (floating license) or on an individual workstation computer (node-locked license) for a specified period of time, as indicated in the accompanying license file. With a floating license the Licensee is granted the right to run the software according to the individual number of each License Feature on any computer in the network during the time period determined in the license file. With a node-locked license the Licensee is granted the right to use the software on 1 cpu on 1 workstation, during the time period determined in the license file. Part of this software is covered by other licenses. Where relevant, these are enclosed in the installation in their original form, in conjunction with the software component they refer to. 3. Restrictions a. The Licensee may not lease, sub-license, rent, loan, translate, merge, adapt vary, modify or otherwise exploit the Software other than for the Licensee's internal business purposes. In case of an academic or non-profit license, the Licensee may use the Software exclusively for non-profit research. b. The Licensee may not de-compile, reverse engineer, or disassemble the Software, or otherwise reduce it to a human-perceivable form. c. The Licensee may not incorporate, or let others incorporate, the Software, in part or in whole, into another program that may reasonably be considered to constitute, in part or in whole, directly or indirectly, now or in the future, a potential competitor to the licensed Software. d. The Licensee may only copy the Software as part of backup and maintenance of the Licensee's computer. These archive copies may not be in use at any time and must remain in the possession and control of the Licensee. e. Under no circumstances may the Licensee publish anything based on a trial license. f. The Licensee undertakes to supervise and control the use of the Software and ensure that the Software is used in accordance with the terms of this Agreement by Licensee's employees. g. Licensee must permit the Licensor and it's representatives, at all reasonable times and on reasonable advance notice, to inspect and have access to any premises, and to the computer equipment located there, at which the Software is being kept or used, and any records kept pursuant to this Licence, for the purpose of ensuring that you are complying with the terms of this Agreement. 4. Intellectual Property Rights a. Licensee acknowledges that all intellectual property rights in the Software throughout the world belong to the Licensor, that rights in the Software are licensed (not sold) to Licensee, and that Licensee has no rights in, or to, the Software other than the right to use it in accordance with the terms of this Agreement. b. Licensee acknowledges that it has no right to have access to the Software in source code form or in unlocked coding or with comments. c. The integrity of this Software is protected by technical protection measures (TPM) so that the intellectual property rights, including copyright, in the Software of the Licensor are not misappropriated. Licensee must not attempt in any way to remove or circumvent any such TPM, nor to apply,

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5 TABLE OF CONTENTS 1. Preface Introduction The VNL Toolbar The Nanoscope Using the Molecular Builder Methane, silane, carbon tetrachloride, and 2,2-dimethyl propane with automatic adjustments Methane without automatic adjustments Eclipsed ethane Building ethanol using Join and the Molecule Cupboard Acetaldehyde from ethanol by changing oxygen atom properties Naphthalene by fusing of two benzene molecules p-benzene-dithiol from benzene and H 2 S The NanoLanguage Scripter Using the NanoLanguage Scripter Using the Method Editor tool with the NanoLanguage Scripter Optimizing the lattice parameter of a bulk system Current versus geometrical changes of a molecule Molecular systems Periodic systems One-dimensional linear chain Two-probe systems Linear chain the electrodes Linear chain the central region Molecule between metal surfaces Carbon nanotubes Creating a nanotube two-probe system The Magnetic Tunnel Junction Builder Going further with Virtual NanoLab Index v

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7 CHAPTER 1. PREFACE Welcome to Virtual NanoLab (VNL), QuantumWise's electronic structure and transport modeling software. In this Tutorial, we will demonstrate the basic features of VNL by studying a few simple nanoscale systems and show you how to create different molecule systems using the Molecular Builder tool. investigate molecule and bulk system by using the NanoLanguage Scripter tool. use the Atomic Manipulator tool to analyze two-probe systems by building a hydrogen molecule. setting up periodic systems (a lithium bulk crystal and a chain of lithium atoms). use the above molecule and crystal systems to setup two different two-probe systems: a hydrogen molecule wedged in between two semi-infinite lithium chains and a DTB molecule between [111] fcc Li surfaces. investigate ballistic transport properties of carbon nanotubes with the Nanotube Grower tool. The tutorial is organized as a guided tour through VNL where you should carry out each instructions step-by-step to gain practical experience. We recommend that you do the tutorials in order and do not jump between different topics since some steps require that the previous step is completed. You can navigate through the on-line tutorial easily in the intended order by using the links Next and Previous. From within VNL, you can access the tutorial by using the menu selection Help Tutorial. For details on how to install and start the program, please refer to the Installation Guide, which is available from the download section of the QuantumWise web site. In general, this tutorial does not aim to explain all details of the covered topics but mainly focus on presenting the basic usage of the program. For further (specific and technical) information about VNL, take a look at the section Going further with Virtual NanoLab. In addition, the following style guidelines are used throughout the tutorial Bold text is used to indicate key concepts. In some cases, the words in bold face also correspond to items in the user interface such as the text on buttons. Underlined monospace text is used for menu items (including context menus). 1

8 Preface Regular monospace text corresponds to names of files or directories. With this one exception, text set in underlined blue is a clickable link to other tutorial sections. Good luck and have fun with the tutorial. 2

9 CHAPTER 2. INTRODUCTION Virtual NanoLab (VNL) gives you access to a powerful set of modeling tools for investigating nanoscale structures through a user friendly graphical interface. The VNL software uses advanced software architecture and numerical methods to find solutions of the fundamental quantum mechanical equations describing the electronic properties of nanoscale objects, such as molecules, bulk and two-probe systems by use of the techniques density functional theory (DFT) non-equilibrium Green's functions (NEGF) Based on the these techniques, VNL can simulate the detailed electronic structure and transport properties of molecules, crystals, nanotubes, and two-probe devices. The way you work with VNL is in many aspects similar to what you would do in an actual experiment: First you set up your system using either of the Molecular Builder, the Crystal Cupboard, or the Atomic Manipulator tools. After setting up your system, you specify the details of the DFT method that should be applied to your system. You do this using either the Method Editor or the NanoLanguage Scripter tool. Once the DFT method has been defined, you select the physical properties that should be extracted from the calculation. You do this by using the NanoLanguage Scripter tool. The calculation is then performed by submitting the job to the Job Manager tool or executing it from the command line. Finally, you analyze and inspect the obtained data by using the Nanoscope and the Result Browser tools. In short, VNL is designed to bridge experimental and computational approaches by offering a spectrum of useful tools for performing virtual experiments. The NanoLanguage scripts that are generated with VNL are performed with the Atomistix ToolKit (ATK) calculation engine. Since VNL is designed with ease-of-use in mind, you do not have to be an expert in quantum chemistry and electronic structure calculations to use it. Instead, you can focus on the physical properties of the systems under investigation, and let the program handle the details of the numerical models. The numerical methods used in VNL are primarily based on first principles (ab initio) and do not, in principle, require any input parameters regarding the quantum-mechanical description 3

10 Introduction of the atomic systems. Nevertheless, as is the case in most numerical simulations, a number of accuracy parameters must be specified to define the DFT and NEGF methods. Even though detailed knowledge of the input parameters is essential for users who wish complete control of their calculations and results, non-expert users should certainly not feel intimidated by this requirement; only a small subset of the parameters are really important, and it is not difficult to understand how they work. The most relevant parameter settings are discussed in this tutorial, whereas more esoteric and complex parameters are described in detail in the VNL Manual. Note The Atomistix ToolKit (ATK) is the underlying engine performing all calculations in VNL. A complete description of all the parameters, and in many cases a longer discussion about their physical relevance, can be found in the ATK manual, which can be obtained as a PDF file from the Support section of the QuantumWise web site. Finally, we are ready to begin the tour of Virtual NanoLab. 4

11 CHAPTER 3. THE VNL TOOLBAR When you launch Virtual NanoLab (VNL), the first thing which appears is the VNL Toolbar window. Figure 3.1: The contents of the VNL Toolbar. The Toolbar provides access to all the individual tools that are used in VNL. In summary, these are Tool Icon Description Crystal Cupboard Database of bulk crystals Magnetic Tunnel Junction Builder Nanotube Grower Build your basic magnetic tunnel junction ready to be used in other VNL tools (for further modifications, use the Atomic Manipulator). Create and visualize perfect carbon nanotubes Atomic Manipulator Molecular Builder Set up two-probe systems and make modifications to magnetic tunnel junctions. Build and construct your own molecules ready to be used in other VNL tools 5

12 The VNL Toolbar Tool Icon Description Bulk Builder NanoLanguage Scripter Build and construct bulk systems ready to be studied and analyzed with other VNL tools Create complete calculation set-ups and store these as Nano- Language script. Method Editor Script Editor Job Manager Predefine DFT and NEGF parameters for reuse in the Nano- Language Scripter when generating NanoLanguage scripts. Manually edit and extend NanoLanguage scripts constructed by the different set of VNL tools. Execute scripts using the ATK computation engine. Nanoscope Visualize atomic geometries and calculated properties in 3D Result Browser Browse the contents of VNL files including all stored samples and results within them. The Toolbar icons give you quick access to tools used for creating and modifying molecule, bulk, and two-probe systems. setting up DFT calculations and defining the physical properties that should be extracted from the calculations. executing calculations, as well as inspecting and analyzing results. Before you can study the electronic properties of a system, you first have to construct a model of the atomic configuration you wish to investigate. VNL provides you with several tools that assists you in defining the geometry of complex nanoscale systems. We refer to the systems that you build as configurations. Once a configuration has been build, you store it in a NanoLanguage script on your file system. The script files can then be imported for use in other tools, where it, for example, can be modified 6

13 and exported to a new script file. Configurations from different scripts can also be combined in tools in order to define composite two-probe geometries or to perform calculations. All configurations as well as the specification of the DFT methods and calculations is stored on disk as an editable NanoLanguage script. This implies that you seamlessly can include other software application in the handling of the data flow generated by VNL: Use your favorite text editor to produce a script for setting up a skeleton model of the system you wish to study Copy-and-paste the configuration directly into the VNL tools for further fine-tuning and modification. Add the final configuration to the NanoLanguage Scripter to setup a final computation method and specify the physical analysis of your system. In VNL, results calculated for a particular sample are stored in a so-called VNLFile (stored VNLFiles carry the extension vnl). VNLFiles can be browsed, analyzed, and their data can be extracted by using the Result Browser tool, which is backwards compatible with previous versions of VNL (2.01 and earlier). Note For more information about the VNLFile and NanoLanguage Script format, please consult the section called Data handling in VNL in the VNL Manual. During the tutorial, we will become acquainted which each particular tool in VNL. To jump in, we start off by using and exploring the Nanoscope tool. 7

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15 CHAPTER 4. THE NANOSCOPE 1. Open the Nanoscope Before we start looking at the electronic structure of various systems, we will have a quick look at the Nanoscope, the tool used in Virtual NanoLab (VNL) for visualizing atomic geometries (and other things, as we shall see later). For this purpose, we will use the water molecule, defined by the icon H20 which already is present on the examples folder. navigate to the examples directory located in the directory where you installed VNL import the file molecules/h2o.vnl Now, drag-and-drop the H2O file onto a Nanoscope and a representation of the molecule appears Figure 4.1: A water molecule visualized by the Nanoscope. By default, the covalent radius is used to determine the size of the atoms. The context menu is opened by right-clicking anywhere in the Nanoscope window. 9

16 The Nanoscope 2. Rotate, zoom, and pan the camera You may think of the Nanoscope as a camera through which you observe the atomic system. The camera can be zoomed, rotated, and moved (panned) in order to obtain a different view of the system: To rotate the camera angle, hold down the left mouse button (without pressing any other keys) and move the mouse around. To zoom in and out, use the scroll-wheel of the mouse, or hold down the Ctrl key while pressing the left mouse button and move the mouse backwards and forwards. To pan the camera across the molecule, press the middle mouse button (or hold down the Shift key and press the left mouse button) and move the mouse. Initially, you may find it a bit difficult to master the mouse to obtain the desired view, but with some practice the movements should appear natural. The mouse commands described above are used also in other tools to zoom, rotate. and pan the camera in the 3D preview windows. 3. Change the properties of the plots You can change the size of the atoms and the thickness of the bonds, by choosing Properties from the context menu which appears when you right-click anywhere on the Nanoscope window. In the appearing dialog, you will find a left panel containing a list of all plots currently defined for this particular Nanoscope. To change the appearance or options for a plot, select the respective entry in the tree to see the available options. Right-clicking a plot (either in the 3D preview window or in the Properties dialog) offers the possibility to delete or rename the plot. Figure 4.2: The Properties dialog for the water molecule in the Nanoscope. 10

17 If you want to export or print the image which is displayed in the Nanoscope, right-click the plot windows and choose the corresponding entry from the Camera context menu. Exit the Nanoscope by closing the window. 11

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19 CHAPTER 5. USING THE MOLECULAR BUILDER The Molecular Builder tool provides advanced features that enable you to build and fine-tune both simple and complex molecular structures. Typical molecular properties such as bond length and bond order, hybridization, and other geometric properties are handled automatically by the Molecular Builder making the construction of even complex structures a simple task. In this chapter, we will use the Molecular Builder to set up a selection of molecules. The examples are structured in such a way that the main functionalities of the Molecular Builder has covered once you have completed all the tutorials. If you need a detailed reference account of the functional elements of Molecular Builder, please consult the VNL Manual. METHANE, SILANE, CARBON TETRACHLORIDE, AND 2,2-DIMETHYL PROPANE WITH AUTOMATIC ADJUSTMENTS The first basic operation you need to learn in order to start building your own molecules with the Molecular Builder is to insert the atomic elements of the molecule that you wish to build. There are two ways of accomplishing this task in VNL All atomic elements can be inserted using the Periodic Table tool. In addition, elements whose atomic symbol is a single letter, can be inserted by pressing the corresponding symbol on your keyboard. For example, to insert an oxygen atom, press the O key on the keyboard. In this tutorial, we will use both approaches to construct the two simple molecules shown below, namely methane (CH 4 ) and silane (SiH 4 ). 13

20 Using the Molecular Builder 1. Launching the Molecular Builder To launch the Molecular Builder tool, double-click the Molecular Builder icon on the VNL Toolbar. The main window of the Molecular Builder tool now appears Figure 5.1: The main the Molecular Builder window with an empty 3D-View. 2. Inserting a carbon atom 14

21 Methane, silane, carbon tetrachloride, and 2,2-dimethyl propane with automatic adjustments First, make sure that the option Autoadjust has been enabled. Now, insert a carbon atom by pressing the C key. This inserts an sp 3 hybridized carbon atom into the 3D-View. In addition, since Autoadjust is active, the Molecular Builder by default inserts four monovalent hydrogen atoms to satisfy the valency of the carbon atom. Since the carbon atom is sp 3 hybridized, the hydrogen atoms are positioned as the four corners of a tetrahedron with the sp 3 hybridized carbon atom as the tetrahedron center. As a result, the finished methane molecule has been constructed. The Molecular Builder main window should now displays the CH 4 molecule, as shown in Figure 5.2. Figure 5.2: A methane molecule constructed by the Molecular Builder. Note Make sure that the 3D-View of the builder is empty before you insert the carbon atom. If not, either Press Ctrl-A followed by pressing the Delete key. Right-click and choose Select all from the context menu, then press the Delete key. 3. Saving the methane molecule To use the methane molecule in a different VNL tool, first save it to the disk as a NanoLanguage script by pressing the Save/Save As button. Drag-and-drop from Molecular Builder into another open VNL tool is also supported in the following cases: the Atomic Manipulator, the Nanoscope, the NanoLanguage Scripter, and the Script Editor; see drag-and-drop. 15

22 Using the Molecular Builder 4. Building silane The carbon atom in the methane molecule was inserted by pressing the C key on the keyboard. This keyboard operation cannot be used for inserting elements whose atomic symbols consist of two letter combinations. Pressing S followed by I to insert the element Si would not work, since one sulfur and one iodine atom would be inserted into the 3D-View instead. Instead, to insert silicon, you must use the Periodic Table tool. 5. Using the Periodic Table tool First, make sure that the 3D-View is empty by pressing either the New button or using the keyboard short cut Ctrl-A + Delete. Then launch the Periodic Table tool by pressing the button Periodic Table. The Periodic Table window then appears. Figure 5.3: The Periodic Table tool. Click on the element symbol Si in the Periodic Table tool and change to the 3D-View of the main window. To insert the selected Si atom, either press the Insert key right-click in the 3D-View and select the entry Insert [Silicon (Si)] from the context menu Since the option Autoadjust is enabled, the four hydrogen atoms of the silane molecule are inserted automatically in a tetrahedral arrangement centered around the sp 3 hybridized silicon atom. The finished silane molecule is shown in Figure

23 Methane, silane, carbon tetrachloride, and 2,2-dimethyl propane with automatic adjustments Figure 5.4: A silane molecule (SiH 4 ). The central silicon atom has been inserted using the Periodic Table tool. The next task we will solve is building the two molecules carbon tetrachloride and 2,2-dimethyl propane. The structure of both molecules is shown below. 6. Building carbon tetrachloride 17

24 Using the Molecular Builder First, keep tapping the undo button until you get back to the state with the finished methane molecule. Then left-click and select all four hydrogen atoms. The 3D-View should now look as follows Then launch the Periodic Table tool by pressing the Periodic Table button and select the element Cl (chlorine). Switch back to the 3D-View, then press the Insert key or right-click and choose Replace [Chlorine (Cl)]. All the selected hydrogen atoms are replaced by chlorine yielding the desired carbon tetrachloride molecule. 7. 2,2-dimethyl propane Again, tap the undo button until you reach the state with the finished methane molecule. Then select all four hydrogen atoms, and press the C key. As a result, all hydrogen atoms are replaced by methyl groups yielding the molecule 2,2-dimethyl propane. The molecule displayed in the 3D-View is shown below. 18

25 Methane without automatic adjustments METHANE WITHOUT AUTOMATIC ADJUSTMENTS As you saw in the previous section, building a molecule such as methane is an almost trivial task in the Molecular Builder provided that the option Autoadjust is enabled. In this case, the properties and geometry of the entire molecule is handled automatically by the Molecular Builder. In many other situations, however, you will need to add some level of hand tuning when constructing your molecules. In this case, you may use the Geometry Manager tool for putting the molecule into place. Doing this will allow you to specify the bond order bond distance bond angle dihedral angle between the atomic elements of a molecule. If Autoadjust is enabled, changing atomic properties (elements, hybridization, charge, or bond order) will trigger automatic adjustments. To avoid this, disable the Autoadjust option. To learn to master the Geometry Manager tool, we will use it for constructing a methane molecule, but this time with Autoadjust disabled. 1. Inserting the atoms 19

26 Using the Molecular Builder First start an empty Molecular Builder window by double-clicking the icon If the 3D-View is not empty, either press Ctrl-A followed by pressing the Delete key. right-click and choose Select all from the context menu, then press the Delete key. Now, insert a carbon atom in the center of the 3D-View by pressing the C key. After this, insert three hydrogen atoms positioned as a triangle centered around the carbon atom. Position one of the hydrogen atoms above the central carbon atom. You insert the hydrogen by first placing the mouse cursor at the desired position followed by pressing the H key. If the initial carbon atom takes up too much space, press Ctrl and drag the mouse in the 3D- View while pressing the left mouse button until an acceptable view has been reached. Your initial setting should now look similar to this 2. Setting bond order, bond length, and angles In the 3D-View, select the top-most hydrogen atom, then the carbon atom, and finally one of the two remaining hydrogen atoms. Select the atoms by left-clicking each atom in the order H C H. Then launch the Geometry Manager tool by pressing the Geometry Manager button. 20

27 Methane without automatic adjustments Now, edit and change the two Distance fields to the value 1.09 corresponding to the correct value of the C H bond length. Since geometric operations performed in the Geometry Manager tool always operate on the last selected atom, the above change will reposition the carbon atom as well as the last selected hydrogen atom. Change the bond angle for the H C H bond to in the Angle field and use the Bond Order drop-down menu to set the bond-order of the two C H bonds to single. Switch back to the 3D-View and deselect the last selected hydrogen atom and select the other non-selected hydrogen atom. In a similar fashion, for the last selected atom, use the Geometry Manager tool for setting the respective bond order, bond length, and bond angle to single, 1.09, and The 3D-View and Geometry Manager tool now look as follows 21

28 Using the Molecular Builder Important All bond distances inserted and displayed in the Geometry Manager tool are measured in units of Ångström (Å). 3. Setting the first dihedral First, switch to the 3D-View and press Clear Selection (Ctrl-A). Then left-click one of the bottom hydrogen atoms, the carbon atom, the top hydrogen atom, and finally the other bottom hydrogen atom. Switch to the Geometry Manager tool and change the Dihedral angle to either 120 or Change to the 3D-View and press Clear Selection (Ctrl-A). Rotate and zoom the view to observe that the four atoms are positioned with the three hydrogen atoms as corners of a tetrahedron face with the carbon atom as the tetrahedron center. 22

29 Methane without automatic adjustments 4. Adding the last atom In the 3D-View, use the mouse to rotate and zoom the system until the carbon atom is centered with the three hydrogen atoms positioned behind the carbon atom Position the mouse cursor slightly off the central carbon atom and insert the fourth hydrogen atom by pressing the H key. Select the carbon atom and the newly inserted hydrogen atom in the order C H and use the Geometry Manager tool to change the bond length to Defining the last dihedral First select an arbitrary H C H bond among the back-facing hydrogen atoms. Then select the last inserted hydrogen atom. Launch the Geometry Manager tool and notice the value of the displayed dihedral angle. Change the dihedral to either 120 or -120 depending on which value is closest to the currently displayed dihedral angle. 23

30 Using the Molecular Builder 6. Final touches To finalize the construction of the methane molecule, choose any H C H bond with the first hydrogen atom chosen among the back-facing atoms and the last hydrogen atom chosen as the newly inserted hydrogen atom. Switch to the Geometry Manager tool. First set the H C H bond angle to Then change the bond order of the last C H bond to single. Press Ctrl-R (or choose Camera Reset in the 3D-View context menu) to reset the 3D-View. The finished methane will look similar to the one seen in this figure ECLIPSED ETHANE In nature, the stable conformation of the molecule ethane (C 2 H 6 ) is the so-called staggered form, where the two methyl groups are rotated 60 relative to each other around the axis connecting the two carbon atoms. In this staggered conformation, all 8 atoms are positioned as far from each other as possible giving rise to the energetically lowest possible conformation of ethane. As the rotation angle between the two methyl groups is increased, the energy of the molecule also increases reaching its maximum value at 60 where the C H bonds of the methyl groups are pairwise parallel. This conformation of ethane is called the eclipsed conformation. The eclipsed conformation is meta-stable since any infinitesimal perturbation will make the molecule relax back to the staggered state. The geometry of both the staggered and the eclipsed state is shown in Figure

31 Eclipsed ethane Figure 5.5: The staggered (a) and the eclipsed (b) configuration of an ethane molecule. When you build ethane and have the option Autoadjust enabled, the Molecular Builder will always construct the staggered version of ethane. In this tutorial, we will show you how to construct an eclipsed ethane molecule with the Molecular Builder. 1. Constructing staggered ethane Our first step will be to construct a staggered ethane molecule. Afterwards, we then convert this into the desired eclipsed conformation. First, launch an empty the Molecular Builder window by double-clicking the icon and check that the 3D-View is empty (Ctrl-A + Delete). In addition, make sure that the option Autoadjust has been enabled. Now, position the mouse cursor in the center of the screen and build a methane molecule by pressing the C key. Position the mouse cursor over one of the four hydrogen atoms and press the C key. As shown below, the entire structure will be converted into a staggered ethane molecule. 25

32 Using the Molecular Builder 2. Selecting the right atoms To change the staggered conformation into the eclipsed, select a sequence of four atoms in the order H C C H with the two hydrogen atoms rotated 60 relative to each other. 3. Setting the dihedral The eclipsed conformation can now be obtained by changing the dihedral angle between the two planes spanned by the H C C and C C H bonds. Clearly, the two planes should coincide implying that the dihedral angle should be 0. To accomplish this, launch the Geometry Manager tool by pressing the Geometry Manager button. Change the value of the Dihedral Angle field to 0. This operation generates the eclipsed ethane conformation Note Depending on your choice when selecting the H C C H chain, the dihedral angle displayed in the Geometry Manager tool may be either 60 or -60. In either case, the displayed value should be changed to 0 in order to obtain the eclipsed conformation. BUILDING ETHANOL USING JOIN AND THE MOLECULE CUPBOARD 26

33 Building ethanol using Join and the Molecule Cupboard In this tutorial, we will construct an ethanol molecule (C 2 H 5 OH) using the Join feature of the Molecular Builder as well as the Molecule Cupboard tool. The final goal of the tutorial, the ethanol molecule, is shown below 1. Prerequisites Start by building a staggered ethane molecule as discussed here. 2. Using the Molecule Cupboard tool Launch the Molecule Cupboard tool by pressing the Molecule Cupboard. Either type the string h2 in the search field or use the drop-down list and select the item Functional group. Then select the water molecule (H2O) from the list of displayed molecules. Switch to the 3D-View and position the mouse cursor away from the ethane molecule. Press the Insert key. The water molecule will be inserted into the 3D-View. 3. Joining ethane and water Left-click to select a hydrogen atom on both the water and the ethane molecule. Right-click in the 3D-View and choose Join from the context menu. The water and ethane molecule will be joined at the selected positions. 4. Alternative approaches Once you have selected the water molecule, first notice that one of the hydrogen atoms of the molecule have been selected as displayed in the preview window of the Molecule Cupboard tool. Then switch to the 3D-View, and position the mouse cursor over one of the hydrogen atoms of the ethane molecule. Then press Insert upon which the water and ethane molecule get joined. Alternatively, first select the water molecule in the Molecule Cupboard. Then switch to the 3D- View and select a hydrogen atom on the ethane molecule. Finally, right-click and choose Insert & Join 27

34 Using the Molecular Builder Furthermore, during the Join operation, auto adjustments are always active. For the current setting, this implies that Molecular Builder automatically removes one of the hydrogen atoms in order to obtain a valency preserving bond between the sp 3 hybridized carbon and the oxygen atom. As a result, the molecule ethanol has been built. ACETALDEHYDE FROM ETHANOL BY CHANGING OXYGEN ATOM PROPERTIES Here, we will show you how to construct the aldehyde molecule acetaldehyde. To this end, we will first construct an ethanol molecule and use the bond order parameter from the Geometry Manager to add the required changes to the bond between the C O bond. An acetaldehyde molecule is shown below. 1. Setting up an ethanol template Start the Molecular Builder with an empty 3D-View and make sure that the Autoadjust option is enabled. Then position the mouse cursor in the 3D-View and press the C key. This will construct a methane molecule. Then position the mouse cursor over one of the four hydrogen atoms and press the C key. The hydrogen atom is then converted into a carbon atom changing the methane molecule to ethane. Finally, position the mouse cursor over one of the six hydrogen atoms and press the O key. As displayed below, the ethane molecule is converted into ethanol. 28

35 Acetaldehyde from ethanol by changing oxygen atom properties 2. Changing the bond order of the C O bond In order to finalize the construction of the acetaldehyde molecule, we need to change the bond order of the C O from a single to a double bond. First, left-click to select both the oxygen and carbon atom that make up the C O bond. 29

36 Using the Molecular Builder Then press the Geometry Manager button and use the drop-down menu to change the bond order of the C O bond from single to double. As a result, the desired acetaldehyde molecule has been generated. Note also, that the hybridization of both the carbon and the oxygen atom has been changed from sp 3 to sp 2 as expected in a double bond. Note The automatic adjustment of the hybridization is only done if the initial hybridization of the two atoms are identical. The only exception to this rule is allene structures. 30

37 Naphthalene by fusing of two benzene molecules Figure 5.6: The molecule acetaldehyde generated by changing the bond order of the C O bond in an ethanol molecule. NAPHTHALENE BY FUSING OF TWO BENZENE MOLECULES We have already seen how the Join feature can be used for attaching molecular structures to each other. When molecules are joined in the Molecular Builder, a single bond between the two are established. In some situations, however, more than a single bond must be established in order to obtain the desired structure. In this case, you should use the Fuse functionality to build your molecule. Here, we will illustrate the use of Fuse operations by constructing the molecule naphthalene from two benzene rings: 31

38 Using the Molecular Builder 1. Adding the benzene rings Start the Molecular Builder with an empty 3D-View and launch the Molecule Cupboard. Scroll through the Molecules list and select benzene (C 6 H 6 ). Switch back to the 3D-View and press the Insert key twice. To avoid overlaps between the inserted rings, make sure to reposition the mouse cursor in-between the insertions. Your Molecular Builder window should look as shown below. 32

39 Naphthalene by fusing of two benzene molecules 2. Fusing the rings Now, left-click to select the following two sequences of atoms H C C H and C C C C. Notice, that the order of selections is important. Your selections should look as below 33

40 Using the Molecular Builder Finally, in the 3D-View, right-click on any of the selected atoms and select Fuse from the context menu. As a result of the operation, the two benzene rings get fused at the selected atoms thereby generating the desired naphthalene molecule. A 3D representation is shown below. 34

41 p-benzene-dithiol from benzene and H 2 S P-BENZENE-DITHIOL FROM BENZENE AND H 2 S The final molecule that we will construct here is p-benzene-dithiol that is, a benzene ring where two oppositely positioned hydrogen atoms have been substituted by thiol groups. A 3D representation of p-benzene-dithiol is shown below. 35

42 Using the Molecular Builder Figure 5.7: p-benzene-dithiol molecule. 1. Gathering the building blocks Start the Molecular Builder with an empty 3D-View and press Molecule Cupboard to launch the Molecule Cupboard tool. Scroll though the list of Molecules and select benzene. Switch to the 3D-View and press Insert to add the selected benzene molecule. Switch back to the Molecule Cupboard dialog and select Hydrogen sulfide. In the 3D-View, press the Insert key twice to insert an H 2 S molecule above and below the benzene ring. The 3D-View should look as follows: 36

43 p-benzene-dithiol from benzene and H 2 S 2. Joining the two H2S molecules Now, select a hydrogen atom belonging to one of the two H 2 S molecules. In addition, select the hydrogen atom located closest to the previously selected hydrogen atom. Right-click in the 3D-View, and choose Join from the context menu. As a result, the first thiol group has been added to the benzene ring. To obtain a p-benzene-dithiol molecule, similar to the one shown in Figure 5.7, repeat the above procedure to add the remaining thiol group. 3. Alternative approaches Once the benzene ring has been added to the 3D-View, position the mouse cursor over two mutually para oriented hydrogen atoms and do one of the following operations for each hydrogen atom: press S select S from the Periodic Table tool, and press Insert. select two para-h atoms. Then press S. select two para-h atoms in the 3D-View and then select S in the Periodic Table tool. Finally, press Insert or right-click and choose Replace. select two para-h atoms in the 3D-View and then select H 2 S in the Molecule Cupboard. Finally, press Insert or right-click and choose Insert & Join. 37

44 38

45 CHAPTER 6. THE NANOLANGUAGE SCRIPTER The NanoLanguage Scripter and the Method Editor tool are the main components used in VNL for setting up calculations for the molecule, bulk, or two-probe systems that you have generated using the Molecular Builder, the Crystal Cupboard, and the Atomic Manipulator tools. The basic work-flow when using the NanoLanguage Scripter typically involves the following steps: 1. Import NanoLanguage scripts (molecule, bulk, or two-probe). 2. Define the parameters that control the DFT and NEGF calculations for your configuration. 3. Determine which physical quantities should be extracted from the converged results. 4. Save all calculation settings as a script. 5. Execute your scripts using the Job Manager. In this chapter, we provide a set of tutorials, that will guide you through some of the typical steps that are required to master the usage of the NanoLanguage Scripter and the Method Editor. The complexity of the tutorials will increase as we progress, so if you are a relatively inexperienced VNL user, we recommend that you follow the tutorials in the order that they are presented. USING THE NANOLANGUAGE SCRIPTER In this tutorial, we will use the organic molecule biphenyl (C 12 H 10 ) as our system configuration. For this relatively simple molecular structure, we will demonstrate some of the most common and basic features of the NanoLanguage Scripter tool. In particular, we will cover: Importing the biphenyl molecule to the NanoLanguage Scripter. Setting up suitable parameters for the DFT calculation. Choosing the physical quantities that should be calculated for the system. In this particular case, we have chosen the total energy and the electron density of the biphenyl molecule. Saving and executing the calculation. 39

46 The NanoLanguage Scripter Accessing and visualizing the calculated physical quantities of the biphenyl system. Figure 6.1: The organic molecule biphenyl (C 12 H 10 ) used in the tutorial. 1. A short preliminary building the biphenyl molecule The first thing we need to do, is setting up the biphenyl molecule that we want to analyze. Please follow these steps in the VNL manual describing how to use the Molecular Builder tool for setting up a biphenyl molecule. Once you have completed the steps, your file system should contain a file corresponding to the created biphenyl molecule. Just for clarity, let us assign the biphenyl configuration with an appropriate file name: Rename the file to C12H10.py. We could also have used drag-and-drop to transfer the configuration from the Molecular Builder to the NanoLanguage scripter without saving it on the file system. However, since we are going to use it in more than one tutorial, we create the configuration on the disk. 2. Starting the NanoLanguage Scripter To launch the NanoLanguage Scripter tool, double-click the NanoLanguage Scripter icon As a result, the NanoLanguage Scripter window will appear: 40

47 Using the NanoLanguage Scripter 3. Adding a configuration to the NanoLanguage Scripter To add the biphenyl molecule to the NanoLanguage Scripter, drag-and-drop the file C12H10.py from your file browser to the open NanoLanguage Scripter window. The NanoLanguage Scripter window should now look as follows: 41

48 The NanoLanguage Scripter 4. Previewing the configuration If you left-click the Configuration tab in the NanoLanguage Scripter, the biphenyl molecule will be displayed. Use the mouse to rotate, zoom, and translate the displayed biphenyl molecule. 42

49 Using the NanoLanguage Scripter 5. Setting method parameters Our next task is to fine-tune some of the parameters that control the DFT calculation of the biphenyl molecule. In the NanoLanguage Scripter, we use the Method tab for that purpose. To do this, first left-click the Method tab. The NanoLanguage Scripter then changes back to: 43

50 The NanoLanguage Scripter The first thing we want to alter, is the basis set that will be used in the DFT calculation for the biphenyl molecule. You do that by using the Basis Set dialog: First, left-click and change the basis set Type from DoubleZetaPolarized to SingleZetaPolarized. This change implies that the SingleZetaPolarized basis set will used as the default basis set for all atoms of the biphenyl molecule. Since hydrogen atoms have a relatively simple electronic structure, these particular atoms do not require the application of very complex basis sets. To set a specific basis set for hydrogen only, first check the option Specify basis set by element type. Navigate to H in the Element list and then left-click to check the element. 44

51 Using the NanoLanguage Scripter Finally, change the basis set type from SingleZetaPolarized to SingleZeta. As a result, the SingleZetaPolarized basis set is now applied to all carbon atoms whereas SingleZeta is selected for all the hydrogen atoms Note The same result could have been achieved by first selecting SingleZeta for all atoms followed by assigning SingleZetaPolarized explicitly for the carbon atoms. 6. Changing additional method parameters The next thing we want to do, is to change the default size of the mesh cut-off from its default value of 150 to 100. First, select the item Electron Density from the drop-down list in the main Method tab. The following dialog window then appears inside the Method tab 45

52 The NanoLanguage Scripter Left-click in the field entitled Mesh Cut-off and change the default value from 150 to 100. We have now modified the desired set of parameters. The next task is to select the list of physical properties that should be extracted from the DFT calculation that we just finished setting up. 7. Calculating the total energy In this tutorial, we want to calculate the total energy E tot as well as the electron density of the biphenyl molecule. These quantities, as well as many other physical quantities that also can be extracted from the DFT calculation, are set via the Analysis tab. Access the Analysis tab by left-clicking it from the NanoLanguage Scripter window. As a result, the NanoLanguage Scripter window changes to: 46

53 Using the NanoLanguage Scripter Now, left-click to select the item Total energy from the Available Quantities list and press the > button. The Total energy item now appears in the Selected Quantities list. To enable the calculation of the electron density, repeat the above steps for the Electron density item. 8. Creating and running the NanoLanguage script At this point, all method and analysis parameters are defined. The next step is to perform the corresponding computation. We do this by saving the state of the NanoLanguage Scripter as a NanoLanguage Script on the file system, which we then execute. To create the file containing the script, press the Save/Save as button located on the main NanoLanguage Scripter window. As a result, the file C12H10_script.py will be created on your file system. 47

54 The NanoLanguage Scripter To execute the script, drag and drop the script icon from your file system browser into the Job Manager tool. The script is now executed resulting in the appearance of the following Log- Window The LogWindow displays a summary of both the system configuration as well as the parameters used in setting up the method and analysis. As the actual DFT calculation is started a progress log from the calculation is appended to the contents of the LogWindow. Once the script has finished, the LogWindow contains the following green lines indicating that the script has finished successfully: Use the scroll bar of the LogWindow to investigate the log output from the script execution. 9. Examining the results 48

55 Using the Method Editor tool with the NanoLanguage Scripter Once a script has finished execution, a VNLFile with the extension.vnl has been created on your file system. This VNLfile contains a copy of the configuration originally used to set up the script the calculated results (physical quantities) obtained from running the script In this particular case, the file C12H10<1>.vnl has been added to your file system. In order to examine the calculated data, do the following: To determine the total energy, do the following: From your file browser, drop the newly created file on the Result Browser tool. As a result, a new sample icon appears. Then, right-click and choose Logbook NanoLanguage. A LogBook window opens displaying the entire output generated when the script was executed. Use the scroll bar to locate the line starting with # Total Energy. Here you will find values for all energy components of the biphenyl system. In particular, we see that the total energy satisfies E tot = ev. The electron density is stored in the sample as a 3D grid structure. This data set can be visualized by using the Nanoscope tool. To visualize and investigate the electron density, drag-and-drop the sample icon C12H10<1> on a Nanoscope tool and choose Insert plot Contour plot Real Space Electron Density NanoLanguage. A plot similar to the one shown below will appear In this case, we have chosen to visualize the electron density using a 3D contour plot. Other visual representations of the grid data, such as isosurfaces and volume plots can also be generated via the context menu of the Nanoscope tool. This finishes our first NanoLanguage Scripter tutorial. If you want to continue, we suggest you continue with the next tutorial, where we will use the NanoLanguage Scripter in combination with the Method Editor tool to investigate the twisting potential energy surface of biphenyl. USING THE METHOD EDITOR TOOL WITH THE NANOLANGUAGE SCRIPTER The Method Editor tool provides you with a fast and convenient way to set-up and store calculation parameters for the optimization of the electron density. Once you have set it up, it also provides a fast way to specify all these parameters in the NanoLanguage Scripter by a drag-and- 49

56 The NanoLanguage Scripter drop action instead of going through all parameter dialogs and changing them by hand. In this section, you will learn how to Use the Method Editor tool to define calculation parameters Export the script directly to the file system Execute the job from the command line. This will be illustrated by calculating the potential energy surface when the dihedral angle between the two phenyl rings in biphenyl is changed. It is assumed that you have gone through the basic tutorial and are familiar with basic operations in VNL. We will also assume that your working folder contains the items that were used in the previous section. If this is not the case, you might need to go through some of those steps before you can continue. 1. Create configurations Similar to the previous section, we first need to generate the biphenyl configuration that we want to study. In this case, however, we will study a series of configurations, and have chosen to calculate the energy of biphenyl for the dihedral angles 0, 25, 35, 45, 55, and 90. The corresponding molecular configurations will be generated with the Molecular Builder tool. To do this you need to I. Open the Molecular Builder by dropping the biphenyl configuration from the previous section onto the molecular builder icon. II. Select the four carbon atoms that defines the dihedral angle between the two rings (see Figure 6.2). III. IV. Open the Geometry Manager by left-clicking on the Geometry Manager button. Change the dihedral angle by clicking in the input section for atom 4, change the value from 45 to 0, and close the Geometry Manager. V. Clicking on the Save/Save As button, and save the configuration on your file system in a file with the name biphenyl_0.py. 50

57 Using the Method Editor tool with the NanoLanguage Scripter Figure 6.2: Then create a number of biphenyl configurations with various dihedral angles with the Molecular Builder and save them. After you have generated all the needed configurations, the following files will be present in your working directory: biphenyl_0.py biphenyl_25.py, biphenyl_35.py, biphenyl_45.py, biphenyl_55.py, biphenyl_90.py. 2. Create and set-up the method tool Before starting to use the Method Editor tool, we need to set the calculation parameters to the values we want. In this case we are going to set up a comparatively crude but fast calculation so that running the calculations will not take too long time. In order to do this I. Open a molecule Method Editor tool by double-clicking on the associated icon in the VNL Toolbar II. Once the tool is open, we need to specify the calculation parameters we are going to use. The calculation parameters are divided into groups and can be accessed in separate dialogs. You can navigate through the dialogs by using the drop-down menu. i. Change the basis set Type in the Basis Set dialog from the default DoubleZetaPolarized to SingleZetaPolarized, (Figure 6.3). ii. Make sure the Energy Shift in the Basis Set dialog is set to 0.01 Ry, (Figure 6.3). 51

58 The NanoLanguage Scripter III. iii Change the Mesh cut-off in the Electron Density dialog to 100 Ry, (Figure 6.3).. iv. Change the Exchange Correlation Functional in the Exchange Correlation Functional dialog to GGA.PBE, (Figure 6.3). v. Make sure the Tolerance in the Iteration Control dialog is set to , (Figure 6.3). Save the settings of the Method Editor tool by pressing the Save/Save As button. Name the corresponding file approximate.py. Basis set parameters Electron density parameters Exchange correlation functional Iteration control parameters Figure 6.3: The dialog windows for the calculation parameters that are changed in this tutorial. 3. Create scripts with the NanoLanguage Scripter 52

59 Using the Method Editor tool with the NanoLanguage Scripter After defining the configuration with the Molecular builder and the calculation parameters by setting up the approximate method, we combine these elements to create a script with the NanoLanguage scripter tool. To do this, you need to I. Open the NanoLanguage Scripter that you created in the previous tutorial by drag-and-dropping the first configuration (biphenyl_0.py) on the NanoLanguage Scripter. This action loads the NanoLanguage Scripter with a biphenyl configuration associated with a dihedral angle of 0. II. Drag-and-drop the approximate method icon onto the open scripter window. This sets all the calculation parameters under the scripter Method tab to those defined in the method in step 2 Create and set-up the Method Editor. III. IV. Instruct the NanoLanguage Scripter to calculate the total energy by selecting Total energy in the Available Quantities list in the Analysis tab in the same way as was done in the previous section. Save the script to the file system by pressing the Save/Save As button. A file dialog is presented where you can specify the name of the script and in which directory you want to create it. Save the script as biphenyl_0_nls.py, and close the scripter. 4. Run the scripts and extract the data Now that your script is stored on disk, you can to execute it like any other script by typing atk biphenyl_0_nls.py > biphenyl_0.log from the command line. When the calculation has finished, open the file biphenyl_0.log and locate the line starting with # Total potential energy towards the end of the file. Note You could just as well have used the Job Manager tool to start a local execution of the script. This, however, could be inconvenient for jobs that require substantial computation time in order to finish. Now, repeat the calculation for the remaining configurations with dihedral angles 25, 35, 45, 55, and 90 using the same set-up of calculation parameters (steps 3 and 4). The energies you obtain are collected in Table 6.1, and presented in Figure 6.4. Table 6.1: Total energies for the biphenyl molecule with various dihedral angle between the two phenyl rings. ϕ / Energy / ev This is where the tutorial on the Method Editor tool ends. However, as an extra and informative exercise, you could also set up the Method Editor tool with higher accuracy, calculate the total energy using the same biphenyl configurations, and compare how different parameters affect the calculated result. A suggestion of parameters to change and values to choose is given in 53

60 The NanoLanguage Scripter Table 6.2. Just keep in mind that more accurate calculations require longer time to run. In the next tutorial, we will use the NanoLanguage Scripter to calculate some of the properties of a silicon bulk crystal system. Table 6.2: Suggested parameters and values for testing the accuracy of your calculation. The outcome of these calculations are plotted in Figure 6.4. approximate intermediate accurate Basis Set Type SingleZetaPolarized DoubleZetaPolarized DoubleZetaDoublePolarized Energy Shift 0.01 Ry Ry Ry Mesh Cut-off 100 Ry 200 Ry 300 Ry Exchange Functional Correlation GGA.PBE GGA.PBE GGA.PBE Tolerance ev ev ev Figure 6.4: The energy of biphenyl as a function of the twisting dihedral angle for the approximate (red), intermediate (green), and accurate (blue) set of calculation parameters defined in Table 6.2. Note that all curves have been shifted such that the value of the lowest point in each curve is zero. Note The accuracy of these parameters is very system-dependent, so intermediate parameters for one molecule can still be good parameters for another. You should always check how your result depends on your choice of parameters. OPTIMIZING THE LATTICE PARAMETER OF A BULK SYSTEM In this tutorial, we will look at a silicon bulk system and use the NanoLanguage Scripter tool to find the optimal lattice constant for silicon. 54

61 Optimizing the lattice parameter of a bulk system We will do this by storing six configurations each with different lattice constants. Once the NanoLanguage scripts have been created, the NanoLanguage Scripter tool will be used to create the necessary scripts for calculating the total energy of the six systems. By plotting the total bulk energy against the six lattice constants, the lattice constant α min associated with the minimum bulk energy can be deduced. 1. Creating the silicon configurations The first step will be used to create the different silicon bulks. Do this by double-clicking the the Crystal Cupboard tool and enter the string Si in the Filter field. Then left-click to choose the structure Si (alpha) followed by pressing the Save/Save as. Then drag-and-drop the saved NanoLanguage script onto the Atomic Manipulator tool. Here we will be able to change the lattice parameters for the silicon crystal. Under the Lattice tab change the Lattice parameter a to 5.0 Å and click Save/Save As to save the bulk in a NanoLanguage script called Si (alpha) 5.0.py Now, repeat the above step until you have a total of six crystal configurations on disk with lattice parameters ranging from 5.0 Å to 6.0 Å separated by increments of 0.2 Å. Once these steps are completed, the following files should be available: Si (alpha) 5.0.py, Si (alpha) 5.2.py, Si (alpha) 5.4.py, Si (alpha) 5.6.py, Si (alpha) 5.8.py, Si (alpha) 6.0.py. 2. Launching the NanoLanguage Scripter We will create the scripts by importing the six different NanoLanguage script one at a time in the NanoLanguage Scripter tool. After this, we will change some appropriate parameters and choose the physical quantity (the total energy) that we wish to calculate. First open the NanoLanguage Scripter tool, by double-clicking on its associated icon As a result, the NanoLanguage Scripter window appears 55

62 The NanoLanguage Scripter Note Observe that at this particular moment, it is not possible to change any of the parameters, since the NanoLanguage Scripter has not been informed about the system type that should be used for setting up the calculation. As a consequence, almost all tabs in the window are inactive (grayed out). 3. Importing a bulk configuration To activate the NanoLanguage Scripter functionality, import the first configuration Si (alpha) 5.0.py by drag-and-dropping it from your file browser to the NanoLanguage Scripter window (it does not matter where you drop on the window). Now that the NanoLanguage Scripter has been informed about the system type (a bulk system), the various tabs become active. Notice that the System type in the top right corner has changed from None to Bulk. In addition, the name of the NanoLanguage script file (Si (alpha) 5.0) has also appeared in the top left corner of the NanoLanguage Scripter window: 56

63 Optimizing the lattice parameter of a bulk system 4. Defining parameters for the DFT calculation The first task we will solve, is choosing some appropriate parameters for the DFT calculation; these are defined in the Method tab, which you activate by left-clicking the associated tab 57

64 The NanoLanguage Scripter To obtain more accurate results, we will change the basis set type that will be used in the DFT calculation. Click on the drop-down list and change the basis set type from DoubleZetaPolarized to DoubleZetaDoublePolarized. Many other DFT relevant settings can be changed and fine-tuned from the Method tab. You access these by choosing the relevant parameter groups from the top-level drop-down list on the Method tab. For this particular tutorial though, we leave the remaining default values. 5. Choosing the calculated physical properties Our final step in setting up the NanoLanguage Scripter is to specify the physical quantities that should be calculated from the main DFT calculation. These are accessed via the Analysis tab: left-click on the tab to display all the quantities that the NanoLanguage Scripter offers. 58

65 Optimizing the lattice parameter of a bulk system When the Analysis tab has been activated, all the available quantities for the calculation are displayed on the left side in the Available Quantities list. On the right, the list Selected Quantities displays all the quantities that you have selected (at this moment the list is empty since no choices have been made so far). In this tutorial, we are only interested in the total energy corresponding to the list term Total Energy. Therefore, left-click to select the item Total Energy in the Available Quantities list and add it to the Selected Quantities list by pressing the > button located in-between the two lists. The content of the Analysis has changed to 59

66 The NanoLanguage Scripter 6. Generating the scripts After setting up the DFT calculation using the Method tab and adding the desired physical quantity from the Analysis tab, we are ready to generate the scripts that will be used to perform the actual calculation: Simply left-click the Save button and the script file will be saved in your working directory. The generated script is named using the convention: configuration_name + _script. So in this case, the script will given then name Si (alpha) 5.0_script.py. Since the NanoLanguage Scripter stores all Method and Analysis parameters internally, it is an easy matter to generate the five additional scripts for the remaining bulks: Just drag-and-drop each bulk configuration from your file browser onto the open NanoLanguage Scripter tool and press the Save/Save As button. Repeat this procedure for the last five bulks. Once you are done, you should have created the following files: Si (alpha) 5.0_script.py, Si (alpha) 60

67 Optimizing the lattice parameter of a bulk system 5.2_script.py, Si (alpha) 5.4_script.py, Si (alpha) 5.6_script.py, Si (alpha) 5.8_script.py, Si (alpha) 6.0_script.py. 7. Executing the scripts We are now ready to perform the calculation of the total energy for the six silicon bulk systems. To execute the scripts in one single batch, do as follows: 1. Select all the bulk silicon script files on your file browser 2. Drag-and-drop the selected group of files onto the Job Manager icon located in the Toolbar. For each submitted script, a LogWindow will appear, displaying informative output about the status of the script execution. Notice also, that the title bar of the LogWindow informs you whether the script is NanoLanguageScript [Running] or NanoLanguageScript [Waiting]. In this case, the scripts are executed in successions with only one active script running at a time. Once a script has successfully finished execution, the title bar of the LogWindow changes to NanoLanguageScript [Finished]. In addition, the log output in LogWindow also contains the following line (type set in green): Terminated Normally. After all scripts have finished execution, we are ready to extract the total energy value from each of the runs. 8. Extracting and analyzing data After each successful script execution, a new VNLFile will be added to your file system. So after execution of the six scripts, the contents of your working directory will be extended with the following files: Si (alpha) 5.0(1).vnl, Si (alpha) 5.2(1).vnl, Si (alpha) 5.4 (1).vnl, Si (alpha) 5.6(1).vnl, Si (alpha) 5.8(1).vnl, Si (alpha) 6.0(1).vnl. Each of the new VNLFiles files, Si (alpha) 5.0(1).vnl,, Si (alpha) 6.0(1).vnl, contain the results (the total energy) that we specified in the Analysis tab of the NanoLanguage Scripter. You can access the results by dropping the file into the Result Browser tool. The result of examining the filer 61

68 The NanoLanguage Scripter Locate the line in the log text that reads # Total Energy. Here you will find values for all the energy components of the silicon bulk in question. In particular, for the bulk system with a lattice constant equal to 5.0 Å, the total energy E tot should be equal to ev. From all the new samples generated by the script executions, collect the values of the calculated total energies. Your result should be equal to the values displayed in the following table Table 6.3: Total energies for a silicon bulk system calculated for six different values of the bulk lattice constant α. α / Å Energy / ev A plot of the data set together with a parabolic fit is shown in Figure 6.5. The data values already reveal that the minimum energy lattice constant α min must be located somewhere between 5.2 and 5.6. Using the minimum of the parabolic fit, a more precise estimate of α min becomes 5.41 Å. 62

69 Current versus geometrical changes of a molecule Figure 6.5: The variation of the total energy E tot of a silicon bulk as a function of the lattice constant (blue circles). A parabolic fit to the points around the minimum is also shown (solid line). CURRENT VERSUS GEOMETRICAL CHANGES OF A MOLECULE In this tutorial, we will combine what we have learned in the previous tutorials to perform computations of the electron ballistic current through a molecule of experimental interest. We will do the following: 1. Use the the Molecular Builder tool to create a set of diamino biphenyl (DABP) molecules with different dihedral angles ϕ. 2. Create two-probe NanoLanguage scripts by using the Atomic Manipulator tool to place the DABP molecules in-between two gold electrodes. 3. Use the NanoLanguage Scripter tool to create NanoLanguage scripts for computing the electronic current. 4. Execute the generated scripts. 5. Obtain and analyze the calculated results, which, for example, will enable us to predict how the ballistic electron current changes as a function of the dihedral angle ϕ. 1. Creating the molecules The molecule diaminobiphenyl (DABP) has the molecular formula C 12 N 2 H 12, and is very similar to the biphenyl (C 12 H 10 ) molecule investigated in the tutorial Using the NanoLanguage Scripter. We will create several DABP molecules that only differ in their dihedral angles ϕ. To create the molecules, follow these steps: 63

70 The NanoLanguage Scripter I. Open the Molecular Builder tool by double-clicking its icon in the Toolbar. II. Left-click on the Molecule Cupboard button and select C6H6 (Benzene) from the list displayed in the Molecule Cupboard window. III. IV. Press the Insert key while the mouse cursor is placed in the 3D-View of the Molecular Builder window. A benzene ring will appear. Select one of its H atoms and press Insert again. Another ring appears, both rings are joined at the selected position. As a result, a biphenyl molecule has been created. Note that you might need to rotate or zoom out to get a clear view of the biphenyl molecule. Select one of the H atoms at the longitudinal extreme, press N. Select the opposite H atom, and press N again. This leads to the creation of the DABP molecule by inserting two amino groups in the biphenyl molecule. At this point your Molecular Builder window should look like this: Figure 6.6: One of the molecules diamino biphenyl (DABP) used in the tutorial. V. To change the dihedral angle ϕ between the planes spanned by the two rings of the DABP molecule, select a sequence of four carbon atoms, as shown in Figure 6.7. Note, that the order of the selection matters and it is color coded; so make sure that yours follow the same color sequence as that displayed in Figure 6.7: 64

71 Current versus geometrical changes of a molecule VI. VI I. Figure 6.7: The same molecule after the selection has been done aiming to change a dihedral angle. Now, launch the Geometry Manager and change the value of the dihedral angle from 45 to 0. Left-click Save/Save As in the main Molecular Builder window to save the configuration in your working directory with the name dabp0.py (where 0 stands for its dihedral angle value). Using the Molecular Builder tool, change the dihedral angle to 22, save the configuration as a NanoLanguage script, and name this dabp22.py. Repeat this procedure and create Nano- Language scripts for the dihedral angles 45, 67, and 90. VI Once you have completed these steps, your working directory should contain the following II. files: dabp0.py, dabp22.py, dabp45.py, dabp67.py, dabp90.py. 2. Placing the DABP molecules in between the gold electrodes Our next task is to place the generated DABP molecules in between the electrodes. We will use gold electrodes since it is the material of choice in actual experiments. The outcome will be five two-probe systems, each one consisting of a DABP molecule positioned in between two gold electrodes. These systems will only differ from each other in the dihedral angle ϕ of the DABP molecules. Follow these steps: 65

72 The NanoLanguage Scripter I. Open the Crystal Cupboard tool by double-clicking on its icon. Select Au from the displayed list of crystals and then left-click Save/Save As to create a NanoLanguage script called Au.py containing a gold bulk crystal. II. Open the Atomic Manipulator tool and drop the Au NanoLanguage script file on it. Rightclick on the 3D-View and select Cleave from the context menu. In the left dialog, change Surface Vector 1 (S1) from (1,0) to (2,0) Surface Vector 2 (S2) from (0,1) to (0,2) In the Two-Probe tab, change Left Surface Layers to 3. Your Atomic Manipulator tool now looks like this (you might need to press the Show button to update the window): III. Figure 6.8: The Atomic Manipulator after cleaving a gold bulk and changing the values of the surface vectors. Drop the molecule dabp45.py in between the electrodes. Set its respective origin and orientation to (0,0,15.2) and (0,90,0) in the corresponding edit fields of the molecule dialog. Set the central region width in the Two-Probe tab to Your Atomic Manipulator now looks similar to this: 66

73 Current versus geometrical changes of a molecule IV. Figure 6.9: The appearance of Atomic Manipulator after placing a DABP molecule in between two gold electrode followed by setting the DABP origin, orientation, and the central region width correctly. Click Save/Save As to save the configuration in NanoLanguage script called Au-dabp45- Au.py. Get back to the Atomic Manipulator tool again and delete the molecule: Right-click on molecule dialog and choose Delete... from the context menu. Check that the molecule has been removed and that the electrodes still remain. V. Drop another molecule, say dabp90.py in-between the electrodes. Set the same values as above and create the corresponding NanoLanguage script. Continue this procedure until you have produced two-probe configuration scripts for each of the five molecules. After this has been done, your working folder contains five additional NanoLanguage scripts: Au-dabp0- Au.py, Au-dabp22-Au.py, Au-dabp45-Au.py, Au-dabp67-Au.py and Au-dabp90- Au.py. 3. Creating the scripts. We will now create a NanoLanguage script for each of the constructed two-probe scripts. The goal is to produce a minimal intensity-voltage curve composed of two points only. We will first do this for the relaxed configuration with a dihedral angle of 45. I. Open the NanoLanguage Scripter tool and drop the file Au-dabp45-Au.py on it. In the Method tab, choose Basis Set from the drop-down list. Set Type to SingleZeta and check Specify Basis Set by Element Type. Choose the chemical element C (carbon) and set its basis set Type to DoubleZetaPolarized and Energy Shift to Except for carbon, we have chosen simple parameters for all chemical elements. This permits for a relatively quick calculation that still preserves a correct description of π-conjugated bonds. 67

74 The NanoLanguage Scripter Figure 6.10: The NanoLanguage Scripter while setting the chosen basis sets parameters. II. The next step is to customize the names of some of the files that will be generated during the execution of the actual calculation: In the Self Consistent Calculation tab, type audabp45au.nc in the Checkpoint Filename field. In the Analysis tab, type audabp45au.vnl in the VNLFile Name field. Here are the contents of the NanoLanguage Scripter window, after completion of these steps 68

75 Current versus geometrical changes of a molecule III. Figure 6.11: The Self Consistent Calculation tab after setting the Checkpoint Filename to audabp45au.nc. From the Available Quantities list, select and add the following items to the Selected Quantities list: Atomic forces Current Electron density Mulliken population Total energy Transmission spectrum. 69

76 The NanoLanguage Scripter Finally, left-click Save/Save As. This generates a script file containing all the necessary information for performing a computation with a zero-bias voltage. IV. Figure 6.12: The Analysis tab after selecting the quantities. Select the Self-Consistent Calculation tab. In the Runtime Parameters dialog, change the value of Checkpoint Filename from audabp45au.nc to audabp45au01.nc. Then check Restore calculation from checkpoint file, and type audabp45au.nc in the Checkpoint Filename field. Check Only use initial density. V. In the Analysis tab, change VNLFile Name from audabp45au.vnl to audabp45au01.vnl. Then, select the Method tab. Finally, in the menu entry labeled Electrode Voltages, change the value of Right Electrode from 0 to 0.1. Click Save/Save As to produce a new script file. Close the NanoLanguage Scripter tool. On your file system, two new script files will now be available. Make sure that these are called: Au-dabp45-Au_script.py and Au-dabp45- Au_script(1).py. 70

77 Current versus geometrical changes of a molecule VI Repeat the steps I V this time using the dabp90.py. Make sure that all file names (check. point and VNLFile names) have a 90 instead of a 45. Carry out the same steps for the remaining samples: dabp0.py, dabp22.py and dabp67.py. 4. Running the computations To run the computations, beware that the order in which the jobs are submitted matters. We will create a batch queue where the calculations are done in the order in which they have been submitted. In this case, we will simply use the local computer. I. Drop the script file labeled Au-dabp45-Au_script.py on the Job Manager tool. The execution of the script starts, and the associated log window appears. While the job is running, launch the script labeled Au-dabp45-Au_script(1).py. A log window also appears, but it will be in a waiting state until the previous job either finishes or is canceled. In this fashion, all committed jobs are placed in a simple job queue. II. Repeat these steps until all scripts have been committed to the execution queue. III. Note Remember to preserve the order in which the jobs are submitted: Since the script Audabp45-Au_script(1).py depends on the output generated by the script Audabp45-Au_script.py, Au-dabp45-Au_script.py must be submitted first. Furthermore, for computations at high bias voltage, it is recommended to use the following technique: First perform computations at zero bias and store the resulting density. Then use this density as the initial density for the computation with a higher bias. Then increase the bias voltage stepwise by reusing the previous computations as starting points. Often, this will give convergence for systems under high bias voltages, that otherwise would not converge. The required computation time for the jobs you just have committed depends on your computer power. Since it very well may take several hours, we suggest that you leave the computer overnight working on finishing the jobs. For very computational demanding tasks, we recommend that you execute the job(s) on a cluster and use the Atomistix ToolKit (ATK) directly for processing the scripts. For more information, please consult your system administrator or consult the ATK manual. Inspection of the produced log and VNLFiles will allow you to predict changes in the current for a bias voltage of 0.1 V as a function of the dihedral angle. In addition, you will be able to predict changes in the zero bias conductance, the atomic forces, and atomic charges as a function of both the bias voltage and the dihedral angle ϕ. The following figure shows the obtained current as a function of the dihedral angle. The dashed line is a function proportional to the square of the cosine of the dihedral angle. As can be seen, there is an approximate correspondence as observed in experimental studies for similar π-conjugated systems 1. 1 L. Venkataraman, J. E. Klare, C. Nuckolls, M. S. Hybertsen, and M. L. Steigerwald, Dependence of single-molecule junction conductance on molecular conformation, Nature 442,

78 The NanoLanguage Scripter Figure 6.13: The computed current for the DABP molecules between gold leads (points). The bias voltage is 0.1 V, and the current is computed for different dihedral angles ϕ ranging from 0 to 90. To highlight the approximate correspondence to a cosine-square function (dashed line), the results are displayed symmetric around ϕ = 90. Note: we include here 4 extra points that are not computed in the present tutorial. Figure 6.14: Zero bias conductance as a function of cos 2 ϕ, where ϕ is the dihedral angle. The zero bias conductance is proportional to the current at 0.1 V (as expected for the low bias regime), and is therefore also roughly proportional to cos 2 ϕ as highlighted here. 72

79 CHAPTER 7. MOLECULAR SYSTEMS 1. Open the Atomic Manipulator The first step in constructing a model for a nanoscale system is to define its atomic geometry. For this purpose, we use the tool Atomic Manipulator: To open the tool, double-click the corresponding icon in the VNL Toolbar. Note If you open an Atomic Manipulator which has been used before, the tool remembers the last used configuration. In the Atomic Manipulator, it is possible to to import existing molecules from your file system. build molecules by hand, simply by inserting the atoms at their positions. For convenience, you can define groups of atoms, which will be moved or rotated together as one single object. For complicated systems, the grouping of atoms provides a very handy way of defining different parts of the system separately (such as side-groups), and then putting them all together without distorting the internal configuration of the groups. The different groups are called molecules in the interface, but note that when saving the system, the entire system will be treated as a single molecule. By default, the Atomic Manipulator always contains at least one (empty) molecule. To insert or delete molecules 1. right-click the left gray area 2. choose Insert new molecule or Delete new molecule from the context menu Molecules can also be renamed from the context menu. 2. Insert two hydrogen atoms Atoms are inserted into a specific molecule groups by right-clicking the white area belonging to the molecule, and choosing Insert Atom from the context menu. To delete an atom from a group, 73

80 Molecular systems right-click on the corresponding line and select Delete Atom from the context menu. To create the hydrogen molecule, insert two hydrogen atoms (by default, new atoms are always inserted at the origin). The interatomic distance in a hydrogen molecule has experimentally been determined to be Å, so specify this as the X-value for one of the atoms, and let the other one remain at the origin. Note It is of course completely arbitrary whether we choose the X, Y, or Z direction as the molecular axis, but it is highly recommended to always align the molecular geometry symmetrically with respect the coordinate axes. If not, it becomes complicated to plot quantities such as the electron density as a contour plane in the Nanoscope, since this type of plot requires the specification of the normal surface. Generally, the contour surface normal should be related to the molecular symmetry directions if not, the plots can be very difficult to interpret. Figure 7.1: Using the Atomic Manipulator for creating a hydrogen molecule. The context menu shows where to click in order to insert or delete molecules. The 3D representation of the molecule in the Preview window to the right can be zoomed, rotated, and panned by using the mouse in the same way as in the Nanoscope. In order to rotate, zoom, or pan the camera, however, it is necessary to click on a part of the preview area which does not contain any atoms (i.e. the background). If you instead click on an atom and then move the mouse, the camera will be fixed while the molecule is rotated (or translated, if the Shift button is held down). This can, in principle, be used to position or orient a group, but it is difficult to achieve high precision by using this method with just the mouse. A more controlled way of positioning the groups is offered either by the entries Translate and Rotate from the context menu, or directly by specifying the origin and orientation of the group in the corresponding boxes above the atom list for each group. We will discuss these features a bit later on. 74

81 3. Save the configuration Save the hydrogen molecule to a NanoLanguage script by clicking the button Save/Save As. It is a good idea to name the file with a descriptive name such as hydrogen.py or H2.py. 75

82 76

83 CHAPTER 8. PERIODIC SYSTEMS Virtual NanoLab (VNL) is also capable of handling periodic systems. Let us first briefly look at a bulk crystal, and then move on to a linear chain of atoms, which we later will use a one of the building blocks for constructing a two-probe system. 1. Open the Crystal Cupboard The Crystal Cupboard contains over 500 predefined crystals. You are free to include any of these directly in the calculations, or use them as templates and modify certain parameters, such as the lattice constants or the chemical species of the atoms in the unit cell. Launch the Crystal Cupboard tool by double-clicking the associated icon on the VNL Toolbar. Then browse down the list to locate Li (beta) (the stable phase of Li (bcc) at room temperature). The lattice constant is already provided, corresponding to the experimental value. Note, that other allotropes of Li also are shown in the list: these are low-temperature phases, as indicated in the Crystal Information box. Here you can also find details about the lattice parameters and other relevant quantities. 77

84 Periodic systems Figure 8.1: The bcc Li crystal in the Crystal Cupboard. In the Preview window, you will find a visualization of the atoms in the basis and the primitive unit cell, spanned by the three primitive lattice vectors. In VNL, these are labeled A, B and C. The view can be rotated, zoomed, and panned in the same way as in the Nanoscope tool. 2. Create the crystal configuration Click Save/Save As to create a NanoLanguage script containing the crystal configuration. Note General periodic structures, which are not covered by any of the templates in the Crystal Cupboard, can be defined externally using a NanoLanguage script. The resulting script can then be used in VNL as any other VNL generated script file. 3. Visualize the crystal Drop the new NanoLanguage script containing the Li crystal on a Nanoscope tool. By default, the basis (a single atom in our case) and the primitive unit cell are displayed. However, when viewing periodic systems in the Nanoscope, the option Repetition is available under Bulk Atomic Configuration in the Properties dialog. Use this to repeat the basis a given number of times in the directions of the primitive lattice vectors, and in this way visualize the structure of the periodic crystal. The repetition option is also available in the Crystal Cupboard. As another example of a periodic system, we will study a linear chain of Li atoms. ONE-DIMENSIONAL LINEAR CHAIN As the second example of a periodic system, we will consider a linear chain of lithium atoms. 78

85 One-dimensional linear chain The numerical methods used in VNL cannot handle truly one-dimensional systems, but we can always represent a linear chain as a crystal with an artificially large lattice constant in two directions. This symmetry corresponds exactly to a tetragonal lattice, and we will use this for our one-dimensional system, although in reality it means that we will rather be studying a bundle of chains. However, as long as the distance between the chains is kept sufficiently large, interactions between different chains can be completely neglected. 1. Open the Crystal Cupboard Return to the Crystal Cupboard. Use the Search function to locate the available tetragonal lattices (type in tet in the search field and click the button). Among the results returned, you will find a template for a linear chain. 2. Manipulating a crystal template The provided chain is defined with a carbon atom instead of lithium, but we can easily change this by doing the following: 1. press the Save/Save As button to store the bulk configuration as a NanoLanguage script. 2. drag-and-drop the saved script onto the Atomic Manipulator tool. 1. position the cursor in the 3D preview window of the Crystal Cupboard. 2. hold down the Z key and then drag-and-drop the crystal configuration onto the Atomic Manipulator tool. This open in the crystal template in the Atomic Manipulator tool, where we can modify the elements in the basis, as well as the lattice constants. First of all, we need to replace the carbon atom by lithium. Click the tab Basis, and change C to Li in the drop-down list. Then switch back to the Lattice tab, where we will set up the lattice constants. For later purposes, we need the chain to be directed along the Z direction, so we need to make sure that the lattice constant in this direction is the right one for a chain of Li atoms. In fact, a distance of 2.88 Å between the Li atoms corresponds to a minimum in the total energy, so we enter this value for the c lattice constant. The lattice constants in the other two directions provides the spacing between the repeated copies of the chains, which we will set to something large, like 10 Å. The interested user can perform a whole series of calculations to check how large the separation needs to be in order to obtain converged results. 79

86 Periodic systems Figure 8.2: The linear lithium chain as it is defined in the Atomic Manipulator. In this figure, we have also used the possibility to repeat the basis twice in the A and B directions and 6 times in the C direction, to show how the periodic boundary conditions effectively give rise to an array of chains, with a large separation in the A and B directions. The box shows the unit cell. 3. Create the crystal configuration To store the configuration to a NanoLanguage script, click Save/Save As, and choose the file name Li 1D chain.py. We are now ready to look at transport properties of two-probe systems, the most interesting and complicated systems that VNL can handle. 80

87 CHAPTER 9. TWO-PROBE SYSTEMS In this part, we will construct two-probe systems, in which two semi-infinite electrodes are in contact through a nano-scale piece of material (or vacuum), the so called central or scattering region). In the following we will build three different two-probe configurations: A linear atomic chain A molecule between two metal surfaces A carbon nanotube While setting up each of these system, we will demonstrate different important and useful aspects of Virtual NanoLab (VNL). For a complete understanding, it is therefore important to go through all three cases. We will start with the linear chain. LINEAR CHAIN THE ELECTRODES The simplest two-probe system one can imagine is a linear chain. Let us create one as a combination of two of the previous systems of this tutorial, namely a hydrogen molecule coupled to two linear lithium chains. Provided that you followed each of the previous steps in the tutorial, you already have both of these systems present as separate files on your file system. Our first two-probe system will be constructed by joining these sub-systems using the Atomic Manipulator tool. 1. Drop the Li chain on the Atomic Manipulator The Li chain is imported in the Atomic Manipulator as a bulk crystal, which extends periodically up to infinity. But to create a two-probe system we need a couple of semi-infinite electrodes ending in surfaces. In Atomic Manipulator these are obtained by cleaving the bulk. 2. Cleave the crystal To create a surface from a bulk crystal, right-click the left panel in the Manipulator, and choose Cleave from the context menu. The tool now changes mode, from bulk crystal to two-probe manipulator, and the Li chain has been turned into two electrodes, as can be seen in the preview window. The left-hand panel has also changed, and displays the relevant properties of the electrodes. We will consider these parameters before importing the hydrogen molecule. 81

88 Two-probe systems Figure 9.1: To cleave a crystal in the Atomic Manipulator, right-click the left panel and choose Cleave from the context menu. 3. Set up the electrode cell The immediate question which arises is why there are so many lithium atoms ; the original Li configuration only contained a single Li atom (in the unit cell). There are two reasons for this, and it is important to understand these in order to judge the quality of the results obtained from the calculations. First of all, the numerical models used in VNL only account for interactions between atoms within the electrode cell plus those in the nearest repeated cell. If, in reality, there are interactions also with atoms in the next-nearest cell, these will be neglected. By making the electrode cell long enough it is always possible to make sure that all interactions are included, but unfortunately this can lead to time-consuming calculations. It is therefore up to the user to set the appropriate level of accuracy by choosing the length of the electrode cell in the C direction. This length is set by choosing the number of layers in the C direction of the surface unit cell, under the Surface tab. VNL assists the user in this process by suggesting a reasonable value for the number of layers (2, in this case). In this way, the electrode cell is constructed as small as possible, while still including enough atoms to account for all first order interactions. In addition, warnings are issued if interactions are neglected: A NOTE is displayed if only second order interactions are unaccounted for (which almost always is an acceptable approximation). A WARNING is issued if also direct interactions are disregarded due to a too short electrode cell. In addition, the surface cell must be periodic in the transport direction, which is trivially fulfilled by the Li chain. Later, we will return to this point as well as the parameters on the Surface tab. 4. Set up the screening layers Now switch to the Two-Probe tab. Note how there is a sequence of lithium atoms outside the electrode cell, extending inwards to the center of the system. These atoms are part of the central region, and are so-called surface atoms. The number of surface layers is controlled via the parameters called Surface Layers and can be set separately for the two (left/right) surfaces. It is sometimes necessary to use different values to obtain a symmetric coordination of the atoms in the central region to the surface. In the surface regions, the electron density in the electrodes 82

89 Linear chain the central region is allowed to differ from its bulk equivalent. If these regions are not long enough, such that the influence of the central region is not sufficiently screened by the surface layers, the resulting transmission spectrum will not be accurate. If, on the other hand, the surface regions are taken too wide, the calculations will take unnecessarily long time. For our calculation, two Li atoms is reasonable, and we set both left and right Surface Layers to 2. There is no strict rule for choosing a proper width of the surface region, although a good guess (at least for metallic electrodes) is to use a value that gives a surface region width comparable to the screening length. The recommended approach is to choose a conservative and small value for the Surface Layers, and then increase it systematically until the results converge. All in all, as we see the default suggestions for both the electrode cell and the surface layers provided by VNL are sufficient for this system, and we do not have to change any parameters. We will complete the two-probe system in the next section. LINEAR CHAIN THE CENTRAL REGION We still have to put in the hydrogen molecule in the central region to complete our first twoprobe system. 1. Import the hydrogen molecule Select the hydrogen molecule file and drop it on the open Atomic Manipulator window. Now, we just need to position it properly between the electrodes. 2. Rotate the molecule We used the X axis as the molecular axis earlier, so in order to make a chain in the Z direction we need to rotate it first. In this case, we may simply move the X coordinates to the Z coordinate column. A general and more powerful operation for rotating a molecule is also available: 1. right-click the molecule 2. choose Rotate from the context menu Clearly we can obtain the desired orientation of the hydrogen molecule by rotating it 90 about the Y axis. 83

90 Two-probe systems After closing the rotate dialog box, notice that the coordinates of the molecule are unchanged. This is because the numbers in the table for the atomic positions are internal coordinates referring to a given local coordinate system centered at a local origin. Each molecule has such a local coordinate system, which in turn provides a convenient method for controlling both the internal configuration of each molecule as well as the global orientation and position of all molecules. So, in order to position and orient the hydrogen molecule as desired, we need not change the coordinates, but merely provide a new origin and orientation. As noted above, the desired orientation corresponds to a single rotation of 90 about the Y axis. Instead of using the rotation tool, we could have entered this in the Orientation fields directly. In more complicated cases, however, it is not always this obvious to determine the orientation; in this case, the rotation tool is more intuitive tool to use. 3. Align the molecule with the electrode surface cell We now need to position the local coordinate system of the hydrogen molecule with respect to the global origin. Since the size of the tetragonal Li unit cell in the X and Y directions was chosen as 9.6 Å, we set the X and Y origin to 4.8 Å to center the atoms in the cell. 4. Position the molecule between the electrodes The remaining task is to position the molecule in the Z direction. Ideally, the atomic distances in this direction should be determined by relaxing the system to minimize the energy and the interatomic forces. This is a time-consuming process, which yields a H-H chain distance larger than in a free hydrogen molecule, about 0.98 Å. The Li-H separation is in turn smaller than the lattice constant in the chain (which is 2.88 Å); about 2.18 Å is a reasonable value. As an example of the power of using internal coordinates in action, let us therefore change the X position of the second H atom to 0.98 Å. To actually see the molecule while working on it, set the Z coordinate of the Origin of the molecule to 13 Å. Next, determine the position of the last Li atom in the left electrode by positioning the mouse over it (do not click it, just leave the mouse cursor placed over). If you did not change any other values, it should be positioned at 3*2.88=8.64 Å. 84

91 Linear chain the central region Note The left electrode is the one with the axes attached to it; you may have to rotate the camera to actually have the left electrode to the left in the plot! In order to position the left hydrogen atom 2.18 Å to the right of the last Li atom, it should sit at Å. This can be achieved in a very simple and general way. Right-click the atom you wish to position (i.e. the hydrogen atom closest to the left electrode), and choose Translate from the context menu. In the dialog that appears we can read off the absolute position (i.e. its coordinates in the global coordinate system); change the Z coordinate to 8.64 Å to position it on top of the last Li atom in the electrode. Click Apply ; the molecule seems to disappear, but that is just because it lies inside the Li atom. Note that the translation operation applies to the molecule as a whole (i.e. does not change the internal coordinates), but the position displayed refers to a specific atom, namely the one which was right-clicked to open the dialog. Next, Translate the molecule 2.18 Å to the right, click Apply, and then Close. Hover the mouse over the left hydrogen atom to verify that the position was set properly. Obviously, we could immediately have set the Position of the atom in the Translate dialog box to Å, but the method described above is generally very useful. Note If you forgot to change the distance between the hydrogen atoms earlier, and instead modified it after positioning the molecule, the position of the left atom will not be correct any more, since the right hydrogen atom has been positioned at the origin of the internal coordinate system. In general, be aware that changes to the internal sample of the molecule also may modify its alignment. For instance, had we chosen a counter-clockwise rotation of 90 for the hydrogen molecule, we could have changed the bond length without moving the left atom. 5. Position the right electrode Finally, we need to position the right electrode with respect to the right hydrogen atom. The Z coordinate of this H atom is Å, and to set the desired distance (again 2.18 Å) to the electrode, we right-click the first atom in the right electrode (the atom closest to the hydrogen molecule) and again choose Translate from the context menu. Set the Z coordinate of this atom to Å. Clearly, it is not possible to move the electrode in the X and Y directions. 85

92 Two-probe systems Figure 9.2: The finished setup of the Li-H2 two-probe configuration. Note that the parameter width of the central region on the Region tab changed as a result of the above operation. This particular parameter essentially describes the amount of empty space that should reserved for the molecule between the two electrodes. You may also specify the parameter, either by dragging an electrode using the left mouse button while pressing Shift simply typing in a new value The first approach demonstrated above provides the necessary control of the distance between the atoms in the central region and the right electrode, and is the recommended way for setting the width of the central region. Nevertheless, in some cases, it is straightforward to determine the width of the central region, which is defined as the distance between the two outermost layers of the electrode surfaces. In that case, simply type in the value of the width of the central region parameter. 6. Store the two-probe configuration Once the two-probe system is finished, save it as a NanoLanguage script by clicking Save/Save As; accept the suggested file name or choose a descriptive label your self. In the next section, we will consider a more advanced two-probe system, namely a molecule between two metal surfaces. MOLECULE BETWEEN METAL SURFACES In the previous section, we studied a very basic two-probe system composed of linear chain electrodes. We will now move on to a somewhat more complicated and more realistic system. The next system we consider is one of the benchmark structures for molecular electronics namely a dithiol-benzene (DTB) molecule positioned between two Au [111] surfaces. A disad- 86

93 Molecule between metal surfaces vantage of this system is that gold has 11 valence electrons resulting in very time-consuming calculations. To overcome this bottleneck, we will therefore use lithium electrodes instead of gold. Of course this means that the results will not really be comparable with the original system, but the aim of this tutorial is just to demonstrate the functionality of VNL. Once you know how to set up the structure with Li, it is a trivial matter to replace Li by Au, and redo the calculations. 1. Define an fcc Li crystal To define the Li electrode, we start out with the Crystal Cupboard. Select the Au template, and press Save/Save As. Then drag-and-drop the stored NanoLanguage script onto the Atomic Manipulator tool. Change the basis atoms to Li on the Basis tab, but keep the Au lattice constant. In this way, you can later compare the results with those of the original DTB system. Figure 9.3: To define a fcc Li crystal, we use the Au fcc template from the Crystal Cupboard, and add to the Atomic Manipulator. With this tool, we can exchange the Au basis atoms with Li atoms. Note that the configuration is still called Au in the Manipulator, so it is a good idea to rename it by right-clicking the left panel and choosing Rename from the context menu. 2. Cleave the Li crystal Right-click the left panel and choose Cleave from the context menu. Clicking the Surface tab, we then see that the default cleaving plane is [001]. It is however simple to cleave along any desired plane, by just editing the Miller indices [hkl]; in our case, we wish to use [111]. When you cleave the bulk along the [111] plane, observe that the surface unit cell contains three atoms (or, more generally, three layers, as indicated in the dialog). This is because the cleaving does not actually produce a general surface based just on the Miller indices, but rather one that can be used as an electrode in a two-probe configuration. For this to be possible, the cell must first of all have two surface unit vectors (called SA and SB in the interface) perpendicular to the transport direction. In addition, the electrode cell should be periodic in the transport direction. While it is not always possible to satisfy the latter requirement with an arbitrary combination of Miller indices and crystal symmetry, it is generally not a problem for cubic structures. As discussed earlier, the default cell suggested by VNL is always the smallest periodic cell which includes all second-order matrix elements. If you would like to make an even more precise calculation, however, it is not sufficient to increase the number of layers to 4 or 5; this introduces a stacking fault; only layer sizes of 6,9,12, will satisfy the periodicity requirement. 3. Set up the surface unit cell 87

94 Two-probe systems One of the crucial things to keep in mind when setting up two-probe systems is that VNL uses periodic boundary conditions in the directions perpendicular to the transport direction (which always is the Z direction). Therefore, the two-probe system will be repeated periodically along the surface vectors SA and SB. As a consequence, a two-probe system is effectively always equivalent to a system where two infinite surfaces are linked together by an infinite number of central regions. From this view point, it is clear that the surface cell determines the distance between points where molecules can be adsorbed on the surface. As long as the distance between these points is large enough (compared, among other things, to the size of the molecule in the relevant directions), the results are independent of the boundary conditions. The above consideration did not have to be taken into account for the Li chain system, since the lattice constants in the perpendicular directions were chosen large enough to ensure that these repeated copies did not interact with each other. This is not an option with the present Li- DTB system, as the surface unit cell is determined by the cleavage of the Li fcc crystal. We can, however, increase the distance between the repeated copies of the DTB molecule by extending the surface cell. In general, the surface vectors S1 and S2 can be expressed as linear combinations of the primitive surface vectors SA and SB, but unless there is a particular reason to change the shape of the surface cell, it is recommended to simply let S1 and S2 be multiples of SA and SB, respectively. The calculations will also run faster in this case, due to certain numerical algorithms implemented in ATK. In our case, a 4x4 unit cell provides a sufficient separation of the DTB molecules, so we set S1=4*SA and S2=4*SB (see Figure 9.4). Figure 9.4: Do the following to define a 4x4 [111] surface: Specify the Miller indices and the surface vectors on the Surface tab in the Atomic Manipulator. The Li atoms in the respective surface layers are automatically generated according to the specification of the surface unit cell. 4. Screening layers Just as for the Li chain, we need to consider the screening layers. In fcc [111] structure, we have the stacking sequence ABC. Furthermore, as shown in the interface, the left and right electrodes follow the same sequence, if we read from left to right, whereas the layers on the right electrode are added backwards. If we wish both surfaces to be of the B-type, we need two surface layers, both to the left and to the right in order to achieve an [ABC]AB-BC[ABC] stacking ordering (with [ABC] being the electrode cell). On the other hand, if we wanted the surface to be an A-type, we would need 4 layers to the left and 3 layers to the right, that is [ABC] ABCA-ABC[ABC]. For this tutorial, let us use a B surface to reduce the number of atoms in the central region. This is achieved by setting the width of the left and right surface to 4 Å and 5 Å, respectively. 88

95 Molecule between metal surfaces 5. Import the DTB molecule It is straightforward to build a DTB molecule from scratch in the Atomic Manipulator. This molecule is distributed as a VNLFile with VNL. So, in order to use the DTB molecule, just import it by choosing 1. navigate to the examples/molecules directory under the installation directory 2. open the DTB.vnl file. Note You may also find it interesting to have a look at some of the other examples shipped with VNL. Observe also, that it is possible to drag-and-drop VNLFiles onto VNL tools from a system folder. 6. Coordinate the molecule The S atoms in the DTB molecule are generally assumed to sit above a hollow site of the surface. To find such a site, we can use the fact that the Li atoms in the surface layer form equilateral triangles, so we can pick any three atoms and find the center of mass by summing the X and Y coordinates and divide by 3. One choice of 3 atoms gives the result ( , ) Å. To find the coordinates of the atoms in the surface layer, it is convenient to hide the right electrode for the moment. Right-click the right electrode, and choose Properties from the context menu. Depending on the exact position of your right-click, the Atom entry of either the bulk (electrode) or surface will be selected. Above this tree level, there is an entry called Li (or Au if you forgot to rename it earlier!). Click this, and deselect the Visible option (see below). 89

96 Two-probe systems The internal X and Y coordinates of the S atoms in the DTB molecule are (0,0); so to position the molecule correctly, we just need to use the values given above for the X and Y Origin of the entire molecule. Of course, we also need to set the correct distance from the S atom to the left surface. We will use the value 1.70 Å, and since the Z coordinate of the Li atoms in the left surface layer (the B layer) is Å, we enter the value Å for the Z coordinate of the molecule Origin. This, however, places the molecule inside the left electrode, since the original origin of the molecule was not on the S atom, but at the center of the benzene ring. The internal Z coordinate of the left S atom is Å, so to find the final position of the DTB molecule, we right-click the molecule and choose Translate from the context menu, and translate the molecule by 3.15 Å to the right. 7. Position the right electrode The final step is to set the correct distance between the right S atom and the right electrode. Start by making the right electrode visible (follow the same steps, and tick the option Visible). Then right-click an atom in the right surface layer (in the B layer) and position it at Å (the Z coordinate of the right S atom) plus 1.70 Å (same separation as before), that is at Å, using the Translate function. 90

97 Molecule between metal surfaces Figure 9.5: The finished setup of the Li-DTB-Li two-probe system. Click Save/Save As to save the two-probe setup in a file. The third and final two-probe system we will investigate is a carbon nanotube. We will create the tube using the Nanotube Grower tool and then construct a pseudo two-probe system corresponding to perfect carbon nanotube; from there it should be easy to produce, for example, a nanotube with a defect to compute its electron transport properties. 91

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99 CHAPTER 10. CARBON NANOTUBES One of the hottest research areas within nanotechnology is the topic of carbon nanotubes. For that reason, Virtual NanoLab (VNL) also comes with a Nanotube Grower tool that can be used to construct and design carbon nanotubes. To demonstrate some of the principal capabilities of the Nanotube Grower, we will describe the steps needed for building and computing the band structure of a perfect carbon nanotube. 1. Open the Nanotube Grower The Nanotube Grower is opened by double-clicking the associated icon on the VNL Toolbar. An active Nanotube Grower window is shown in Figure A nanotube is essentially characterized by just two integer parameters, known as the tube indices (n,m). The tube indices and distance between the carbon atoms can be specified in the left panel, which also shows some general information about the chosen tube. Just as for any 3D plot in VNL, the object in the Preview window can be transformed by rightclicking the preview window and choosing Properties. Similar to the Nanoscope, you may use the dialog for changing the radius of the atoms, the background color, as well as other properties of the 3D scene. 93

100 Carbon nanotubes Figure 10.1: Geometry preview of a (4,1) carbon nanotube. The size of the atoms has been reduced to emphasize the tube bond structure. The entire tube has been repeated 6 times along the tube axis. 2. Inspect the tight-binding band structure Click the Band Structure tab to get a preview of the band structure of the nanotube in the energy area around the Fermi energy. Like the 3D preview, this plot usually updates automatically when the tube indices are changed. Sometimes, however, if there are many atoms/bands, the program waits to re-display the plots until the button Show (or any point inside the plot window) is clicked, in order not to slow down the interface too much. This is automatically handled by VNL (in fact, all 3D windows behave the same way) by continuously measuring the time it takes to set up the plots. 94

101 Creating a nanotube two-probe system Figure 10.2: Tight-binding band structure of a (4,1) carbon nanotube. If we stick to the default (4,1) tube for the moment, VNL predicts that this particular tube is semimetallic. At the same time, the band structure plot appears to show a metallic structure. This is due to the fact that the preview of the band structure is generated on-the-fly using an analytic third-nearest-neighbor tight-binding formula. In this approximation, all tubes with indices n and m offset by an integer multiple of 3 will turn out metallic. This happens because the tight-binding formula does not take the proper hybridization of s and p orbitals into account. The hybridization effects are due to the fact that the graphene sheet is rolled up into a tube. On the other hand, the band gap displayed in the left side of the panel is extracted from a semi-empirical interpolation formula, which does include the curvature effect. The measurements on which this method is based reveal that only armchair tubes (n = m) are truly metallic which also follows from a more careful theoretical analysis. 3. Create a metallic (4,4) tube Here we will construct a metallic nanotube, which would is more suitable for building conductive electrodes, which we will do in a later step. Therefore, change the tube indices to (4,4) and click Save/Save As. The configuration stored in the resulting NanoLanguage script is of bulk type. In the following, we demonstrate how to create a perfect nanotube by setting this up as a two-probe system. CREATING A NANOTUBE TWO-PROBE SYSTEM Constructing a perfect carbon nanotube as a two-probe system will serve as a starting point for studying transport properties of the tube under high bias voltages as well as in the presence of defects. In this tutorial, we will limit ourselves to the first necessary step: the construction of a perfect nanotube not as a bulk, but as a two-probe system. For this purpose, we need to define 95

102 Carbon nanotubes one part of the infinite, perfect nanotube as the left electrode one part as the central region one part as the right electrode. As a consequence, we first need to cleave the tube in half and then glue it back together. All these operations are carried out using the Atomic Manipulator. In this case, it would appear that a central region is redundant; by just gluing the two electrodes together, we would immediately have a perfect nanotube. For numerical reasons, this is not recommended. If we did set up the system this way, there would be direct interactions between the two electrodes and this is not allowed in the algorithms used for calculating two-probe systems. This is a general consideration that always must be observed: Always make the number of surface layers large enough, even if the central region is identical to the electrodes. 1. Cleave the nanotube The first thing you must do is to locate the NanoLanguage script that contains the nanotube configuration created above. Then drop the file onto an open Atomic Manipulator tool. Since the Nanotube Grower creates tubes that are aligned along the Z-axis, the tubes can immediately be turned into electrodes by right-clicking the left panel and choose Cleave from the context menu. In this case, there are no surface parameters, since its definition makes no sense for one-dimensional systems; cleaving a nanotube just means cutting it in half. In order not to neglect any matrix elements, you may still set the number of tube Periods within the electrode cell. Normally, however, a single period is sufficient for including all second-order matrix elements even for armchair tubes, which have the shortest possible period (they consist of just two layers). 2. Check the electrode cell Although the nanotube is one-dimensional, the electrode unit cell is kept three-dimensional for numerical reasons. As discussed earlier, the size of the electrode cell is chosen sufficiently large to make sure that the nanotube does not interact with its own repeated copies (due to the periodic boundary conditions in the transverse plane). Where you not able to control the size of the electrode unit cell in the X-Y plane, this would lead to problems for two-probe systems: Imagine a molecule inserted between the two tube electrodes; if the molecule is larger than the electrode unit cell, the two-probe system will not be valid due to overlaps between the repeated copies of the molecule caused by the periodic boundary conditions in the transverse plane. So, when nanotubes are used as electrodes, an additional parameter, called the Padding Factor, is available for extending the electrode unit cell in the X-Y plane. By default, the padding factor is zero; a value of 1 corresponds to twice as large a cell, whereas a negative value (which is not recommended) makes the cell smaller than the default size. 3. Represent the perfect nanotube as a two-probe system As described above, we are forced to add a few additional nanotube periods to the central region in order to avoid any direct interactions between the electrodes. Therefore, drop the (4,4) carbon nanotube again on the opened Manipulator. If a nanotube is dropped on a Manipulator that already contains a two-probe system, it does not replace the electrodes. Instead, it is imported as part of the central region where it can be positioned and repeated (but not rotated). This feature makes it possible to set up e.g. metal-nanotube-metal two-probe systems. We also need to take make sure that the surfaces correspond to an integer number of tube periods. Let us use two layers (i.e. one nanotube period) both to the left and the right, and two 96

103 Creating a nanotube two-probe system periods in the middle. In total, there will be 8 layers (four periods) and thereby 64 atoms in the central region. To obtain one full period in both the left and right segments, we need to set the left/right surface layers to 2 (see the VNL Manual for more details). Note It is actually not the number of repetitions or the number of surface layers which is relevant, but rather the total number of layers in the central region, which must be of a sufficient size to achieve proper screening for a perfectly periodic system. This is simply a requirement in the algorithms used to calculate two-probe systems. So, alternatively, we could have used a single period in the central region, and compensate for this by increasing the surface layers accordingly; in fact, we could have skipped the nanotube in the central region completely and just used the surfaces to define the central region. The motivation for setting up the system as we did was pedagogical (rather than physical or numerical) with a primary purpose of illustrating how to include a nanotube in the central region. It should also be noted that a surface layer is defined as atoms that have a unique Z- value. For the (4,4) nanotube, it is pretty convenient, but for other tube indices it means that a layer can contain a single atom, which might require a bit more attention to get the correct alignment. Figure 10.3: A perfect carbon nanotube, set up as a two-probe system in order to prepare it for a calculation. For clarity, the unit cells of the left electrode and the nanotube in the central region have been hidden. Finally, to obtain a perfect match for the periodicity of the tube, we need to position the nanotube in the central region and set the central region width. If the periodicity is broken just slightly, you will typically see a gap in the transmission spectrum around the Fermi level. The same will happen if the electrode cell is too small in the transverse directions resulting in residual electrostatic interactions (or direct basis set overlaps) between the repeated copies of the electrodes. A perfect match is achieved by setting the origin of the nanotube 3 times the nanotube period length (7.389 Å), whereas the central region width should be one layer (half a period) shorter, that is Å. 97

104 Carbon nanotubes Click Save/Save As to create ananolanguage script file containing a perfect nanotube, but now stored as a two-probe configuration. The configuration is now ready for setting up electronic transport calculations. 98

105 CHAPTER 11. THE MAGNETIC TUNNEL JUNCTION BUILDER The Magnetic Tunnel Junction Builder tool is used in VNL for setting up calculations for a special type of two-probe systems: A magnetic tunnel junction. Magnetic tunnel junctions are devices that can be modeled as an insulating thin layer sandwiched between magnetic metal electrodes. In this tutorial we will: 1. Use the Magnetic Tunnel Junction Builder tool to build several Fe-MgO-Fe junctions with increasing depth of the insulating magnesium oxide layers. 2. Create NanoLanguage scripts with the NanoLanguage Scripter tool to calculate the zero-bias conductance for the configurations we have created both with anti-parallel and parallel magnetic polarization of the electrodes. 3. Create a simple batch queue using the Job Manager tool to run all the jobs. 4. Analyze the resulting data. We will guide you through some of the steps that you typically will do when you are working with magnetic tunnel junctions. Even though the tutorial takes you through everything step-bystep, it is assumed that you know the basics of how to work with VNL. 1. Building the magnetic tunnel junctions. To launch the Magnetic Tunnel Junction Builder tool, double-click the icon in the Virtual NanoLab Toolbar. The tool will open up, displaying the magnetic tunnel junction initialized with default settings: 99

106 The Magnetic Tunnel Junction Builder Figure 11.1: The Magnetic Tunnel Junction Builder tool main window. Using this tool, we will create a series of systems to model iron-magnesium oxide-iron interfaces, Fe-MgO-Fe, where the depth of the insulating magnesium oxide layer is of just a few atomic layers. We will first adjust a few geometrical parameters to make the structures closer to the relaxed one: the minimum of the total potential energy. Note that this tutorial does not aim to fully relax the structure by finely adjusting all lattice constants and geometrical parameters, but to give a general scope of how to work with magnetic tunnel junctions. Define your system by taking the following steps. I. Choose Fe in the Material (bcc, 100) drop-down list located under Electrodes. Make sure that the other values are set as follows: Lattice constant (A) = 2.866, and Layers = 4. II. Under Surface layers set: Left surface= 2, Right surface= 2, Last layer separation (A)= 1.2, and Surface-oxygen distance (A) = 2.0. III. IV. Under Scattering region set: Material (B2)= MgO, Number of Layers= 2, Oxygen buckling (A)= 0.2, and all Layer separations = (the default value). Under Global repetition set: Repetition along A= 1, Repetition along B= 1. Now, all parameters have been set to produce the first magnetic tunnel junction (with 2 layers of MgO between Fe electrodes). Next, create the configuration with these settings by left-click- 100

107 ing the button labeled Save/Save As. This will create a file called Fe-MgO-Fe.py, in your working folder. Rename it to Fe-MgO_2Layers-Fe.py. Next, return to the Magnetic Tunnel Junction Builder tool, and change the Number of Layers to 3 in the Scattering region group box. Then create the corresponding NanoLanguage script and name this Fe-MgO_3Layers-Fe.py. Analogously, create the configurations and associated files for systems with 4 and 5 MgO layers. Now, you should have the following files in your working directory: Fe-MgO_2Layers- Fe.py, Fe-MgO_3Layers-Fe.py, Fe-MgO_4Layers-Fe.py, Fe-MgO_5Layers-Fe.py. The files should contain the configuration for magnetic tunnel junctions with, respectively, 2, 3, 4 and 5 layers of MgO between Fe electrodes. 2. Creating the scripts for the calculations. The next step is to set up NanoLanguage scripts using the NanoLanguage Scripter tool to calculate the spin polarized transport properties (i.e. the transmission spectrum) for all the magnetic tunnel junction configurations you have just built. This you do by Loading a magnetic tunnel junction configuration Setting the calculation parameters that specifies how to calculate the electron density Setting the density file Selecting what properties to calculate Modifying the created script Open the NanoLanguage Scripter tool by double-clicking the icon. Loading a configuration Once you have opened the NanoLanguage Scripter, add one of the configurations you created by drag-and-dropping the configuration file Fe-MgO_2Layers-Fe.py from your file browser onto the open NanoLanguage Scripter window. The system is now loaded into the NanoLanguage Scripter, and the Configuration tab shows the structure. You can also open and load the NanoLanguage Scripter directly by drag-and-drop the configuration directly from the Magnetic Tunnel Junction Builder 3D-window to the Scripter icon on the toolbar. 101

108 The Magnetic Tunnel Junction Builder Figure 11.2: The Configuration tab in the NanoLanguage Scripter showing the magnetic tunnel junction system with two layers of insulating MgO material. Setting calculation parameters The next step is to specify the parameters for the calculation. It is far from trivial to select an optimal set of parameters, but the general rule of thumb is to select something that is reasonable (typically, the default initial guesses will), and then vary some of the most pertinent parameters to see if the result changes. In this tutorial, we have chosen to change quite a few parameters from their default values in order to increase the convergence and accuracy of the calculation. Note It is far from obvious that these settings are good for your system, instead you should always check how your result depends on your choice of parameters. 102

109 Start by left-clicking the Method tab. This opens the first of the method dialog windows: Figure 11.3: The Method tab in the NanoLanguage Scripter. You navigate through the different method dialog windows by using the drop-down list, which is initially set to Basis set. The parameters regulating how to solve the SCF equation is divided into groups that are displayed on different dialog windows. These can be navigated through using the top-level dropdown list of the Method tab, and is set to Basis set in Figure In this tutorial, we leave most parameters to their default values, but find that changing some of the parameters increase accuracy and convergence. I. Navigate to the Brillouin-Zone-Integration dialog window by choosing Brillouin Zone Integration from the drop-down list. Set the Number of k-points to 5 in the A and B directions, 103

110 The Magnetic Tunnel Junction Builder and 100 in the C direction. C is always taken as the transport direction and typically requires much higher k-point sampling than the transversal directions (A and B). II. Navigate to the Eigenstate-Occupation dialog window by choosing Eigenstate Occupation from the drop-down list, and set the Electrode Temperature to 1300 K for both the left and the right electrodes. III. IV. Navigate to the Electron-Density dialog window by choosing Electron Density from the drop-down list, and check the Heterogeneous check box under the frame for Spin. This enables you to specify the parameters in this window individually for the central region, for the left, and the right electrodes. Check the Initial Scaled Spin radio button and set the value to 1 in the three input fields (left, central, and right). This instructs the program to start with the highest possible spin polarization on all atoms when solving the SCF equation. Note It is not necessary to specify the electrodes separately in the case of electrodes with parallel spin configuration, but since it is necessary in the anti-parallel, we also do it for the parallel case in this tutorial. For the anti-parallel spin configuration, you specify 1 for the left electrode and -1 for the right electrode. Navigate to the Energy-Contour dialog window by choosing Energy Contour from the dropdown list. Set the Integral Lower Bound to 30 Ry and the Real Axis Infinitesimal to 0.1 ev. V. Navigate to the Exchange-Correlation-Functional dialog window by choosing Exchange Correlation Functional from the drop-down list, and select GGA.PBE from the Exchange Correlation Functional drop-down list. VI. VI I. Navigate to the Iteration-Control dialog window by choosing Iteration Control from the drop-down list, and set the Max Steps to This is usually not necessary with these parameters, but it is always better to specify too many iterations than too few. Navigate to the Iteration-Mixing dialog window by choosing Iteration Mixing from the dropdown list, and set the Diagonal Mixing Parameter to 0.05 and the History Steps to 10. VI Navigate to the TwoProbe-Algorithm dialog window by choosing TwoProbe Algorithm from II. the drop-down list, and set the Electrode constraint to RealSpaceDensity, Setting the checkpoint file After you have set up all the calculation parameters in the Method tab, left-click on the Self- Consistent Calculation tab. Type Fe-MgO_2Layers-Fe.nc in the Checkpoint Filename input field to specify the name of the checkpoint file. The scripter window now looks like this 104

111 Figure 11.4: The Self-Consistent Calculation tab in the NanoLanguage Scripter after you have set the checkpoint filename. Setting properties Now that we have set up all the parameters to calculate and store the electron density, we also need to specify which properties to calculate for the system. This is done from the Analysis tab. Left-click the Analysis tab. Figure 11.5 shows the Analysis tab when you are done setting up the properties in this tutorial. First, make sure the Store Results in VNL File is checked, and specify the name of the VNLFile by typing Fe-MgO_2Layers-Fe.vnl in the VNLFile Name input field. Second, select Total energy from the Available Quantities list and press the > button to calculate and print out the total energy. Total energy now appears in the Selected Quantities list to the right. Similarly, select Transmission spectrum from the Available Quantities list and press the > button. Transmission spectrum appears now in the Selected Quantities list to the right. Left-click the Transmission spectrum in the Selected Quantities list; a Calculate Transmission Spectrum panel appears. Specify that the transmission spectrum is calculated for 41 energies equally distributed from -0.2 to 0.2 ev by typing 41, -0.2, and 0.2 in the three Energies input fields. Change the number of k-points in the Brillouin zone integration to 5 by modifying Number of k-points both for the A and B directions. The scripter window looks now like this 105

112 The Magnetic Tunnel Junction Builder Figure 11.5: The Analysis tab in the NanoLanguage Scripter. You select the properties you want to calculate by selecting a function from the Available Quantities list and moving it over to the Available Quantities list by pressing the > button. When you have specified all the parameters in the scripter, create your NanoLanguage script by left-clicking Save/Save As. A script named twoprobe_configuration_script.py is created in your working folder. Rename it to Fe-MgO_2Layers-Fe.py. Now, we have created the NanoLanguage script for the parallel spin configuration and are ready to submit the script. However, before we do that we go back to the Method tab to generate a script to calculate the anti-parallel spin system. Generating the anti-parallel case and modifying the script Return to the Method tab and navigate to the electron-density dialog window. Change the initial scaled spin for the right electrode from 1 to -1; leave the other parameters the way they are. Generate a new script by left-clicking Save/Save As, and rename the script. Open the generated NanoLanguage script with your favorite editor, and locate the section where the density parameters are defined for the central region, it should be lines if you have followed this tutorial, which looks like this: electron_density_parameters = electrondensityparameters( mesh_cutoff = 150.0*Rydberg, 106

113 ) initial_scaled_spin = [ 1., 1., 1., 1., 1., 1., 1., 1., 1., 1. ] Modify the elements in the list to look like this: electron_density_parameters = electrondensityparameters( mesh_cutoff = 150.0*Rydberg, initial_scaled_spin = [ 1., 1., 0., 0., 0., 0., 0., 0., -1., -1. ] ) This sets the initial spin-polarization of each surface atom to the maximum spin-up value for the left electrode and the maximum spin-down value for the right electrode. This is also what we want for the anti-parallel spin configuration. The insulating MgO layer is spin unpolarized and should therefore have the values 0; since MgO is a closed shell system, however, it does not make any difference if you leave these at the value 1. Now, create the scripts for the remaining configurations, i.e. Fe-MgO_3Layers-Fe.py, Fe- MgO_4Layers-Fe.py, and Fe-MgO_5Layers-Fe.py. 3. Running the jobs. To create a simple batch queue for execution on a local system, the Job Manager tool can be used. From your file browser, simply drag-and-drop all the script files created in the previous section one by one onto the icon of the Job Manager tool (the tool is located in the Virtual NanoLab Toolbar. The calculations will be executed in the order that they were submitted. Note that these calculations are relatively time consuming and it will take a powerful CPU and some patience to get the corresponding results. Depending on your CPU and memory, you might need to leave a single computer running for a couple of days. An alternative method, that would eventually allow you to save time, is to execute the computations externally and in parallel if possible, using ATK. Note that several licenses for the Atomistix ToolKit are needed in this case. 4. Analyzing the obtained results. We expect that the conductance of the magnetic tunnel junction device drops exponentially with the thickness of the central insulating layer (in this case the MgO layer). This is caused by the fact that the insulating layer acts as a tunneling barrier for the incident electrons, which is well-known property of 1D systems. Note that this is approximately a 1D case since the important variations of the system are only along the Z axis. The other expectation and this is why these devices have a high technological interest is that the electrical conductance is strongly dependent on the magnetic polarization of the electrodes. When both electrodes have the same magnetic polarization (parallel polarization case) the conductance should be higher than in the case when both electrodes have opposite magnetization. In fact, for some devices, the difference in conductance between the parallel case and the anti-parallel can be of several orders of magnitude. The results of this tutorial already show both of the above mentioned effects. In the following figure, we have plotted the conductance of the iron-magnesium oxide-iron junctions as a function of the number of MgO layers, both for the parallel and anti-parallel cases. 107

114 The Magnetic Tunnel Junction Builder Figure 11.6: Conductance of the Fe-MgO-Fe junction as a function of the number of MgO layers. Both the parallel (red dots) and anti-parallel (green dots) magnetic polarization cases can be seen. As expected, the conductance of the device is much larger for the parallel polarization case and it decreases exponentially with the number of layers (solid lines are exponential fits). 108