Computer laboratory exercise 1 (LAB2): Quantum chemical calculations Introduction: The objective of the second computer laboratory exercise is to get acquainted with a program for performing quantum chemical ab initio calculations and to perform calculations on different molecules to study electronic properties and reaction mechanisms. A lab report is required for LAB2. Hand in the report by submitting it on It s learning in Computer labs > Computer lab2 > Lab report LAB2, select Submit answer and upload your file. Quantum chemical calculations using Gaussian98 In this computer laboratory exercise, the quantum chemical program Gaussian98 will be used. Gaussian98 is one version of the Gaussian series of programs, where the latest and most advanced version is called Gaussian09. 1 Gaussian is one of the most widely used quantum chemical program packages for molecular applications, and is used both in industry and in many scientific areas in academia. It is a licensed software that runs on different platforms, on single CPU systems or in parallel multiprocessor systems. The program was created by John A. Pople, which received the Nobel prize in chemistry in 1998 for his development of computational methods in quantum chemistry. 2 The prize was shared with Walter Kohn for his development of the density-functional theory, a type of calculation that can be performed using Gaussian. Practical guide The terms L-, M-, and R-click refers to clicking with the left, middle and right mouse button, respectively. The g98 input file: The basic structure of a Gaussian input file (filename.inp) consists of a series of lines in an ASCII text file, and includes several different sections. Example of the contents of an input file: Sections in input file: # RHF/6-31G** Opt Freq Route section Blank line Route section done A water molecule Title section Blank line Title done 0 1 Charge and multiplicity O 0.000000 0.000000 0.000000 H 0.000000 0.756792-0.585760 H 0.000000-0.756792-0.585760 Molecular geometry Blank line Molecular specification done (Additional sections for specific job types) (Blank line) 1 http://www.gaussian.com/ 2 http://nobelprize.org/nobel_prizes/chemistry/laureates/1998/index.html 1
Route section: line begins with #. Specifies level of theory, calculation type, and other options, e.g. print options o Level of theory: QC method/basis set, e.g. HF/STO-3G, MP2/6-31G**, B3LYP/6-31G* o Calculation type: single point calculation no keyword, optimization Opt keyword, frequency calculation Freq keyword, scan along predefined coordinates Scan keyword o Print options: to be able to visualize molecular orbitals in Molekel, add print options GFPrint and Pop=Full Title section details about the calculation, not interpreted by program Molecular specification o Charge: first entry on fifth row specifies the systems total charge, e.g. 0, 1, -1 etc. o Multiplicity: is given by M = 2 S + 1, where S is the total spin. M = 1 for a singlet (all electrons paired), 2 for a doublet (i.e. one unpaired spin), 3 for a triplet (two unpaired spins) etc. o Molecular geometry: specifies the type and the position of the atomic nuclei of the system in Cartesian coordinates or Z-matrix Start a g98 calculation: Start the calculation by typing: g98.run filename & (Note filename and not filename.inp) in a terminal window. The calculation will generate an output file called filename.out. The g98 output file: The output file (filename.out) contains a lot of information about the calculation and the results. The content depends on what type of calculation that has been performed and on what print options that was specified. The units are usually Hartree (atomic unit) for energy and Ångström for distance. Examine the output file by e.g. reading it in a text editor, or using the more command in a terminal window. Alternatively, extract information from the output file by the grep command and appropriate text search string 3. Examples of important text strings in output files: It is good to make sure that the calculation has finished successfully by checking that the last line of the output file contains Normal termination of Gaussian 98. Use for instance the tail command. The total energy of the system is printed after SCF Done. In a single point calculation only one such line is found, in an optimization one line for each iteration is found. Use for instance the more or grep commands. Detailed information about molecular orbitals is listed after Molecular Orbital Coefficients. The number of steps required for convergence in a geometry optimization can be found by searching for Step number. The Mulliken charges are listed after Total atomic charges. The dipole moment is written after Tot=, one line below Dipole moment. To check the progress of an optimization the command grep -A4 Item filename.out can be useful. 3 grep text string filename.out Prints lines of filename.out matching the pattern text string 2
Visualization using Molekel4.3: Start the program by typing molekel4.3 & in a terminal window. Two windows will appear, a Molekel Main Window and a Main Interface Window. Read a molecule in xyz-format by R-click and hold in the Main Window. Choose Load > xyz, tick atomic symbol, and L-click OK. Select a file and L- click Accept. Note that Molekel4.3 does not read Gaussian input files. Load a g98 output file by R-click and hold in the Main Window. Choose Load > gaussian log. Select a file and L-click Accept. Inspect the molecule in the Main Window by rotating the molecule with the left mouse button and translating with the middle button. Zoom in or out by holding down the Shift key and using the middle button. It is possible to save the coordinates of a new molecule orientation by Write > xyz (current orient.). Change the appearance of the molecule to Ball & Stick by clicking that option in the Interface Window. Display atom labels by R-clicking the Main Window, choosing Labels and marking atom labels (unmark to remove labels). To display atomic charges (Mulliken), R-click the Main Window, choose Labels and tick atom charges ( un-tick to remove). To display dipole moment, R-click the Main Window, choose Dipole moment and read the value in Debye and/or display the dipole moment graphically by ticking the box show dipole moment. Measure atomic distances by R-clicking in the Main Window, and selecting Geometry > Distance to enter picking mode. Click on the two atoms of interest to measure the distance. The measured values are displayed in the Main Window and printed in the terminal window. Angles and dihedrals are measured similarly by Geometry > Angle and Geometry > Dihedral. Exit picking mode by M-clicking. To display molecular orbitals: o create a file (filename.macu) by R-clicking in the Main Window, choosing Compute > Orbital, selecting an orbital in the list, and clicking Accept. Type a name for the molecular orbital (filename.macu), and click Accept. o load existing macu files by R-clicking in the Main Window, and selecting Surface. Select load, choose a file from the list, and click Accept. Tick both signs, change the cutoff to e.g. 0.05 and click create surface. When loading an output file from a geometry optimization, the last (and hopefully converged) geometry is shown. To view the previous geometries, go to Animate > Series of coords. Click on first to view the starting structure, and then go through the geometries of the optimization, step by step, with next >. Unmark keep bonds for bonds to be formed and broken. Display vibrations with Animate > Frequency. Select a vibrational mode by clicking choose and then selecting a vibration in the list and clicking Accept. Click on animate to display the vibration and end with stop. Select another vibration in the same way. Click cancel to exit animation mode. 3
Exercises Save all your files for the second computer laboratory exercise in the directory Lab2 created in LAB1. Start the calculations from this directory. Download the prepared input files from the folder Computer lab 2 > Input files LAB2 on It s learning. 1. Molecular orbitals of H 2 and F 2 Calculations: Perform single point Hartree-Fock calculations using the STO-3G basis set on the diatomic molecules H 2 and F 2. Use the experimentally determined geometries (R H H =0.74 Å, and R F F =1.42 Å) and print the molecular orbitals and basis functions in the output file (keywords GFPrint and Pop=Full). Input files for these calculations are found in the files H2_MO.inp and F2_MO.inp. Analysis: Visualize the molecular orbitals using Molekel and draw molecular orbital energy diagrams for the two molecules. Verify that the molecular orbital coefficients in the output file are in agreement with the visualized molecular orbitals. Classify the molecular orbitals with symmetry labels, i.e σ or π, and indicate with an asterisk (*) if the orbital is antibonding. 2. Equilibrium geometries and reaction energy of HCN + 3 H 2 CH 4 + NH 3 Calculations: Optimize the geometries of HCN, H 2, CH 4, and NH 3 using Hartree- Fock and the 6-31G** basis set (keyword Opt). Input files are available in HCN.inp, H2.inp, CH4.inp, and NH3.inp. Analysis: Measure the covalent bond lengths of the optimized geometries using Molekel or Molden. Calculate the reaction energy (in kj/mol) for the reaction HCN + 3 H 2 CH 4 + NH 3 from the total energies of the optimized structures. Compare the computed value with the experimental U obtained from H in e.g. SI Chemical Data (remember that H = U + n RT). 3. Molecular orbitals, Mulliken charges and dipole moments of H 2 O Calculations: Perform a single point calculation at the HF/6-31G** level of theory on the experimental geometry of H 2 O, in order to study the molecular orbitals (use keywords GFPrint and Pop=Full), Mulliken charges, and dipole moment. An input file is available in H2O_MO.inp. Perform another single point calculation on the same geometry using the correlation method MP2 and the 6-31G** basis set (exchange the keyword RHF with MP2 and add the keyword Density). Analysis: In X-ray Photoelectron Spectroscopy (XPS), the ionization energy of H 2 O is about 18 ev. On the basis of the HF calculation, from which molecular orbital does the ionization occur? What does the molecular orbital look like (use Molekel to visualize)? What are the Mulliken charges of the atoms in H 2 O? How does the dipole moment calculated with the HF and MP2 methods compare to the experimental dipole moment of 1.85 Debye? Extra: Perform RHF and MP2 calculations using the near-hartree-fock-limit basis set 6-311++G(3d2f,3p2d) and compare the obtained dipole moments. 4. Product and binding energy of the HF + OH reaction Calculations: Study the acid-base reaction between HF and OH by performing a geometry optimization of the geometry enclosed in the input file OH_HF.inp using Hartree-Fock and the 6-31G** basis set. With the same method, study the reaction between Be 2+ and LiF starting from Be_LiF.inp. 4
Analysis: Describe what happens in the reactions? What product is formed? Calculate the binding energy 4 of the product complex. 5. Reaction coordinate and activation energy of a proton transfer reaction Calculations: Proton transfer reactions occur in many catalytic and biochemical reactions. Use the model system H 3 O + + H 2 O to study the energy barrier of proton transfer. A potential energy surface (PES) scan is the mapping of the PES by calculating the energy of the system at several distinct values of for instance a bond length or bond angle. In a rigid PES scan, a series of single point energies are performed on geometries in which a certain parameter is varied and the other parameters kept fixed. In a relaxed scan, however, a certain parameter is systematically varied while all other degrees of freedom are optimized. Perform a rigid potential energy surface scan at the B3LYP/6-31G** level of theory by scanning the O-H distance in steps of 0.1 Å. A starting geometry is available in H3O_H2O.inp. Analysis: In plotting program of your choice, plot the energy as a function of the O-H distance. What is the activation energy? 6. Identify the OH vibrational modes of the formic acid monomer and dimer Calculations: Perform geometry optimization and frequency calculation on formic acid (HCOOH) at the HF/6-31G* level. The input file HCOOH.inp is available. Construct a starting geometry for a hydrogen bonded HCOOH dimer 5, optimize the geometry and calculate the vibrational frequencies. Analysis: In Molekel, examine the OH vibrational modes (vibration/displacement and frequency) of the two systems. How does the dimerization affect the OH vibrational frequency? 7. Changes in molecular orbital energies of PEDOT with increasing chain length Calculations: Perform single point calculations using the B3LYP hybrid density functional and the 6-31G** basis set for 1, 2 and 3 fused monomers of 3,4- ethylenedioxythiophene (EDOT) (input files: pedot1.inp etc). Analysis: Study how the HOMO and LUMO energies change with increasing length of the organic polymer poly(3,4-ethylenedioxythiophene) (PEDOT). Identify the molecular orbital energy of the HOMO (the highest occupied orbital) and of the LUMO (the lowest unoccupied/virtual orbital), and plot both MO energies as a function of the number of fused monomers in a diagram. In addition, plot the LUMO-HOMO energy difference versus chain length. If time permits, construct polymers consisting of 4, 5 and so on molecules, geometry optimize these structures, calculate the MO energies, and extend the diagrams. 4 Binding energy = energy of the product complex sum of the energies of the monomers (opposite sign) 5 Tip for construction of dimer: in Molekel, read the HCOOH geometry twice, orient the molecules relative to each other, write current orientation of both molecules, and combine coordinates in one file. 5