Introduction to Computational Chemistry Exercise 2

Transcription

1 Introduction to Computational Chemistry Exercise 2 Intermolecular interactions and vibrational motion Lecturer: Antti Lignell Name

2 Introduction In this computer exercise, we model intermolecular interactions and vibrational properties of molecules by using computational chemistry methods. Vibrational properties of molecules are important when thermodynamic properties are studied and especially important for molecular spectroscopy. For the infrared absorption and Raman scattering measurements, the frequencies and intensities of vibrational modes are used for identification of novel and existing species. Visualization of molecular geometries and vibrations is a good tool to characterize different vibrational modes. The importance of intermolecular interactions for biological, chemical, and physical systems is difficult to overestimate. A major part of biological processes, e.g. the structure and function of proteins and DNA, is based on weak intermolecular interactions (mainly hydrogen bonding) between different species. Two molecules interacting with each other form a complex dimer, three molecules a complex trimer etc. Large systems containing a large amount of molecules are called clusters. It is an important fact that all bulk properties of materials are originating from the molecular-scale weak intermolecular forces. 2

3 1. Modeling and visualization of vibrational motion Computational part Find a minimum energy structure for formic acid molecule. The structure and parameters for preparation of a z-matrix are presented in Fig. 1. Figure 1 Trans- formic acid molecule (planar geometry) Input file: %mem=1gb #B3LYP/gen opt=z-matrix freq HCOOH B3LYP/6-31++G(d,p) opt freq 0 1 Z-matrix Z-matrix variables Basis set in general form %mem sets the maximum amount of dynamic memory for program (now 1GB) Computational method is density functional theory (DFT) -based B3LYP Freq is a keyword for frequency calculation The basis set will be given in general form. Go to webpage: 3

4 Find G** basis [different notation for G(d,p)] and choose the atoms and the proper basis set format (Gaussian94). Basis set will be opened to a separate window. Copy/Paste (after! s) the basis to your Gaussian input file. After the basis set description, always leave empty line to the input file (otherwise Gaussian job will crash). Run your Gaussian input. Make sure, that Gaussian has ended normally and fill in the following Table 1: Bond length Angle Freq mode frequency Intensity Description of mode* O1-C2 = O1-C2-O3 = 1 cm -1 C2-O3 = C2-O3-H4 = 2 cm -1 O3-H4 = O1-C2-H5 = 3 cm -1 C2-H5 = 4 cm -1 5 cm -1 6 cm -1 7 cm -1 8 cm -1 9 cm -1 * to be done by using gopenmol program Visualization part Make a new folder c:\temp\xvibs\formic to your local computer (e.g. using Windows Explorer). Transfer your Gaussian output file (filename.log) to this folder by using Putty FTP (psftp) program (instructions below). Note capital and small letters. Open Putty FTP -program go to your local xvibs-directory: lcd c:\temp\xvibs\formic Connect to the corona: open corona.csc.fi Then give your login and password. After that go to your remote work directory: cd /wrk/jlkx/ (jlkx is your login name) Download your Gaussian output file to your local computer: 4

5 get filename.log Now you can check that the file transfer was successful. Open gopenmol program from the Kurssit-folder. Make Xvibs conversion (Xvibs is a small program implemented into the gopenmol program): Run Xvibs Browse your Gaussian output and type all for the box below (makes conversion for all vibrational modes. Import molecular coordinates to the gopenmol window: File Import Coords... Browse you xvibs/formic-folder and open one of the filename.xmol-files and apply. Now you see the atoms in a gopenmol display window. You can rotate molecules by holding down left mouse button and moving cursor. Molecule can be zoomed by holding down right mouse button and moving cursor up/down. Edit molecular structure: Edit Molecule Create/Brake bonds Change atom type: View Atom type After finishing the molecular structure and the atom type, open trajectory control: Trajectory Main Select vibrational mode for visualization: *freq001.xmol refers to the mode 1 etc., remember to Import File before starting the animation. If animation runs too fast, it can be slowed down in Slowdown display (e.g. 50 ms). Check all vibrational modes and fill in description of mode in the Table 1. 5

6 2. Optimization of complex structure and calculating its energies Optimization Calculate a minimum energy structure for a complex between N 2 and HHeF molecules. The starting structure of complex is presented in Fig. 2. For the interaction energy calculation, find also minimum energy structures for N 2 and HHeF monomers. For the monomers, use the same bond lengths that for complex calculation. Figure 2 N 2 HHeF complex Xi is a dummy atom i Input file for the complex calculation: %Mem=1GB #MP2/gen opt=z-matrix pop=npa freq N2-HHeF opt MP2/6-311G(d,p) 0 1 Z-matrix Z-matrix variables Basis set in general form In principle, input file is very similar to that in the previous exercise, only additional keyword is pop=npa. This relates to the atomic charge calculation using a Natural Population Analysis method, which gives much better accuracy than default Mulliken analysis. This is important especially for estimating charges in complexes. Write down a Z-matrix and Z-matrix variables according to Fig. 2. Find general basis from the same webpage This time 6-311G(d,p) basis set (same as 6-311G**) is used. Because intermolecular forces are strongly dependent on electron correlation, we use 2 nd -order Møller-Plesset perturbation theory (MP2) for complex calculations. 6

7 Optimize the complex structure and fill in Table 2. Bond length Freq mode frequency Int Description of mode N1-N2 = 1 cm -1 N2-H4 = 2 cm -1 H4-He6 = 3 cm -1 He6-F8 = 4 cm -1 Atom NPA-charge 5 cm -1 N1 6 cm -1 N2 7 cm -1 H4 8 cm -1 He6 9 cm -1 F8 10 cm -1 * This will be done with gopenmol if we have time After that calculate the N 2 and HHeF monomers and Fill in Table 3 Bond length Freq mode frequency Int. Description of mode* Atom NPA-charge N1-N2 = 1 cm -1 N1 Bond length Freq mode frequency Int. Description of mode* N2 H1-He2 = 1 cm -1 Atom NPA-charge He2-F4 = 2 cm -1 H1 3 cm -1 He2 4 cm -1 F4 *Can be done intuitively Finally, calculate the changes in monomer bond lengths, charges, and frequencies upon complexation (value in complex value in monomer): Bond length Freq. mode frequency Atom NPA-charge N1-N2 = 1 cm -1 N1 Bond length Freq. mode frequency N2 H1-He2 = 1 cm -1 Atom NPA-charge He2-F4 = 2 cm -1 H4 Interaction energy calculations 3 cm -1 He6 4 cm -1 F8 The most simple way, interaction energy of a complex can be written as a difference between complex [E(AB)] and monomer [E(A) and E(B)] energies as presented in Eq. 1. Small letters in the same equation refer to complex (ab) and monomer (a) based basis sets. A means that a system is in complex geometry: (1) E = E AB E A E B Int ab a b 7

8 Because of the incompleteness of basis sets, monomers can steal a part of the complex partner s basis set and this artificially leads to lower values of monomer energies. This effect often overestimates the values of interaction energy (Eq. 1). The effect is referred as basis set superposition error or BSSE. Computationally, the BSSE effect can be taken into account by doing counterpoise BSSE correction where monomer energies are calculated in dimer based basis sets. This means, that the atoms of a complex partner are removed but their basis functions are left to their original positions. Then monomer energies are calculated and subtracted from the energy of the complex (Eq. 2). (2) E = E AB E A E B BSSE Int ab ab ab We calculate the counterpoise BSSE corrected interaction energy of N 2 HHeF by using following Gaussian input: %Mem=1GB #MP2/gen geom=coord counterpoise=2 N2-HHeF bsse MP2/6-311G(d,p) 0 1 N X Y Z 1 N X Y Z 1 H X Y Z 2 He X Y Z 2 F X Y Z 2 Basis set in general form geom=coord tells for the Gaussian that atoms in a molecule are given in Cartesian coordinates. Counterpoise=2 means that our complex consist of two monomers. Now instead of a Z-matrix, molecular geometry is given in Cartesian coordinates. Minimum energy structure of the complex in Cartesian can be Copy/Pasted from the output file of complex calculation. Numbers 1 and 2 in the right-most column refer to the monomer 1 and monomer 2. Finally, calculate the interaction energy, BSSE-corrected interaction energy, and BSSE error in N 2 HHeF complex by using Equations 1 and 2. = cm -1 BSSE -1 = cm BSSE error % E Int E Int 8

9 3. Questions Answer in English or Finnish to the following questions. Fill in this handout and return it to my mailbox (Antti Lignell) in Physical chemistry lab by Oct 20 th. Reviewed handout can be collected from my office (B432) after Oct 27 th. 1. What changes take place in the properties of HHeF molecule upon its complexation with N 2? 2. Why are diffuse functions important to be included into basis sets for complex calculations? (not used in this work for complexes due to limited cpu-time) 3. Explain a harmonic approximation in vibrational frequency calculations, what are its weaknesses? 4. Explain all terms in the basis sets G(2d,2p) and aug-cc-pvtz. 5. Why is counterpoise basis set superposition error (BSSE) correction used? 6. Construct a Z-matrix for the water dimer (Fig. 3). How many vibrational modes does it have? Figure 3 Water dimer (planar structure) 4. References [1] T. Engel, Quantum Chemistry and Spectroscopy (Pearson 2006), chapter 16 (computational chemistry) [2] F. Jensen, Introduction to Computational Chemistry (Whiley 2002) [3] J. B. Foresman and Æ. Frisch, Exploring Chemistry with Electronic Structure Methods (Gaussian inc., 1996) [4] Gaussian webpage 9