Advanced Quantum Chemistry Lecture: MO Calculations and Gaussian Program Usage

CHE-30042 Inorganic, Physical & Solid State Chemistry Advanced Quantum Chemistry: lecture 5 Rob Jackson LJ1.16, 01782 733042 r.a.jackson@keele.ac.uk www.facebook.com/robjteaching @robajackson

Lecture 5 contents 1. An example of molecular orbital calculations: HF Showing how MO diagrams and calculation results relate to each other. 2. Using the Gaussian program: Setting up the calculation Extracting the results Comparison with Coulson s results from 1937. 2 che-30042 Advanced QC lecture 5

Illustration of the result of MO calculations on HF Details of HF MO scheme: Diagram of scheme: The 1s and 2s orbitals from F are too low in energy to be involved in bonding. The F 2pz orbital has the right symmetry to overlap with the H 1s orbital to form 2 orbitals, one bonding, one antibonding. The 2px and 2py orbitals form orbitals. 3 che-30042 Advanced QC lecture 5

How are the MOs in HF written? In lecture 4, we used expressions for the MOs: = cA A + cB B If we carry out an SCF calculation on HF we get, for the orbitals: ( ) = 0.33 H, 1s + 0.94 F, 2pz and ( ) = 0.94 H, 1s + 0.33 F, 2pz This shows that the bonding orbital is mainly from the F 2pz, and the antibonding orbital is mainly from H 1s. 4 che-30042 Advanced QC lecture 5

Using the Gaussian program Gaussian is a computer program for computational chemistry initially released in 1970 by John Pople and his research group at Carnegie-Mellon University, USA. It has been continuously updated since then. The name originates from Pople's use of Gaussian orbitals to speed up calculations compared to those using Slater-type orbitals, a choice made to improve performance considering the limited computing capacities of the then available computer hardware. We will use the Windows version of Gaussian 03, available on the PCs in the Faculty Lab. 5 che-30042 Advanced QC lecture 5

What information does the program need? (i) Molecular geometry and Z matrices The program needs to know the molecular geometry and this is represented by a Z matrix. For H2 it is: H H 1 R This means that the first atom is H, and the second is also H, bonded to atom 1 at a distance R (if you know R you can specify it). A starting value for R is specified for geometry optimisation. Try HCl as another example. 6 che-30042 Advanced QC lecture 5

What information does the program need? (ii) As well as the molecular geometry, the type of calculation and the basis set information needs to be specified. e.g. for H2, we specify # RHF STO-3G OPT This gives the type of calculation (RHF is a closed- shell SCF calculation), the basis set, e.g. STO-3G (lecture 4), and the keyword OPT , which tells the program to optimise the geometry (i.e. the H2 bond length). 7 che-30042 Advanced QC lecture 5

The Gaussian dataset summarised # RHF STO-3G OPT Calculation type, basis set, keyword (blank line) Title (blank line) Molecule charge, state (singlet) Z matrix line 1 Z matrix line 2 (blank line) Starting value of R (in ) Hydrogen geometry optimisation 0 1 H H 1 R R=1.0 8 che-30042 Advanced QC lecture 5

Extracting information from the output file (i) In the workshop you are asked to produce a table like this: Re/ Basis set STO-3G STO-6G 3-21G 6-31G Experimental Total Energy/H - 9 che-30042 Advanced QC lecture 5

Extracting information from the output file (ii) Search for the last occurrence* of the following: SCF Done: E(RHF) = SCF Done: E(RHF) = -1.11750585060 A.U. after 1 cycles Further down is confirmation that the structure is optimised: Optimization completed. -- Stationary point found. * To ensure you have the minimum value of the energy. 10 che-30042 Advanced QC lecture 5

Extracting information from the output file (iii) NB different from script! Just below Stationary point found , it says: Optimized Parameters ! ! (Angstroms and Degrees) ! -------------------------- ---------- ---------------- ! Name Definition Value Derivative Info. ! ---------------------------------------------------------------- ---------------- ! R1 R(1,2) 0.712 -DE/DX = 0.0002 ! The value R(1, 2) = 0.712 is the H-H bond length in . Also DE/DX should be small (energy gradient). 11 che-30042 Advanced QC lecture 5

Coulson: the first MO calculations (1937) This paper (available from the describes first calculations on H2. Keele trivia point he did his PhD with Lennard-Jones in Cambridge, who later became one of the first Principals of UCNS, which in turn became Keele. KLE) Coulson s 12 che-30042 Advanced QC lecture 5

Comparing results with those of Coulson Coulson carried out one of the first MO calculations on H2 in 1937 Note: these calculations were probably largely done by hand! He initially used a MO based on free atom atomic orbitals, 1sA + 1sB This gives Re= 0.850 , which becomes 0.732 if the orbitals are scaled to account for the molecular environment. 13 che-30042 Advanced QC lecture 5

Further comparison See The Gaussian Programs as a Teaching Tool: A Case Study on Molecular Hydrogen Calculations (copy on KLE). It is seen that the minimal basis sets STO-3G & STO-6G give better results than Coulson s free atom orbitals, but not as good as his scaled result. This paper also shows you how to set up a calculation that closely emulates what Coulson did. Try it and see if you can get it to work! 14 che-30042 Advanced QC lecture 5

Lecture summary An example of MO calculations has been given for HF, relating MO diagrams to calculation results. The Gaussian program has been introduced, and the procedure for running calculations and extracting results explained. Results for molecular hydrogen have been compared with those obtained by Coulson, and the differences have been discussed. 15 che-30042 Advanced QC lecture 5