Advanced Electronic Structure Theory Density functional theory. Dr Fred Manby
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1 Advanced Electronic Structure Theory Density functional theory Dr Fred Manby
2 Course overview This is a course about density functional theory (DFT) Aims and objectives Understand the role of DFT in modern chemistry Understand how DFT works Be able to assess critically uses of DFT Recommended books A Chemist s Guide to DFT; W Koch and M C Holthausen (Wiley, 2001) DFT of Atoms and Molecules; R G Parr and W Yang (OUP, New York, 1989) Introduction to Computational Chemistry; F Jensen (Wiley, 1998) 1
3 Relation to other courses 1. Quantum concepts Level 2, Prof Balint-Kurti 2. Understanding structure and reactivity Level 2, Prof Allan and Dr Mulholland 3. Molecular Electronic Structure level 3, Dr Harvey 4. Molecular Modelling level 4, Dr Mulholland 2
4 Lecture summaries 1. DFT in modern computational chemistry 2. How it works: background 3. How it works: the mechanics 4. How it works: specific approximations 5. Where DFT goes wrong 6. Strengths of DFT, and summary 3
5 1 DFT in modern computational chemistry 1.1 Computational chemistry Based on quantum mechanics and statistical mechanics Can predict structures Interpret spectroscopy Predict reaction rates and mechanisms Compute thermochemical properties 4
6 1.2 The potential energy surface vibrational frequencies transition state: mechanism kinetics thermochemistry structure 5
7 1.3 DFT in context Molecular mechanics cf. Molecular Modelling course (Dr Mulholland) Simple empirical expressions for energy Very fast Cannot describe chemical reactions (no bond formation) Quantum mechanics Exact solutions only for very simple problems Accurate approximations for larger systems 6
8 Hartree-Fock (cf Dr Harvey s level 3 course) Semi-empirical methods HF AM1, PM3 Very fast can treat 100s of atoms Reduced accuracy Second order Møller-Plesset theory MP2 Goes beyond HF theory by including correlation Coupled cluster theory CCSD(T) Achieves chemical accuracy for many problems Terribly expensive (O(N 7 )) 7
9 8
10 1.4 Basic reminder of Hartree-Fock theory Require approximate solution to n-electron Schrödinger equation Build this by solving n coupled 1-electron Schrödinger equations ( ˆv eff ) ψ i = ɛ i ψ i No longer need to think about the whole wavefunction Enough to think about orbitals (1-electron wavefunctions) 9
11 1.5 Electron correlation Working definition: that which HF theory doesn t have The instantaneous position of electrons should be correlated He 2+ He 2+ e e e e Situation on the left should be more probable than on the right In HF theory both of these have equal probability Electrons do not avoid each other enough in HF theory 10
12 1.6 Basic outline of how DFT works Quite similar to Hartree-Fock (HF) theory In HF the effective potential has the form: ˆv eff = v nuc + v J ˆK In DFT exchange and correlation effects are modelled v eff = v nuc + v J + v xc 11
13 Exact DFT v nuc 1/r ij v nuc + v J + v xc 12
14 This simple model of electrons in molecules is the basis of DFT The main problem is how to determine v xc (this is the focus of the next three lectures) But successful approximations can be made And DFT can be used for all sorts of things 13
15 1.7 Examples of uses of DFT Elucidating enzyme mechanisms Mechanism for methane formation in methanogenic bacteria CO 2 + 4H 2 CH 4 + 2H 2 O PDB 1e6y CoB S H + CH 3 S CoM CoB S S CoM + CH 4 14
16 Mechanism thought to involve methyl radical/nickel complex DFT allowed the correct mechanism to be found Pelmenschikov, Blomberg, Siegbahn and Crabtree, JACS (2002) 15
17 1.7.2 Prediction of novel molecules WAu 12 Manninen, Pyykkö and Häkkinen, PCCP (2005) 16
18 1.7.3 Prediction of properties Experimental and DFT NMR chemical shifts of retinal Touw, de Groot and Buda, J Mol Struct THEOCHEM (2004) Retinal image from edudev/labtutorials/vision/vision.html 17
19 1.7.4 Other applications Thermochemistry Dynamics of chemical reactions Treatment of condensed phase Literally thousands of other... 18
20 1.8 Summary Computational methods are used in all branches of chemistry Prediction Interpretation DFT is one of the central tools It is fast (can be applied to large molecules) It is accurate (excellent structure, good energies) Next week: the density and the beginning of how DFT works 19
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