Molecular Modeling Elementary Principles and Applications

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1 Course for Molecular Modelling Elementary Principles and Applications Jian Wan Department of Chemistry Central China Normal University Wuhan , China Tel:

2 Molecular Modelling

4 Outline 1. The Theoretical Background Gaussian98/GaussView 2. Single Point Energy Calculations 3. Geometry Optimizations 4. Frequency Calculations 5. Reaction Pathways

5 References Exploring Chemistry with Electronic Structure Methods, J. R. Fores man, A. Frisch, Second Edition Gaussian, Inc. Molecular Modelling, A. R. Leach, Addison Wesley Long-man Limit ed,

6 Chapter One The Theoretical Background

7 1.1 Molecular Modelling (Computational Chemistry ) Molecular Modelling 1. Molecular Mechanics (MM ) 2. Molecular Dynamics (MD ) 3. Electronic Structure Theory ( ) Quantum Mechanics, QC & Semiempirical QC (Ab initio Methods) 4. Quantum Statistics ( )

8 1 2 3 (local minimum)

9 1.1.1 Molecular Mechanics Advantages Disadvantages

10 .1.2 Electronic Structure Theory a) Semi-empirical QC Methods HMO AM1 MNDO PM3 INDO/S b) Ab initio Hartree-Fock c) Density Functional Theory DFT/B3LYP DFT/X3LYP Gaussian MOPAC HyperChem

11 homework Functions in Gaussian98 Molecular energy and structures Energies and structures of transition states Bond and reaction energies Molecular obitals Multipole moments Atomic charges and electrostatic potentials Vibrational frequency IR and Raman spectra NMR properties Polarizabilities and hyperpolarizabilities Thermochemical properties Reaction pathways

12 1.2 Model Chemistry

13 1.2.1 [Gaussian98 ] PM3 HF B3LYP MP2 Hartree-Fock Becke 3 Moller-Plesset

14 1.2.2 Open shell Close shell :, (Restricted) R RHF, (Unrestricted) U HF UHF

17 1.,

18 1.3 Basis set LCAO-MO H 1s H 2s ψ ψ 3 ς exp( ς ) π 1s = r 5 ς r 3π 2s = r exp( ς )

20 Basis Sets Slater type orbitals (STO) Gaussian type orbitals (GTO) - functional form - zeroth-order Gaussian function r n n nl e r n r R ζ ζ + = 1 2 1/ 2 1/ )!] [(2 ) (2 ) ( / 2 ), ( r s e r g α π α α = 2 ar c b a e z y x

21 Slater Gauss GTO STO STO STO GTO ( 3 6, STO-NG)

22 Property of Gaussian functions is that the product of two G aussians can be expressed as a single Gaussian, located alon g the line joining the centers of the two Gaussians c mn n m n m n n m m ar r a a a a r a r a e e e e + =

23 STO VS. GTO

24 1.3.1 Minimal Basis Sets H He 1s Li Be C Ne 1s, 2s, 2px, 2py, 2pz

25 1.3.2 Split Valence Basis Sets H He 1s, 1s' Li Be C 1s, 2s, 2s', 2Px, 2Py, 2Pz, 2Px', 2Py', 2Pz' 3-21G 6-31G 3-21G Gauss 2 Gauss 1 Gauss

27 1.3.3 Polarized Basis Sets (size) (shape) 6-31G(d) 6-31G* 6-31G(d,p) 6-31G** 6-31G(d) 6-31G d 6-31G(d,p) 6-31G(d) p

30 1.3.4 Diffuse Functions s p 6-31+G(d) 6-31G++(d) 6-31+G(d) 6-31G(d), G(d)

31 1.3.5 High Angular Momentum Basis Sets 6-31G(2d) 6-31G d G(3df,3pd) d f p d G(3df,2df,p) d f, d f

33 1.3.6 Effective Core Potential Basis Sets (Effective Core Potential, ECP) LanL2DZ

34 STO-3G: [H-Xe] 3-21G:[H-Xe] 6-31G(d):[H-Cl] 6-31G(d,p):[H-Cl] 6-31+G(d):[H-Cl] 6-31+G(d,p):[H-Cl] G(d,p):[H-Br] G(2d,p):[H-Br] G(2df,2p):[H-Br] G(3df,2pd):[H-Br]

36 1.4 * (semi-empirical) * : Hartree-Fock SCF ( ): Moller-Plesset CI QCI * (DFT)

37 1.4.1 AM1 PM3 MNDO Gaussian MOPAC HyperChem Spartan * * HF DFT * *

38 1.4.2 HF AM1,PM3,HF/6-31+G(d) MP2/ G(2d,2p) AM1 PM3 HF MP2 R(H-F) R(H4-F2) R(F-F) A(F-H4-F) A(H3-F-F)

39 1.4.3 Hartree-Fock Hartree-Fock Electron Correlation( ) Fermi( ) ---- Pauli Couloub( ) ----

40 Electron Correlation The most significant drawback to HF theory is that it fails to adequately represent electron correlation. E corr = E NR E HF Configuration Interactions - excited states are included in the description of an electronic state Many Body Perteubation Theroy - based upon Rayleigh-Schrödinger perturbation theroy.

41 1.4.4 Electron Correlation and Post-SCF Methods SCF Gaussian Moller-Plesset MP2, MP3, MP4, MP5 MP2 MP3, MP4( MP4SDQ) MP2 Quadratic CI QCISD, QCISD(T), QCISD(TQ),QCISD Coupled Cluster methods ( ) ( ) CCD, CCSD, CCSD(T)

42 HF HF/STO-3G 73.9 HF 97.9 MP MP MP4(SDTQ) QCISD QCISD(T)

43 1.4.5 Density Functional Theory Methods DFT - Gaussian B3LYP B3PW91

44 1.5

46 6-31+G(d,p) G(d,p)

47 H, He STO-3G 3-21G 6d 6-31G* 6-31G** 6-31+G(d) 6-31+G(d,p) G(d,p) 5d

BBS Gaussian Gaussian Gaussian Gaussian98 Gaussian Gaussian Gaussian94 98 Exploring Chemistry with Electronic Structure Methos Second Edition James B

Exploring Chemistry with Electronic Structure Method Second Edithion James B. Foresman Aeleen Frisch Gaussian, Inc Pittsburgh, PA 2002 9 25 BBS Gaussian Gaussian Gaussian Gaussian98 Gaussian Gaussian Gaussian94