Overview to Molecular Modeling Computational Chemistry
E of a molecular structure Geometry optimization Related properties vibrational frequencies nmr e ) density Energy method / Energy basis set // Geometry method / Geometry basis set Computational Chemistry
Molecular Mechanics
Atoms obey laws of classical physics No e) structure MM2, MM3, MM+, others Useful Large (bio) molecules Small molecules N O energy value Computational Chemistry
Molecular Mechanics 3 E = E i Large number of parameters C 2 H 6 C-C, 6 @ C-H 6 @ C - C - H 9 @ H - C - C - H C 6 H 6 6 @ C - H, 6 @ C -/= C (not C - C or C = C) 6 @ C - C - H, 24 torsion Parameters determined empirically Computational Chemistry
Molecular Quantum Mechanics Mechanics
Electronic structure based on , ø = E ø , is known exactly ø is unknown except for simple systems (H-like atoms, SHO, RR, particles in boxes, etc.) Computational Chemistry Problems Molecular Quantum Mechanics Mechanics
Overlap Integral Exchange Integral Exchange Functional (HF theory) Correlation Functional Computational Chemistry
Molecular Quantum Mechanics Mechanics
Semiempirical Methods Ignore part of , Hückel molecular orbital theory MOPAC theory ZINDO theory Computational Chemistry
Molecular Quantum Hückel Theory Mechanics Mechanics
Semiempirical Methods
HMO Hückel molecular orbital theory Applied to conjugated hydrocarbons Assumes ALL overlap integrals are zero EHT Extended Hückel theory Applied to any molecule type Useful for “quick and dirty” calculations and starting point for more advanced calculations Computational Chemistry
Molecular Quantum MOPAC Mechanics Mechanics Molecular Orbital Package
Semiempirical Methods CNDO Complete Neglect of Differential Overlap INDO Intermediate Neglect of ... NDDO Neglect of Diatomic ... MINDO Modified INDO MINDO/3 MNDO Modified Neglect of ... AM1 Austin Model 1 PM3 Parameterized Model Series 3 AM1/d and MNDO-d (MOPAC 2000, d e- ’s) Useful for ground state energy and geometry Computational Chemistry
Molecular Quantum ZINDO Mechanics Mechanics Zerner’s INDO
Semiempirical Methods
ZINDO/1, ZINDO/3, ZINDO-d, etc Useful for Transition states Energies Spectroscopy Transition elements Not useful for optimizations Computational Chemistry
Molecular Quantum Mechanics Mechanics
Semiempirical ab initio Methods Methods Use complete , Estimate ø $ Variation Principle (E trial E experimental) Computational Chemistry
Molecular Quantum Mechanics Mechanics Level of Theory
Semiempirical ab initio Methods Methods HF-SCF Hartree-Fock Self-Consistent Field B3LYP Density Function Theory (DFT) Becke Exchange with Lee-Yang-Parr Correlation MP2/MP4 Second/Fourth Order Møller-Plesset perturbation theory QCISD(T) Quadratic configuration interaction Computational Chemistry
Molecular Quantum Mechanics Mechanics Trial Wave Functions
Semiempirical ab initio (Basis Sets) Methods Methods Computational Chemistry
Molecular Quantum Mechanics Mechanics Electron Spin
Semiempirical ab initio Methods Methods Open Shell (unrestricted) Odd number of electrons Excited states 2 or more unpaired electrons Bond dissociation processes Closed Shell (restricted) Even number of electrons--all paired Comparison of ab initio Methods (p 94) Comparison of Models (F/F p 96)
Comparison of Commercial Software Basis Sets Basis Set Criteria
Capable of describing actual wave function well enough to give chemically useful results Can be used to evaluate I ’s accurately and “cheaply” Basis Functions Hydrogenlike Orbitals Hydrogenlike Orbitals
( n - l - 1) nodes Basis Functions Slater-type Orbitals (STO’s) Basis Functions Gaussian-type Orbitals (GTO’s) GTO’s
Advantages Complete Favorable math properties Disadvantages Not mutually orthogonal Poor representation of electron probability near and far away from nucleus (overcome using large number of GTO’s Use of STO’s
One or more STO on each nucleus Accuracy of calculation increases as Orbital exponents chosen well Number of STO’s used increases Number of STO’s used Minimal Basis Set
Use STO for occupied AO’s Examples H 1s C 1s 2s 2px 2 p y 2 p z Number of STO’s used Split (Double Zeta æ ) Basis Set Linear combination of two similar orbitals with different orbital exponents (different sizes)
ö 2 p = a ö 2p,inner + b ö 2p,outer If a > b charge cloud contracted around nucleus If b > a diffuse cloud Number of STO’s used Split (Double Zeta æ ) Basis Set
Examples: H 1s, 1sN N N N N C 1s, 2s, 2s , 2px , 2py , 2pz , 2px , 2py , 2pz
Triple Zeta basis sets are also used Number of STO’s used Diffuse Basis Set Extra s and p wave functions included that are significantly larger than usual ones Useful for Distant electrons Molecules with lone pairs Anions Species with significant negative charge Excited states Species with low ionization potentials Describing acidities Number of STO’s used Polarized Basis Set
Linear combination of different types of orbitals Examples H 1s and 2p C 1s, 2s, 2p and 3d Shifts charge in/out of bonding regions Number of STO’s used
Other attempts Place STO’s in center of bonds instead of on only nuclei Problems with increasing number of STO’s used Number of I ’s increases as N4 where N is the number of basis functions As minimization occurs, orbital exponents change thus defining a new basis set to rebegin the calculation Use of STO’s/GTO’s
Wrong shape of GTO’s accounted for by Choosing several á ’s to get set of “primitive” gaussians for compact and diffuse Linear combination of primitives (usually 1-7) to get STO Optimize “Freeze” as “contracted” gaussian function Use minimal, split/double zeta, polarization, diffuse sets Use of STO’s / GTO’s Jargon: minimal basis set
STO-NG where N is the number of primitive gaussians
STO-3G 3 primitve gaussians per basis set not the simplest minimal basis set popular Use of STO’s / GTO’s Jargon: split basis set
K-LMG where K is the number of sp type inner shell primitive gaussians L is the number of inner valence s and p primitive gaussians M is the number of outer valence s and p primitive gaussians Use of STO’s / GTO’s Jargon: split basis set
3-21G 3 primitives for inner shell 2 sizes of basis functions for each valence orbital
6-311G 6 primitives for inner shell 3 sizes of basis functions for each valence orbital Use of STO’s / GTO’s Jargon: polarization
* d-type orbital added to atoms with Z > 2 ** d-type orbital added to atoms with Z > 2 and p-type orbital added to H and He d’s added: STO-NG are 5 regular 3d’s
L-KMG are 6 3d’s dx x , d y y , d z z , d x y , d y z , d x z (formed by linear combination of 5 regular 3d’s and 3s) Use of STO’s / GTO’s Jargon: polarization
6-31G* or 6-31G(d) 6-31G with d added for Z > 2 (FF choice)
6-31G** or 6-31G(d,p) 6-31G with d added for Z > 2 and p added to H
6-31G(2d) 6-31G with 2d functions added for Z > 2 Use of STO’s / GTO’s Jargon: diffuse
+ diffuse function included for Z > 2 ++ diffuse function included for Z > 2 and for H
6-31+G(d) 6-31G(d) with diffuse function added for Z > 2
6-31++G(d) 6-31+G(d) with diffuse function added for H Some Recommended Standard Basis Sets (F/F p 102)
~DZVP
~TZVP Common Basis Sets