Overview toMolecular Modeling

�E of a molecular structure

�Geometry optimization

�Related properties� vibrational frequencies� nmr� e) density

�Energy method / Energy basis set // Geometry method / Geometry basis set

ComputationalChemistry

�Atoms obey laws of classical physics

�No e) structure

�MM2, MM3, MM+, others

�Useful� Large (bio) molecules� Small molecules

�NO energy value

ComputationalChemistry

MolecularMechanics

�E = 3 Ei

�Large number of parameters� C2H6

� C-C, 6 @ C-H� 6 @ C - C - H� 9 @ H - C - C - H

� C6H6

� 6 @ C - H, 6 @ C -/= C (not C - C or C = C)� 6 @ C - C - H, 24 torsion

�Parameters determined empirically

ComputationalChemistry

MolecularMechanics

�Electronic structure based on , ø = E ø

�, is known exactly

�ø is unknown except for simple systems (H-likeatoms, SHO, RR, particles in boxes, etc.)

ComputationalChemistry

MolecularMechanics

QuantumMechanics

�Overlap Integral

�Exchange Integral� Exchange Functional (HF theory)� Correlation Functional

Problems

ComputationalChemistry

MolecularMechanics

QuantumMechanics

�Ignore part of ,

�Hückel molecular orbital theory

�MOPAC theory

�ZINDO theory

ComputationalChemistry

MolecularMechanics

SemiempiricalMethods

QuantumMechanics

�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 andstarting point for more advanced calculations

Hückel Theory

ComputationalChemistry

MolecularMechanics

SemiempiricalMethods

QuantumMechanics

� 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

MOPACMolecular Orbital Package

ComputationalChemistry

MolecularMechanics

SemiempiricalMethods

QuantumMechanics

�ZINDO/1, ZINDO/3, ZINDO-d, etc

�Useful for� Transition states� Energies� Spectroscopy� Transition elements

�Not useful for optimizations

ZINDOZerner’s INDO

ComputationalChemistry

MolecularMechanics

SemiempiricalMethods

QuantumMechanics

�Use complete ,

�Estimate ø

�Variation Principle (Etrial $ Eexperimental)

ComputationalChemistry

MolecularMechanics

SemiempiricalMethods

ab initioMethods

QuantumMechanics

�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 configurationinteraction

Level of Theory

ComputationalChemistry

MolecularMechanics

SemiempiricalMethods

ab initioMethods

QuantumMechanics

Trial Wave Functions(Basis Sets)

ComputationalChemistry

MolecularMechanics

SemiempiricalMethods

ab initioMethods

QuantumMechanics

�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

Electron Spin

ComputationalChemistry

MolecularMechanics

SemiempiricalMethods

ab initioMethods

QuantumMechanics

Comparison of ab initio Methods (p 94)

Comparison of Models (F/F p 96)

Comparison of Commercial Software

�Capable of describing actual wave functionwell enough to give chemically useful results

�Can be used to evaluate I’s accurately and“cheaply”

Basis SetsBasis Set Criteria

Basis FunctionsHydrogenlike Orbitals

(n - l - 1) nodes

Hydrogenlike Orbitals

Basis FunctionsSlater-type Orbitals (STO’s)

Basis FunctionsGaussian-type Orbitals (GTO’s)

�Advantages� Complete� Favorable math properties

�Disadvantages� Not mutually orthogonal� Poor representation of electron probability near and

far away from nucleus (overcome using largenumber of GTO’s

GTO’s

�One or more STO on each nucleus

�Accuracy of calculation increases as� Orbital exponents chosen well� Number of STO’s used increases

Use of STO’s

�Use STO for occupied AO’s

�Examples� H 1s� C 1s 2s 2px 2py 2pz

Number of STO’s usedMinimal Basis Set

Number of STO’s usedSplit (Double Zeta æ) Basis Set

Linear combination of two similar orbitals withdifferent orbital exponents (different sizes)

ö2p = aö2p,inner + bö2p,outer

If a > b charge cloud contracted around nucleusIf b > a diffuse cloud

Examples:

H 1s, 1sN

C 1s, 2s, 2sN, 2px, 2py, 2pz, 2pxN, 2pyN, 2pzN

Triple Zeta basis sets are also used

Number of STO’s usedSplit (Double Zeta æ) Basis Set

�Extra s and p wave functions included thatare 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 usedDiffuse Basis Set

�Linear combination of different types oforbitals

�Examples� H 1s and 2p� C 1s, 2s, 2p and 3d

�Shifts charge in/out of bonding regions

Number of STO’s usedPolarized Basis Set

�Other attempts� Place STO’s in center of bonds instead of on only

nuclei

�Problems with increasing number of STO’sused� 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 thecalculation

Number of STO’s used

�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

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’sJargon: minimal 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’sJargon: 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’sJargon: split basis set

* d-type orbital added to atoms with Z > 2

** d-type orbital added to atoms with Z > 2 and p-typeorbital added to H and He

d’s added:

STO-NG are 5 regular 3d’s

L-KMG are 6 3d’s dxx, dyy, dzz, dxy, dyz, dxz (formed bylinear combination of 5 regular 3d’s and 3s)

Use of STO’s / GTO’sJargon: 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’sJargon: polarization

+ 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

Use of STO’s / GTO’sJargon: diffuse

SomeRecommendedStandardBasis Sets(F/F p 102)

~DZVP

~TZVP

Common Basis Sets