Overview to Molecular Modeling

8/3/2019 Overview to Molecular Modeling

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Overview toMolecular Modeling


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Eof a molecular structureGeometry optimization

Related properties vibrational frequencies

nmr e) density

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

ComputationalChemistry


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Atoms obey laws of classical physicsNo e) structure

MM2, MM3, MM+, others

Useful Large (bio) molecules Small molecules

NO energy value


MolecularMechanics


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E= 3EiLarge 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


MolecularMechanics


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Electronic structure based on , =E

, is known exactly

is unknown except for simple systems (H-like

atoms, SHO, RR, particles in boxes, etc.)


MolecularMechanics

QuantumMechanics


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Overlap IntegralExchange Integral Exchange Functional (HF theory) Correlation Functional

Problems


MolecularMechanics

QuantumMechanics


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Ignore part of,

Hckel molecular orbital theory

MOPAC theory

ZINDO theory


MolecularMechanics

SemiempiricalMethods

QuantumMechanics


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HMO Hckel molecular orbital theory Applied to conjugated hydrocarbons Assumes ALL overlap integrals are zero

EHT Extended Hckel theory Applied to any molecule type

Useful for quick and dirty calculations andstarting point for more advanced calculations

Hckel Theory


MolecularMechanics


QuantumMechanics


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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


MolecularMechanics


QuantumMechanics


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ZINDO/1, ZINDO/3, ZINDO-d, etcUseful for Transition states Energies Spectroscopy Transition elements

Not useful for optimizations

ZINDOZerners INDO


MolecularMechanics


QuantumMechanics


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Use complete ,

Estimate

Variation Principle (Etrial$Eexperimental)


MolecularMechanics


ab initio

Methods

QuantumMechanics


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HF-SCF

Hartree-Fock Self-Consistent Field

B3LYP Density Function Theory (DFT) Becke Exchange with Lee-Yang-Parr Correlation

MP2/MP4 Second/Fourth Order Mller-Plesset perturbation

theory

QCISD(T) Quadratic configuration

interaction

Level of Theory


Molecular

Mechanics


ab initio

Methods

Quantum

Mechanics


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Trial Wave Functions(Basis Sets)


MolecularMechanics


ab initio

Methods

QuantumMechanics


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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


MolecularMechanics


ab initio

Methods

QuantumMechanics


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Comparison ofab initio Methods (p 94)


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Comparison of Models (F/F p 96)


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Comparison of Commercial Software


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Capable of describing actual wave function

well enough to give chemically useful resultsCan be used to evaluate Is accurately and

cheaply

Basis SetsBasis Set Criteria


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Basis FunctionsHydrogenlike Orbitals


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(n - l- 1) nodes

Hydrogenlike Orbitals


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Basis FunctionsSlater-type Orbitals (STOs)


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Basis FunctionsGaussian-type Orbitals (GTOs)


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Advantages

Complete Favorable math properties

DisadvantagesNot mutually orthogonal

Poor representation of electron probability near andfar away from nucleus (overcome using largenumber of GTOs

GTOs


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One or more STO on each nucleus

Accuracy of calculation increases as Orbital exponents chosen wellNumber of STOs used increases

Use of STOs


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Use STO for occupied AOs

Examples H 1s C 1s 2s 2px 2py 2pz

Number of STOs usedMinimal Basis Set


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Number of STOs usedSplit (Double Zeta ) Basis Set

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

2p = a2p,inner + b2p,outer

Ifa > b charge cloud contracted around nucleusIfb > a diffuse cloud


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Examples:

H 1s, 1sNC 1s, 2s, 2sN, 2px, 2py, 2pz, 2pxN, 2pyN, 2pzN

Triple Zeta basis sets are also used

Number of STOs usedSplit (Double Zeta ) Basis Set


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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 STOs usedDiffuse Basis Set


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Linear combination of different types of

orbitalsExamples H 1s and 2p C 1s, 2s, 2p and 3d

Shifts charge in/out of bonding regions

Number of STOs usedPolarized Basis Set


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Other attempts

Place STOs in center of bonds instead of on onlynuclei

Problems with increasing number of STOsused

Number ofIs increases as N4 where N is thenumber of basis functions

As minimization occurs, orbital exponents changethus defining a new basis set to rebegin thecalculation

Number of STOs used


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Wrong shape of GTOs accounted for by

Choosing several s to get set of primitivegaussians for compact and diffuse

Linear combination of primitives (usually 1-7) to getSTO

Optimize Freeze as contracted gaussian function

Use minimal, split/double zeta, polarization,diffuse sets

Use of STOs/GTOs


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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 STOs / GTOsJargon: minimal basis set


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K-LMG

whereKis the number of sp type inner shell primitivegaussians

L is the number of inner valence s and p

primitive gaussians

Mis the number of outer valence s and pprimitive gaussians

Use of STOs / GTOsJargon: split basis set


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3-21G

3 primitives for inner shell2 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 STOs / GTOsJargon: split basis set


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* d-type orbital added to atoms withZ> 2

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

ds added:

STO-NG are 5 regular 3ds

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

Use of STOs / GTOsJargon: polarization


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6-31G* or 6-31G(d)

6-31G with d added forZ> 2 (FF choice)

6-31G** or 6-31G(d,p)

6-31G with d added forZ> 2 and p added to H

6-31G(2d)

6-31G with 2d functions added forZ> 2

Use of STOs / GTOsJargon: polarization


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+ diffuse function included forZ> 2

++ diffuse function included forZ> 2 and for H

6-31+G(d)6-31G(d) with diffuse function added forZ> 2

6-31++G(d)6-31+G(d) with diffuse function added for H

Use of STOs / GTOsJargon: diffuse


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SomeRecommended

StandardBasis Sets(F/F p 102)

~DZVP

~TZVP


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Common Basis Sets

Documents

Overview to Molecular Modeling