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
ComputationalChemistry
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
ComputationalChemistry
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.)
ComputationalChemistry
MolecularMechanics
QuantumMechanics
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Overlap IntegralExchange Integral Exchange Functional (HF theory) Correlation Functional
Problems
ComputationalChemistry
MolecularMechanics
QuantumMechanics
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Ignore part of,
Hckel molecular orbital theory
MOPAC theory
ZINDO theory
ComputationalChemistry
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
ComputationalChemistry
MolecularMechanics
SemiempiricalMethods
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
ComputationalChemistry
MolecularMechanics
SemiempiricalMethods
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
ComputationalChemistry
MolecularMechanics
SemiempiricalMethods
QuantumMechanics
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Use complete ,
Estimate
Variation Principle (Etrial$Eexperimental)
ComputationalChemistry
MolecularMechanics
SemiempiricalMethods
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
ComputationalChemistry
Molecular
Mechanics
SemiempiricalMethods
ab initio
Methods
Quantum
Mechanics
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Trial Wave Functions(Basis Sets)
ComputationalChemistry
MolecularMechanics
SemiempiricalMethods
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
ComputationalChemistry
MolecularMechanics
SemiempiricalMethods
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