�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
�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
�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