Semi-Empirical Methods:Where is the Rest?

Matthew GrandboisCHEM 381Spring 2004

IntroductionIntroductionComputational chemistry is one of the fastest growing

areas of chemistry

Used to computationally determine vital information Geometry

Bond Angles, Bond Distances, Dihedral AnglesDipole MomentEnthalpy of FormationIonization Potentials

Electronic StructureElectronic Structure

Calculations based on determining electronic structures

Different Approaches:Density Functional TheoryAb InitioSemi-empirical

Semi-Empirical MethodsSemi-Empirical Methods

Some of the electrons are considered explicitly

Reduces computational demand of the problem

Pilar, F.L. Elementary Quantum Mechanics. Second Edition. Dover Publications, Inc. Mineola, New York, 1990, 454.

Semi-Empirical ApproximationsSemi-Empirical Approximations

“Ignoring” of core electronsCore electrons reduce nuclear chargeIntroduction of function to model combined repulsion

due to nuclei and core electronsMinimum basis set of functions to account for

valence electronsMajority of basis functions are taken to be STOs

Jensen, F. Introduction to Computational Chemistry. John Wiley & Sons, England 1999, 81.

Huckel ApproximationsHuckel Approximations

1931, E. Huckel showed depiction of conjugated hydrocarbons by use of quantum mechanical model which only considered pi electrons.

Applicable to chain and cyclic conjugated systems

- C = C – C = C – C = C -

Central AssumptionCentral Assumption

Zero Differential Overlap approximationNeglects all products of basis functions depending on

the same electron coordinates when located on different atoms

How many integrals are neglected is which determines the various Semi-Empirical methods

Jensen, pg 81

Neglect of Diatomic Differential Overlap (NDDO)

Neglect of Diatomic Differential Overlap (NDDO)

Only uses the previously mentioned central assumption

Overlap Integral

S = < A| B > = vAB

Jensen, pg 82

Intermediate Neglect of differential Overlap (INDO)

Intermediate Neglect of differential Overlap (INDO)

In addition to NDDO:Neglects all two-centre 2 electron integrals which are

not of the Coulomb typeTo preserve rotational invariance, some integrals

must be made independent of orbital type

Jensen, pg 83

Complete Neglect of Differntial Overlap (CNDO)

Complete Neglect of Differntial Overlap (CNDO)

Only the Coulomb one-centre and two-centre 2 electron integrals remain:

< AB | CD> = ACBD < AB | AB>

< µAB | µAB> is independent of orbital type (s or p)

Jensen, pg. 83

ParameterizationParameterization Direct use of ZDO approximations is not useful

due to only qualitative picture of MOs 3 Methods to transform NDO approximations into

useful computational models1) Remaining integrals calculated from functional form of AO’s2) Remaining integrals made into parameters, assigned

values based on experimental data3) Remaining integrals made into parameters, assigned

values based on fitting to experimental data

Jensen, pg. 84

Modified NDDO ModelsModified NDDO Models

MNDO

AM1

PM3

Modified Neglect of Diatomic Overlap (MNDO)

Modified Neglect of Diatomic Overlap (MNDO)

One of first paramaterization models usedParameterizes: H, B, C, N, O, F, Al, Si, P, S, Cl, Zn,

Ge, Br, Sn, I, Hg, and Pb. Some LimitationsSucceeded by AM1 and PM3 Models

Jensen, pg. 87

Austin Model 1 (AM1)Austin Model 1 (AM1)

Developed by Dewar at the University of Texas at Austin, 1985.

Came from systematics errors of MNDOToo high repulsion between atoms 2-3 Å apart

Parameterized for:H, B, C, N, O, F, Al, SI< P, S, Cl, Zn, Ge, Br, I, and

Hg.Some Limitations

Jensen, pg. 87

AM1AM1

- Heats of Formation (kcal/mol )- 1,4-pentadiene: 25.2 (expt), 25.0 (Dewar), 25.2

(CAChe)- MNDOd calculations yielded 26.0- 2-propyl cation: 192 (expt), 192 (Dewar), 208

(CAChe)- Ammonium: 155 (expt), 151 (Dewar), 151 (CAChe)

AM1 GeometriesAM1 Geometries

EtheneCC 1.339

1.326CH 1.086

0.964HCC 121.2 114.64

NitrogenNN 1.094 1.106

FuranOC1 1.362 1.431C2C3 1.361 1.526C3C4 1.431 1.522C2H 1.075 1.121C3H 1.077 1.117HC2O 115.9 107.2HC3C4 128.0 111.2

Modified Neglect of Diatomic Overlap, Parametric Method

Number 3 (PM3)

Modified Neglect of Diatomic Overlap, Parametric Method

Number 3 (PM3)MNDO and AM1 parameters were done by hand,

limiting number of reference compoundsEssentially, AM1 with all parameters fully optimizedStill needs some human interventionParameterized for:

H, Li, C, N, O, F, Mg, Al, Si, P, S, Cl, Zn, Ga, Ge, As, Se, Br, Cd, In, Sn, Sb, Te, I, Hg, Tl, Pb, Bi, Po, and At

Additional transition metals are being developed to include d orbitals

LimitationsLimitations

~1000 atoms, due to diagonzalization of Fock matrix

Calculations are extremely close, but not exactlyUnable to predict unknown compound typesNo guarantee to trust calculations

AdvantagesAdvantages

Once atom has been parameterized, all possible compounds can be calculated

Ability to describe bond breaking and forming reactions

Provide methods for calculating electronic wave functions

Save on amount of time for calculations

SummarySummary

Use of Semi-Empirical methods provides relatively-reliable, time-efficient calculations of chemical systems via minimal basis sets

Several different methods have been discussed:NDO’s, MINDO, AM1, PM3

Thank YouThank You

Dr. Brian Moore

Augustana College