Semi-Empirical Methods: Where is the Rest?

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Semi-Empirical MethodsWhere is the Rest?

• Matthew Grandbois
• CHEM 381
• Spring 2004

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Introduction

• Computational chemistry is one of the fastest
  growing areas of chemistry
• Used to computationally determine vital
  information

• Geometry
• Bond Angles, Bond Distances, Dihedral Angles
• Dipole Moment
• Enthalpy of Formation
• Ionization Potentials

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Electronic Structure

• Calculations based on determining electronic
  structures
• Different Approaches
• Density Functional Theory
• Ab Initio
• Semi-empirical

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Semi-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.
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Semi-Empirical Approximations

• Ignoring of core electrons
• Core electrons reduce nuclear charge
• Introduction of function to model combined
  repulsion due to nuclei and core electrons
• Minimum basis set of functions to account for
  valence electrons
• Majority of basis functions are taken to be STOs

Jensen, F. Introduction to Computational
Chemistry. John Wiley Sons, England 1999,
81.
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Huckel 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 -
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Central Assumption

• Zero Differential Overlap approximation
• Neglects 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
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Neglect of Diatomic Differential Overlap (NDDO)

• Only uses the previously mentioned central
  assumption
• Overlap Integral

Sm? lt mA ?B gt dmvdAB
Jensen, pg 82
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Intermediate Neglect of differential Overlap
(INDO)

• In addition to NDDO
• Neglects all two-centre 2 electron integrals
  which are not of the Coulomb type
• To preserve rotational invariance, some integrals
  must be made independent of orbital type

Jensen, pg 83
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Complete Neglect of Differntial Overlap (CNDO)

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

lt mAnB lCsDgt dACdBDdmldns lt mAnB mAnBgt lt
µAnB µAnBgt is independent of orbital type (s or
p)
Jensen, pg. 83
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Parameterization

• Direct use of ZDO approximations is not useful
  due to only qualitative picture of MOs
• 3 Methods to transform NDO approximations into
  useful computational models
• Remaining integrals calculated from functional
  form of AOs
• Remaining integrals made into parameters,
  assigned values based on experimental data
• Remaining integrals made into parameters,
  assigned values based on fitting to experimental
  data

Jensen, pg. 84
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Modified NDDO Models

• MNDO
• AM1
• PM3

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Modified Neglect of Diatomic Overlap (MNDO)

• One of first paramaterization models used
• Parameterizes H, B, C, N, O, F, Al, Si, P, S,
  Cl, Zn, Ge, Br, Sn, I, Hg, and Pb.
• Some Limitations
• Succeeded by AM1 and PM3 Models

Jensen, pg. 87
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Austin Model 1 (AM1)

• Developed by Dewar at the University of Texas at
  Austin, 1985.
• Came from systematics errors of MNDO
• Too high repulsion between atoms 2-3 Å apart
• Parameterized for
• H, B, C, N, O, F, Al, SIlt P, S, Cl, Zn, Ge, Br,
  I, and Hg.
• Some Limitations

Jensen, pg. 87
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AM1

• 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)

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AM1 Geometries

• Ethene
• CC 1.339 1.326
• CH 1.086 0.964
• HCC 121.2 114.64
• Nitrogen
• NN 1.094 1.106

• Furan
• OC1 1.362 1.431
• C2C3 1.361 1.526
• C3C4 1.431 1.522
• C2H 1.075 1.121
• C3H 1.077 1.117
• HC2O 115.9 107.2
• HC3C4 128.0 111.2

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Modified Neglect of Diatomic Overlap, Parametric
Method Number 3 (PM3)

• MNDO and AM1 parameters were done by hand,
  limiting number of reference compounds
• Essentially, AM1 with all parameters fully
  optimized
• Still needs some human intervention
• Parameterized 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

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Limitations

• 1000 atoms, due to diagonzalization of Fock
  matrix
• Calculations are extremely close, but not exactly
• Unable to predict unknown compound types
• No guarantee to trust calculations

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Advantages

• 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

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Summary

• Use of Semi-Empirical methods provides
  relatively-reliable, time-efficient calculations
  of chemical systems via minimal basis sets
• Several different methods have been discussed
• NDOs, MINDO, AM1, PM3

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Thank You

• Dr. Brian Moore
• Augustana College