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Semi-Empirical Methods: Where 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 S = = v AB 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: = AC BD 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 1) Remaining integrals calculated from functional form of AOs 2) Remaining integrals made into parameters, assigned values based on experimental data 3) 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, SI< 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 1.3391.326 CH 1.0860.964 HCC 121.2114.64 Nitrogen NN 1.0941.106 Furan OC11.3621.431 C2C31.3611.526 C3C41.4311.522 C2H1.0751.121 C3H1.0771.117 HC2O115.9107.2 HC3C4128.0111.2

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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

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