Parameterization of Semiempirical MO Methods

The parameterization process allows assignment of specific values to quantities not directly available from experiment and difficult to estimate accurately a priori. As important as the theoretical model in semiempirical methodology is, often the philosophy of parameterization that was used to derive the parameters for each element from the experimental data is at least as important. This is certainly the case with AMI and the closely related PM3 method. These two methods employ the same theoretical model, but differ only by the approach taken in parameterization. This resulted in two very different chemical models. Parameterizations may be based on either experimental data or the results of more complete HF calculations. AMI, along with most other currently used methods, depended on experimental data. This has significant advantages. First, any theoretical inadequacy of higher level ab initio methods are circumvented. Second, relaxation of the parameters in such a way as to reproduce experiment handles in one step a multitude of chemical factors not directly includable or includable only at vast expense (i.e., dynamic electron correlation) in the model. The procedure and philosophy used in AMI and the other Dewar-style methods (except PM3) will be discussed below (see also Parameterization of Semiempirical MO Methods). 

Configuration Interaction Semiempirical Calculations MNDO MNDO/d Parameterization of Semiempirical MO Methods PM3 Semiempirical Vibrational Frequencies (Including Scaling). 

AMI AMBER A Program for Simulation of Biological and Organic Molecules CHARMM The Energy Function and Its Parameterization Combined Quantum Mechanics and Molecular Mechanics Approaches to Chemical and Biochemical Reactivity Density Functional Theory (DFT), Hartree-Fock (HF), and the Self-consistent Field Divide and Conquer for Semiempirical MO Methods Electrostatic Catalysis Force Fields A General Discussion Force Fields CFF GROMOS Force Field Hybrid Methods Hybrid Quantum Mechanical/Molecular Mechanical (QM/MM) Methods Mixed Quantum-Classical Methods MNDO MNDO/d Molecular Dynamics Techniques and Applications to Proteins OPLS Force Fields Parameterization of Semiempirical MO Methods PM3 Protein Force Fields Quantum Mechanical/Molecular Mechanical (QM/MM) Coupled Potentials Quantum Mecha-nics/Molecular Mechanics (QM/MM) SINDOI Parameterization and Application. 

Parameterization of Semiempirical MO Methods Pharmacophore and Drug Discovery Quantitative Structure-Property Relationships (QSPR) Shape Analysis Structural Similarity Measures for Database Searching Structure and Substructure Searching Structure Databases Superfamily Analysis Understanding Protein Function from Structure and Sequence Three-dimensional Structure Searching. 

AMI Divide and Conquer for Semiempirical MO Methods Green s Function Ionization Potentials in Semiempirical MO Theory Hydrogen Bonds Semiempirical Methods Localized MO SCF Methods MNDO/d Parameterization of Semiempirical MO Methods PM3 Polymers Semiempirical Calculations Population Analyses for Semiempirical Methods Semiempirical Vibrational Frequencies (Including Scaling). 

Electrostatic Potentials Chemical Applications Parameterization of Semiempirical MO Method. 

Some of the more widely used semiempirical MO methods in recent years have been the MNDO and AMI approximations developed by Dewar and co-workers [20, 21]. They have been parameterized for calculations on systems containing first row elements and some heavier atoms and their reliability has been extensively documented, both in tests of the parameterization and in applications to real problems. 

Most of the semiempirical MO methods currently used are based on SCF theory and differ in the approximations that are made so as to simplify the evaluation of the two-electron repulsion integrals. The approximations are then corrected for by parametrization, wherein parameters are included in the fundamental protocol to make the results match ab initio calculations on known systems. Examples of these semiempirical methods are CNDO (complete neglect of differential overlap), INDO (intermediate neglect of differential overlap), and NDDO (neglect of diatomic differential overlap). An alternative approach is to parameterize the calculations to optimize agreement with measured molecular properties, such as thermochemical, structural, or spectral data. 

The extent of approximation and parameterization varies with the different MO methods. As computer power has expanded, it has become possible to do MO calculations on larger molecules and with larger basis sets and fewer approximations and parameters. The accuracy with which calculations can predict structure, energy, and electron density has improved as better means of dealing with the various approximations have been developed. In the succeeding sections, we discuss three kinds of MO calculations (1) the Htickel MO method, (2) semiempirical methods, and (3) ab initio methods, and give examples of the application of each of these approaches. 

That said above does not mean that a semiempirical parameterization based on the HFR MO LCAO scheme and valid for a certain narrow class of compounds or even for a specific purpose cannot be built. It is done for example in [69] for iron(H) porphyrins. But in a more general case there is no way to arrive to any definite conclusion [76] about the validity of a semiempirical parameterization in the HFR context. On the other hand we have to mention that the semiempirical method ZINDO/1 [77] which allows for... 

The agreement between theory and experiment for commonly computed properties can be judged from the data in Tables 6-8. These data were drawn from the literature. Ab initio calculations give results that are close to experiment on average. Since the semiempirical and ab initio tests were not done on identical sets of molecules, it is hard to evaluate exactly how much better ab initio is. Although an ab initio molecular orbital calculation is based on first principles, predictions from such a calculation are not necessarily better than those from some of the recent semiempirical molecular orbital or empirical force field methods. A carefully parameterized, general force field can, in fact, predict molecular geometries as well as or better than an ab initio MO calculation. Overall, however, molecular models built quantum mechanically will be quite realistic. 

Warren Hehre has used Thiel s theoretical model to parameterize several transition metals, beginning with the PM3 approach rather than MNDO. The resulting model is called PM3(tm) and is available from Wavefunction, Inc. in Spartan. A primary difference between previous general semiempirical methods and PM3(tm) is that data for the parameterization focused on geometries (some solid state) rather than a more balanced range of properties. PM3(tm) parameters are available for Ti, Cr, Mn, Fe, Co, Ni, Cu, Zn, Zr, Mo, Ru, Rh, Pd, Cd, Hf, Ta, W, Hg, and Gd. 

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