Limitations and Advantages of Semi-empirical Methods

The neglect of all three- and four-centre two-electron integrals reduces the constructioi of the Fock matrix from a formal order of to M. However, the time required fo 

The parameterization of MNDO/AM1/PM3 is performed by adjusting the constants involved in the different methods so that the results of HF calculations fit experimental data as closely as possible. This is in a sense wrong. We know that the HF method cannot give the correct result, even in the limit of an infinite basis set and without approximations. The HF results lack electron correlation, as will be discussed in Chapter 4, but the experimental data of course include such effects. This may be viewed as an advantage, the electron correlation effects are implicitly taken into account in the parameterization, and we need not perform complicated calculations to improve deficiencies in fhe HF procedure. However, it becomes problematic when the HF wave function cannot describe the system even qualitatively correctly, as for example with biradicals and excited states. Additional flexibility can be introduced in the trial wave function by adding more Slater determinants, for example by means of a Cl procedure (see Chapter 4 for details). But electron cori elation is then taken into account twice, once in the parameterization at the HF level, and once explicitly by the Cl calculation. 

Semi-empirical methods are zero-dimensional, just as force field mefhods are. There is no way of assessing the reliability of a given result within the method. This is due to the selection of a fixed (minimum) basis set. The only way of judging results is by comparing the accuracy of other calculations on similar systems with experimental data. 

Semi-empirical models provide a method for calculating the electronic wave function, which may be used for predicting a variety of properties. There is nothing to hinder the 

Szabo and N. S. Ostlund Modem Quantum Chemistry, McGraw-Hill, 1982 R. McWeeny, Methods of Molecular Quantum Mechanics, Academic Press, 1992 W. J. Hehre, L. Radom, J. A. Pople and P. v. R. Schleyer Ah Initio Molecular Orbital Theory, Wiley, 1986 J. Simons, J. Phys. Chem., 95 (1991), 1017 J. Simons and J. Nichols, Quantum Mechanics in Chemistry, Oxford University Press, 1997. 

Atoms are assigned types , much as in force field methods, i.e. the parameters depend on the nuclear charge and the bonding situation. The and Pab parameters for atom types A and B are related to the corresponding parameters for sp -hybridized carbon by means of the dimensionless constants Ha and A ab- 

The carbon parameters cfc and Pec are normally just denoted aand P, and are rarely assigned numerical values. Simple Htickel theory thus only considers the connectivity of the ji-atoms there is no information about the molecular geometry entering the calculation (e.g. whether some bonds are shorter or longer than others, or differences in bond angles). 

In analogy to extended Htickel theory, there are also charge iterative methods for simple Htickel theory. The equivalent of eq. (3.99) is given in eq. (3.104). 

The Htickel method is essentially only used for educational purposes or for very qualitative orbital considerations. It has the abihty to produce qualitatively correct MOs, involving a computational effort that is within reach of doing by hand. 

ELECTRONIC STRUCTURE METHODS INDEPENDENT-PARTICLE MODELS 

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For polyatomic molecules the situation is more complex, and detailed knowledge of the potential hypersurface is available only for few systems. Semi-empirical methods are therefore introduced. As in the construction of the LEPS surface one should in the semi-empirical method, use expressions which behave correctly in the asymptotic limit. Thus for the molecule ABC the potential should approach Vab for bc oo Vbc for Rab oo, and Vac for Rab oo. The LEPS function discussed above has this property. However, it is advantageous to have a recipe which uses the extensive information on force-field potentials which is available from spectroscopic measurements. For a molecule as CO2, the... 

Each of these tools has advantages and limitations. Ab initio methods involve intensive computation and therefore tend to be limited, for practical reasons of computer time, to smaller atoms, molecules, radicals, and ions. Their CPU time needs usually vary with basis set size (M) as at least M correlated methods require time proportional to at least M because they involve transformation of the atomic-orbital-based two-electron integrals to the molecular orbital basis. As computers continue to advance in power and memory size, and as theoretical methods and algorithms continue to improve, ab initio techniques will be applied to larger and more complex species. When dealing with systems in which qualitatively new electronic environments and/or new bonding types arise, or excited electronic states that are unusual, ab initio methods are essential. Semi-empirical or empirical methods would be of little use on systems whose electronic properties have not been included in the data base used to construct the parameters of such models. 

Although electronic transition energies are mainly obtained by semi-empirical SCF methods with limited configuration interaction (LCI) based on delocalized orbitals, the use of localized orbitals has some advantages for the interpretation of data. The latter procedure is known as the Molecules-in-Molecule (MIM) method. An extension of this method to ir-electron systems with heteroatoms has been given and exemplified for sulphur-containing compounds. Differences in the calculated spectral data between the PPP and MIM methods are small where the participating localized tt systems are weakly coupled. ... 

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