Semiempirical methods INDEX

Those who applied quantum mechanics to atoms and molecules had a wealth of chemists data at hand well-defined bond properties including dipole moments, index of refractions, and ultraviolet absorption qualities and polarizability as well as well-defined valence properties of atoms in molecules. If one attempted to set up a wave equation for the water molecule, for example, there were 39 independent variables, reducible to 20 by symmetry considerations. But the experimental facts of chemistry implied or required certain properties that made it possible to solve equations by semiempirical methods. "Chemistry could be said to be solving the mathematicians problems and not the other way around," according to Coulson. 148... 

The established semiempirical methods developed until 1990 have been applied extensively in chemical research. There are thousands of publications with applications of semiempirical methods to solve chemical problems, as indicated by the Science Citation Index where the number of citations for the original papers on CNDO/2 [13], MINDO/3 [15], MNDO [16], AMI [18], PM3 [19], and INDO/S [23] currently (June 2004) exceeds 2500, 2100, 5800, 9800, 4500, and 1200, respectively. This is further illustrated in Fig. 21.1 which shows the corresponding citations per year between 1966 and 2003. Assuming that the number of citations reflects the actual use of these methods, it is obvious that AMI and PM3 are presently the most popular semiempirical tools in computational work. 

With respect to the metal-adsorbate interaction it is of interest, for comparison with the experimental results, to develop theoretical calculations based on molecular models that involve the adsorbate molecules and a metal cluster. The INDO/1 semiempirical method has been proved to be very useful in the stmc-ture optimization and in the evaluation of the bond characteristics throughout the Wiberg index - ° The interaction of azamacrocycle complexes with simulated copper surfaces studied by the same method was performed -... 

Hall and Kier investigated the possible relationship between topological indices and the partial charge computed by semiempirical MO methods The following model was obtained in a comparison of atomic indices from MO theory (partial charge) and a modified version of the chi indices. In this case the chi indices were partitioned into atomic contributions. Of course, the index is already defined as an atom index the others are given the strike-through symbol, x (equation 24) ... 

The links with the underlying theory become feeble. The computers arc omnivorous observables or other statutory quantities attract their interest as well as molecular indexes or other interpretative tools, these last often considered at the same degree of "realism" as the physical observables. The selection of the level of the theory and of the method is basal on the criterion of "continuity", i.e. by looking at the methods used by other computers and trying to do something better. A criterion to decide what is better is simply the cost of the method ab initio methods are better that the semiempirical ones which m turn are better than the semiclassical ones. A larger basis set is better than a smaller one, and so on. 

A calculation with the semiempirical SIND01 method yields a ring current index of 1.720 for indicative of an aromatic ion. The anion c-NgH " was found to be unstable,... 

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