Semiempirical wave functions surfaces

SMI [50], SMla [50], SM2 [52], SM2.1 [54], SM2.2 [55], SMS [52,56], and SM3.1 [54] methods were parametrized only for water, and the partial charges for the electrostatic contribution were based on a Mulliken analysis of the semiempirical molecular orbital wave functions, in particular the wave functions obtained by the Austin Model 1 (AMI) [57] and the Parametrized Model 3 (PM3) [58]. These charges, like those calculated from ab initio minimum-basis-set Hartree-Fock calculations, tend to overestimate the charge separations and polarities. Since the errors are systematic, the parametric expressions for surface tensions compensate these errors. 

After the discovery of the relativistic wave equation for the electron by Dirac in 1928, it seems that all the problems in condensed-matter physics become a matter of mathematics. However, the theoretical calculations for surfaces were not practical until the discovery of the density-functional formalism by Hohenberg and Kohn (1964). Although it is already simpler than the Hartree-Fock formalism, the form of the exchange and correlation interactions in it is still too complicated for practical problems. Kohn and Sham (1965) then proposed the local density approximation, which assumes that the exchange and correlation interaction at a point is a universal function of the total electron density at the same point, and uses a semiempirical analytical formula to represent such universal interactions. The resulting equations, the Kohn-Sham equations, are much easier to handle, especially by using modern computers. This method has been the standard approach for first-principles calculations for solid surfaces. 

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