Semiempirical Calculations

Semiempirical quantum mechanical calculations are based on the Schrödinger equation. This chapter deals with SCF semiempirical methods, in which repeated (in contrast to the simple and extended Hückel methods) diagonalization of a Fock matrix refines the wavefunction and molecular energy. These calculations are much faster than ab initio ones, mainly because the number of integrals to be dealt with is greatly reduced by ignoring some and approximating others with the help of experimental quantities or with values from high-level ab initio or DFT calculations. In order of increasing sophistication, these SCF semiempirical methods have been developed: PPP (Pariser-Parr-Pople), CNDO (complete neglect of differential overlap), INDO (intermediate neglect of differential overlap), and NDDO (neglect of diatomic differential overlap). Today, the most popular SCF semiempirical methods are variations of NDDO: AM1 (Austin model 1, from Austin, Texas) and its offshoot PM3 (parametric method 3), and refinements up to PM7, which are carefully parameterized to reproduce experimental quantities, mainly heats of formation. Extensions of AM1 (RM1, Recife model 1, from Recife, Brazil) and PM3-PM7 seem to represent substantial improvements, and PM7 may be, or may become, the standard semiempirical “general SCF-type” method.