Method for the evaluation of normal modes and molecular mechanics with reduced sets of force constants. 1. Principles and reliability test

A novel method was developed for molecular mechanics calculations and norma l mode analysis. In this approach, the number of free parameters is strongl y reduced compared with other empirical force fields, and in contrast to th em is generally smaller than the number of available wavenumber values. The molecule is subdivided into local units, each of which is constituted by a distinct atom and its nearest neighbors. The vibrational force field is th en expressed as the sum over the contributions from all local units, and ea ch local unit's potential function is assumed to depend solely on the atomi c positions within the unit. Local units often exhibit high symmetry, becau se each atom forms bonds which are characteristic of its valencies and hybr idization state, and the bonds are therefore arranged in a symmetrical way. This local (pseudo)symmetry imposes group theoretical restrictions that re duce the number of possible interaction parameters. As suggested by ab init io results, the internal force constants of each local unit are transferabl e to other molecules. It is therefore possible to calculate the internal fo rce constants of each local unit from small molecules and these are then us ed to calculate the potential of large molecules such as porphyrins. A seri es of alkanes, ethene, some homo- and heterocyclic aromatic compounds and p orphyrins were analyzed. The results for the normal mode wavenumbers and th eir eigenvectors are comparable to those reported in the literature and to results from DFT calculations [B3-LYP/6-31G(d)]. The force constants were c lose to those obtained from ab initio calculations using local symmetry coo rdinates for ethene, ethane and propane. Moreover, the above procedure repr oduces very well the vibrational wavenumbers and mode compositions of aroma tic compounds and porphyrins, as shown by comparison with DFT calculations. In contrast to general valence force field calculations, the number of fre e parameters is reduced by 40-80%. Copyright (C) 1999 John Wiley & Sons, Lt d.