Redundant internal coordinates, compliance constants and non-bonded interactions – some new insights

Abstract

A long standing problem in normal mode analysis is identifying the right internal coordinates given only the cartesian coordinates, the masses of the atoms and the cartesian force constants without using any other additional chemical information. A possible solution is suggested here as drawing the normal modes obtained from the mass weighted cartesian force constant matrix and identifying the correct bonds and angles from the normal mode pictures. If chosen properly, the internal coordinates will have minimum mixing in the normal mode representation. This can in principle lead to an automation algorithm. A complete basis of internal coordinates is defined as the minimum number of valence internal coordinates that describe all the normal modes as completely as possible. It was shown in the literature that the relaxed force constants could be used as a measure of bond order in all atom–atom distance coordinates. Some of the bonded and non-bonded atom pairs can have similar values of the relaxed force constants and hence to use the relaxed force constant as a measure of bond order we need to separate the bonded pairs from the non-bonded ones. This needs extra chemical information of which pairs are bonded. The new definition of complete basis of non-redundant valence internal coordinates helps to identify the bonded pairs effectively without extra information. The hydrogen bonded water clusters (H2O)n, n = 2–6, methane dimer and methane–water complex are used as examples to verify that the relaxed force constants of bonded pairs are indeed a measure of bond order. A new definition of a complete basis of valence internal coordinates and a way of choosing them from the normal mode pictures is provided. The meaning of redundancy in redundant internal coordinates is explored. This new definition helps to identify the bonded pairs for which the relaxed force constants are a measure of bond order. Hydrogen bonded clusters are used as examples.