A novel decomposition of torsional potentials into pairwise interactions: A study of energy second derivatives

Abstract

A general method of analyzing intramolecular torsional potentials in terms of energy second derivatives that couple the rotating atoms is presented. The method offers a rigorous decomposition of the total torsional potential into pairwise (dihedral) interactions and enables one to derive nonbonded torsional interactions between 1-4 atoms as well as between more distant atoms and sites. The method is demonstrated on ethane, propane and acetaldehyde. It is shown that the 1-4 H . . . H dihedral potentials in ethane and propane are very similar, thereby supporting the notion of transferable force field potential functions. However, the dihedral potentials that are obtained differ from 1-4 potentials that are used in current force fields. Intramolecular three body effects are clearly seen in this method and are found to be relatively large for the dihedral interactions, although in the one case studied (propane) the overall effect on the methyl-methyl interaction is negligible due to cancellation of terms. The analysis explicitly shows that the barrier in acetaldehyde is due mainly to the dihedral H . . . H interaction.

Derivation of class II force fields. VIII. Derivation of a general quantum mechanical force field for organic compounds

“…This comprehensive set of coupling and anharmonic terms is an essential feature of the class II force field. In previous articles 7,8,10 we have demonstrated the appreciable increase in accuracy of computed molecular properties that results from including these additional terms, which reflect the coupling interactions between valence coordinates observed in intramolecular interactions. The major improvements occur in the energetic and dynamic properties, although the structural properties improve as well.…”

“…Finally, structures at both the extrema and intermediate torsional angles are distorted along linear combinations of all internal coordinates (normal modes), using an approach we have described previously. 7,8,10 At each sampled structure the ab initio energy and the first and second derivatives of the energy with respect to atomic Cartesian displacements are computed. Finally, it is necessary to examine all the computed structures and verify that they adequately span the regions about the equilibrium values of their internal coordinates.…”

On the suitability of semiempirical calculations as sources of force field parameters

“…The determination of force field parameters from experimental data is a long and tedious process, for which a great amount of experimental data are needed. This explains the considerable research effort directed towards the development of strategies to determine force field parameters from quantum mechanical calculations [1,[17][18][19][20][21][22][23][24][25][26][27][28]. In this respect, some strategies have recently been reported to compute the nonbonded force field parameters, i.e.…”

“…the van der Waals and hydrogen bond constants [18419], as well as the atomic charges and bond dipoles [24][25][26][27][28]. Moreover, other strategies have been developed to calculate the bonded force field parameters [17,[19][20][21][22][23], among which Hagler's [17,19,20] and Hopfinger's [21] procedures are probably the most widely used.…”

“…Thus, in practice, ab initio derived force field parameters are usually obtained from calculations on small molecules, which are very different to those of real interest. As a consequence, even the ab initio methods provide excellent force field parameters [17][18][19][20]22,23,29,30], since such parameters are obtained in a very different molecular environment, their ability to describe the large molecule which will be studied by molecular mechanical dynamical techniques can be poor. Here, out attention is focused on the study of the reliability of the semiempirical RHF wave function computed from MINDO/3 [2], MNDO [3], and AM 1 [4] Hamiltonians to correctly represent the molecular characteristics in its perturbed geometries.…”