The energy well connection graph: a use of curvilinear coordinates to achieve dimension reduction for graph representation of molecular conformation energy data

Abstract

In the conformation space of a flexible molecule, curvilinear coordinate paths connecting conformations of segments of the given molecule are used to reduce the number of variables required for describing barriers between preferred conformations of the molecule as a whole. The technique is applied to a hypothetical example, then to m-trinuoromethyl-N-ethyl-amphetamine (fenfluramine), and to N-methyl-3-phenyl-3-(o-methoxyphenoxy)-propylamine (nisoxetine). In the latter example, the number of variables is thus reduced from six to three. In all three examples, a graph representation of low-energy well connection is achieved. The limit of easy comprehension has thus been moved back from about three torsion angles to three effective segments. Within this limit the procedure leads to a quantitative diagram, which is no harder to read than a contour map, showing the barriers to low-energy interconnection among the favorable conformations of a moderately complex molecule.