EFFICIENT COMPUTATION OF POTENTIAL-ENERGY FIRST AND 2ND DERIVATIVES FOR MOLECULAR-DYNAMICS, NORMAL-COORDINATE ANALYSIS, AND MOLECULAR MECHANICS CALCULATIONS

By using two- and three-body internal coordinates and their derivative s as intermediates, it is possible to enormously simplify formulas for three- and four-body internal coordinates and their derivatives. Usin g this approach, simple formulas are presented for stretch (two-body), two types of bend (three-body), and wag and two types of torsion (fou r-body) internal coordinates and their first and second derivatives. T he formulas are eminently suitable for economizing molecular dynamics and molecular mechanics calculations and normal coordinate analysis of complicated potential energy surfaces. Efficient methods for computin g derivatives of entire potential energy terms, and in particular cros s terms or terms with switching functions, are presented.