A Method of Rapid Calculation of a Second Derivative Matrix of Conformational Energy for Large Molecules

A new algorithm is described to calculate a second derivative matrix of the conformational energy surface for non-cyclic molecules, in which bond lengths and bond angles are treated as fixed and only torsional angles are treated as independent variables. This algorithm involves a number of operations proportional to n 2 , where n is the number of rotatable torsional angles, while conventional methods require a number of operations proportional to n 4 . Therefore, the present method is a very rapid one for large molecules. A method is developed for rapid calculation of first derivatives, as well.