ANGULAR AND TORSIONAL FORCES VIA QUANTUM-MECHANICS

First the applications of angular and oscillatory radial forces that a re derived quantum mechanically for metals are reviewed, emphasizing t he ''mu(4)'' methods of generating angular forces, The dominant conclu sion from several applications that are discussed is that bcc transiti on metals will often sacrifice bond-length constraints in order to obt ain an energetically favorable angular environment, Then the derivatio n of angular and torsional forces for polymers such as proteins, in wh ich chemical bonds remain fairly intact, are discussed. The derivation of the mu(4) methodology is briefly reviewed, and it is shown that th e earlier mu(4) analysis of the angular forces can be understood in te rms of overlap repulsion between bond orbitals. This overlap repulsion is used to develop simplified forms for angular interactions in well- bonded systems. These angular interactions are consistent with the str uctures of P and S, A result of this analysis is that some of the ''im proper'' torsion terms that are typically used in polymer simulations may be unnecessary, It is then shown that torsional forces in polymers can be understood by a second-order perturbation analysis, in which o ne takes into account the interaction between hybridized bond orbitals on one atom with hybridized antibond orbitals on other atoms, The res ulting torsional forces are consistent with the structures of elementa l S and the ethane molecule.