Models for polymers and biopolymers based on quantum mechanics

Abstract

A study has been made of several types of 3-dimensional macromolecular chains: open and closed-ring linear chains, star polymers and double-stranded chains. Chains in thermal equilibrium at room temperature are assumed, and typical harmonic-oscillator-like vibrational potentials with frequencies ωi for the interactions of nearest-neighbour atoms along the same chain. For the double-stranded chain, the interactions between atoms in different strands behave like the Morse potential. In physically interesting cases ωi is large, so that all rapidly varying vibrational degrees of freedom have to be treated quantum mechanically, and these are represented approximately by ground state wavefunctions; they decouple consistently, yielding constant bond lengths. This generates effective quantum Hamiltonians and partition functions for the macromolecules, depending only on the remaining and relevant slowly varying degrees of freedom (angles determining internal rotations). At room temperature, the classical limit of the slowly varying quantum description yields simpler effective classical Hamiltonians and partition functions. Previous results for the open linear chain are discussed together with former work for the closed-ring linear chain, and new models are presented for star polymers and double-stranded macromolecules. The model appears to describe consistently a double-stranded chain at temperatures below thermal denaturation.