Hindered macromolecular chains: A quantum mechanical model

Abstract

A model for an open hindered three-dimensional macromolecular chain, based upon quantum mechanics, is proposed, which improves previous work. The chain is formed by N particles (so that all bond lengths between successive particles take on given values) and harmonic-like vibrational potentials in the high-frequency limit constrain all successive bond angles. This formulation leads, via a variational procedure and a suitable choice of variables, to a specific quantum Hamiltonian for the chain. Issues related to overall rotational invariance are clarified. Some properties of the resulting classical partition function are analyzed. Several checks of consistency are given.