Conjugate symmetry of molecular systems and determination of their conformations

Abstract

In nonrigid molecules and molecular aggregates, the dependence of a property on conformation may be expressed in the form of a limited expansion in terms of appropriate harmonics. The use of the conjugate symmetry of the molecular groups to reduce such an expansion may have several advantages: (i) it helps decrease, sometimes drastically, the time required to calculate the conformational dependence of the considered property; (ii) it provides a parameterized functional form that can be used by experimentalists to rationalize their results. The symmetry rules that define the distinct non-zero harmonics are determined by a set of indices that depend on both the form and type of the property (scalar, polar, axial, tensorial; aggregate, mononuclear, binuclear) and the nature of the isodynamic operations characterizing the system. We have applied Altmann's isodynamic groups to the analysis of Wigner's harmonic expansions of dynamical, electric, and magnetic properties of various molecular structures: binary molecular associations, quasi-atoms in molecular fields, rigid molecules in crystal lattices, and non-rigid molecules involving one to three rotors. A few examples are given to illustrate these considerations.