Extensions and foundations of the continuous symmetry measure

A quantum mechanical extension of the continuous symmetry measures (CMS) proposed by Avnir et al. is described. The theoretical framework is essentially based in a simple extension of the HMO approach, leading to compute molecular CSM energy spectra, constituting a useful step for construction of first and higher order CSM terms. This permits in turn to connect the general CMS theoretical framework with the fundaments of structure-property relationships and allows the evaluation of statistical mechanics CMS partition functions and the deduction of CMS thermodinamical functions as well.