Quantifying the symmetry content of the electronic structure of molecules: molecular orbitals and the wave function

Abstract

A scheme to quantify the symmetry content of the electronic wave function and molecular orbitals for arbitrary molecules is developed within the formalism of Continuous Symmetry Measures (CSMs). After defining the symmetry operation expectation values (SOEVs) as the key quantity to gauge the symmetry content of molecular wavefunctions, we present the working equations to be implemented in order to carry out real calculations using standard quantum chemistry software. The potentialities of a symmetry analysis using this new method are shown by means of some illustrative examples such as the changes induced in the molecular orbitals of a diatomic molecule by an electronegativity perturbation, the breaking of orbital symmetry along the dissociation path of the H₂ molecule, the changes in the molecular orbitals upon a geometrical distortion of the benzene molecule, and the inversion symmetry content in the different spin states of the [Fe(CH₃)₄]²⁻ complex.