An orbital-based definition of radical and multiradical character

Abstract

A definition for radical and general m-fold multiradical character of molecular systems is formulated. The orbitals in which lone or odd electrons most often reside are identified; these orbitals are found by maximizing their probability of (m-fold simultaneous) single occupancy over orbital rotations. The maximum such probability functions as a scalar measure of (multi)radical character. The method is general and applicable to wavefunctions of any form. The radical character, as defined here, obeys strict bounds of zero and unity and has a well-defined meaning. The method has been implemented generally, and it has been tested on simple radical, diradical (biradical), and triradical systems. The results agree with chemical experience for these cases, and in the diradical case, we show that it agrees qualitatively with earlier proposed characterization schemes. Specific implementation for monoradical character requires only two-particle density matrix information, and furthermore, a promising approximation for the diradical analogue can be constructed from quantities that we call the first and second monoradical characters and orbitals. An algebraic connection can be made to a reinterpretation of the widely discussed distribution of total odd electrons.