A Unique QP Partitioning and Siegert Width Using Real-Valued Continuum-Remover Potential

A simple, practical quantum chemical procedure is presented for computing the energy position and the decay width of autoionization resonances. It combines the L²-stabilized resonance wave function obtained using the real-valued continuum-remover (CR) potential [Y. Sajeev Chem. Phys. Lett. 2013, 587, 105-112] and the Feshbach projection operator (FPO) partitioning technique. Unlike the conventional FPO partitioning of the total wave function into its resonant $$ space and background $$ space components, an explicit partitioning of the total wave function into its interaction region and noninteraction region components is obtained with the help of real-valued continuum-remover potential. The molecular system is initially confined inside a CR potential which removes the electronic continuum of the molecular system in which its resonance state is embedded and, thus, unravels the $$ space component of the resonance wave function as a bound, localized eigenstate of the confined system. The eigenfunctions of the molecular Hamiltonian represented in the $$ space constitute a complementary, orthogonal $$ space. A unique $$ partition is obtained when the level-shift of the $$ space function due to its coupling with the $$ space is zero, and the resonance width is computed using these unique partitioned spaces. This new procedure, which we refer to as CR-FPO formalism, is formally very simple and straightforward to implement, yet its applications to the resonance state of a model Hamiltonian and to the doubly excited resonance states of atomic and molecular systems at the full-CI level are very accurate as compared to the alternative, very precise L² methods. In addition, the CR-FPO formalism is implemented in the multireference configuration interaction (MRCI) method, and uses it for calculating the energy position and the autionization decay width of ²Π shape resonance in N₂^-.