Generalized diatomics-in-molecules method for polyatomic anions

Abstract

The diatomics-in-molecules (DIM) method for the construction of polyatomic potential-energy functions from the potential energies of atomic and diatomic fragments is generalized to obtain a description of potential-energy functions of both quasistationary and bound states of polyatomic anions. The formulation is based on the combination of the DIM method with the projection-operator approach of scattering theory. The proposed theory allows the construction of diabatic discrete states, electron-molecule scattering continua, and discrete-continuum coupling elements from the corresponding data of the fragments. The polyatomic projection-operator description obtained in this way provides the basis for a rigorous treatment of the nuclear dynamics in short-lived electron-molecule collision complexes and ion-molecule collisions in terms of energy-dependent, complex, and nonlocal effective potentials. More approximate local complex potential-energy surfaces of quasistationary states of polyatomic anions also can be obtained with the generalized DIM method via the determination of the poles of the multichannel electron-molecule scattering matrix in the fixed-nuclei limit. Although the focus of the present work is on anions, the proposed theory is also applicable to quasistationary states of neutral and positively charged polyatomic systems including clusters. To illustrate the concepts, the generalized DIM method is applied to obtain the potential-energy functions of the ground and first excited states of the ${\mathrm{H}}_{3}^{\ensuremath{-}}$ anion, making use of information that is available for the bound and resonance states of ${\mathrm{H}}^{\ensuremath{-}}$ and ${\mathrm{H}}_{2}^{\ensuremath{-}}.$