Radiative and radiationless decay of resonances resulting from electronically nonadiabatic interactions: A computational approach valid for both narrow and broad linewidths and large energy shifts

Abstract

The description of resonances originating from several coupled electronic states in a diabatic or approximate diabatic basis can offer both conceptual insights and computational challenges. In a three-state problem, two bound electronic states strongly coupled to a single dissociative continuum, large resonance energy shifts (thousands of cm−1), and linewidths varying over 4 orders of magnitude can be encountered. In this work a nonperturbative computational approach is developed to treat this class of resonances. Expressions for both the radiative and radiationless decay rates are developed. Although the approach is nonperturbative, the linewidth is expressed in a Golden-Rule-type formula. The resonance energy is obtained from the iterative solution of an eigenvalue problem in the bound state space. These attributes enable efficient determination both narrow and broad linewidths and large resonance energy shifts. The approach is used to characterize both radiative and radiationless decay of the 2,3 3Πg states of Al2 using a rigorous three-state diabatic basis. Lifetimes ranging from tenths of picoseconds to nanoseconds are determined. The corresponding resonance energy shifts are on the order of 4000 cm−1.

Nonadiabatic Predissociation Studies of the (1-3)3Πg System of Al2 by Means of a Complex Rotated Finite Element Method

“…The presented E(v (2) , 0) and E(v (3) , 0) levels agree quite well with the results reported by Han et al (13) and Han and Yarkony (14). In Table 2, a selected number of energies for rotationless vibrational levels are presented.…”

“…We have neglected the spin-orbit coupling terms because no such data, consistent with the PECs used here, are available. This implies that we, as well as Han et al (13,14), use the case (b) rotational quantum number, N , i.e., {J (J + 1) − 2 } → {N (N + 1)} in Eq. [20].…”

“…The index a denotes results from the present calculations while the indices b and c denote results reported in Refs. (13,14).…”

“…This three-state system, illustrated in Fig. 1 (13,14), consists of one repulsive ( (1) 3 g ) and two attractive ((2, 3) 3 g ) electronic states. Each pair of these states is coupled to each other through nonadiabatic derivative couplings (13).…”

Rovibronic Levels for the (1–3)3Π Manifold of B2: Exterior Complex Scaling Finite Element Calculations Based on an Adiabatic and a Strictly Diabatic Basis

“…A similar behavior of the wavefunctions was discussed by Han and Yarkony (38,39). The main components for the four highest N = 0 levels are shown in Figs.…”