Radiationless decay of the 1,2,3 3Πg states of Al2: A fully first principles treatment using adiabatic and rigorous diabatic states

Abstract

The decay mechanisms of the metastable 2,3 3Πg states of Al2 are investigated. Both nonadiabatic radiationless decay to the dissociative 1 3Πg state and radiative decay to the ground X 3Πu state are considered. The 1,2,3 3Πg states are described using state averaged multiconfiguration self consistent field/configuration interaction wave functions [ψam(r,Q)]. The derivative couplings famn(Q)≡〈ψam(r, Q)‖(d/dQ)ψan(r,Q)〉r are determined and used to construct a rigorous diabatic basis for this strongly interacting three state problem. The 2 3Πg state and somewhat surprisingly the 3 3Πg state are rapidly predissociated by the dissociative 1 3Πg state. The lifetimes for nonradiative decay of the vibrational levels of the 2 3Πg state are on the order of picoseconds while those of the 3 3Πg state are on the order of nanoseconds being reduced from the direct coupling (3 3Πg∼1 3Πg) rate of milliseconds by indirect coupling through the 2 3Πg state, (3 3Πg∼2 3Πg∼1 3Πg). Radiative decay is found to be on the order of 102 and 30 ns for the 2 3Πg and 3 3Πg states, respectively, so that radiationless decay is principal decay mechanism. Significant variation in the lifetimes of the individual vibrational levels of the 2,3 3Πg states is expected. This is attributed to the mechanism of the predissociation which involves nonadiabatic interactions near the ‘‘inner walls’’ of the 1,2 3Πg states. Although avoided crossings strongly affect the properties of the 1,2,3 3Πg states the adiabatic basis is preferred over the diabatic basis both conceptually and computationally.

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

“…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].…”

“…for Al 2 was obtained from Huber and Herzberg (15). The initial data, in the form of adiabatic PECs and nonadiabatic derivative coupling elements for the (1-3) 3 g system, were obtained from Han et al (13) and are here represented as tension splines (42). The ADT was carried out by applying the RKF45 method on the system of coupled Eqs.…”

“…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).…”

“…The conclusion was that the nonradiative transitions are the dominating decay mechanism in this three-state system. We here apply a general diabatization procedure to the (1-3) 3 g system of Al 2 , using the adiabatic PECs and nonadiabatic derivative couplings from Han et al (13). The resulting diabatic representation is used to form a coupled-channel Schrödinger problem which is numerically solved by means of a complex rotated, one-dimensional finite element method.…”

“…al. (13), using multiconfiguration self-consistent field interaction wavefunctions, and by Han and Yarkony (14) by means of a nonperturbative computational approach. Vibrational levels as well as radiative and nonradiative lifetimes, for a number of (2,3) 3 g vibrational levels, were reported in these studies.…”