Vibrational spectrum of Li3 first-excited electronic doublet state: Geometric-phase effects and statistical analysis

Abstract

We present J s 0 calculations of all bound and pseudobound vibrational states of Li in its first-excited electronic doublet state by using a realistic double 3 many-body expansion potential-energy surface and a minimum-residual filter diagonalization technique. The action of the system Hamiltonian on the wave function was evaluated by the spectral transform method in hyperspherical coordinates. Calculations of the vibrational spectra were carried out both without consideration and with consideration of geometric-phase effects. Dynamic Jahn᎐Teller and geometric-phase effects are found to play a significant role, while the calculated fundamental symmetric stretching frequency is larger by 8.3% than its reported experimental value of 326 cm y1 . From the neighbor-spacing distributions of the levels, it is observed that the title vibrational spectrum is quasiregular in the short range and quasi-irregular in the long range. By the ⌬ standard defined in this article, it is found that the spectra are more 2 nonuniform than those of the ''trough'' states for the ground electronic state.

Singularities in the Hamiltonian at electronic degeneracies

“…This result is corroborated from calculations of the vibrational spectrum for the ground and the ®rst excited states of Li 3 [18,19]. In fact, we have then found the fundamental vibrational frequency of the symmetric stretching mode to be insensitive to inclusion of the geometric phase eect.…”

“…Note that bR must change by p for any nuclear motion which encircles the conical intersection (i.e., a pseudo-rotation). In order to meet this boundary condition, it is commonly used [4,9,10,16,18,19,23,25,32,57±61] for X 3 systems the form…”

“…Instead, Billing and Markovic [33] adopted hyperspherical coordinates to include the GP eect in the nuclear wave function of X 3 molecules, which have a D 3h conical intersection seam. A similar method has been utilized by the authors to study the vibrational spectra and transition state resonances of H 3 [16] and Li 3 [18,19]. Such an approach has most recently been extended to isotopomers of X 3 systems [34].…”

Complex States of Simple Molecular Systems

“…As of late, non-linear coupling has become of increased interest, partly through evidence for a weak linear coupling in the metallic cluster N a 3 [53,270] (computations of vibrational levels in a related molecule Li 3 were performed in [271,272]), and partly by attempts to computationally locate ci's in the potential energy landscape with a view to estimate their effect on inter-surface, non-adiabatic transitions [273]. The method used in the last reference was based on the acquisition of the geometric phase by the total function as a ci is circled [274,157,158,9].…”

Vibrational Calculations for the HD2 First-Excited Electronic State Using a Coordinate-Transformation Technique

“…In this case, the complex phase factor is incorporated into the nuclear wave function so as to make the total electronuclear wave function single-valued. A similar method has been employed by us 15,17,18 to study the resonance and vibrational spectra of H 3 and Li 3 . This work has recently been reviewed, 34 while J ) 0 calculations of the vibrational states of Li 3 in its lowest electronic doublet state by using a reliable double many-body expansion 35,36 (DMBE) potential energy surface 37,38 and a minimum-residual filter diagonalization 39 (MFD) technique, both without consideration (NGP) and with consideration (GP) of the GP effect, can be found elsewhere.…”