Theoretical Predictions of the Vibrational Frequencies of Singlet Li₄

Abstract

The geometry of the singlet ground state of Li₄, has been optimized using gradient methods in a 6–21G and 6–21G* basis using MICROMOLE and HONDO/5 computer programs respectively. The geometries were exhaustively optimized to provide the best energy minimum point at which to calculate the force constant matrix from a finite gradient difference and thus estimate the vibrational frequencies of the cluster. The lowest energy vibration is estimated as 100 to 106 cm in energy and offers a vibronic mechanism to a quasi-tetrahedral triplet state. The triplet geometry was optimized in an ST0–6G basis and both singlet and triplet geometries were compared in a Van Duijneveldt (10s, 2p/4s, 1p) basis with configuration interaction (C.I.) treatment including valence shell single, double, and selected quadruple excitations. The 99 C.I. singlet energy at the 6–21G geometry is -29.782356 au and the 100 C.I. triplet energy at the ST0–6G geometry is -29.754456 au. Three quadruple excitations contributed only 0.064 ev to the singlet, and split-double (11) excitations were more important than quadruple excitations in the triplet C.I. This study suggests an electronic singlet-triplet transition in Li₄ at about 0.8 ev (1550 nm. wavelength) which may couple with a vibrational mode of about 100 cm^-1.