Physical and Theoretical Chemistry

Biography

Biography: Per Jensen

Abstract

Traditionally, molecules are theoretically described as near-static structures rotating in space. Vibrational motion causing small structural deformations induces a perturbative treatment of the rotation-vibration interaction. This treatment fails in highly flexible molecules, where all vibrational motions have amplitudes comparable in size to the linear dimensions of the molecule. An example is protonated methane (CH₅⁺). For these molecules, customary theory fails to simulate reliably even the low-energy spectrum. Within the traditional view of rotation and vibration being near-separable, rotational and vibrational wavefunctions are symmetry classified separately in the molecular symmetry (MS) group. All MS groups discussed so far are isomorphic to subgroups of the special orthogonal group in three dimensions SO(3). This leads to a group theoretical foundation of the technique of equivalent rotations. The group G₂₄₀ (the MS group of protonated methane) represents, to the best of our knowledge, the first example of an MS group which is not isomorphic to a subgroup of SO(3). Because of this, a separate symmetry classification of vibrational and rotational wavefunctions becomes impossible in this MS group, consistent with the fact that a decoupling of vibrational and rotational motion is impossible. The talk will discuss the consequences of this and propose an alternative description making use of the fact that G₂₄₀ and SO(3) are both subgroups of the group SO(5) of rotations in five-dimensional space. We take SO(5) to be a near-symmetry group for CH₅⁺ and develop a theoretical model that successfully explains recent experimental observations of rotation-vibration transitions in cold CH₅⁺. Two of the vibrational degrees of freedom are essentially free and, in an initial approximation, these vibrations are combined with the “usual” rotation in 3D space with the resulting motion being viewed as free rotation in 5D space, consistent with the symmetry group SO(5).

Figure 1: The effect of the proton permutation (15432) on a CH₅⁺ ion. It rotates the quantization axis z and so the customary technique of equivalent rotations cannot be applied.