Infrared photoconversion of rotational isomers: Theoretical treatment and isometric group selection rules

Abstract

A treatment of the dynamical problem of molecules featuring both infinitesimal internal modes (“vibrations”) and finite internal modes (e.g., internal rotations) is presented, which might serve as a theoretical basis of the interconversion by infrared radiation of conformers of molecules isolated in matrices. Basing on definitions for nuclear configurations of semirigid and quasi semirigid molecular models (SRMs and QSRMs) and the isometric groups associated with these models the internal classical kinetic and potential energy functions for systems characterized by inf infinitesimal and fin finite internal coordinates are formulated to various degrees of approximation. By the use of the isometric group X(gx) and procedures for construction of symmetrized infinitesimal internal coordinates derived in a foregoing paper a number of general Wigner-Eckart type theorems for subblocks of the kinetic and potential energy matrix are proven. For SRMs whose covering group X(ξ) is nontrivial, it is shown that the dynamical problem to lowest order decomposes into two problems which belong to engendered and nonengendered irreducible representations of X(ξ) respectively. Subjecting the symmetrized infinitesimal coordinates to Mathieu transformations the classical energy function is transformed to a standard form which resembles closely that commonly used for quasi rigid molecules (QRMs) and which can be transcribed into the quantum mechanical energy operator in a straightforward way. The energy eigenvalue problem for general QSRMs is discussed in terms of a solution by diagonalization of (truncated) infinite matrices. All matrix elements of the energy operator to lowest order will be calculated; their dependence on isometric symmetry closely parallels that of the classical system, in particular decomposition into parts belonging to engendered and nonengendered irreducible representations is the dominant structural aspect of the quantum mechanical treatment. This decomposition represents general selection rules (based on isometric symmetry) for interconversion of conformations of molecules through excitation of specific vibrational modes and energy transfer to highly excited internal rotation states. Asymptotic approximations to highly excited internal rotation states will be derived. A number of applications to further problems will briefly be mentioned.