Molecular Rotation in the Solid State. Theory of Rotation of Trapped Molecules in Rare-Gas Lattices

Abstract

A theory is presented to explain the rotational perturbations experienced by a molecule trapped substitutionally in a rare‐gas lattice at low temperatures (4°—20°K). The nonbonded repulsive interaction due to the Pauli exclusion principle between the molecule and the host lattice has been ignored in preference to the multipole charge interaction. In the case of an octahedral substitutional trapping site the dominant interacting term is the rotation of a permanent molecular hexadecapolar charge distribution interacting with the fourth gradient of the electric potential at the molecular center of mass due to all of the lattice charges. A general method of computing the fourth gradient of the potential due to the rotational independent induced‐dipole—induced‐dipole effect is given in the Appendix in terms of the molecular and atomic polarizabilities and ionization constants. Matrix elements are given for linear, spherical‐top, symmetric‐top, and asymmetric‐top molecules. The theory for a trapped linear molecule is applied to the vibration—rotation data of HCl trapped in an Ar lattice yielding a value of the single molecular hexadecapole moment in HCl of 3.9×10⁻⁴² esu cm⁴. Other effects discussed are: (1) higher‐order terms in the potential expansion, (2) isotopic substitution in the molecule, and (3) the rotation of HCl in the other rare‐gas lattices.