Dipole moments of symmetrical molecular systems

Abstract

It is shown that quantization of nuclear motion causes the intrinsic dipole moment of a molecular system to depart from the classical representation, e.g., it is different from zero for symmetrical molecules. A formula is derived for the mean dipole moment ¯p as a function of temperature with allowance for the internal motion of the nuclei, which is functionally related to the dipole moment. Calculations are performed for ammonia with allowance for the inversion splitting, which is due to tunneling between two equivalent equilibrium configurations having their dipole moments in opposite directions. The temperature coefficient of ¯p may be positive or negative, in accordance with the relation between the tunneling frequency and the temperature; the formula usually employed is valid only in the limiting case of low frequencies and high temperatures. A deduction is given for the criterion for instability of the maximally symmetrical configuration with respect to odd nuclear displacements (dipole distortions); this is based on a simple model system having an inversion center, a totally symmetric ground state, and a triply degenerate odd excited state of the T_1u type. The experimental consequences of the results are discussed, as well as the concept of symmetry for a molecular system in which the maximally symmetrical configuration is unstable.