Novel theory of the HD dipole moment. I. Theory

A novel theory of the electric dipole moments of homopolar but isotopically asymmetric molecules (such as HD, HT, or DT) is formulated, such that electrical asymmetry and the resulting dipole moment arise as purely electronic properties within a suitable Born-Oppenheimer approximation, and nonadiabatic (rovibronic) perturbations play no part in the theory. It is shown thereby that a much simpler and more direct explanation for these dipole moments can be given than that invoking non- adiabatic perturbations: The dipole moment arises from isotopic variation of the local effective electronic reduced mass and its effects on binding energies and sizes of orbitals. It is an odd function of the isotopic splitting parameter ${\alpha }_0$=(1/2)λm/μ, where λ=($M_A$-$M_B$)/($M_A$+$M_B$) is the nuclear mass asymmetry for nuclei A,B and (m/μ) is the electron-nuclear mass ratio (for HD, this parameter is 1.36×${10}^{\mathrm{-}4}$). A canonical transformation exhibiting these effects (in the form of an asymmetric effective potential) is the basis for the new formulation. Since ${\alpha }_0$ is small the resulting dipole moment function is essentially linear in ${\alpha }_0$, and hence the dipole moment functions for HT and DT may be computed by rescaling the results for HD. Since the problem is purely electronic in the new formulation, variational and convergence studies are easy to carry out. In this and the following paper we formulate the new theory in detail and carry out variation-perturbation calculations of the HD dipole moment. The results are in good agreement with theoretical results obtained by nonadiabatic perturbation theory and demonstrate that this approach to isotopically induced dipole moments is valid.