Theory of Hydrogen Deuteride in Magnetic Fields

The Hamiltonian for the diatomic ${}_{}{}^1{}_{}{}^{}\Sigma$ heteronuclear molecule HD in a magnetic field is discussed. Included in the Hamiltonian are the effects of the nuclear and rotational magnetic moments interacting with the external magnetic field, magnetic shielding, molecular diamagnetism, and spin-spin magnetic interaction of the two nuclei, the interaction of the nuclear magnetic moments with the field due to the rotation of the molecule, the interaction of nuclear electric quadrupole moment, and the electron coupled nuclear spin-spin interaction. General expressions for the matrix elements of such a Hamiltonian are developed. Perturbation theory expressions for the energy of HD in the first rotational state are obtained in both strong and weak-field limits. General expressions are given up to third order and numerical perturbation coefficients as calculated with a digital computing machine are given up to ninth order. The secular equation for HD is numerically solved for intermediate fields. Curves are given showing the theoretical dependence of the energy upon the field. Effects of zero-point molecular vibration and centrifugal stretching are discussed.