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Dependence of the multipole moments, static polarizabilities, and static hyperpolarizabilities of the hydrogen molecule on the H-H separation in the ground singlet state


Miliordos, Evangelos
Hunt, Katharine L. C.


In this work, we provide values for the quadrupole moment Theta, the hexadecapole moment Phi, the dipole polarizability alpha, the quadrupole polarizability C, the dipole-octopole polarizability E, the second dipole hyperpolarizability gamma, and the dipole-dipole-quadrupole hyperpolarizability B for the hydrogen molecule in the ground singlet state, evaluated by finite-field configuration interaction singles and doubles (CISD) and coupled-cluster singles and doubles (CCSD) methods for 26 different H-H separations r, ranging from 0.567 a.u. to 10.0 a.u. Results obtained with various large correlation-consistent basis sets are compared at the vibrationally averaged bond length r(0) in the ground state. Results over the full range of r values are presented at the CISD/d-aug-cc-pV6Z level for all of the independent components of the property tensors. In general, our values agree well with previous ab initio results of high accuracy for the ranges of H-H distances that have been treated in common. To our knowledge, for H-2 in the ground state, our results are the first to be reported in the literature for Phi for r > 7.0 a.u., gamma and B for r > 6.0 a.u., and C and E for any H-H separation outside a narrow range around the potential minimum. Quantum Monte Carlo values of Theta have been given previously for H-H distances out to 10.0 a.u., but the statistical error is relatively large for r > 7.0 a.u. At the larger r values in this work, alpha(xx) and alpha(zz) show the expected functional forms, to leading order in r(-1). As r increases further, Theta and Phi vanish, while alpha, gamma, and the components of B converge to twice the isolated-atom values. Components of C and E diverge as r increases. Vibrationally averaged values of the properties are reported for all of the bound states (vibrational quantum numbers upsilon = 0-14) with rotational quantum numbers J = 0-3. Published by AIP Publishing.