Finite field configuration interaction calculations on the distance dependence of the hyperpolarizabilities of H2

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

In this work, we provide values for the quadrupole moment Θ, the hexadecapole moment Φ, the dipole polarizability α, the quadrupole polarizability C, the dipole-octopole polarizability E, the second dipole hyperpolarizability γ, 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 r₀ 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 H₂ in the ground state, our results are the first to be reported in the literature for Φ for r > 7.0 a.u., γ 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 Θ 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, α_xx and α_zz show the expected functional forms, to leading order in r^-1. As r increases further, Θ and Φ vanish, while α, γ, 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 υ = 0-14) with rotational quantum numbers J = 0-3.

Variationally stable calculations for molecular systems: polarizabilities and two-photon ionization cross section for the hydrogen molecule

The variationally stable method of Gao and Starace [B. Gao and A. F. Starace, Phys. Rev. Lett. 61, 404 (1988); Phys. Rev. A 39, 4550 (1989)] has been applied for the first time to the study of multiphoton processes in molecular systems. The generalization in theory is presented, as well as the calculation of properties such as the static and dynamic polarizabilities of the hydrogen molecule and the generalized two-photon ionization cross section. The Schwinger variational iterative method [R. R. Lucchese and V. McKoy, Phys. Rev. A 21, 112 (1980)] has been applied in the achievement of the photoelectron wave function, while a Hartree-Fock representation has been used for the target. This research has been motivated by the scarceness of ab initio calculations of molecular multiphoton ionization cross sections in the literature.