Modified adiabatic approximation: Charge asymmetry in HD+ and HD

Abstract

The modified adiabatic approximation is discussed, in which the interaction of electrons with nuclei is partitioned between the electronic and nuclear Hamiltonian, in order to simulate the finite nuclear mass effect. The proposed formalism is universal and can be used in calculations for molecules of any size. The effect of electron localization on the deuteron in vibrationally excited states of HD(+) and the permanent dipole moment of HD, typically both explained in terms of nonadiabatic couplings between g and u states, are well reproduced with this method.

Hyperfine transitions in the first overtone mode of hydrogen deuteride

“…Solving the Schrödinger Equation beyond the BOA, i.e., without considering the associated corrections [5], and even including relativistic effects [6], is nowadays possible. Remarkable computational progresses have been attained on the hydrogen isotopologues thanks to the nonadiabatic perturbation theory (NAPT) or to a modified nonadiabatic approach [7]. The relativistic effects can be in principle considered [8,9] as well as the QED theory [10].…”

“…where X=H, D, etc..) makes these species rigorously nonpolar, a small permanent electric dipole moment exists in the corresponding heteroisotopic isotopologues (like HD), thereby making vibrational dipolar transitions of these molecules weakly allowed. While it is perhaps traditional to associate this weak electrical charge asymmetry (the density of charge located on the deuteron differs slightly from that located on the proton) with "nonadiabatic effects" that mix different (clamped-nucleus) adiabatic wave functions [23][24][25][26][27][28][29][30], recent works, like those based on the so called Post-BO approach [7,[31][32][33], on the so-called non-BO variational approach [34,35], or on the approximate adiabatic variational approach [36] have convincingly demonstrated that the overwhelming majority of this effect resides in the so-called adiabatic (diagonal Born-Oppenheimer) correction. Hence within this perspective, the intensity of fundamental and overtone vibrational transitions in molecules like HD can be calculated by the usual methods as currently done for the calculation of the hyperfine couplings.…”

Isotopic dipole moments in water clusters

“…In high resolution experiments, however, the isotopic effects on the electronic structure must be considered. This problem is normally treated on a nonadiabatic level for very small systems 17, 18, but it is now clear that it can be treated also on the pure electronic level, though beyond the clamped‐nuclei BO approximation 13, 14, 19–24, so that larger systems can be considered. After the implementation of upgrades of molecular structure packages to include corrections for finite nuclear masses on the correlated Molecular Orbital 25, 26 and Density Functional 27, 28 methods, it became possible to handle large isotopic systems with the same computational burden of common BO calculations.…”