Non-Born–Oppenheimer molecular structure and one-particle densities for H2D+

Abstract

We show that the nonadiabatic (non-Born-Oppenheimer) ground state of a three-nuclei system can be effectively calculated with the use of an explicitly correlated Gaussian basis set with floating centers. Sample calculations performed for the H2D+ system with various basis set sizes show good convergence with respect to both the total energy and the expectation values of the internuclear distances (molecular geometry), the distances between the nuclei and the electrons, and between the electrons. We also provide a derivation of the formulas for one-particle density calculations and some density plots showing the spatial distribution of the H2D+ nuclear and electronic densities.

Nonadiabatic corrections to rovibrational levels of H2

“…It is not always true, especially for rovibrational levels close to the dissociation threshold. In spite of this fact, we claim that each power of E el +H n −E a in these particular matrix elements is at least of the order O( m e /µ n ), which we demonstrate in next sections for the leading terms δ (2) E na and δ (3) E na of the nonadiabatic perturbative expansion.…”

“…In the fully nonadiabatic approach the total nonrelativistic energy of a molecular state is obtained by solving the Schrödinger equation with kinetic energy of electrons and of nuclei on the same footing. This approach has been applied to vibrational states of several small diatomic molecules [1,2,3,4,5]. Much more commonly though, the total energy of a molecular state is obtained in a two-step procedure based on the Born-Oppenheimer (BO) approximation [6,7] in which a separation of electronic and nuclear motion is assumed.…”

Molecular structure calculations: A unified quantum mechanical description of electrons and nuclei using explicitly correlated Gaussian functions and the global vector representation

“…Of course, the space rotationinversion symmetry for floating geminals could be restored numerically in a variational procedure, which was pursued by Adamowicz and Cafiero for L = 0, for example, in Ref. 22. It would also be interesting to consider this numerical reconstruction of the spatial symmetry for higher L values, but for the present work we stick to the analytic expressions and employ Eq.…”

Hidden aspects of the Structural theory of chemistry: MC-QTAIM analysis reveals “alchemical” transformation from a triatomic to a diatomic structure

“…To answer this question, novel quantum chemical methodologies must be developed being capable of using non-BO wavefunctions, instead of adiabatic electronic wavefunctions, as input to extract essentials of molecular structure. In contrast to some primary progress in this direction, [29][30][31][32][33][34][35][36][37][38][39][40][41] currently, such novel non-BO methodologies are in their infancy and it is not clear whether they will survive in long term as reliable sources to derive essentials of molecular structure. 18,[42][43][44][45][46] A more modest strategy is extending the known BO-based methodologies to the non-BO realm; the use of various "extended population analysis" methodologies using non-BO wavefunctions as input is a prime example.…”