On the Calculation of Resonances in Pre-Born–Oppenheimer Molecular Structure Theory

Abstract

The main motivation for this work is the exploration of rotational–vibrational states corresponding to electronic excitations in a pre-Born–Oppenheimer quantum theory of molecules. These states are often embedded in the continuum of the lower-lying dissociation channel of the same symmetry and thus are thought to be resonances. To calculate rovibronic resonances, the pre-Born–Oppenheimer variational approach of [J. Chem. Phys. 2012, 137, 024104], based on the usage of explicitly correlated Gaussian functions and the global vector representation, is extended with the complex coordinate rotation method. The developed computer program is used to calculate resonance energies and widths for the three-particle positronium anion, Ps(–), and the four-particle positronium molecule, Ps(2). Furthermore, the excited bound and resonance rovibronic states of the four-particle H2 molecule are also considered. Resonance energies and widths are estimated for the lowest-energy resonances of H(2) beyond the b (3)∑(u)(+) continuum.

Computation of rovibronic resonances of molecular hydrogen: EFΣg+1 inner-well rotational states

“…In retrospect, we can confirm that the largest basis set of Ref. [9] gives EF energies accurate within ca. 10 nE h , which we can estimate now from the convergence pattern and behaviour of the states upon the systematic refinement of the basis set.…”

“…The Born-Oppenheimer (BO) potential energy curve of EF 1 Σ + g shows a double-well feature due to an avoided crossing with the nearby GK 1 Σ + g state ( Figure 1). In a pre-Born-Oppenheimer (pre-BO) description [8][9][10], 'all' nonadiabatic couplings and 'effects' are automatically included, so we will not use po-tential energy curves, nor coupling vectors in the computations, but the curves are useful to look at and we will continue to use the electronic state labels to have a short description and reference for the computed four-particle states. Since all non-adiabatic couplings are included, also the coupling with the X 1 Σ + g (ground) state continuum is present (we cannot separate it), and thus the EF states can only be obtained as resonances within the four-body problem [9].…”

“…In a pre-Born-Oppenheimer (pre-BO) description [8][9][10], 'all' nonadiabatic couplings and 'effects' are automatically included, so we will not use po-tential energy curves, nor coupling vectors in the computations, but the curves are useful to look at and we will continue to use the electronic state labels to have a short description and reference for the computed four-particle states. Since all non-adiabatic couplings are included, also the coupling with the X 1 Σ + g (ground) state continuum is present (we cannot separate it), and thus the EF states can only be obtained as resonances within the four-body problem [9]. The lower-energy vibrations of EF have been estimated to have a very long predissociative lifetime (much longer than their radiative lifetime) due to their very weak coupling to the dissociation continuum of the X 1 Σ + g ground electronic state [9,11].…”

Pre-Born–Oppenheimer molecular structure theory

“…A general (n p + 1)-particle variational approach was developed in Refs. [36,37] for the solution of the time-independent many-particle Schrödinger equation, Eq. (3), beyond spectroscopic accuracy [38] and for various combinations of the non-relativistic quantum numbers, N, N z , p, S a , S z,a , S b , S z,b , .…”

The any particle molecular orbital approach: A short review of the theory and applications

“…[6][7][8][9] Other groups have presented alternative explicitly correlated non-BO methods, in which selected coordinates are included in the ECG functions. [10][11][12][13][14][15][16][17][18][19][20] In spite of their accuracy, the overall applicability of ECG methods is limited to very small molecular because of their high computational costs which in many cases display formal scalings of O(N! ).An alternative to ECG methods to investigate non-BO phenomena are the multicomponent (MC) methods.…”