Qualitative failure of a multiconfiguration method in prolate spheroidal coordinates in calculating dissociative photoionization ofH2+

Abstract

A formulation of multiconfiguration time-dependent Hartree-Fock (MCTDHF) with nuclear motion is tested by application to a three-body breakup problem, the dissociative photoionization cross section of the H + 2 ion. The representation of the wave function in terms of a set of Slater determinants used for all nuclear geometries, with a prescribed parametric dependence upon the nuclear geometry such that the cusps follow the nuclei, times a complete basis expansion in the nuclear degrees of freedom shows promise as a method for treating nonadiabatic electronic and nuclear motion in molecules. However, the method used here for diatomics, in which the parametric dependence is prescribed through the choice of prolate spheroidal coordinates, produces qualitatively incorrect step-like behavior in the calculated cross section near onset. Modifications to the prolate spheroidal coordinate system that would improve this nonadiabatic diatomic MCTDHF representation are proposed.

Systematically expanding nondirect product bases within the pruned multi-configuration time-dependent Hartree (MCTDH) method: A comparison with multi-layer MCTDH

“…We are using the state-averaged formalism, 54 which is advantageous whenever one wishes to compute more than one wavefunction. In contrast to the original MCTDH approach, 36,37 Optimised SPFs, obtained from the Dirac-Frenkel variational principle δΨ|iΨ −ĤΨ = 0, [55][56][57] have been derived for a pruned MCTDH method designed for fermionic 58 and bosonic 59 systems. Analogous equations could also be used for a P-MCTDH approach for vibrational problems.…”

Time-dependent optimized coupled-cluster method for multielectron dynamics IV: Approximate consideration of the triple excitation amplitudes

“…However, these methods scale factorially with the number of correlated electrons, re-stricting large scale applications. By limiting the configuration interaction (CI) expansion of the wavefunction up to an affordable level, various less demanding methods [29][30][31][32][33] like the time-dependent restricted-activespace self-consistent field (TD-RASSCF) 29,30 and timedependent occupation-restricted multiple-active-space (TD-ORMAS) 32 have been developed. These methods have proven to be of great utility 34 even though not sizeextensive.…”

Molecular second-quantized Hamiltonian: Electron correlation and non-adiabatic coupling treated on an equal footing

“…This method showed rapid convergence in vibronic states of HD + , HD, H 2 and LiH, 55 but did not perform as well at calculating the dissociative photoionization cross section of H 2 + . 56 It was conjectured that prolate spheroidal coordinates do not behave physically in the asymptotic region, and some alternatives were suggested. Nonetheless, one of the important contributions of this work is to show that one can choose geometry-dependent AOs that satisfy key physical conditions to get around the strong electron-nuclear coupling.…”