Generalized elimination of the global translation from explicitly correlated Gaussian functions

Abstract

This paper presents the multi-channel generalization of the center-of-mass kinetic energy elimination approach [B. Simmen et al., Mol. Phys. 111, 2086 (2013)] when the Schrödinger equation is solved variationally with explicitly correlated Gaussian functions. The approach has immediate relevance in many-particle systems which are handled without the Born-Oppenheimer approximation and can be employed also for Dirac-type Hamiltonians. The practical realization and numerical properties of solving the Schrödinger equation in laboratory-frame Cartesian coordinates are demonstrated for the ground rovibronic state of the H={p,p,e} ion and the H = {p, p, e, e} molecule.

Lower Bounds for Nonrelativistic Atomic Energies

“…In principle, the methodology described in this work can be adapted also for the computation of electronic energies of molecules within and even without the Born–Oppenheimer approximation. , This will require the replacement of the plain ECG functions, eq , with “floating” ECGs and the corresponding generalization of the newly implemented 1/ r ij r kl integral expressions (see ref and the Supporting Information). It would be of significance to complement the five-particle upper bound , with a similarly precise lower bound for selected rovibronic states of the H 3 + molecular ion, for which a 10 ppm relative precision would allow for the assessment of the importance of nonadiabatic (in comparison with Born–Oppenheimer results and corrections to them) and relativistic quantum electrodynamics (in comparison with experiment) “effects.”…”

Fundamental vibration frequency and rotational structure of the first excited vibrational level of the molecular helium ion (He2+)

“…Ab initio calculations of the properties of few-electron molecules are currently in a phase of rapid progress and methodological change [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]. To reach the high accuracy required for the comparison with the latest experimental results, it now appears advantageous to abandon the traditional approach starting with calculations of Born-Oppenheimer potential-energy functions, or surfaces, and of adiabatic and nonadiabatic corrections, followed by a perturbative treatment of relativistic and radiative corrections.…”

Gaussians for Electronic and Rovibrational Quantum Dynamics

“…In the first part of this work, we review the ECFs used in the atomic and molecular calculations of stationary bound states, and we discuss the features of these functions that may make them particularly useful in QM calculations of atomic and molecular systems. We particularly focus on Gaussian ECFs (ECGs), as these are the most popular functions used in non-BO atomic and molecular calculations. − In the second part, two-dimensional time-propagation calculations are performed for two model systems involving Coulomb and Morse potentials using a grid approach. Next, the time-dependent grid wave functions are fitted with ECGs that are chosen to best represent the key features that appear in the wave function due to the interaction of the system with ultrashort intense laser pulses.…”