Explicitly correlated Gaussian functions with shifted-center and projection techniques in pre-Born-Oppenheimer calculations

Abstract

Numerical projection methods are elaborated for the calculation of eigenstates of the non-relativistic many-particle Coulomb Hamiltonian with selected rotational and parity quantum numbers employing shifted explicitly correlated Gaussian functions, which are, in general, not eigenfunctions of the total angular momentum and parity operators. The increased computational cost of numerically projecting the basis functions onto the irreducible representations of the three dimensional rotation-inversion group is the price to pay for the increased flexibility of the basis functions. This increased flexibility allowed us to achieve a substantial improvement for the variational upper bound to the Pauli-allowed ground-state energy of the H${}_3^{+}=\{$p${}^{+},$p${}^{+},$p${}^{+},$e${}^{-},$e${}^{-}\}$ molecular ion treated as an explicit five-particle system. We compare our pre-Born-Oppenheimer result for this molecular ion with rovibrational results including non-adiabatic corrections.

arXiv comment29 pages, 3 figures, 4 tables

References in corpus (13)

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• Nonadiabatic corrections to rovibrational levels of H${}_2$
• Bounds on fifth forces from precision measurements on molecules
• Fundamental transitions and ionization energies of the hydrogen molecular ions at the few ppt level
• Relativistic corrections of mα^6 order to the ro-vibrational spectrum of H_2^+ and HD^+ molecular ions
• Dissociation energy of the hydrogen molecule at 10${}^{-9}$ accuracy
• New representation of orbital motion with arbitrary angular momenta
• Hydrogen molecular ions for improved determination of fundamental constants
• Calculation of the relativistic Bethe logarithm in the two-center problem
• Nonadiabatic rotational states of the hydrogen molecule
• Elimination of the Translational Kinetic Energy Contamination in pre-Born-Oppenheimer Calculations
• Precision spectroscopy of the hydrogen molecular ions HD${}^{+}$
• Generalized elimination of the global translation from explicitly correlated Gaussian functions

Cited by in corpus (9)

• Nuclear-Electronic All-Particle Density Matrix Renormalization Group
• Effective non-adiabatic Hamiltonians for the quantum nuclear motion over coupled electronic states
• Non-adiabatic quantum dynamics without potential energy surfaces based on second-quantized electrons: application within the framework of the MCTDH method
• H${}_3^{+}$ as a five-body problem described with explicitly correlated Gaussian basis sets
• Relativistic two-electron atomic and molecular energies using $LS$ coupling and double groups: role of the triplet contributions to singlet states
• Gaussians for Electronic and Rovibrational Quantum Dynamics
• Analytically projected rotationally symmetric explicitly correlated Gaussian Functions with one-axis-shifted centers
• Sub-percent accuracy for the intensity of a near infrared water line at 10670 cm${}^{-1}$: experiment and analysis
• Deformed Explicitly Correlated Gaussians