Theory and application of explicitly correlated Gaussians

Mitroy, Jim; Bubin, Sergiy; Horiuchi, W.; Suzuki, Y.; Adamowicz, Ludwik; Cencek, Wojciech; Szalewicz, Krzysztof; Komasa, Jacek; Blume, D.; Varga, K.

doi:10.1103/revmodphys.85.693

Cited by 316 publications

(345 citation statements)

References 567 publications

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“…Correlated Gaussian (CG) basis functions [15,16] are used to expand the radial part of Φ. This approach is sufficiently flexible to describe both short-and long-range properties of the wave function accurately, a necessary condition when dealing with systems such as kaonic deuterium in which very…”

Section: Solving the Three-body Schrödinger Equationmentioning

confidence: 99%

Kaonic deuterium and low-energy antikaon-nucleon interaction

Horiuchi

Hyodo

Weise

2018

EPJ Web of Conferences

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Abstract.A new evaluation of the 1s level shift and width of kaonic deuterium is presented based on an accurateKNN three-body calculation, using as input a realistic antikaon-nucleon interaction constrained by the SIDDHARTA kaonic hydrogen data. The three-body Schrödinger equation is solved with a superposition of a large number of correlated Gaussian basis functions extending over distance scales up to several hundred fm. The resulting energy shift and width of the kaonic deuterium 1s level are ∆E 0.67 keV and Γ 1.02 keV, with estimated uncertainties at the 10 % level.

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Section: Solving the Three-body Schrödinger Equationmentioning

confidence: 99%

Kaonic deuterium and low-energy antikaon-nucleon interaction

Horiuchi

Hyodo

Weise

2018

EPJ Web of Conferences

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“…71 However, this methodology has yet to make significant impact on polyatomic systems, even ones containing few electrons such as H + 3 . Here a more pragmatic model based on high-accuracy electronic structure calculations using explicitly correlated Gaussians 72 and a simplified treatment of non-adiabatic effects using effective vibrational and rotational masses 73 has been found to provide excellent predictions of ro-vibrational transition frequencies 74 and intensities.…”

Section: Hydrogenic Systems As Benchmarksmentioning

confidence: 99%

Perspective: Accurate ro-vibrational calculations on small molecules

Tennyson

2016

The Journal of Chemical Physics

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In what has been described as the fourth age of quantum chemistry, variational nuclear motion programs are now routinely being used to obtain the vibration-rotation levels and corresponding wavefunctions of small molecules to the sort of high accuracy demanded by comparison with spectroscopy. In this perspective, I will discuss the current state-of-the-art which, for example, shows that these calculations are increasingly competitive with measurements or, indeed, replacing them and thus becoming the primary source of data on key processes. To achieve this accuracy ab initio requires consideration of small effects, routinely ignored in standard calculations, such as those due to quantum electrodynamics. Variational calculations are being used to generate huge lists of transitions which provide the input for models of radiative transport through hot atmospheres and to fill in or even replace measured transition intensities. Future prospects such as the study of molecular states near dissociation, which can provide a link with low-energy chemical reactions, are discussed. Published by AIP Publishing. [http://dx

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“…To determine the eigenenergies of the two-particle system numerically, we expand the eigenstates in terms of basis functions that contain explicitly correlated Gaussians whose parameters are optimized semi-stochastically and solve the resulting generalized eigenvalue problem [67,68]. We first consider the situation where the first particle feels the spin-orbit coupling while the second…”

Section: Appendix A: Basis Set Expansion Approachmentioning

confidence: 99%

Harmonically trapped two-atom systems: Interplay of short-ranges-wave interaction and spin-orbit coupling

Yin

Gopalakrishnan²,

Blume

2014

Phys. Rev. A

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The coupling between the spin degrees of freedom and the orbital angular momentum has a profound effect on the properties of nuclei, atoms and condensed matter systems. Recently, synthetic gauge fields have been realized experimentally in neutral cold atom systems, giving rise to a spin-orbit coupling term with "strength" kso. This paper investigates the interplay between the single-particle spin-orbit coupling term of Rashba type and the short-range two-body s-wave interaction for cold atoms under external confinement. Specifically, we consider two different harmonically trapped two-atom systems. The first system consists of an atom with spin-orbit coupling that interacts with a structureless particle through a short-range two-body potential. The second system consists of two atoms that both feel the spin-orbit coupling term and that interact through a short-range two-body potential. Treating the spin-orbit term perturbatively, we determine the correction to the ground state energy for various generic parameter combinations. Selected excited states are also treated. An important aspect of our study is that the perturbative treatment is not limited to small s-wave scattering lengths but provides insights into the system behavior over a wide range of scattering lengths, including the strongly-interacting unitary regime. We find that the interplay between the spin-orbit coupling term and the s-wave interaction generically enters, depending on the exact parameter combinations of the s-wave scattering lengths, at order k 2 so or k 4 so for the ground state and leads to a shift of the energy of either sign. While the absence of a term proportional to kso follows straightforwardly from the functional form of the spin-orbit coupling term, the absence of a term proportional to k 2 so for certain parameter combinations is unexpected. The well-known fact that the spin-orbit coupling term couples the relative and center of mass degrees of freedom has interesting consequences for the trapped two-particle systems. For example, we find that the spin-orbit coupling term turns, for certain parameter combinations, sharp crossings into avoided crossings with an energy splitting proportional to kso. Our perturbative results are confirmed by numerical calculations that expand the eigenfunctions of the two-particle Hamiltonian in terms of basis functions that contain explicitly correlated Gaussians.

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Theory and application of explicitly correlated Gaussians

Cited by 316 publications

References 567 publications

Kaonic deuterium and low-energy antikaon-nucleon interaction

Kaonic deuterium and low-energy antikaon-nucleon interaction

Perspective: Accurate ro-vibrational calculations on small molecules

Harmonically trapped two-atom systems: Interplay of short-ranges-wave interaction and spin-orbit coupling

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