On distributed Gaussian bases for simple model multidimensional vibrational problems

Hamilton, Ian; Light, John C.

doi:10.1063/1.450139

Cited by 413 publications

(146 citation statements)

References 23 publications

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“…As shown in ref. 26, a distributed Gaussian basis (DGB), as popularized by Hamilton and Light, 30 is a good first choice. To achieve a minimal representation of the wavefunction in the PRODG approach, expansion coefficients [eqn (1)] and the corresponding basis functions are only stored at places where they have a non-negligible contribution to the total wavefunction (these are the ''active'' coefficients or basis functions).…”

Section: A Adaptive Basismentioning

confidence: 99%

Quantum-mechanical wavepacket propagation in a sparse, adaptive basis of interpolating Gaussians with collocation

Sielk

Horsten

Krüger

et al. 2009

Phys. Chem. Chem. Phys.

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We present an extension of our earlier work on adaptive quantum wavepacket dynamics [B. Hartke, Phys. Chem. Chem. Phys., 2006, 8, 3627]. In this dynamically pruned basis representation the wavepacket is only stored at places where it has non-negligible contributions. Here we enhance the former 1D proof-of-principle implementation to higher dimensions and optimize it by a new basis set, interpolating Gaussians with collocation. As a further improvement the TNUM approach from Lauvergnat and Nauts [J. Chem. Phys., 2002, 116, 8560] was implemented, which in combination with our adaptive representation offers the possibility of calculating the whole Hamiltonian on-the-fly. For a two-dimensional artificial benchmark and a three-dimensional real-life test case, we show that a sparse matrix implementation of this approach saves memory compared to traditional basis representations and comes even close to the efficiency of the fast Fourier transform method. Thus we arrive at a quantum wavepacket dynamics implementation featuring several important black-box characteristics: it can treat arbitrary systems without code changes, it calculates the kinetic and potential part of the Hamiltonian on-the-fly, and it employs a basis that is automatically optimized for the ongoing wavepacket dynamics.

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Section: A Adaptive Basismentioning

confidence: 99%

Quantum-mechanical wavepacket propagation in a sparse, adaptive basis of interpolating Gaussians with collocation

Sielk

Horsten

Krüger

et al. 2009

Phys. Chem. Chem. Phys.

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“…As suggested by Hamilton and Light [15], each one-dimensional function ϕ p is chosen to be a DGF centered at the R p position 4 F o r P e e r R e v i e w O n l y…”

Section: The Dgf Methodsmentioning

confidence: 99%

Searching for many-body effects and Efimov states in very weakly bound triatomics: HeNeH⁻and HeNeH

2008

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“…We notice that the DGF method was proposed to deal also with excited vibrational states. 82 Concerning the inclusion of the inter-particle correlation, the transcorrelated Hamiltonian approach 84 seems to be quite attractive. By using a single determinant (permanent) Jastrow ansatz, HF-like equations are obtained and, therefore, this approach seems to be well-suited to interfaces with standard electronic structure codes.…”

Section: Applicationsmentioning

confidence: 99%

Including nuclear quantum effects into highly correlated electronic structure calculations of weakly bound systems

Aguirre

Villarreal

Delgado‐Barrio

et al. 2013

The Journal of Chemical Physics

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An interface between the APMO code and the electronic structure package MOLPRO is presented. The any particle molecular orbital APMO code [González et al., Int. J. Quantum Chem. 108, 1742 implements the model where electrons and light nuclei are treated simultaneously at Hartree-Fock or second-order Möller-Plesset levels of theory. The APMO-MOLPRO interface allows to include highlevel electronic correlation as implemented in the MOLPRO package and to describe nuclear quantum effects at Hartree-Fock level of theory with the APMO code. Different model systems illustrate the implementation: 4 He 2 dimer as a protype of a weakly bound van der Waals system; isotopomers of [He-H-He] + molecule as an example of a hydrogen bonded system; and molecular hydrogen to compare with very accurate non-Born-Oppenheimer calculations. The possible improvements and future developments are outlined.

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On distributed Gaussian bases for simple model multidimensional vibrational problems

Cited by 413 publications

References 23 publications

Quantum-mechanical wavepacket propagation in a sparse, adaptive basis of interpolating Gaussians with collocation

Quantum-mechanical wavepacket propagation in a sparse, adaptive basis of interpolating Gaussians with collocation

Searching for many-body effects and Efimov states in very weakly bound triatomics: HeNeH⁻and HeNeH

Including nuclear quantum effects into highly correlated electronic structure calculations of weakly bound systems

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On distributed Gaussian bases for simple model multidimensional vibrational problems

Cited by 413 publications

References 23 publications

Quantum-mechanical wavepacket propagation in a sparse, adaptive basis of interpolating Gaussians with collocation

Quantum-mechanical wavepacket propagation in a sparse, adaptive basis of interpolating Gaussians with collocation

Searching for many-body effects and Efimov states in very weakly bound triatomics: HeNeH−and HeNeH

Including nuclear quantum effects into highly correlated electronic structure calculations of weakly bound systems

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Searching for many-body effects and Efimov states in very weakly bound triatomics: HeNeH⁻and HeNeH