N-body quantum-mechanical Hamiltonians: Extrapotential terms

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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“…. .,q 3NÀ6 ) T , the general expression of the kinetic energy operator can be written in a very compact form: [40][41][42][43] Tðq;pÞ ¼ À h…”

Section: E Numerical Kinetic Energy Operatormentioning

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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“…(33) and (27). The equality of the respective terms is readily apparent from the following identities…”

Section: An Alternative Form Of the Kinetic Energymentioning

confidence: 84%

“…(27) can be placed in a different form, that of Eq. (33), which is more common in the rovibrational literature. Sect.…”

Section: Introductionmentioning

confidence: 99%

The rovibrational kinetic energy for complexes of rigid molecules

MITCHELL¹

1999

Molecular Physics

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The rovibrational kinetic energy for an arbitrary number of rigid molecules is computed. The result has the same general form as the kinetic energy in the molecular rovibrational Hamiltonian, although certain quantities are augmented to account for the rotational energy of the monomers. No specific choices of internal coordinates or body frame are made in order to accommodate the large variety of such conventions. However, special attention is paid to how key quantities transform when these conventions are changed. An example system is explicitly analysed as an illustration of the formalism.

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“…59,61 To explain how this is done, consider a (J = 0) Hamiltonian in orthogonal polyspherical coordinates, [117][118][119] …”

Section: General Pes/iterative-eigensolver/contracted-basis (G/i/cmentioning

confidence: 99%

Perspective: Computing (ro-)vibrational spectra of molecules with more than four atoms

Carrington

2017

The Journal of Chemical Physics

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In this perspective, I review methods for computing (ro-)vibrational energy levels and wavefunctions of molecules with more than four atoms. I identify three problems one confronts (1) reducing the size of the basis; (2) computing hundreds of eigenvalues and eigenvectors of a large matrix; (3) calculating matrix elements of the potential, and present ideas that mitigate them. Most modern methods use a combination of these ideas. I divide popular methods into groups based on the strategies used to deal with the three problems. Published by AIP Publishing. [http://dx

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N-body quantum-mechanical Hamiltonians: Extrapotential terms

Cited by 79 publications

References 7 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

The rovibrational kinetic energy for complexes of rigid molecules

Perspective: Computing (ro-)vibrational spectra of molecules with more than four atoms

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