Simulation of a hydrogen atom in a laser field using the time-dependent variational principle

Rowan, Keefer; Schatzki, Louis; Zaklama, Timothy; Suzuki, Yasumitsu; Watanabe, Kazuyuki; Varga, K.

doi:10.1103/physreve.101.023313

Cited by 6 publications

(3 citation statements)

References 67 publications

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“…Rowan et al showed that only their counterparts with time-dependent parameters are able to reasonably describe the wavefunction propagation in laser fields. 134 Recently, Coccia and co-workers have decided to revisit and extend the work of Kaufmann et al with the primary goal of constructing basis sets for an accurate description of atomic and molecular HHG spectra. 131,[135][136][137][138][139] They combined the K functions with augmented Dunning basis sets 140 containing a very large number of diffuse functions.…”

Section: Introductionmentioning

confidence: 99%

A systematic construction of Gaussian basis sets for the description of laser field ionization and high-harmonic generation

Woźniak

Lesiuk

Przybytek

et al. 2021

The Journal of Chemical Physics

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A precise understanding of mechanisms governing the dynamics of electrons in atoms and molecules subjected to intense laser fields has a key importance for the description of attosecond processes such as the high-harmonic generation and ionization. From the theoretical point of view, this is still a challenging task, as new approaches to solve the time-dependent Schrödinger equation with both good accuracy and efficiency are still emerging. Until recently, the purely numerical methods of real-time propagation of the wavefunction using finite grids have been frequently and successfully used to capture the electron dynamics in small one-or two-electron systems. However, as the main focus of attoscience shifts toward many-electron systems, such techniques are no longer effective and need to be replaced by more approximate but computationally efficient ones. In this paper, we explore the increasingly popular method of expanding the wavefunction of the examined system into a linear combination of atomic orbitals and present a novel systematic scheme for constructing an optimal Gaussian basis set suitable for the description of excited and continuum atomic or molecular states. We analyze the performance of the proposed basis sets by carrying out a series of time-dependent configuration interaction calculations for the hydrogen atom in fields of intensity varying from 5 × 10 13 W/cm 2 to 5 × 10 14 W/cm 2 . We also compare the results with the data obtained using Gaussian basis sets proposed previously by other authors.

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Section: Introductionmentioning

confidence: 99%

A systematic construction of Gaussian basis sets for the description of laser field ionization and high-harmonic generation

Woźniak

Lesiuk

Przybytek

et al. 2021

The Journal of Chemical Physics

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“…Now, gaussians are very flexible, which means that there may be several distinct LCGs that approximate the same wavefunction to a very high accuracy, i.e., the nonlinear parameters are almost redundant. This leads to the system of ODEs being very stiff, and time-propagation with the Dirac-Frenkel variational principle is therefore very challenging for the LCG ansatz [4].…”

Section: The Methods Of Vertical Linesmentioning

confidence: 99%

“…Perhaps ironically, the flexibility of the LCG wavefunctions make them very hard to propagate using the standard Dirac-Frenkel variational principle [2], leading to ill-conditioned variational equations [3,4]. The propagation scheme described in this Letter is based on the method of vertical lines, or Rothe's method [5,6].…”

Section: Introductionmentioning

confidence: 99%

No need for a grid: Adaptive fully-flexible gaussians for the time-dependent Schrödinger equation

Kvaal¹,

Lasser²,

Pedersen³

et al. 2022

Preprint

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Linear combinations of complex gaussian functions, where the nonlinear parameters are allowed to vary, are shown to be an extremely flexible representation for the solution of the time-dependent Schrödinger equation in one spatial dimension. Propagation of such wavefunctions using the Dirac-Frenkel variational principle is notoriously hard, and we present instead a scheme based on the method of vertical lines, or Rothe's method. We apply the method to a simple test system mimicking an atom subject to an extreme laser pulse, producing complicated ionization dynamics. The scheme is shown to perform very well on this model. Since the propagation method can be formulated entirely in terms of gaussian integrals and expectation values, we eliminate the need for large grids using only a handful of gaussian functions but with the same accuracy. This paves the way for accurate and affordable solutions of the time-dependent Schrödinger equation for multi-atom molecules beyond the Born-Oppenheimer approximation.

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Deformed explicitly correlated Gaussians

Beutel

Ahrens

Huang

et al. 2021

The Journal of Chemical Physics

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Deformed explicitly correlated Gaussian (DECG) basis functions are introduced, and their matrix elements are calculated. All matrix elements can be calculated analytically in a closed form, except the Coulomb one, which has to be approximated by a Gaussian expansion. The DECG basis functions can be used to solve problems with nonspherical potentials. One example of such potential is the dipole self-interaction term in the Pauli–Fierz Hamiltonian. Examples are presented showing the accuracy and necessity of deformed Gaussian basis functions to accurately solve light–matter coupled systems in cavity QED.

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Simulation of a hydrogen atom in a laser field using the time-dependent variational principle

Cited by 6 publications

References 67 publications

A systematic construction of Gaussian basis sets for the description of laser field ionization and high-harmonic generation

A systematic construction of Gaussian basis sets for the description of laser field ionization and high-harmonic generation

No need for a grid: Adaptive fully-flexible gaussians for the time-dependent Schrödinger equation

Deformed explicitly correlated Gaussians

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