Grid-based methods for diatomic quantum scattering problems: A finite-element discrete-variable representation in prolate spheroidal coordinates

Tao, Liang; McCurdy, C. William; Rescigno, T. N.

doi:10.1103/physreva.79.012719

Cited by 77 publications

(80 citation statements)

References 30 publications

(36 reference statements)

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“…In the following, we will work out the formulas for the onedimensional (1D) case. Analogous expressions in 3D spherical coordinates [46] or prolate spheroidal coordinates [69] are straightforward and pose no conceptual difficulties. In short, the technique can be summarized by using localized HF-like orbitals for the description of the bound part of the spectrum and a grid-like representation for the continuum part.…”

Section: A Partially Rotated Basismentioning

confidence: 99%

Time-dependent generalized-active-space configuration-interaction approach to photoionization dynamics of atoms and molecules

2014

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We present a wave-function based method to solve the time-dependent many-electron Schrödinger equation (TDSE) with special emphasis on strong-field ionization phenomena. The theory builds on the configuration-interaction (CI) approach supplemented by the generalized-active-space (GAS) concept from quantum chemistry. The latter allows for a controllable reduction in the number of configurations in the CI expansion by imposing restrictions on the active orbital space. The method is similar to the recently formulated time-dependent restricted-active-space (TD-RAS) CI method [D. Hochstuhl, and M. Bonitz, Phys. Rev. A 86, 053424 (2012)]. We present details of our implementation and address convergence properties with respect to the active spaces and the associated account of electron correlation in both ground state and excitation scenarios. We apply the TD-GASCI theory to strong-field ionization of polar diatomic molecules and illustrate how the method allows us to uncover a strong correlation-induced shift of the preferred direction of emission of photoelectrons.

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Section: A Partially Rotated Basismentioning

confidence: 99%

Time-dependent generalized-active-space configuration-interaction approach to photoionization dynamics of atoms and molecules

2014

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“…37. At this internuclear distance (R AB = 3), the resonance has a position of 0.02555645961 and a width of 0.02354423918 in units natural to the problem.…”

Section: A Numerical Detailsmentioning

confidence: 99%

Stabilizing potentials in bound state analytic continuation methods for electronic resonances in polyatomic molecules

White

Head‐Gordon

McCurdy

2017

The Journal of Chemical Physics

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The computation of Siegert energies by analytic continuation of bound state energies has recently been applied to shape resonances in polyatomic molecules by several authors. We critically evaluate a recently proposed analytic continuation method based on low order (type III) Padé approximants as well as an analytic continuation method based on high order (type II) Padé approximants. We compare three classes of stabilizing potentials: Coulomb potentials, Gaussian potentials, and attenuated Coulomb potentials. These methods are applied to a model potential where the correct answer is known exactly and to the 2 Π g shape resonance of N − 2 which has been studied extensively by other methods. Both the choice of stabilizing potential and method of analytic continuation prove to be important to the accuracy of the results. We conclude that an attenuated Coulomb potential is the most effective of the three for bound state analytic continuation methods. With the proper potential, such methods show promise for algorithmic determination of the positions and widths of molecular shape resonances.

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“…The present implementation for diatomics is based on a previously described [35][36][37] basis set treatment in prolate spheroidal coordinates using a finite element implementation of the Discrete Variable Representation (DVR) [38][39][40][41]. The DVR basis functions are localized on grid points in the prolate spheroidal coordinates ξ and η, with angular basis functions e imφ in the azimuthal angle.…”

Section: Methodsmentioning

confidence: 99%

Ultrafast population transfer to excited valence levels of a molecule driven by x-ray pulses

Haxton

McCurdy

2014

Phys. Rev. A

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First-principles quantum mechanical calculations of an intense-field ultrafast two-color core hole stimulated Raman process in nitric oxide are presented. They employ the Multiconfiguration TimeDependent Hartree-Fock (MCTDHF) method with all 15 electrons active. These calculations demonstrate a robust excitation localized on an atom through a core-electron stimulated Raman transition, the first step in proposed stimulated X-ray Raman spectroscopy experiments. A total population transfer of approximately 41% into valence excited states and 30% ionization is obtained via two concurrent 1.31fs pulses of maximum intensity 0.5 and 3 ×10 17 W cm −2 . It is found that both resonant and nonresonant (via the continuum) Raman transitions contribute. All aspects of these calculations except for AC stark shifts are converged with a modest basis of 11 orbitals, demonstrating the efficiency of MCTDHF for the treatment of nonperturbative electronic dynamics in molecules.

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Grid-based methods for diatomic quantum scattering problems: A finite-element discrete-variable representation in prolate spheroidal coordinates

Cited by 77 publications

References 30 publications

Time-dependent generalized-active-space configuration-interaction approach to photoionization dynamics of atoms and molecules

Time-dependent generalized-active-space configuration-interaction approach to photoionization dynamics of atoms and molecules

Stabilizing potentials in bound state analytic continuation methods for electronic resonances in polyatomic molecules

Ultrafast population transfer to excited valence levels of a molecule driven by x-ray pulses

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