Sensitivity analysis of state-specific multireference perturbation theory

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19 Citations (Scopus)

Abstract

State-specific multireference perturbation theory (SS-MRPT) developed by Mukherjee [Int. J. Mol. Sci. 3, 733 (2002)] is examined focusing on the dependence of the perturbed energy on the initial model space coefficients. It has been observed earlier, that non-physical kinks may appear on the potential energy surface obtained by SS-MRPT while related coupled-cluster methods may face convergence difficulties. Though exclusion or damping of the division by small coefficients may alleviate the problem, it is demonstrated here that the effect does not originate in an ill-defined division. It is shown that non-negligible model space coefficients may also be linked with the problem. Sensitivity analysis is suggested as a tool for detecting the coefficient responsible. By monitoring the singular values of sensitivity matrices, orders of magnitude increase is found in the largest value, in the vicinity of the problematic geometry point on the potential energy surface. The drastic increase of coefficient sensitivities is found to be linked with a degeneracy of the target root of the effective Hamiltonian. The nature of the one-electron orbitals has a profound influence on the picture: a rotation among active orbitals may screen or worsen the effect.

Original languageEnglish
Article number174113
JournalThe Journal of Chemical Physics
Volume134
Issue number17
DOIs
Publication statusPublished - máj. 7 2011

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Potential energy surfaces
sensitivity analysis
Sensitivity analysis
perturbation theory
Hamiltonians
coefficients
Damping
division
potential energy
Geometry
Electrons
Monitoring
electron orbitals
sensitivity
exclusion
damping
orbitals
matrices
geometry

ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Physical and Theoretical Chemistry

Cite this

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title = "Sensitivity analysis of state-specific multireference perturbation theory",
abstract = "State-specific multireference perturbation theory (SS-MRPT) developed by Mukherjee [Int. J. Mol. Sci. 3, 733 (2002)] is examined focusing on the dependence of the perturbed energy on the initial model space coefficients. It has been observed earlier, that non-physical kinks may appear on the potential energy surface obtained by SS-MRPT while related coupled-cluster methods may face convergence difficulties. Though exclusion or damping of the division by small coefficients may alleviate the problem, it is demonstrated here that the effect does not originate in an ill-defined division. It is shown that non-negligible model space coefficients may also be linked with the problem. Sensitivity analysis is suggested as a tool for detecting the coefficient responsible. By monitoring the singular values of sensitivity matrices, orders of magnitude increase is found in the largest value, in the vicinity of the problematic geometry point on the potential energy surface. The drastic increase of coefficient sensitivities is found to be linked with a degeneracy of the target root of the effective Hamiltonian. The nature of the one-electron orbitals has a profound influence on the picture: a rotation among active orbitals may screen or worsen the effect.",
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