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How to compute the Fukui matrix and function for systems with (quasi-)degenerate states

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Abstract
A system in a spatially (quasi-)degenerate ground state responds in a qualitatively different way to a change in the external potential. Consequently, the usual method for computing the Fukui function, namely, taking the difference between the electron densities of the N- and N +/- 1 electron systems, cannot be applied directly. It is shown how the Fukui matrix, and thus also the Fukui function, depends on the nature of the perturbation. One thus needs to use degenerate perturbation theory for the given perturbing potential to generate the density matrix whose change with respect to a change in the number of electrons equals the Fukui matrix. Accounting for the degeneracy in the case of nitrous oxide reveals that an average over the degenerate states differs significantly from using the proper density matrix. We further show the differences in Fukui functions depending on whether a Dirac delta perturbation is used or an interaction with a true point charge (leading to the Fukui potential).
Keywords
FRONTIER-ELECTRON THEORY, ELECTRONEGATIVITY EQUALIZATION, SOFT ACIDS, DUAL-DESCRIPTOR MATRICES, DEGENERATE GROUND-STATES, CHEMICAL-REACTIVITY, MAXIMUM HARDNESS, ATOMIC CHARGES, CONCEPTUAL DFT, BASES HSAB

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Chicago
Bultinck, Patrick, Carlos Cardenas, Patricio Fuentealba, Paul Johnson, and Paul W Ayers. 2014. “How to Compute the Fukui Matrix and Function for Systems with (quasi-)degenerate States.” Journal of Chemical Theory and Computation 10 (1): 202–210.
APA
Bultinck, P., Cardenas, C., Fuentealba, P., Johnson, P., & Ayers, P. W. (2014). How to compute the Fukui matrix and function for systems with (quasi-)degenerate states. JOURNAL OF CHEMICAL THEORY AND COMPUTATION, 10(1), 202–210.
Vancouver
1.
Bultinck P, Cardenas C, Fuentealba P, Johnson P, Ayers PW. How to compute the Fukui matrix and function for systems with (quasi-)degenerate states. JOURNAL OF CHEMICAL THEORY AND COMPUTATION. 2014;10(1):202–10.
MLA
Bultinck, Patrick, Carlos Cardenas, Patricio Fuentealba, et al. “How to Compute the Fukui Matrix and Function for Systems with (quasi-)degenerate States.” JOURNAL OF CHEMICAL THEORY AND COMPUTATION 10.1 (2014): 202–210. Print.
@article{4342465,
  abstract     = {A system in a spatially (quasi-)degenerate ground state responds in a qualitatively different way to a change in the external potential. Consequently, the usual method for computing the Fukui function, namely, taking the difference between the electron densities of the N- and N +/- 1 electron systems, cannot be applied directly. It is shown how the Fukui matrix, and thus also the Fukui function, depends on the nature of the perturbation. One thus needs to use degenerate perturbation theory for the given perturbing potential to generate the density matrix whose change with respect to a change in the number of electrons equals the Fukui matrix. Accounting for the degeneracy in the case of nitrous oxide reveals that an average over the degenerate states differs significantly from using the proper density matrix. We further show the differences in Fukui functions depending on whether a Dirac delta perturbation is used or an interaction with a true point charge (leading to the Fukui potential).},
  author       = {Bultinck, Patrick and Cardenas, Carlos and Fuentealba, Patricio and Johnson, Paul and Ayers, Paul W},
  issn         = {1549-9618},
  journal      = {JOURNAL OF CHEMICAL THEORY AND COMPUTATION},
  language     = {eng},
  number       = {1},
  pages        = {202--210},
  title        = {How to compute the Fukui matrix and function for systems with (quasi-)degenerate states},
  url          = {http://dx.doi.org/10.1021/ct400874d},
  volume       = {10},
  year         = {2014},
}

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