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Performance of Shannon-entropy compacted N-electron wave functions for configuration interaction methods

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Abstract
The coefficients of full configuration interaction wave functions (FCI) for N-electron systems expanded in N-electron Slater determinants depend on the orthonormal one-particle basis chosen although the total energy remains invariant. Some bases result in more compact wave functions, i.e. result in fewer determinants with significant expansion coefficients. In this work, the Shannon entropy, as a measure of information content, is evaluated for such wave functions to examine whether there is a relationship between the FCI Shannon entropy of a given basis and the performance of that basis in truncated CI approaches. The results obtained for a set of randomly picked bases are compared to those obtained using the traditional canonical molecular orbitals, natural orbitals, seniority minimising orbitals and a basis that derives from direct minimisation of the Shannon entropy. FCI calculations for selected atomic and molecular systems clearly reflect the influence of the chosen basis. However, it is found that there is no direct relationship between the entropy computed for each basis and truncated CI energies.
Keywords
COLLINS CONJECTURE, SPIN-ADAPTED SPACES, NATURAL ORBITALS, DENSITY-MATRICES, INFORMATION ENTROPY, NUMERICAL EVIDENCE, QUANTUM-THEORY, OPTIMIZATION, SYSTEMS, ORDER REPLACEMENT OPERATORS, DOCI, Seniority, Configuration interaction, Entropy

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MLA
Alcoba, Diego R., et al. “Performance of Shannon-Entropy Compacted N-Electron Wave Functions for Configuration Interaction Methods.” THEORETICAL CHEMISTRY ACCOUNTS, vol. 135, no. 6, 2016, doi:10.1007/s00214-016-1905-x.
APA
Alcoba, D. R., Torre, A., Lain, L., Massaccesi, G. E., Oña, O. B., Ayers, P. W., … Van Neck, D. (2016). Performance of Shannon-entropy compacted N-electron wave functions for configuration interaction methods. THEORETICAL CHEMISTRY ACCOUNTS, 135(6). https://doi.org/10.1007/s00214-016-1905-x
Chicago author-date
Alcoba, Diego R, Alicia Torre, Luis Lain, Gustavo E Massaccesi, Ofelia B Oña, Paul W Ayers, Mario Van Raemdonck, Patrick Bultinck, and Dimitri Van Neck. 2016. “Performance of Shannon-Entropy Compacted N-Electron Wave Functions for Configuration Interaction Methods.” THEORETICAL CHEMISTRY ACCOUNTS 135 (6). https://doi.org/10.1007/s00214-016-1905-x.
Chicago author-date (all authors)
Alcoba, Diego R, Alicia Torre, Luis Lain, Gustavo E Massaccesi, Ofelia B Oña, Paul W Ayers, Mario Van Raemdonck, Patrick Bultinck, and Dimitri Van Neck. 2016. “Performance of Shannon-Entropy Compacted N-Electron Wave Functions for Configuration Interaction Methods.” THEORETICAL CHEMISTRY ACCOUNTS 135 (6). doi:10.1007/s00214-016-1905-x.
Vancouver
1.
Alcoba DR, Torre A, Lain L, Massaccesi GE, Oña OB, Ayers PW, et al. Performance of Shannon-entropy compacted N-electron wave functions for configuration interaction methods. THEORETICAL CHEMISTRY ACCOUNTS. 2016;135(6).
IEEE
[1]
D. R. Alcoba et al., “Performance of Shannon-entropy compacted N-electron wave functions for configuration interaction methods,” THEORETICAL CHEMISTRY ACCOUNTS, vol. 135, no. 6, 2016.
@article{8042643,
  abstract     = {{The coefficients of full configuration interaction wave functions (FCI) for N-electron systems expanded in N-electron Slater determinants depend on the orthonormal one-particle basis chosen although the total energy remains invariant. Some bases result in more compact wave functions, i.e. result in fewer determinants with significant expansion coefficients. In this work, the Shannon entropy, as a measure of information content, is evaluated for such wave functions to examine whether there is a relationship between the FCI Shannon entropy of a given basis and the performance of that basis in truncated CI approaches. The results obtained for a set of randomly picked bases are compared to those obtained using the traditional canonical molecular orbitals, natural orbitals, seniority minimising orbitals and a basis that derives from direct minimisation of the Shannon entropy. FCI calculations for selected atomic and molecular systems clearly reflect the influence of the chosen basis. However, it is found that there is no direct relationship between the entropy computed for each basis and truncated CI energies.}},
  articleno    = {{153}},
  author       = {{Alcoba, Diego R and Torre, Alicia and Lain, Luis and Massaccesi, Gustavo E and Oña, Ofelia B and Ayers, Paul W and Van Raemdonck, Mario and Bultinck, Patrick and Van Neck, Dimitri}},
  issn         = {{1432-881X}},
  journal      = {{THEORETICAL CHEMISTRY ACCOUNTS}},
  keywords     = {{COLLINS CONJECTURE,SPIN-ADAPTED SPACES,NATURAL ORBITALS,DENSITY-MATRICES,INFORMATION ENTROPY,NUMERICAL EVIDENCE,QUANTUM-THEORY,OPTIMIZATION,SYSTEMS,ORDER REPLACEMENT OPERATORS,DOCI,Seniority,Configuration interaction,Entropy}},
  language     = {{eng}},
  number       = {{6}},
  pages        = {{11}},
  title        = {{Performance of Shannon-entropy compacted N-electron wave functions for configuration interaction methods}},
  url          = {{http://doi.org/10.1007/s00214-016-1905-x}},
  volume       = {{135}},
  year         = {{2016}},
}

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