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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.

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Acknowledgments

D.R.A. and P.B. acknowledge the Ministerio de Ciencia, Tecnología e Innovación Productiva (Argentina) and the FWO Vlaanderen (Belgium) for collaborative research grant VS.0001.14N. D.R.A. acknowledges the Universidad de Buenos Aires (Argentina) and the Consejo Nacional de Investigaciones Científicas y Técnicas (Argentina) for research Grant Nos. UBACYT 20020100100197, PIP 11220090100061 and PIP 11220130100377CO. A.T. and L.L. acknowledge the Universidad del Pais Vasco (Spain) for research Grant Nos. GIU12/09 and UFI11/07. O.B.O. acknowledges the Consejo Nacional de Investigaciones Científicas y Técnicas (Argentina) for research Grant Nos. 11220090100369 and 11220130100311CO. M.V.R., D.V.N. and P.B. acknowledge the support from the Research Foundation Flanders (FWO Vlaanderen). The computational resources and services used in this work were provided by the Universidad de Buenos Aires and the Universidad del Pais Vasco and the Stevin Supercomputer Infrastructure, provided by the VSC (Flemish Supercomputer Center), funded by Ghent University, the Hercules Foundation and the Flemish Government-department EWI. M.V.R., P.B. and D.V.N. are members of the QCMM alliance Ghent-Brussels.

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Authors and Affiliations

  1. Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, 1428 Buenos Aires, Argentina

    Diego R. Alcoba

  2. Instituto de Física de Buenos Aires, Consejo Nacional de Investigaciones Científicas y Técnicas, Ciudad Universitaria, 1428, Buenos Aires, Argentina

    Diego R. Alcoba

  3. Departamento de Química Física, Facultad de Ciencia y Tecnología, Universidad del País Vasco, Apdo. 644, 48080, Bilbao, Spain

    Alicia Torre & Luis Lain

  4. Departamento de Ciencias Exactas, Ciclo Básico Común, Universidad de Buenos Aires, Ciudad Universitaria, 1428, Buenos Aires, Argentina

    Gustavo E. Massaccesi

  5. Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas, Universidad Nacional de la Plata, CCT La Plata, Consejo Nacional de Investigaciones Científicas y Técnicas, Diag. 113 y 64 (s/n), Sucursal 4, CC 16, 1900, La Plata, Argentina

    Ofelia B. Oña

  6. Department of Chemistry and Chemical Biology, McMaster University, 1280 Main Street West, Hamilton, ON, L8S 4M1, Canada

    Paul W. Ayers

  7. Department of Inorganic and Physical Chemistry, Ghent University, Krijgslaan 281 (S3), 9000, Gent, Belgium

    Mario Van Raemdonck & Patrick Bultinck

  8. Center for Molecular Modeling, Ghent University, Technologiepark 903, 9052, Zwijnaarde, Belgium

    Dimitri Van Neck

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  1. Diego R. Alcoba
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  2. Alicia Torre
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  4. Gustavo E. Massaccesi
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Correspondence to Patrick Bultinck.

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Alcoba, D.R., Torre, A., Lain, L. et al. Performance of Shannon-entropy compacted N-electron wave functions for configuration interaction methods. Theor Chem Acc 135, 153 (2016). https://doi.org/10.1007/s00214-016-1905-x

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