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Potential energy function information from quantum phase shift using the variable phase method

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Abstract

The present work discusses quantum phase shift sensitivity analysis with respect to the potential energy function. A set of differential equations for the functional derivative of the quantum phase shift with respect to the potential energy function was established and coupled with the variable phase equation. This set of differential equations provides a simple, exact and straightforward way to establish the sensitivity matrix. The present procedure is easier to use than the finite difference approach, in which several direct problems have to be addressed. Furthermore, integration of the established equations can be used to demonstrate how the sensitivity phase shift is accumulated as a function of the interatomic distance. The potential energy function was refined to produce a better quality function. The average error on the phase shift decreased from 9.8 % in the original potential function to 0.13 % in the recovered potential. The present procedure is an important initial step for further work towards recovering potential energy functions in upper dimensions or to recovering this function from cross sections.

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Acknowledgments

We would like to thank Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) and Fundação de Amparo à Pesquisa do Estado de Minas Gerais (FAPEMIG) for their financial support.

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Authors and Affiliations

  1. Instituto de Química, Universidade Federal de Alfenas, Rua Gabriel Monteiro da Silva 700 - Centro, Alfenas, MG, 37130-000, Brazil

    Nelson H. T. Lemes & Éderson D’M. Costa

  2. Departamento de Química, Universidade Federal de Minas Gerais, Av. Antônio Carlos 6627 - Pampulha, Belo Horizonte, MG, 31270-010, Brazil

    João P. Braga & Márcio O. Alves

Authors
  1. Nelson H. T. Lemes
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  2. João P. Braga
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  3. Márcio O. Alves
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  4. Éderson D’M. Costa
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Corresponding author

Correspondence to João P. Braga.

Additional information

This paper belongs to Topical Collection Brazilian Symposium of Theoretical Chemistry (SBQT2013)

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Lemes, N.H.T., Braga, J.P., Alves, M.O. et al. Potential energy function information from quantum phase shift using the variable phase method. J Mol Model 20, 2317 (2014). https://doi.org/10.1007/s00894-014-2317-2

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  • DOI: https://doi.org/10.1007/s00894-014-2317-2

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