Application of Fisher information in estimation of nuclear configurations of molecules

Document Type : Original Article

Authors

1 Department of Mathematics, University of Qom

2 Department of Chemistry, Faculty of Science, University of Qom, Qom, I.R. Iran

10.22036/cr.2023.376437.1199

Abstract

Abstract
In this paper, we first review the relationship between the electronic density function of a chemical molecule and a parameterization space via the solution of the Schrödinger equation. Then, using the charge density functions corresponding to a molecule, we study the molecular structures via information theory. To do this, we assign a parameterized family of electron density functions to any molecule, and consider a quantity for them, named Fisher information. Finally, Applying the presented model, a lower bound for the estimation error of configurations of a molecule is given. Then, the model presented in the paper is applied on Hydrogen molecule ion, and the Fisher information corresponding to this molecule is calculated, using the electronic density function of the Hydrogen molecule ion . Finally, applying the Cramer-Rao inequality, a lower bound for the estimation error of the nuclear configuration of Hydrogen molecule ion is attained and the results are described using some plots. It is expected that the results of this research can open new horizons in the investigation and analysis of the quantum configuration of molecular subsystems.

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Iranian Journal of Chemistry
Volume 5, Issue 2 - Serial Number 9
March 2023
Pages 187-195

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History

  • Receive Date: 21 December 2022
  • Revise Date: 10 March 2023
  • Accept Date: 14 April 2023

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