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

作者：Lemes Nelson H T; Braga Joao P^*; Alves Marcio O; Costa Ederson D' M

来源：Journal of Molecular Modeling, 2014, 20(7): 2317.

DOI：10.1007/s00894-014-2317-2

• Variable phase method
• Phase shift
• Quantum inversion
• Sensitivity analysis

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.

• 出版日期2014-7