The Lehmann-Maehly approach and Bazley’s method of special choice are matrix eigenvalue problems that allow the calculation of lower bounds to energies of atomic and molecular systems. We introduce a common derivation of their scalar versions using the overlap of a trial function with the unknown ground-state wave function. In the scalar setting, the Lehmann-Maehly approach reduces to the Temple formula. The common derivation allows us to easily unite and improve both methods in several stages within this restricted application. Finally we offer a different union that allows generalization to arbitrary dimension matrix methods. Calculations on the helium atom ground state illustrate the improvements and mergers.
%0 Journal Article
%1 noKey
%A Marmorino, M.G.
%D 2013
%I Springer Netherlands
%J Journal of Mathematical Chemistry
%K chemistry inequality mechanics physics quantum unread variational
%N 8
%P 2062-2073
%R 10.1007/s10910-013-0199-7
%T Comparison and union of the Temple and Bazley lower bounds
%U http://dx.doi.org/10.1007/s10910-013-0199-7
%V 51
%X The Lehmann-Maehly approach and Bazley’s method of special choice are matrix eigenvalue problems that allow the calculation of lower bounds to energies of atomic and molecular systems. We introduce a common derivation of their scalar versions using the overlap of a trial function with the unknown ground-state wave function. In the scalar setting, the Lehmann-Maehly approach reduces to the Temple formula. The common derivation allows us to easily unite and improve both methods in several stages within this restricted application. Finally we offer a different union that allows generalization to arbitrary dimension matrix methods. Calculations on the helium atom ground state illustrate the improvements and mergers.
@article{noKey,
abstract = {The Lehmann-Maehly approach and Bazley’s method of special choice are matrix eigenvalue problems that allow the calculation of lower bounds to energies of atomic and molecular systems. We introduce a common derivation of their scalar versions using the overlap of a trial function with the unknown ground-state wave function. In the scalar setting, the Lehmann-Maehly approach reduces to the Temple formula. The common derivation allows us to easily unite and improve both methods in several stages within this restricted application. Finally we offer a different union that allows generalization to arbitrary dimension matrix methods. Calculations on the helium atom ground state illustrate the improvements and mergers.},
added-at = {2013-08-12T17:34:56.000+0200},
author = {Marmorino, M.G.},
biburl = {https://www.bibsonomy.org/bibtex/27ecd070feadcf433ec51c58329c5573a/drmatusek},
doi = {10.1007/s10910-013-0199-7},
interhash = {d26664603085211785589f17e328e522},
intrahash = {7ecd070feadcf433ec51c58329c5573a},
issn = {0259-9791},
journal = {Journal of Mathematical Chemistry},
keywords = {chemistry inequality mechanics physics quantum unread variational},
language = {English},
month = sep,
number = 8,
pages = {2062-2073},
publisher = {Springer Netherlands},
timestamp = {2013-08-12T17:34:56.000+0200},
title = {Comparison and union of the Temple and Bazley lower bounds},
url = {http://dx.doi.org/10.1007/s10910-013-0199-7},
volume = 51,
year = 2013
}