Least‐Squares Local‐Energy Method for Molecular Energy Calculations Using Gauss Quadrature Points

1961 ◽  
Vol 35 (3) ◽  
pp. 827-831 ◽  
Author(s):  
A. A. Frost ◽  
R. E. Kellogg ◽  
B. M. Gimarc ◽  
J. D. Scargle
Keyword(s):  
Least Squares ◽  
Energy Method ◽  
Gauss Quadrature ◽  
Local Energy ◽  
Energy Calculations

Local-Energy Method in Electronic Energy Calculations

1960 ◽  
Vol 32 (2) ◽  
pp. 313-317 ◽  
Author(s):  
Arthur A. Frost ◽  
Reid E. Kellogg ◽  
Earl C. Curtis
Keyword(s):  
Energy Method ◽  
Electronic Energy ◽  
Local Energy ◽  
Energy Calculations

Nonlinear parameters in the Least-Squares Local Energy Method

1968 ◽  
Vol 9 (4) ◽  
pp. 303-311 ◽  
Author(s):  
Donald K. Harriss ◽  
Ronald K. Roubal
Keyword(s):  
Least Squares ◽  
Energy Method ◽  
Local Energy ◽  
Nonlinear Parameters

Energy of the Lithium Atom by the Least‐Squares Local Energy Method

1963 ◽  
Vol 39 (7) ◽  
pp. 1698-1702 ◽  
Author(s):  
B. M. Gimarc ◽  
A. A. Frost
Keyword(s):  
Least Squares ◽  
Energy Method ◽  
Lithium Atom ◽  
Local Energy

RELIABILITY OF ELECTRONIC ENERGY CALCULATIONS BY A MODIFIED LOCAL-ENERGY METHOD

1967 ◽  
Vol 45 (8) ◽  
pp. 2755-2767 ◽  
Author(s):  
T. A. Rourke ◽  
E. T. Stewart
Keyword(s):  
Wave Function ◽  
Energy Method ◽  
Statistical Study ◽  
Electronic Energy ◽  
Wave Functions ◽  
Local Energy ◽  
Energy Calculations ◽  
Simple Situation ◽  
Large Numbers

This statistical study of the performance of a modified local-energy method using random selection shows that there is little advantage in using large numbers of electron positions, the quality of the wave functions being a much more significant factor. A relationship is given between the quality of the wave function and the resulting accuracy. Use of as few as 25 sets of electron positions is suggested.A method of avoiding the increase in the calculation time with the size of a system is given and was found to be very accurate in a simple situation.

Remarks on Local Energy and Perturbations

2000 ◽  
Vol 55 (11-12) ◽  
pp. 912-914
Author(s):  
M. G. Marmorino
Keyword(s):  
Energy Method ◽  
Upper Bounds ◽  
Local Energy ◽  
Large Systems ◽  
Soluble Base

Abstract The local energy is first reviewed and compared with the expected energy. We then present the perturbative local energy method which uses an exactly soluble base problem and a perturbing potential to greatly simplify the expression of the local energy. This is demonstrated with two-electron atoms for which the method gives upper bounds with errors from 18% for He to 4% for Ne8+. Finally a call to develop a local energy method for large systems is issued.

Mathematical Properties of Frost's Local‐Energy Method

1966 ◽  
Vol 45 (2) ◽  
pp. 565-569 ◽  
Author(s):  
Richard E. Stanton ◽  
Robert L. Taylor
Keyword(s):  
Energy Method ◽  
Local Energy ◽  
Mathematical Properties
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