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Singer polymals. II. Tempering methods
Author(s) -
Poshusta R. D.
Publication year - 2009
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.560160807
Subject(s) - parallel tempering , tempering , basis (linear algebra) , monte carlo method , statistical physics , mathematics , physics , monte carlo molecular modeling , materials science , statistics , markov chain monte carlo , geometry , composite material
Tempering of Singer polymal basis sets is introduced to reduce the number of variational parameters to be optimized. Two types of tempering are studied and compared: generalized “even tempering” and generalized “Monte Carlo tempering.” Comparisons of total energy are made for various temperings of Singer geminals using the ground state of the helium atom for a model system. Generalized Monte Carlo tempering is found to be superior. The benefit‐to‐cost ratio is measured for extending the basis size versus extending the number of tempering parameters; for small basis and small numbers of parameters it is more beneficial to add more parameters, but for sufficiently large basis it is more beneficial to extend the basis than to add more parameters. Monte Carlo tempering exploits the benefits of extending the basis without increasing the number of variational parameters.