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New lower bound formula from the local energy
Author(s) -
Marmorino M. G.
Publication year - 2007
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.21297
Subject(s) - upper and lower bounds , hamiltonian (control theory) , ground state , bound state , energy (signal processing) , quantum mechanics , quantum , function (biology) , physics , atomic physics , mathematics , mathematical analysis , mathematical optimization , evolutionary biology , biology
A new formula to determine a lower bound to the ground‐state energy of an electronic system is presented making use of the local energy. Two‐electron atoms are considered and each lower bound is not only superior to the traditional lower bound, which is just the minimum of the local energy, but is also closer to the exact energy than the Hamiltonian expectation value that uses the same trial function. In this method, we have removed the restriction that the trial function be non‐zero. Lower bound methods using the local energy have the advantage that the expectation value of the squared Hamiltonian or another potentially difficult integral does not have to be calculated as in many other lower bound methods. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2007