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On optimization procedures based upon the atomic thomas‐fermi energy
Author(s) -
Ten Hoor Marten J.
Publication year - 1986
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.560290605
Subject(s) - normalization (sociology) , kinetic energy , function (biology) , energy minimization , physics , energy (signal processing) , second derivative , mathematics , statistical physics , quantum mechanics , mathematical analysis , evolutionary biology , sociology , anthropology , biology
For the total atomic Thomas‐Fermi (TF) energy many expressions in terms of the kinetic and potential energy contributions can be given. Thirty of these expressions exhibit either a maximum or a minimum if some variational approximation to the TF function is used. Three of these expressions, to note E , G , and J (see text) have been used in an optimization procedure, in which four two‐parameter and two three‐parameter approximate TF functions have been considered. One‐parameter functions cannot be optimized, as the one parameter must be fixed to ensure proper normalization. It is found that optimization of E and G give reasonable and similar results, whereas the results of optimization of J are generally not very impressive. Where possible, expectation values of the type 〈 r n 〉 (with n = −1, 1, 2, and 3) have been calculated from ten approximate TF functions. A new estimate of the exact atomic TF energy, as well as of the derivative of the TF function at the origin, has been obtained.