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An optimized orbital transformation able to reproduce partially prefixed overlaps
Author(s) -
Gianinetti Ermanno,
Vandoni Ida
Publication year - 1992
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.560410306
Subject(s) - transformation (genetics) , basis (linear algebra) , set (abstract data type) , distortion (music) , space (punctuation) , function (biology) , combinatorics , mathematics , basis set , basis function , algorithm , physics , computer science , geometry , mathematical analysis , chemistry , quantum mechanics , telecommunications , biology , amplifier , biochemistry , molecule , gene , programming language , operating system , bandwidth (computing) , evolutionary biology
Given a function space spanned by a basis {ƒ i }, we are interested in finding another basis { g i } for which the overlaps ( g i | g i ) assume arbitrarily prefixed values in a subset ℬ of the full set of the pairs of indices ( i , j ). The other overlaps are let free. We show how it is possible to perform this linear transformation ƒ i → g i minimizing the “distortion” J = Σ i ( g i – ƒ i | g i – ƒ i ).