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Hierarchical construction of finite diabatic sets by Mathieu functions
Author(s) -
Englman R.,
Yahalom A.,
Baer M.
Publication year - 2001
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.10086
Subject(s) - diabatic , adiabatic process , born–oppenheimer approximation , quantum , quantum mechanics , physics , mathematics , statistical physics , mathematical physics , molecule
An extension is given for the standard two component model of adiabatic, Born–Oppenheimer (BO) electronic states in a polyatonic molecule, by use of Mathieu functions of arbitrary order. The curl or compatibility conditions for the construction of a diabatic set of states based on a finite‐dimensional subset of BO states are not satisfied exactly. It is shown, however, that, by successively adding higher order Mathieu functions to the BO set, the compatibility conditions are satisfied with increasingly better accuracy. We then generalize to situations in which the nonadiabatic couplings (the dynamic corrections to the BO approximation) are small (though not necessarily zero) between a finite‐dimensional BO subset and the rest of the BO states. We prove that approximate diabatic sets exist, with an error that is of the order of the square of the neglected nonadiabatic couplings. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001