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The loge theory as a starting point for variational calculations. I. General formalism
Author(s) -
Aslangul C.,
Constanciel R.,
Daudel R.,
Esnault L.,
Ludeña E. V.
Publication year - 1974
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.560080403
Subject(s) - delocalized electron , wave function , observable , formalism (music) , operator (biology) , physics , function (biology) , quantum mechanics , chemistry , art , musical , biochemistry , repressor , evolutionary biology , biology , transcription factor , visual arts , gene
It is shown that any expectation value of any observable associated with a molecule is the sum of loge contributions and of loge pair contributions. This result provides a rigorous theoretical basis for the study of additive properties of molecules. It is demonstrated that molecular wave functions (exact or approximate) can be expressed as a sum of functions corresponding to the various electronic events. Furthermore any of these event functions can be expressed in terms of correlated loge functions. This expression suggests many kinds of variational procedures of calculating wave functions (known methods and new ones). The case in which noncorrelated completely localized loge functions are used is discussed. If continuous functions are used the variational equation reduces to a sum of independent variational equations, each one corresponding to a particular electronic event. This is not so when discontinuous functions are used or when a delocalized function is added to replace the correlation interloge function. The noncorrelated completely localized loge model is analyzed in more detail. It is seen that local spin operators can be introduced and that each event density operator is the product of the loge density operators. Therefore that model is an independent loge model. The corresponding generalized self‐consistent field equations are derived. This treatment helps us to understand how a localized state of a molecule can produce an ion containing a delocalized region, a phenomenon which is sometimes at the origin of some misunderstanding in photoelectron spectroscopy. Finally it is seen how virtual loge functions can be introduced to describe excited states.