Electron correlations exact treatment

The computation of furoxans (l,2,5-oxadiazole-2-oxides) is very demanding. Very strong electron correlation effects hamper a proper treatment of this class of molecules. With respect to the geometric parameters, it is the endocyclic N—O bond that can be treated reliably either at the B3-LYP or at the MP4(SDQ) level [99MI1 ]. Table II demonstrates the problems associated with the exact determination of this bond length. 

The idea of constructing a good wave function of a many-particle system by means of an exact treatment of the two-particle correlation is also underlying the methods recently developed by Brueck-ner and his collaborators for studying nuclei and free-electron systems. The effective two-particle reaction operator and the self-consistency conditions introduced in this connection may be considered as generalizations of the Hartree-Fock scheme. 

The antiferromagnetic state described by the occupation of the lower Hubbard band is stabilized by inclusion of such electron correlation, but the ferromagnetic analog is not. This is a result exactly analogous to the stabilization of the lowest singlet state in cyclobutadiene below the triplet. For the simple density of states used by Hubbard in his treatment he showed in fact that the condition for ferromagnetism was... 

Third, we can draw a vital conclusion about correlated calculations from these benchmarks. They have established that MRCI (or MRCI+Q) calculations on systems with up to ten electrons correlated, for example, involve little or no error from truncation of the iV-particle basis, at least for calculations in DZP (or somehat larger) basis sets. If we assume that this conclusion is independent of any coupling between the one-particle and iV-particle space, an assumption that is supported by the (very limited) available evidence, we can conclude that in any one-particle basis there will be little or no truncation error in MRCI calculations. It then follows that we should expect that MRCI in a complete basis would agree with complete Cl, that is, with the exact result. Hence if our MRCI calculations do not suffer from errors as a result of JV-paxticle space truncation we infer that the main source of errors (if any) must be the one-paxticle basis. This had been suggested on numerous previous occasions — our best correlation treatments handle the correlation problem very well and the errors in our best results actually reflect inadequacies in the one-particle basis. We shall turn our attention to one-particle basis sets in the next chapter. 

An exactly similar criterion obtained by interchanging the roles of M and L, and m, , applies to the optimum L group wavefunctions. This is a well-defined optimization problem which may be solved iteratively starting from some reasonable guess for the group functions, and its solution already gives us a good treatment of electron correlation. 

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