Generalized perturbation theory versions

The recent expansion of the application of perturbation theory formulations is mainly due to the development of the generalized perturbation theory (GPT). Several versions of GPT formulations have been described. They are characterized by their form and their method of derivation. They are also distinguished by the form of the integral parameters to which they apply and by the method they use to allow for the flux and adjoint perturbation. A unified presentation of GPT is given in Section V, together with an elucidation of problems of accuracy and range of applicability of different formulations. Also outlined in Section V is a perturbation theory for altered systems. 

The generalized perturbation theory expressions presented in this section for systems described by the homogeneous Boltzmann equation (excluding Section V,B,2) are in the form proposed by Stacey (40, 41). Had we assumed that the overall alteration in the reactor retains criticality, we would have achieved the Usachev-Gandini version of GPT. Stacey s version is often associated (41, 46, 48, 62) with the variational perturbation theory as distinguished from the GPT of Usachev-Gandini. Does the variational approach provide a different perturbation theory than the GPT derived (35,39) from physical considerations Is one of these versions of perturbation theory more general or more accurate than the other What does the term GPT stand for ... 

The Mpller-Plesset (MP) treatment of electron correlation [84] is based on perturbation theory, a very general approach used in physics to treat complex systems [85] this particular approach was described by M0ller and Plesset in 1934 [86] and developed into a practical molecular computational method by Binkley and Pople [87] in 1975. The basic idea behind perturbation theory is that if we know how to treat a simple (often idealized) system then a more complex (and often more realistic) version of this system, if it is not too different, can be treated mathematically as an altered (perturbed) version of the simple one. Mpller-Plesset calculations are denoted as MP, MPPT (M0ller-Plesset perturbation theory) or MBPT (many-body perturbation theory) calculations. The derivation of the Mpller-Plesset method [88] is somewhat involved, and only the flavor of the approach will be given here. There is a hierarchy of MP energy levels MPO, MP1 (these first two designations are not actually used), MP2, etc., which successively account more thoroughly for interelectronic repulsion. 

G2(MP2)-RAD, which implements restricted-open-shell versions of both coupled cluster and perturbation theories. The latter method has been shown to generally yield reliable results when applied to open-shell systems [66]. 

Although sophisticated electronic structure methods may be able to accurately predict a molecular structure or the outcome of a chemical reaction, the results are often hard to rationalize. Generalizing the results to other similar systems therefore becomes difficult. Qualitative theories, on the other hand, are unable to provide accurate results but they may be useful for gaining insight, for example why a certain reaction is favoured over another. They also provide a link to many concepts used by experimentalists. Frontier molecular orbital theory considers the interaction of the orbitals of the reactants and attempts to predict relative reactivities by second-order perturbation theory. It may also be considered as a simplified version of the Fukui function, which considered how easily the total electron density can be distorted. The Woodward-Hoffmann rules allow a rationalization of the stereochemistry of certain types of reactions, while the more general qualitative orbital interaction model can often rationalize the preference for certain molecular structures over other possible arrangements. 

Passing now to the analytical calculations of the y " tensor elements in solution, there are several SCRF methods in use we quote here some major examples, referring for more details to the relevant papers. " All the quoted methods use spherical or ellipsoidal cavities, with the exception of the PCM version which can treat cavities of general shape, and work at a QM level ranging from semiempirical to MCSCF methods. A MPE approach is generally used to describe solvent effects, with the exception of PCM again, which uses an ASC method. The evaluation of the y " tensor elements is made either with finite differences, response theory and SOS methods, or with coupled perturbed Hartree-Fock (CPHF) methods. ... 

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