SCF perturbation theory

Density-Functional Theory. Transition metals pose a problem for classical quantum chemical methods like self-consistent field (SCF), perturbation theory, configuration interaction (Cl), and variations on these methods, because of the very large electron correlation. SCF underestimates binding substantially, and post-SCF methods are so expensive for transition metals that one can do a calculation only on models with few atoms. DFT on the other hand is relatively cheap it is about as expensive as SCF. Moreover, with the development of the generalized-gradient approximations it is also reasonably accurate. A large majority of quantum chemical... 

Table 10 Representative calculations of 13C magnetic shielding constants relative to 13C in CH4 calculated using SCF perturbation theory and GIAO...

MC-SCF Perturbation Theory Orthogonal Valence Bond Moller-Plesset 2 (OVB-MP2). 

One of the most successful methods of calculating nuclear spin coupling constants involves application of SCF perturbation theory and use of the INDO molecular orbital (MO) approximations. (8-17) In most theoretical studies aAB and bAB are taken as empirical parameters, adjusted to give best agreement between theory and experiment. Values of the individual integrals calculated from Slater exponents (14) are given in Table I. 

An additional source of chemical shielding anisotropies is that of ab initio theoretical calculations.20 25 There has been considerable progress in this area of molecular quantum mechanics, particularly with the use of gauge-invariant atomic orbitals within the framework of self-consistent-field (SCF) perturbation theory.26 In many cases the theoretical quantities have been extremely accurate and have served not only as a corroboration of experimental quantities but also as a reliable source of new data for molecules of second-row atoms (i.e., Li through F). 

SCF perturbation theory with gage-invariant atomic orbitals by R. Ditchfield (private communication, 1972). 

In both the time-dependent and time-independent SCF perturbation theories the equations determining the effect of the perturbation look as if they can generate a finite effect with no applied perturbation. These cases of infinitesimal perturbations" are genuine ones which have important ramifications for the stabilities of the single-determinant states of a many-electron system. 

Both types of SCF perturbation theory generate similar-looking expressions for the first-order corrections to the density matrix ... 

A variety of methods have been developed and tested which exploit features of the physical structure of wavefunctions in order to avoid the shortcomings of brute-force CI(SD), CI(SDTQ) or full Cl calculations. We mention especially internally or externally contracted MR-CI(SD) techniques, full Cl methods in a limited orbital space such as the CAS-SCF, perturbation theory procedures like MP(4), MP(5), etc., " and pair methods like CP-MET (and CCSD), CEPA and CPF. All these methods certainly have their virtues as is obvious from the chapters in this volume. 

Other studies include C chemical shifts in tetrahalogenomethanes, where there is a regular charge with the period of the halogen, and in the fluoro-methanes, where the dependence upon the number of fluorines is decidedly non-linear, and a comparison of theoretical values, obtained by using SCF perturbation theory, with experimental C diemical shifts in fluoro-ethylenes. ... 

McDoull, J. J. W, Peasley, K., and Robb, M. A. (1998) A simple MC SCF perturbation theory Orthogonal valence bond M0ller-Plesset 2 (OVB MP2), Chem. Phys. Lett, 148,183-189. 

Show how the equations of coupled SCF perturbation theory must be modified when the basis functions are non-orthogonal. [HirU The equations already derived would apply if the orbitals were orthonornudized (for example by the transformation, p. 35) reverse the procedure, transforming all equations to the non-orthogonal basis.]... 

This reduces, of course, to the ordinary SCF equation FT = Te when F is time-independent otherwise T will acquire a time dependence and will introduce (through the time-dependent density in the G matrix) a coupling between the density fluctuations and the effective field. When the time-dependent part of h is specified it is therefore necessary to solve (12.6.13) iteratively until the fluctuations of F and p are self-consistent. There is thus a fully coupled time-dependent analogue of the SCF perturbation theory in Section 11.9. 

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