McWeeny approach

At any rate, the projection of the first-order orbitals on the subspace of occupied is not needed within the McWeeny approach [7], where choice (25) is implicitly assumed it is sufficient to calculate the projection on the subspace of virtual... 

However, using the McWeeny approach [7], it is sufficient to calculate only the pro-... 

However, using the McWeeny approach [7], it is sufficient to calculate only the projection P >v/K on the subspace of virtual zero-order orbitals in order to get the second hyperpolarizability tensor. This projection is evaluated via a procedure similar to the one used in solving the first-order equation (21). Taking in (32) the Hermitian product with the unoccupied and using (19), one finds... 

We will now discuss an iterative scheme based on the CHF approach outlined in Sections 11 and 111, using the McWeeny procedure [7] for resolving matrices into components, by introducing projection operators R and R2, with respect to the subspaces spanned by occupied and virtual molecular orbitals. 

Following the approach ofCGM based on McWeeny s [13] decomposition of into C+C, Pecora arrived at results different from CGM. 

T. Thorsteinsson, D.L. Cooper, J. Gerratt and M. Raimondi A New Approach to Valence Bond Calculations CASVB, in R. McWeeny, J. Mamani, Y.G. Smeyers and S. Wilson (Eds.), Quantum Systems in Chemistry and Physics Trends in Methods and Applications, Kluwer Academic Publishers, Dordrecht (1997). 

Good expositions of VB theory are given by Pauling (1960), Cartmell and Fowles (1977) (see Section A.7 of the Appendix) and Lagowski (1973) (see Section A.3). McWeeny s revisions of Coulson s classic book (1979 and 1982) (see Section A.7) emphasise the three-centre bond approach to hypervalent species. See also Dasent (1965) (Section A.8) for discussion of nonexistent compounds. 

In one sense, research in theoretical chemistry at Queen s University at Kingston originated outside the Department of Chemistry when A. John Coleman came in 1960 as head of the Department of Mathematics. Coleman took up Charles Coulson s challenge150 to make the use of reduced density matrices (RDM) a viable approach to the N-electron problem. RDMs had been introduced earlier by Husimi (1940), Lowdin (1955), and McWeeny (1955). The great attraction was that their use could reduce the 4N space-spin coordinates of the wavefunctions in the variational principle to only 16 such coordinates. But for the RDMs to be of value, one must first solve the celebrated N-repre-sentability problem formulated by Coleman, namely, that the RDMs employed must be derivable from an N-electron wavefunction.151 This constraint has since been a topic of much research at Queen s University, in the Departments of Chemistry and Mathematics as well as elsewhere. A number of workshops and conferences about RDMs have been held, including one in honor of John Coleman in 1985.152 Two chemists, Hans Kummer [Ph.D. Swiss Federal Technical... 

Other multiconfiguration VB methods have also been devised, like the biorthogonal valence bond method of McDouall (35,36) or the spin-free approach of McWeeny (37). For an overview of these methods, the reader is advised to consult a recent review (1). 

This kind of approach in which one distinguishes electron pairs as physically or chemically distinct subsystems has been extended by McWeeny in his theory of generalized product functions.99 In this model, one now distinguishes between several groups of electrons and writes the spatial wave-function in the form of a product of group functions ... 

There are many books describing bonding and molecular orbitals, with levels ranging from those even more descriptive and qualitative than the treatment in this chapter to those designed for the theoretician interested in the latest methods. A classic that starts at the level of this chapter and includes many more details is R. McWeeny s revision of Coulson s Valence, 3rd ed., Oxford University Press, Oxford, 1979. A different approach that uses the concept of generator orbitals is that of J. G. Verkade, in A Pictorial... 

In this Section, we will briefly overview the main ab initio methods to evaluate interaction potentials, referring to McWeeny and Sutcliffe s book [2a] and its recent revised edition [2b] for a thorough treatment (see also [9,10]). There are two principal ab initio methods for potentials, the supermolecular and the perturbative approach, each with its own pro s and con s. 

It is worth noting that the same results of the perturbative method can be attained by the elegant approach in terms of group functions due to McWeeny [2b]. 

C. Amovilli and R. McWeeny, A matrix partitioning approach to the calculation of intermolecular potentials. General theory and some examples, Cbem. Phys., 140 (1990) 343-361. 

There are several approaches that may be used to achieve this goal. Many of these methods are discussed in the review of the Cl method of Shavitt, in the review of MCSCF and Cl methodology of McWeeny and Sutcliffe and in the discussion of spin eigenfunctions by Pauncz The method with which the present author is most familiar is the graphical unitary group approach (GUGA) and this approach will be discussed briefly. For more details of this method, the reader is referred, in particular, to the contributions of Paldus and of Shavitt in the volume of Lecture Notes in Chemistry edited by J. Hinze. 

In the present section we will discuss the general statements on diatomic force constants, in particular, their definition, general properties, and intercorrelations. However, we do not examine a large variety of computational approaches for obtaining the force constants—they have been presented in detail elsewhere (Rossikhin and Morozov, 1983 Gos-teminskaya et al., 1977 Morozov and Bezverkhnaya, 1979 Nielsen, 1951 Sahni et al., 1969 Bezverkhnaya and Morozov, 1980 Pulay, 1969, 1970 Schutte, 1971 Ruttink and van Lenthe, 1981 Mukheijee and McWeeny, 1970). In general, as stated in Section I, we are primarily interested in the pure basic principles of the diatomic potential theory. 

R. McWeeny, Coulson s Valence, 3rd Edn, Oxford University Press, Oxford, 1979 A. Szabo and N. S. Ostlund, Modern Quantum Chemistry, Dover, New York, 1996 N. J. B. Green, Quantum Mechanics 1 Foundations, Oxford University Press, Oxford, 1997 D. A. McQuarrie and J. D. Simon, Physical Chemistry A Molecular Approach, University Science Books, Sausalito, CA, 1997 V. M. S. Gil, Orbitals in Chemistry, Cambridge University Press, Cambridge, 2000 A. Vincent, Molecular Symmetry and Group Theory, 2nd Edn, John Wiley Sons, Ltd, Chichester, 2001 A. Rauk, Orbital Interaction Theory of Organic Chemistry, 2nd Edn, John Wiley Sons, Ltd, New York, 2001 D. O. Hayward, Quantum Mechanics for Chemists, Royal Society of Chemistry, Cambridge, 2002 J. E. House, Fundamentals of Quantum Chemistry, 2nd Edn, Elsevier, Amsterdam, 2004 N. T. Anh, Frontier Orbitals A Practical Manual, John Wiley Sons, Ltd, Chichester, 2007 J. Keeler and P. Wothers, Chemical Structure and Reactivity, Oxford University Press, Oxford, 2008. 

R. McWeeny (1979) Coulson s Valence, 3rd edn, Oxford University Press, Oxford - A general treatment of chemical bonding with a detailed mathematical approach. 

Modem quantum chemistry, (Revised 1st Ed, McGraw-Hill, 1989) by A. Szabo and N. S. Ostlund has a slightly more computational and applied approach than McWeeny s book. 

This approach, which was suggested by McWeeny[55] and explored by Reeves and Harrison[56], [57] in the early 1960s, was thoroughly investigated by Ruedenberg and his coworkers[58]-[64] in the 1970s. 

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