Mpller-Plesset direct

The accurate calculation of these molecular properties requires the use of ab initio methods, which have increased enormously in accuracy and efficiency in the last three decades. Ab initio methods have developed in two directions first, the level of approximation has become increasingly sophisticated and, hence, accurate. The earliest ab initio calculations used the Hartree-Fock/self-consistent field (HF/SCF) methodology, which is the simplest to implement. Subsequently, such methods as Mpller-Plesset perturbation theory, multi-configuration self-consistent field theory (MCSCF) and coupled-cluster (CC) theory have been developed and implemented. Relatively recently, density functional theory (DFT) has become the method of choice since it yields an accuracy much greater than that of HF/SCF while requiring relatively little additional computational effort. 

In 1973, the author used the framework of EOM theory [11] as expressed by the McKoy group to develop a systematic (i.e. order-by-order in the Mpller-Plesset perturbation theory sense) approach for directly computing molecular EAs and IPs as eigenvalues of the EOM working equations. It is this development and its subsequent improvement and extensions [12] by our group and others that we now wish to describe. 

These third-order equations have been used in many applications in which molecular EAs have been computed for a wide variety of species as illustrated in Ref. [16]. Clearly, all the quantities needed to form the second- or third-order EOM matrix elements Hj. are ultimately expressed in terms of the orbital energies sj and two-electron integrals j, k l, h) evaluated in the basis of the neutral molecule s Hartree-Eock orbitals that form the starting point of the Mpller-Plesset theory. However, as with most electronic stmcture theories, much effort has been devoted to recasting the working EOM equations in a manner that involves the atomic orbital (AO) two-electron integrals rather than the molecular orbital based integrals. Because such technical matters of direct AO-driven calculations are outside the scope of this work, we will not delve into them further. 

As long as one stays with traditional methods for calculation of correlation energies, it is necessary to perform a transformation of the one- and two-electron integrals into the molecular spinor basis. While Mpller-Plesset perturbation expansions can be cast in a semi-direct form that does not require a complete integral transformation, it is... 

From a technical point of view, we note that the identification of the MP2 quadruples as diseon-nected products of doubles was not easy, requiring a fair amount of tedious algebra. Clearly, it would be convenient if the identification of connected and disconnected terms in the Mpller-Plesset wave functions could be made directly, without having to go through extensive algebraic manipulations in each case - this will be achieved in the CCPT of Section 14.3. 

In this subsection, we give the closed-shell Mpller-Plesset energy corrections to fourth order. As noted in Section 14.2.4, the sum of the zero- and first-order Mpller-Plesset energies is equal to the Hartree-Fock energy. We therefore proceed directly to the higher-order corrections, treating in turn the closed-shell MP2, MP3 and MP4 energies. 

The application of many-body perturbation theory to molecules involves the direct application of the Rayleigh-Schrodinger formalism with specific choices of reference Hamiltonian. The most familiar of these is that first presented by Mpller and Plesset... 

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