Mpller-Plesset theory

Equilibrium geometries, dissociation energies, and energy separations between electronic states of different spin multiplicities are described substantially better by Mpller-Plesset theory to second or third order than by Hartree-Fock theory. 

Pople, J. A., R. Krishnan, H. B. Schlegel, and J. S. Binkley. 1979. Derivative Studies in Hartree-Fock and Mpller-Plesset Theories. Int. J. Quantum Chem. Quantum Chem. Symp. 13, 225-241. 

Subsequently, we performed more sophisticated calculations with a larger basis set and with inclusion of electron correlation at the level of Mpller-Plesset theory. From Figure 7 it is seen that the agreement between experiment and theory is even better than previously. Similar agreement was found for [1,2,3,4- H4]-1. ... 

The relation between the supermolecule coupled cluster approach and the perturbation theory of intermolecular forces in even less obvious than the case of the Mpller-Plesset theory, and no formal analysis has been reported in the literature thus far. Rode et al.68 analyzed the long-range behavior of the CCSD(T) method65, and showed that this method, although very popular and in principle accurate, may lead to wrong results for systems with the electrostatic term strongly depending on the electronic correlation, e.g. the CO dimer. 

MPn n -order Mpller-Plesset theory. Means of including electron correlation. 

Obviously, theory of vibrationally inelastic electron scattering is open to all complications that have been encountered in the theory of elastic electron scattering1,2,21. In contrast to the electronic structure theory, we do not have in the theory of electron scattering any standard procedures as configuration interaction, Mpller-Plesset theory or coupled clusters, not speaking about the... 

Semi-empirical MO methods address electron correlation implicitly they simply adjust parameters until the calculations give the correct answer compared with experiment. EHT does not address electron correlation at all, so quantitative results from such calculations are almost always wrong unless fortuitous. There are, however, several approaches to explicitly account for electron correlation. One approach is to perform post-ab initio (post-H-F) calculations that in effect mix different electronic configurations involving the ground state and several excited states of the molecule. Such calculations are quite computationally intensive and can be performed only on relatively small molecules. Two commonly-seen acronyms associated with the post H-F approach to electron correlation are MP2 and Cl, which stand for Mpller-Plesset theory at the level of second-order and configuration interaction, respectively. 

J. S. Binkley and J. A. Pople, Int. ). Quantum Chem., 9, 229 (1975). Mpller-Plesset Theory for Atomic Ground State Energies. 

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. 

A critical step in the development of any perturbation expansion is the division of the Hamiltonian 5f into a zero-order part Jfo and a perturbation JKi. In second quantized formalism, the Hamiltonian for the Mpller-Plesset theory is written as... 

Because of its relationship to Mpller-Plesset theory (as discussed in Section 14.2), we shall refer to (13.4.10) as the perturbation correction to the coupled-cluster amplitudes. The first correction to the wave function is obtained from (13.4.10) using zero cluster amplitudes, and higher corrections are generated by repeating this procedure. 

The omissions made in (3CISD theory relative to CCSD theoiY may be justified by the observation that the singles amplitudes are usually smaller than the doubles anplitudes. For further justification, we may invoke perturbation theory, noting that, in Mpller-Plesset theory, the doubles amplitudes appear to first order and the singles to second order in the fluctuation potential. Carrying out an... 

In the closed-shell Mpller-Plesset theory of Section 14.4, the construction of an orthonormal basis is more difficult and we shall then instead use a biorthogonal representation. 

Thus, the second-order quadruple exeitations decouple into products of two first-order double excitations. The remaining second-order eorrections do not decouple in this fashion. The decoupling of the quadmple excitations is a special feature of Mpller-Plesset theory. 

In this section, we study the relationship between coupled-cluster and Mpller-Plesset theories in greater detail. We begin by carrying out a perturbation analysis of the coupled-cluster wave functions and energies in Section 14.6.1. We then go on to consider two sets of hybrid methods, where the coupled-cluster approximations are improved upon by means of perturbation theory. In Section 14.6.2, we consider a set of hybrid coupled-cluster wave fiinctions, obtained by simplifying the projected coupled-cluster amplitude equations by means of perturbation theory. In Section 14.6.3, we examine the CCSE)(T) approximation, in which the CCSD energy is improved upon by adding triples corrections in a perturbative fashion. Finally, in Section 14.6.4, we compare numerically the different hybrid and nonhybrid methods developed in the present chapter and in Chapter 13. 

Based on the success of Mpller-Plesset theory for systems dominated by a single electronic configuration, it is natural to enquire whether the zero-order Hamiltonian operator of Mpller-Plesset theory can be extended to multiconfigurational systems. We recall that, in Mpller-Plesset theory, we use the Fock operator in the canonical representation as the zero-order Hamiltonian - see... 

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