Electron Moller-Plesset treatment

Second-order Moller-Plesset treatment for electron correlation... 

Li et studied the monochalcogenocarboxylic acids CH3COXH with X being S, Se, or Te (Fig. 10) both in vacuum and in a THF (tetrahydrofuran) solution. They used the polarizable continuum model and calculated the electronic properties of the solute by using Hartree-Fock calculations with a second order Moller-Plesset treatment of correlation effects. They compared the enol and the keto forms and calculated also the transition state between the two. Finally, they considered both... 

Ab initio calculated geometrical parameters depend on the kind of applied basis sets (which is the main variable when using an ab initio computer programme like, for example, Pople s GAUSSIAN 90 ) and on the kind of calculational procedure The so-called Hartree-Fock limit is the theoretically best result obtainable with a single determinant MO basis. Because of the different weighting of inter-electron repulsion between electron pairs of like and unlike spin, Hartree-Fock calculations are in error. They may be improved by the use of configuration interaction methods (Cl) or by the use of perturbation theory, like the Moller-Plesset treatment of second, third or fourth order (MP2, MP3 or MP4). 

The best estimate of the binding energy, after correction of this error [60], is approximately 23 kJ/mol, 5 of which are associated with electron correlation. Del Bene s recent calculation [36], which employed a 6-31 +G(2 /, 2p) basis set and full fourth-order Moller-Plesset treatment of correlation, found a value of 28 kJ/mol (although superposition error was not removed). Within the context of hydrides of first-row atoms, this complex is the most weakly bound, with the order as follows ... 

If we except the Density Functional Theory and Coupled Clusters treatments (see, for example, reference [1] and references therein), the Configuration Interaction (Cl) and the Many-Body-Perturbation-Theory (MBPT) [2] approaches are the most widely-used methods to deal with the correlation problem in computational chemistry. The MBPT approach based on an HF-SCF (Hartree-Fock Self-Consistent Field) single reference taking RHF (Restricted Hartree-Fock) [3] or UHF (Unrestricted Hartree-Fock ) orbitals [4-6] has been particularly developed, at various order of perturbation n, leading to the widespread MPw or UMPw treatments when a Moller-Plesset (MP) partition of the electronic Hamiltonian is considered [7]. The implementation of such methods in various codes and the large distribution of some of them as black boxes make the MPn theories a common way for the non-specialist to tentatively include, with more or less relevancy, correlation effects in the calculations. 

Using MP2(full)/6-31+G geometries (second-order Moller-Plesset perturbation theory with core electrons included in the perturbation treatment). 

Parallel to these endeavors, work started in Germany on new concepts to account for electron correlation. The independent electron pair approach (lEPA) was developed by Ahlrichs and Kutzelnigg, followed a few years later by the CEPA (coupled electron pair approach).The relation of these methods to contemporary Moller-Plesset second order (MP2) and coupled cluster treatments is discussed in Ref. 60. Work on circular dichroism by Ruch and on the chemical shift by Voitlander showed the variety of ab initio problems treated. The special priority program of the DFG from 1966-1970 demonstrated the intended impact. 

In a mainly experimental work, Fujihara et al performed photoelectron spectroscopy experiments on Na2 in small water clusters, i.e., Na2 (H20)K with w < 6. In addition, they performed electronic-structure calculations with Hartree-Fock plus 2nd order Moller-Plesset perturbation treatment of correlation effects. Further... 

The Moller-Plesset (MP) treatment of electron correlation [64] is based on perturbation theory, a very general approach used in physics to treat complex systems [65] this particular approach was described by Moller and Plesset in 1934 [66] and developed... 

A fundamental characteristic of the FPA is the dual extrapolation to the one-and n-particle electronic-structure limits. The process leading to these limits can be described as follows (a) use families of basis sets, such as the correlation-consistent (aug-)cc-p(wC)VnZ sets [51,52], which systematically approach completeness through an increase in the cardinal number n (b) apply lower levels of theory with extended [53] basis sets (typically direct Hartree-Fock (HF) [54] and second-order Moller-Plesset (MP2) [55] computations) (c) use higher-order valence correlation treatments [CCSD(T), CCSDTQ(P), even FCI] [5,56] with the largest possible basis sets and (d) lay out a two-dimensional extrapolation grid based on the assumed additivity of correlation increments followed by suitable extrapolations. FPA assumes that the higher-order correlation increments show diminishing basis set dependence. Focal-point [2,49,50,57-62] and numerous other theoretical studies have shown that even in systems without particularly heavy elements, account must also be taken for core correlation and relativistic phenomena, as well as for (partial) breakdown of the BO approximation, i.e., inclusion of the DBOC correction [28-33]. 

Physicists and chemists have developed various perturbation-theory methods to deal with systems of many interacting particles (nucleons in a nucleus, atoms in a solid, electrons in an atom or molecule), and these methods constitute many-body perturbation theory (MBPT). In 1934, Mpller and Plesset proposed a perturbation treatment of atoms and molecules in which the unperturbed wave function is the Hartree-Fock function, and this form of MBPT is called Moller-Plesset (MP) perturbation theory. Actual molecular applications of MP perturbation theory began only in 1975 with the work of Pople and co-workers and Bartlett and co-workers [R. J. Bartlett, Ann. Rev. Phys. Chem.,31,359 (1981) Hehre et al.]. 

Purely theoretical data with an accuracy of 0.1 eV have been calculated more recently. Ab initio MO theory corrected by 4th order Moller-Plesset (MP4) perturbation calculations [9], gave Ej = 9.72 and 10.64 (for X and a of PHJ) [1, 10]. A modification of that method (to give also singlet-triplet separations) yielded Ej = 9.77 and 10.64 [11]. A treatment of the electron correlation not only by MP4 but also by quadratic configuration interaction (Cl) [12,13] led to Ej = 9.71 [14]. Older data were obtained by Cl [15,16] and SCF [16,17] calculations. - For orbital energies from SCF calculations, see [17, 18]. 

Two relevant topics have been ignored completely in this short chapter the treatment of electron correlation with more sophisticated methods than DFT (that remains unsatisfactory from many points of view) and the related subject of excited states. Wave function-based methods for the calculation of electron correlation, like the perturbative Moller-Plesset (MP) expansion or the coupled cluster approximation, have registered an impressive advancement in the molecular context. The computational cost increases with the molecular size (as the fifth power in the most favorable cases), especially for molecules with low symmetry. That increase was the main disadvantage of these electron correlation methods, and it limited their application to tiny molecules. This scaling problem has been improved dramatically by modern reformulation of the theory by localized molecular orbitals, and now a much more favorable scaling is possible with the appropriate approximations. Linear scaling with such low prefactors has been achieved with MP schemes that the... 

The high bond stabilities in LaAu and LuAu have been studied by Schwerdtfeger and Dolg (1991) using relativistic as well as nonrelativistic ab initio PPs and correlation treatments like Moller-Plesset perturbation theory up to fourth order (MP , = 2,3,4), configuration interaction with single and double substitutions (CISD) and coupled electron... 

Although small systematic changes in basis sets can frequently lead to erratic alterations of the quantitative nature of the H-bonding phenomenon, subtraction of the superposition error by the counterpoise procedure leads to much more uniform behavior. This argument applies to the correlated as well as SCF level of treatment. Perturbation theory of the Moller-Plesset type furnishes an efficient and accurate means to account for electron correlation. The literature indicates that MP2 calculations are quite reliable for H-bonds, due in large measure to the opposite effects generally observed for the third and fourth-order terms. 

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