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 first order energy is the same as given by the usual Moller-Plesset treatment, < 0 H 0 > and the first order electrostatic contribution to the free energy of solvation is identical to the result obtained at the Hartree-Fock level of flieory. The second order correction to the free energy is given as... 

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. 

Moller-Plesset (MP) perturbation approach. This is an alternative treatment in the solution of the correlation problem. At a given basis set, the MP approach solves the full Hamiltonian matrix within Schrodinger s equation as the sum of two parts. Here, the second part represents a perturbation of the first... 

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... 

S. S b0 and P. Pulay,/. Chem. Phys., 86, 914 (1987). Fourth-Order Moller-Plesset Perturbation Theory in the Local Correlation Treatment. I. Method. 

The form of the SCEP treatment will vary in certain aspects depending upon whether it is employed to carry out a Cl, CC or Moller-Plesset (MP) perturbation theory calculation. However, the differences are modest and the same quantities appear in one place or another. For convenience we utilize here the MP perturbation theory version of SCEP as formulated by Pulay and Saebo [30, 31] for their local correlation treatment. The (Hylleraas) variation condition on the first-order coefficient matrix, C = CP, may be written in the form... 

It is possible to extend the Moller-Plesset perturbation treatment to higher orders. However, the perturbation expansion often oscillates and diverges to higher... 

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... 

The data of Table 3b have been computed by replacing the active space of the CASPT2 treatment by the CIPSI multireference space of the MRPT2 method documented in section 2.1. The selection of the components of the reference space by this technique enables us to reduce the gap between the Moller-Plesset and Epstein-Nesbet total energies to less than 0.01 a.u., and so to improve our evaluation of energy balances, disregarding a possible overestimation of the Moller-Plesset values due to intruder states, as it is the case in the ScNC system. 

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]. 

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