Moller-Plesset perturbation theory method

Problem was solved by application of intrinsic reaction coordinate (IRC) procedure in combination with Density Functional Theory and second order Moller-Plesset perturbation theory methods [35]. It was demonstrated that potential energy surface around boat conformation is extremely fiat (Fig. 19.2) and contains wide plateau where energy of molecule remains almost the same. Conformation of cyclohexene ring is changed from one twist-boat to symmetric another twist-boat via boat conformation representing a central point of plateau. Width of plateau in terms of value of the C3-C4-C5-C6 torsion angle slightly depends on method of calculations (Table 19.2) and is varied within 30 0°. 

The Seetion on More Quantitive Aspects of Electronic Structure Calculations introduees many of the eomputational ehemistry methods that are used to quantitatively evaluate moleeular orbital and eonfiguration mixing amplitudes. The Hartree-Foek self-eonsistent field (SCF), eonfiguration interaetion (Cl), multieonfigurational SCF (MCSCF), many-body and Moller-Plesset perturbation theories. 

A number of types of calculations begin with a HF calculation and then correct for correlation. Some of these methods are Moller-Plesset perturbation theory (MPn, where n is the order of correction), the generalized valence bond (GVB) method, multi-conhgurational self-consistent held (MCSCF), conhgu-ration interaction (Cl), and coupled cluster theory (CC). As a group, these methods are referred to as correlated calculations. 

Correlation can be added as a perturbation from the Hartree-Fock wave function. This is called Moller-Plesset perturbation theory. In mapping the HF wave function onto a perturbation theory formulation, HF becomes a hrst-order perturbation. Thus, a minimal amount of correlation is added by using the second-order MP2 method. Third-order (MP3) and fourth-order (MP4) calculations are also common. The accuracy of an MP4 calculation is roughly equivalent to the accuracy of a CISD calculation. MP5 and higher calculations are seldom done due to the high computational cost (A time complexity or worse). 

Ah initio methods are applicable to the widest variety of property calculations. Many typical organic molecules can now be modeled with ah initio methods, such as Flartree-Fock, density functional theory, and Moller Plesset perturbation theory. Organic molecule calculations are made easier by the fact that most organic molecules have singlet spin ground states. Organics are the systems for which sophisticated properties, such as NMR chemical shifts and nonlinear optical properties, can be calculated most accurately. 

Various theoretical methods and approaches have been used to model properties and reactivities of metalloporphyrins. They range from the early use of qualitative molecular orbital diagrams (24,25), linear combination of atomic orbitals to yield molecular orbitals (LCAO-MO) calculations (26-30), molecular mechanics (31,32) and semi-empirical methods (33-35), and self-consistent field method (SCF) calculations (36-43) to the methods commonly used nowadays (molecular dynamic simulations (31,44,45), density functional theory (DFT) (35,46-49), Moller-Plesset perturbation theory ( ) (50-53), configuration interaction (Cl) (35,42,54-56), coupled cluster (CC) (57,58), and CASSCF/CASPT2 (59-63)). 

Fifth Order Moller-Plesset Perturbation Theory Comparison of Existing Correlation Methods and Implementation of New Methods Correct to Fifth Order. 

Using a single determinant to derive the Hartree-Fock wavefunction does not take into account the correlation between electrons of different spins. If the wavefunction is described by a linear combination of determinants, then configuration interaction is incorporated. Another method to model correlation energy involves Moller-Plesset perturbation theory. A more detailed description of this may be found in Ref. 41. 

Raghavachari K, Pople JA, Repogle ES, Head-Gordon M (1990) Fifth order Moller-Plesset perturbation theory comparison of existing correlation methods and implementation of newmethods correct to fifth order. J Phys Chem 94 5579-5586... 

One of the inherent problems with ab initio calculations is that they do not take full account of electron correlation, which arises from electrons keeping away from the vicinity of other electrons. This can make a significant contribution to the energy and is especially significant for accurate calculations of reaction energies and bond dissociation. One early method used for adding the effects of electron correlation to the Hartree-Fock method incorporated Moller-Plesset perturbation theory and led to methods labeled MP2, MP3, MP4, etc. 

The Moller-Plesset perturbation theory is a popular and most extensively used method to incorporate electron correlation to the HF theory [26, 34], In this method the HF Hamiltonian is treated in a perturbative way. Thus, the total Hamiltonian is written as ... 

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