Moller-Plesset perturbation theory calculations

An MP3 (third-order Moller-Plesset perturbation theory) calculation predicts that the triazir-ine ground state is 126 kJ/mol more energetic than the ground state of linear HN3 [3]. An ab initio SCF Cl calculation predicts an excess energy of - 230 kJ/mol for triazirine thus, immediate dissociation into NH and N2 can be expected [4]. An MP2 calculation did not yield a minimum for C-N3H on the potential energy surface [5],... 

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. 

As can be seen from Table I, the C-C bond distance as described by LDF is closer to experiment than the corresponding HF value obtained with a 6-3IG basis. Including correlation via second and third order Moller-Plesset perturbation theory and via Cl leads to very close agreement with experiment. The C-H bond length is significantly overestimated in the LDF calculations by almost 2%. The HCH bond angle is reasonably well described and lies close to all the HF and post-HF calculations. Still, all the theoretical values are too small by more than one degree compared with experiment the deviation from experiment is particularly pronounced for the semi-empirical MNDO calculation. 

Higher level calculations, based on higher orders of Moller-Plesset perturbation theory, can also be performed, albeit with the consumption of much more computer time. For example, an MP4SDTQ calculation uses fourth-order Moller-Plesset perturbation theory, includes excitations through quadruples, and gives better energies than MP2 does. 

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)). 

Table 6 displays some bonding energies for CI2-, as calculated at the D-BOVB level and at other theoretical levels, including Hartree-Fock and Moller-Plesset perturbation theory. Unlike the F2 case, the Moller-Plesset series converges well around the values of 24-25 kcal/mol which can be taken as references for the bonding energy in this basis set. 

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. 

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