Moller-Plesset theory

Moller-Plesset theory at second order, third order, etc. 

ROMP2 2nd order restricted open shell Moller-Plesset theory... 

Valeev, E.F., Janssen, C.L. Second-order Moller-Plesset theory with linear R12 terms (MP2-R12) revisited auxiliary basis set method and massively parallel implementation. J. Chem. Phys. 2004, 121, 1214-27. 

Thomas B. E. IV, Evanseck J. D., Houk K. N.,J. Am. Chem. Soc., 1993,115, 4165. Geometry optimizations by 3-21 G calculations, energies calculated using Moller-Plesset theory and the 6-31G basis set. 

Most of these extensions have involved electron correlation methods based on variational approaches (DFT, MCSCF, CI,VB). These methods can be easily formulated by optimizing the free energy functional (1.117), expressed as a function of the appropriate variational parameters, as in the case of the HF approximation. In contrast, for nonva-riational methods such as the Moller-Plesset theory or Coupled-Cluster, the parallel extension to solvation model is less straightforward. 

As in my three most recent reviews, "" I have attempted to provide a snapshot of the many applications of many-body perturbation theory in its simplest form, i.e. Moller-Plesset theory designated MP2, during the period under review by performing a literature search for publications with the string MP2 in the title only. During the period covered by the present report, a total of 80 papers were discovered satisfying this criterion. 

Depending on the choice of molecular orbital basis, the earliest terms for certain excitation levels are naturally zero. For example, in Moller-Plesset theory, only... 

Since the zeroth-order component of H consists of just the Fock operator in Moller-Plesset theory, the first-order components of H may be written as... 

This initial guess may then be inserted on the right-hand sides of the equations and subsequently used to obtain new amplitudes. The process is continued until self-consistency is reached. For the special case in which canonical Hartree-Fock molecular orbitals are used, the Fock matrix is diagonal and the T2 amplitude approximation above is exactly the same as the first-order perturbed wave-function parameters derived from Moller-Plesset theory (cf. Eq. [212]). In that case, the Df and arrays contain the usual molecular orbital energies, and the initial guess for the T1 amplitudes vanishes. 

Restricted Moller-Plesset Theory for Open-Shell Molecules. 

Second-order Moller-Plesset theory with linear R12 terms (MP2-R12) revisited Auxiliary basis set method and massively parallel implementation101... 

All calculations have been carried out with the Gaussian 98 series of programs [18]. The geometries of all species, were optimized using the hybrid density functional method B3LYP [19)[20][21] with the standard 6-31G basis set. Second-order Moller-Plesset theory calculations (MP2), with a 6-311++G basis set,... 

A difficulty with this local approach to dynamical correlation is that, in Moller-Plesset theory, for example, the zero-order Fock operator is no longer diagonal in the space of the Slater determinants, making the application of such theories slightly more complicated than theories based on canonical orbitals. Currently, the development of local correlation methods is an active area of research [57-63]. The diatomics-inmolecules (DIM) method and the triatomics-in-molecules (TRIM) method, for instance, recover typically 95% and 99.7%, respectively, of the full MP2 correlation energy [63]. By means of a linear scaling local variant of the CCSDT method,... 

Ayala PY, Scuseria GE. Linear scaling second-order Moller-Plesset theory in the atomic orbital basis for large molecular systems. J Chem Phys 1999 110 3660-3671. 

Pople JA, Seeger R. Electron density in Moller-Plesset theory. J Chem Phys 1975 62 4566. 

The process of thermal decomposition of 13 was also reinvestigated in 1999, using the CASSCF(10,8) method and Moller-Plesset theory (CAS/MP2) in conjunction with the 6-31G basis set. In contrast to the previous calculations, this reaction was predicted to occur in two steps via a nitrene intermediate. Therefore, the predicted reaction mechanism is drastically changed by the method used in the calculations. The authors concluded that the CASCCF predictions should be the more reliable, because this method has sufficient flexibility to describe in a balanced way most of the potential energy surface. ... 

Application of multireference Moller-Plesset theory confirmed the general tendency observed in carotenoids that the first transition of the dications of polyenes is at a higher energy (shorter m) than the intense transition of the radical cation and at a lower energy (longer Xmax) than the first allowed transition of the neutral species [141], cf. Fig. 23. 

The question for a more systematic inclusion of electronic correlation brings us back to the realm of molecular quantum chemistry [51,182]. Recall that (see Section 2.11.3) the exact solution (configuration interaction. Cl) is found on the basis of the self-consistent Hartree-Fock wave function, namely by the excitation of the electrons into the virtual, unoccupied molecular orbitals. Unfortunately, the ultimate goal oi full Cl is obtainable for very small systems only, and restricted Cl is size-inconsistent the amount of electron correlation depends on the size of the system (Section 2.11.3). Thus, size-consistent but perturbative approaches (Moller-Plesset theory) are often used, and the simplest practical procedure (of second order, thus dubbed MP2 [129]) already scales with the fifth order of the system s size N, in contrast to Hartree-Fock theory ( N ). The accuracy of these methods may be systematically improved by going up to higher orders but this makes the calculations even more expensive and slow (MP3 N, MP4 N ). Fortunately, restricted Cl can be mathematically rephrased in the form of the so-called coupled clus-... 

Initio Calculations of Polarizability and Second Hyperpolarizability in Benzene Including Electron Correlation Treated by Moller-Plesset Theory. 

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