MoUer Plesset

Curtiss L A, P C Redfern, K Raghavachari, V Rassolov and J A Pople 1999. Gaussian-3 Theory Using Reduced MoUer-Plesset Order. Journal of Chemical Physics 110 4703-4709. 

Another distinguishing aspect of MO methods is the extent to which they deal with electron correlation. The Hartree-Fock approximation does not deal with correlation between individual electrons, and the results are expected to be in error because of this, giving energies above the exact energy. MO methods that include electron correlation have been developed. The calculations are usually done using MoUer-Plesset perturbation theoiy and are designated MP calculations." ... 

MoUer-Plesset perturbation theory energies through fifth-order (accessed via the keywords MP2, MP3, MP4, and MP5), optimizations via analytic gradients for second-order (MP2), third-order (MP3) and fourth-order (without triples MP4SDQ), and analytic frequencies for second-order (MP2). 

Electron correlation (how well does MoUer-Plesset perturbation theory converge for these problems )... 

The extrapolation to the complete basis set energy limit is based upon the MoUer-Plesset expansion E= + E + E + E + E +. .. as described earlier in this appendix. Recall that E + E is the Hartree-Fock energy. We will denote E and all higher terms as E , resulting in this expression for E ... 

Schwartz has shown that for a helium-like ion, the contribution to the second-order MoUer-Plesset energy from the 1 angular momentum component can be approximated by the following expression ... 

Petersson and coworkers have extended this two-electron formulation of asymptotic convergence to many-electron atoms. They note that the second-order MoUer-Plesset correlation energy for a many-electron system may be written as a sum of pair energies, each describing the energetic effect of the electron correlation between that pair of electrons ... 

MP4(SDQ) MoUer-Plesset 4-th order perturbation theory incorporating single, double, and quadruple excitations... 

What is of more practical interest here is that HF descriptions of the dimer cannot give a DIS term. This may be recovered by introducing Cl descriptions of the system. The simpler Cl description, now largely used in routine calculations on molecules and molecular aggregates, is called MP2. This acronym means that use has been made of a specialized version of the pertiubation theory (called MoUer-Plesset) limited to second order to determine the expansion coefficients. 

Analytic gradient methods became widely used as a result of their implementation for closed-shell self-consistent field (SCF) wavefunctions by Pulay, who has reviewed the development of this topic. Since then, these methods have been extended to deal with all types of SCF wavefunctions, - as well as multi-configuration SCF (MC-SCF), - " configuration-interaction (Cl) wavefunctions, and various non-variational methods such as MoUer-Plesset (MP) perturbation theory - - and coupled-cluster (CC) techniques. - In short, it is possible to obtain analytic energy derivatives for virtually all the standard ab initio approaches. The main use of analytic gradient methods is, and will remain, the location of stationary points on a potential energy siuface, to obtain equilibrium and transition-state geometries. However, there is a specialized use in the calculation of quantities such as dipole derivatives. 

Cl using SCF orbitals, all single and double excitations from two a and three a" orbitals. Cl (two-reference second-order MoUer-Plesset) using SCF orbitals. 

Olsen et al. and others rests on the assumption that the utihty of lower-order Moller-Plesset perturbation theory can be inferred from the behaviour of the higher-order terms in the perturbation series. It is widely appreciated that MoUer-Plesset perturbation theory and the equivalent many-body perturbation theory for a single determinantal reference function are not as robust as, for example, configuration interaction. Some care must therefore be exercised in applications to ensure that an appropriate reference function is employed. 

Its first term, Eypi, has exactly the same functional form as the conventional second order MoUer-Plesset correlabon contribution (MP2). However, in Eos. (4.7 4.8) the represent KS orbitals, which experience the multiplicative KS potential (2.7), rather... 

Tsuzuki, S. Uchimaru, T. Tanabe, K. Intermolecular interaction potentials of methane and ethylene dimers calculated with the MoUer-Plesset, coupled cluster and density functional methods. Chem. Phys. Lett. 1998, 287, 202-208. 

R. H. Nobes, J. A. Pople, L. Radom, N. C. Handy P. J. Knowles. Slow Convergence of the MoUer-Plesset Perturbation Series The Dissociation Energy of Hydrogen Cyanide and the Electron Affinity of the Cyano Radical. Chem. Phys. Lett., 138 (1987) 481. 

V. Termath, W. Klopper, W. Kutzelnigg. Wave functions with terms linear in the interelectrorric coordinates to take care of the correlation cusp. III. Second-order MoUer-Plesset (MP2-R12) calculations on closed-shell atoms. /. Chem. Phys., 94 (1991) 2002-2019. 

K. G. DyaU. Second-order MoUer-Plesset perturbation theory for molecular Dirac-Hartree-Fock wavefunctions. Theory for up to two open-shell electrons. Chem. Phys. Lett., 224 (1994) 186-194. 

Norris LS, Ratner MA, Roitberg AE, Gerber RB (1996) MoUer-plesset perturbation theory applied to vibrational problems. J Chem Phys 105 11261... 

Christiansen O (2003) MoUer-plesset perturbation theory for vibrational wave functions. J Chem Phys 119 5773... 

Frequency-dependent response functions can only be computed within approximate electronic structure models that allow definition of the time-dependent expectation value. Hence, frequency-dependent response functions are not defined for approximate methods that provide an energy but no wave function. Such methods include MoUer-Plesset (MP) perturbation theory, multiconfigurational second-order perturbation theory (CASPT2), and coupled cluster singles and doubles with non-iterative perturbative triples [CCSD(T)]. As we shall see later, it is possible to derive static response functions for such methods. 

Two of the most commonly used electronic structure methods to evaluate Eint are MP2 (second-order MoUer-Plesset perturbation theory) and CCSD(T) (coupled-cluster with singles and doubles and non-iterated triples). Interaction energies calculated using these methods are shown in O Table 6-1. Interaction energies calculated using MP2 are usually close to those calculated using the more sophisticated and computationally expensive CCSD(T), but the exception is the benzene dimer system for which MP2 overestimates the binding by almost a factor of 2. This deserves some explanation. 

The MoUer-Plesset energy corrections maybe calculated up to the fourth order (MP2, MP3, and MP4). 

Energies and gradients may be evaluated for the second-order closed-shell MoUer-Plesset perturbation theory (MP2). 

The interactions present in halogen-bonded systems are in general weak, thus the need to use quantum mechanical methods that include electron correlation for an accurate description. In particular, these interactions are sensitive, not only to the basis set used but also to the level of electron correlation used, the counterpoise correction and the inclusion of spin-orbit effects for bromine and iodine. In contrast with the widely accepted idea that hydrogen bonded systems are reasonably well described with MoUer-Plesset perturbation (MP2) methods, halogen bond interactions are overestimated at this level. Therefore, for an accurate description of these systems a coupled cluster method is advised, preferably with single and double excitations (CCSD) or with perturbative triple excitations (CCSD(T)). This problem pertains also to density functional theory methods (DFT) where some methods lead to better results than others and the choice of the best functional is not straightforward. DFT methods have the advantage over wave function methods that time... 

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