Mpller-Plesset calculations

The Mpller-Plesset (MP) treatment of electron correlation [84] is based on perturbation theory, a very general approach used in physics to treat complex systems [85] this particular approach was described by M0ller and Plesset in 1934 [86] and developed into a practical molecular computational method by Binkley and Pople [87] in 1975. The basic idea behind perturbation theory is that if we know how to treat a simple (often idealized) system then a more complex (and often more realistic) version of this system, if it is not too different, can be treated mathematically as an altered (perturbed) version of the simple one. Mpller-Plesset calculations are denoted as MP, MPPT (M0ller-Plesset perturbation theory) or MBPT (many-body perturbation theory) calculations. The derivation of the Mpller-Plesset method [88] is somewhat involved, and only the flavor of the approach will be given here. There is a hierarchy of MP energy levels MPO, MP1 (these first two designations are not actually used), MP2, etc., which successively account more thoroughly for interelectronic repulsion. 

Jasien and Fitzgerald62 demonstrated that the LDA dipole moments of such molecules as HF, H20, NH3, formamide, imidazole, pyridine, cytosine, match very closely the experimental ones (the relative errors between 1 and 7%). For uracil and thymine, and adenine, the differences between LDA and experimental dipole moments are slightly larger (relative errors up to 12%) and compared better to the ones derived from second-order Mpller-Plesset calculations. The authors underlined the noticeable effect the inclusion of the hydrogen 2p polarization... 

The conventional coupled-cluster and second-order Mpller-Plesset calculations were performed with the Mainz-Austin-Budapest 2005 version of the AcES II program [83] and with the MRCC program [89, 90]. The former program was employed for the conventional CCSD approach with the perturbative correction for connected triple excitations (T). The MRCC code was used for the higher order coupled-cluster treatment, i.e. the full triples (CCSDT) and perturbative quadruples treatment (CCSDT(Q)). The CCSD(F12) method, as implemented in the Turbomole program, was used for the purpose of the explicitly correlated calculations. 

Klopper W, Kutzelnigg W (1987) Mpller-Plesset calculations taking care of the correlation cusp. Chem Phys Lett 134 17-22... 

J. Mavri, M. Hodoscek and D. Hadzi, Ab initio SCF and Mpller-Plesset calculations on the hydrogen bond in hydrogen malonate Effects of neighbor ions and polarizable medium, J. Mol. Struct. (Theochem), 209 (1990) 421. 

In Figure 14.4, we have illustrated the behaviour of the two-state model for two sets of parameters, which represent a back-door intruder dominated by high-order excitations (to the left) and a front-door intruder dominated by low-order excitations (to the right). The numerical values of the parameters were obtained from the Mpller-Plesset calculations discussed in Section 14.5.5. For the high-excitation back-door intruder, the parameters are yS — a = 12.32, S = —0.00034 and... 

HyperChem supports MP2 (second order Mpller-Plesset) correlation energy calculationsusing afe mi/io methods with anyavailable basis set. In order to save main memory and disk space, the HyperChem MP2 electron correlation calculation normally uses a so called frozen-core approximation, i.e. the inner shell (core) orbitals are omitted. A setting in CHEM.INI allows excitations from the core orbitals to be included if necessary (melted core). Only the single point calculation is available for this option. 

Specifies the calculation of electron correlation energy using the Mpller-Plesset second order perturbation theory (MP2). This option can only be applied to Single Point calculations. 

Things have moved on since the early papers given above. The development of Mpller-Plesset perturbation theory (Chapter 11) marked a turning point in treatments of electron correlation, and made such calculations feasible for molecules of moderate size. The Mpller-Plesset method is usually implemented up to MP4 but the convergence of the MPn series is sometimes unsatisfactory. The effect... 

Simon, S., Duran, M., Dannenberg, J. J., 1999, Effect of Basis Set Superposition Error on the Water Dimer Surface Calculated at Hartree-Fock, Mpller-Plesset, and Density Functional Theory Levels , J. Phys. Chem. A, 103, 1640. 

How does a rigorously calculated electrostatic potential depend upon the computational level at which was obtained p(r) Most ab initio calculations of V(r) for reasonably sized molecules are based on self-consistent field (SCF) or near Hartree-Fock wavefunctions and therefore do not reflect electron correlation in the computation of p(r). It is true that the availability of supercomputers and high-powered work stations has made post-Hartree-Fock calculations of V(r) (which include electron correlation) a realistic possibility even for molecules with 5 to 10 first-row atoms however, there is reason to believe that such computational levels are usually not necessary and not warranted. The Mpller-Plesset theorem states that properties computed from Hartree-Fock wave functions using one-electron operators, as is T(r), are correct through first order (Mpller and Plesset 1934) any errors are no more than second-order effects. 

The difference between the Hartree-Fock energy and the exact solution of the Schrodinger equation (Figure 60), the so-called correlation energy, can be calculated approximately within the Hartree-Fock theory by the configuration interaction method (Cl) or by a perturbation theoretical approach (Mpller-Plesset perturbation calculation wth order, MPn). Within a Cl calculation the wave function is composed of a linear combination of different Slater determinants. Excited-state Slater determinants are then generated by exciting electrons from the filled SCF orbitals to the virtual ones ... 

Perturbative approximation methods are usually based on the Mpller-Plesset (MP) perturbation theory for correcting the HF wavefunction. Energetic corrections may be calculated to second (MP2), third (MP3), or higher order. As usual, the open- versus closed-shell character of the wavefunction can be specified by an appropriate prefix, such as ROMP2 or UMP2 for restricted open-shell or unrestricted MP2, respectively. 

A series of single-point energy calculations is carried out at higher levels of theory. The first higher-level calculation is the complete fourth-order Mpller-Plesset perturbation theory [13] with the 6-31G(d) basis set, i.e. MP4/6-31G(d). For convenience of notation, we represent this as MP4/d. This energy is then modified by a series of corrections from additional calculations ... 

There is also a hierarchy of electron correlation procedures. The Hartree-Fock (HF) approximation neglects correlation of electrons with antiparallel spins. Increasing levels of accuracy of electron correlation treatment are achieved by Mpller-Plesset perturbation theory truncated at the second (MP2), third (MP3), or fourth (MP4) order. Further inclusion of electron correlation is achieved by methods such as quadratic configuration interaction with single, double, and (perturbatively calculated) triple excitations [QCISD(T)], and by the analogous coupled cluster theory [CCSD(T)] [8],... 

Very accurate values of the dipole and quadrupole polarizability for the equilibrium internuclear distance of HF can be found in a review article by Maroulis [71], calculated with finite-field Mpller-Plesset perturbation theory at various orders and coupled cluster theory using a carefully selected basis set. 

Subsequently, we performed more sophisticated calculations with a larger basis set and with inclusion of electron correlation at the level of Mpller-Plesset theory. From Figure 7 it is seen that the agreement between experiment and theory is even better than previously. Similar agreement was found for [1,2,3,4- H4]-1. ... 

The calculations are not all at exactly the same bond length R. The basis set is indicated after the slash in the method. R, L, C, and T are basis sets of Slater-type functions. The aug-cc-pVDZ and aug-cc-pVTZ basis sets [360] are composed of Gaussian functions. SCF stands for self-consistent-field MC, for multiconfiguration FO, for first-order Cl, for configuration interaction MR, for multireference MPn, for nth-order Mpller-Plesset perturbation theory and SDQ, for singles, doubles, and quadruples. 

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