M0ller-Plesset perturbation theory energy

Dahlke, E. E., and Truhlar, D. G. (2007). Electrostatically embedded many-body correlation energy, with applications to the calculation of accurate second-order M0ller-Plesset perturbation theory energies for large water clusters,/. Chem. Theory Comput. 3(4), 1342-1348. 

In the BAC-MP4 method, an additional error in determining heats of formation occurs for open-shell molecules. This error arises from the use of the unrestricted Hartree-Fock (UHF) wavefunction in calculating the M0ller-Plesset perturbation theory energy. We include a BAC spin correction energy term, Ebac (Spin), given by... 

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. 

The //v7/ -t -isomerization of 3-chlorothietane-l-oxide 2a has been studied using ab initio methods <2001JMT235>, where for the prediction of this system s thermodynamics, the M0ller-Plesset perturbation theory has been used. The calculation predicted that in the gas phase the cA-isomer was predominantly present, reaching 85%, and that in solution of polar and nonpolar solvents the concentration of the zA-isomer decreased to 25%. Similar results have been found for 3-methylthietane-l-oxide 2b. For both compounds, transition states have been found to have a quasi-planar structure. Activation energies for compounds 2a and 2b have been computed and they were 49 and 45kcalmol 1 in the gas phase as well as 37 and 33 kcal mol 1 in solution, respectively. For... 

The second order energy in M0ller-Plesset perturbation theory (MP2) can be written... 

The valence shell photoelectron spectra of thiophene, 2-Cl-Th, and 3-Cl-Th have been investigated theoretically and experimentally to evaluate the vertical ionization energies. The ground-state geometrical parameters of the three molecules have been optimized at the level of the second-order M0ller-Plesset perturbation theory, and standard... 

M0ller-Plesset perturbation theory at second order (MP2) (61) is the easiest and most popular way of including correlation energy after a Hartree-Fock calcula-... 

In variational methods, the interaction energy is not calculated directly even if the M0ller-Plesset perturbation theory is used. We have to calculate the interaction energy at all calculation levels as a difference... 

Table 2 Contributions Made by Each Order of M0ller-Plesset Perturbation Theory to the Interaction Energy of Water (kcal/mol) ...

An extensive evaluation has been done by Curtiss et al., who tested a number of density functionals on the G3/05 test set. This set includes 454 energies, all of which have experimental uncertainties less than 1 kcalmoH The computed results are based on single-point B3LYP/6-311- -G(3df,2p) energies at second-order M0ller-Plesset perturbation theory (MP2)/6-31G(d) geometries with scaled (0.89) Hartree-Fock (HF)/... 

The asymptotic behavior of the second-order energy of the M0ller-Plesset perturbation theory, especially adapted to take advantage of the closed-shell atomic structure (MP2/CA), is studied. Special attention is paid to problems related to the derivation of formulae for the asymptotic expansion coefficients (AECs) for two-particle partial-wave expansions in powers... 

In the simplest correlated WFT, which is second-order M0ller-Plesset perturbation theory (MP2) [53, 54], the pair energies e are given by a sum over all virtual orbital pairs at... 

Figure 1. Hierarchial diagram of the BAC-MP4 method for determining thermochemical properties of molecules. First, a Hartree-Fock calculation provides the molecular geometries and frequencies. Fourth-order M0ller-Plesset perturbation theory (MP4) provides the ab initio electronic energy to which bond-additivity corrections (BAC) are then added to obtain chemical bond energies. Finally, statistical mechanics calculations are used to determine the enthalpy, entropy, and free energy of the molecule.

Relativistic Muttireference M0ller-Plesset Perturbation Theory 17 1.4 Relativistic MR-MP calculations on aluminumlike ions 1.4.1 Energy levels... 

The initial interest in the HN2 species at NASA centered around its possible role as an intermediate in the three-body recombination of H atoms in the presence of N2. This and other three-body recombination reactions are critical to the design of the SCRAM jet engine since they are important heat producing reactions. The HN2 species is also believed to be important in thermal de-NOj. processes. A key concern here is the lifetime of the HN2 species. One previous calculation of the lifetime of HN2 [6] was based on a potential energy surface derived with M0ller-Plesset perturbation theory which is shown to break down severely for HN2 [5j. 

The M0ller-Plesset perturbation theory [26] corresponds to the application of the stationary perturbation theory to the calculation of the correlation energy using the Hartree-Fock Slater determinant as the zeroth order wavefunction. These methods are denoted MPn where n is the order of the perturbative corrections included. In the M0ller-Plesset method, the unperturbed Hamiltonian operator is chosen as a sum of Fock operators... 

Grimme, S. (2003). Improved second-order M0ller-Plesset perturbation theory by separate scaling of parallel- and antiparallel-spin pair correlation energies. Journal of Chemical Physics, 118, 9095. 

Well-defined variational (Cl-type see Configuration Interaction), perturbational (MPn see M0ller-Plesset Perturbation Theory), and coupled cluster (CC see Coupled-cluster Theory) techniques have all been employed to determine anharmonic force fields. Important conclusions of these studies include (1) Near equilibrium, the correlation energy is a low-order function of the bond distances,even a linear approximation is meaningful(2) For open-shell species, spin contamination can significantly deteriorate results if a... 

Table 2 Results of Correlation Energy Calculations for the Infinite Metallic Hydrogen Chain Using Second-order M0ller-Plesset Perturbation Theory and RHF Reference Functions ...

Results obtained using a 4-31G atomic basis set and second-order M0ller-Plesset/2 perturbation theory energies are in eV. 

Gauss, J. and Cremer, D. (1992). Analytical energy gradients in M0ller-Plesset perturbation and quadratic configuration interaction methods theory and application. Adv. Quantum Chem., 23, 205-299. 

Mpller-Plesset perturbation theory represents a useful approach to the calculation of size-extensive correlation energies for systems dominated by a single electronic configuration. The MP2 model, in particular, represents a successful compromise between computational cost and accuracy. Higher-order corrections may also be calculated, but it should be emphasized that the M0ller-Plesset series does not converge unconditionally. 

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