Mpller-Plesset

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. 

Until the advent of density functional theory (Chapter 13), thinking centred around means of circumventing the two-electron integral transformation, or at least partially circumventing it. The Mpller-Plesset method is one of immense historical importance, and you might like to read the original paper. 

Equilibrium geometries, dissociation energies, and energy separations between electronic states of different spin multiplicities are described substantially better by Mpller-Plesset theory to second or third order than by Hartree-Fock theory. 

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... 

The matrix elements between the HF and a doubly excited state are given by two-electron integrals over MOs (eq. (4.7)). The difference in total energy between two Slater determinants becomes a difference in MO energies (essentially Koopmans theorem), and the explicit formula for the second-order Mpller-Plesset correction is... 

Coupled cluster is closely connected with Mpller-Plesset perturbation theory, as mentioned at the start of this section. The infinite Taylor expansion of the exponential operator (eq. (4.46)) ensures that the contributions from a given excitation level are included to infinite order. Perturbation theory indicates that doubles are the most important, they are the only contributors to MP2 and MP3. At fourth order, there are contributions from singles, doubles, triples and quadruples. The MP4 quadruples... 

Curtiss, L. A. Raghavachari, K. Pople, J. A. Gaussian-2 theory use of higher level correlation methods, quadratic configuration interaction geometries, and second-order Mpller Plesset zero-point energies. J. Chem. Phys. 1995, 103, 4192-4120. 

Niu, S., Hall, M. B., 1997, Comparison of Hartree-Fock, Density Functional, Mpller-Plesset Perturbation, Coupled Cluster, and Configuration Interaction Methods for the Migratory Insertion of Nitric Oxide into a Cobalt-Carbon Bond , J. Phys. Chem. A, 101, 1360. 

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. 

Pople, J. A., R. Krishnan, H. B. Schlegel, and J. S. Binkley. 1979. Derivative Studies in Hartree-Fock and Mpller-Plesset Theories. Int. J. Quantum Chem. Quantum Chem. Symp. 13, 225-241. 

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 ... 

As usual, the Hartree-Fock model can be corrected with perturbation theory (e.g., the Mpller-Plesset [MP] method29) and/or variational techniques (e.g., the configuration-interaction [Cl] method30) to account for electron-correlation effects. The electron density p(r) = N f P 2 d3 2... d3r can generally be expressed as... 

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. 

H. J. Werner, F. R. Manby, and P. J. Knowles, Fast linear scaling second order Mpller Plesset perturbation theory (MP2) using local and density fitting approximations. J. Chem. Phys. 118, 8149 8160 (2003). 

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