Mpller

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. 

Note on an Approximate Treatment for Many-Electron Systems Chr. Mpller and M. S. Plesset Physical Review 46 (1934) 618... 

Some methods of describing electron correlation are compared from the point of view of requirements for theoretical chemical models. The perturbation approach originally introduced by Mpller and Plesset, terminated at finite order, is found to satisfy most of these requirements. It is size consistent, that is applicable to an ensemble of isolated systems in an additive manner. On the other hand, it does not provide an upper bound for the electronic energy. ... 

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... 

Oedegaard A, Hebling C, Schmitz A, Mpller-Holst S, Tunold R. 2004. Influence of diffusion layer properties on low temperature DMFC. J Power Sources 127 187-196. 

Bojsen-Mpller F. (1975). Demonstration of terminalis, olfactory, trigeminal and perivascular nerves in the rat nasal septum. J Comp Neurol 159, 245-256. 

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. 

Costantini, D. and Mpller, A. P. 2008. Carotenoids are minor antioxidants for birds. Fund. Ecol. 22 367-370. 

H5rak, P., Ots, I., Vellau, H., Spottiswoode, C., and Mpller, A. P. 2001. Carotenoid-based plumage coloration reflects hemoparasite infection and local survival in breeding great tits. Oecologia 126 166-173. 

H5rak, P., Surai, P. F., and Mpller, A. P. 2002. Fat-soluble antioxidants in the eggs of great tits Parus major in relation to breeding habitat and laying sequence. Avian Sci. 2 123-130. 

Mpller, A. P., Biard, C., Blount, J. D., Houston, D. C., Ninni, P., Saino, N., and Surai, P. F. 2000. Carotenoid-dependent signals Indicators of foraging efficiency, immunocompetence, or detoxification ability Avian Poult. Biol. Rev. 11 137-159. 

Saino, N., Ferrari, R., Romano, M., Martinelli, R., and Mpller, A. P. 2003. Experimental manipulation of egg carotenoids affects immunity of barn swallow nestlings. Proc. R. Soc. Lond. B 270 2485-2489. 

Maury, J., Asadollahi, M.A., Mpller, K. et al. (2005) Microbial isoprenoid production an example of green chemistry through metabolic engineering. Advances in Biochemical Engineering/Biotechnology, 100, 19-51. 

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. 

Mpller, C., and M. S. Plesset. 1934. Note on an Approximation Treatment for Many-Electron Systems. Phys. Rev. 46, 618. 

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