Fourth-order Mpller-Plesset

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 ... 

In this subsection, we give the closed-shell Mpller-Plesset energy corrections to fourth order. As noted in Section 14.2.4, the sum of the zero- and first-order Mpller-Plesset energies is equal to the Hartree-Fock energy. We therefore proceed directly to the higher-order corrections, treating in turn the closed-shell MP2, MP3 and MP4 energies. 

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... 

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],... 

To test the MR-CI/BK method used in the present study, the isotropic hfcc s were also calculated with various other methods, e.g. the UHF method, Mpller-Plesset perturbation theory up to the fourth order (MP2 - MP4), Cou-... 

The dimers of Be, Mg and Ca are very weakly bound by the electron correlation effects, at the self-consistent field (SCF) level they are not stable. The binding energy of alkaline earth dimers is only 2-4 times larger than that in Kr2 and Xe2 dimers. Thus, alkaline dimers can be attributed to the van der Waals molecules. The situation is changed in many-atom clusters, even in trimers (Table II). This is evidently a manifestation of the many-body effects. The crucial role of the 3-body forces in the stabilization of the Be clusters was revealed at the SCF level previously [3-5], and more recently was established at the Mpller-Plesset perturbation theory level up to the fourth order (MP4) [6,7]. The study of binding in the Ben clusters [8-10] reveals that the 3-body exchange forces are attractive and give an important contribution to... 

The RB potential is based on 1332 points at the Mpller-Plesset fourth-order (MP4) level with 6-31 lG(d,p) basis set. The fit involves 174 parameters. One deficiency of this surface is that none of the 1332 distances has both monomers simultaneously displaced from equilibrium. 

AMBER = assisted model building with energy refinement force field CHARMM = chemistry at Harvard macromolecu-lar mechanics force field MP4SDQ = Mpller-Plesset fourth-order perturbation theory with corrections for single, double, and quadruple excitations OPLS = optimized potentials for liquid simulation force field TZP = triple-zeta -f polarization. 

For closed-shell Mpller-Plesset perturbation theory, we shall use the exponential CCPT para-metrization of Section 14.3. To calculate the energy to fourth order, we must determine the singlet wave function to second order, constructing the cluster operator T from singles, doubles and triples operators of singlet spin symmetry. We shall employ operators of the form... 

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