Second-order many-body perturbation

Table 8 Second-order many-body perturbation theory corrections to beryllium-like ions using non-relativistic (E ), Dirac-Coulomb (E ) and Dirac-Coulomb-Breit (E ) hamiltonians, obtained using the atomic precursor to BERTHA, known as SWIRLES. Basis sets are even-tempered S-spinors of dimension N= 17, with exponent sets, Xi generated by Xi = abi-i, with a = 0.413, and p = 1.376. Angular momenta in the range 0 < / < 6 have been included in the partial wave expansion of each second-order energy, and the total relativistic correction toE has been collected as Ef. All energies in hartree.

For Three Molecules in Valence Double-Zeta Basis Sets, a Comparison of Energies in Hartrees (H) from the 2-RDM Method with the T2 Condition (DQGT2) with the Energies from Second-Order Many-Body Perturbation Theory (MP2), Coupled-Cluster Method with Single-Double Excitations and a Perturbative Triples Correction (CCSD(T)), and Full Configuration Interaction (FCI)... 

The Hartree-Fock ground state of the F anion is described by orbitals of s Emd of p symmetry. In the first part of this study, attention was restricted to the convergence of the second order many-body perturbation theory component of the correlation energy for stematically constructed even-tempered basis sets of primitive Gaussian-typ>e functions of s and p symmetry. 

Ab initio quantum-chemical calculations are reported at the level of second-order many-body perturbation theory aimed at the equilibrium between the all -trans (ttt) and the trans-gauche-trans (tgtl conformations of dlmethoxyethane. It is concluded that the gauche effect in dimethoxyethane and by analogy POE is mainly due to the presence of a polarizable environment and not to some intrinsic conformational preference. 

Computational Details. Restricted Hartree-Fock (RHF) calculations were carried out using Gaussian 94 (45) and ACES II (46) on an IBM RISC/6000 computer. The gauge independent atomic orbitals (GIAO) method was used for the shielding calculations (47). All second-order many-body perturbation theory (MBPT2, also referred to as MP2) calculations were performed with ACES II (46). 

The partitioned equation-of-motion second-order many-body perturbation theory [P-EOM-MBPT(2)] [67] is an approximation to equation-of-motion coupled-cluster singles and doubles (EOM-CCSD) [17], which will be fully described in Section 2.4. The EOM-CCSD method diagonalizes the coupled-cluster effective Hamiltonian H = [HeTl+T2) in the singles and doubles space, i.e.,... 

Gauss, J., Calculation of NMR chemical shifts at second-order many-body perturbation theory using gauge-including atomic orbitals, Chem. Phys. Lett. 191, 614-620 (1992). 

MBPT(2) stands for second-order many-body perturbation theory, which is also known by the Hamiltonian partitioning scheme it employs, Moeller-Plesset (see references 68 and 69). 

In section 4, we turn our attention to the many applications of second order many-body perturbation theory in chemical modelling. We provide a brief S5mopsis of the applications of MP2 theory during the reporting period. 

In previous reports to this series, the increasing use of many-body perturbation theory in molecular electronic structure studies was measured by interrogating the Institute for Scientific Information (ISI) databases. In particular, I determined the number of incidences of the string MP2 in titles and/or ke5rwords and/or abstracts. This acronym is frequently associated with the simplest form of many-body perturbation theory. This assessment of the use of second order many-body perturbation theory will undoubtedly miss many routine applications but should serve to convey both the extent and the breadth of contemporary application areas. 

Synopsis of applications of second order many-body perturbation theory... 

In volume 1 of this series, I compared the use of second-order many-body perturbation theory in its MP2 form with that of density functional theory and coupled cluster theory. I recorded how the number of hits in a literature search on the string MP2 rises from 3 in 1989 to 854 in 1998. The corresponding results for DFT, the most widely used semi-empirical method, are 7 in 1989 growing to 733 by 1998. By 1998, the number of hits recorded for CCSD stood as 244. 

Some progress has been made during the reporting period towards incorporating a description of correlation elfects in periodic solids using second order many-body perturbation theory. The aim research in this area is to provide a powerful and general-purpose computational tool, which can be used to study a variety of applications in condensed matter physics and solid state chemistry. 

The incorporation of correlation effects in calculations for periodic solids requires the use of a many-body formalism. Second order many-body perturbation theory, in its MP2 form, should provide the basis of an efficient computational approach to this problem. In particular, the local MP2 methods originally developed for large molecules can be adapted for the treatment of periodic solids. 

M. Kollwitz, M. Haser, and J. Gauss,/. Chem. Phys., 108, 8295 (1998). Non-Abelian Point Group Symmetry in Direct Second-Order Many-Body Perturbation Theory Calculations of NMR Chemical Shifts. 

Solution of the matrix equations associated with an independent particle model gives rise to a representation of the spectrum which is an essential ingredient of any correlation treatment. Finite order many-order perturbation theory(82) forms the basis of a method for treating correlation effects which remains tractable even when the large basis sets required to achieve high accuracy are employed. Second-order many-body perturbation theory is a particularly simple and effective approach especially when a direct implementation is employed. The total correlation energy is written... 

All in all, inclusion of correlation effects can be quite important if one is interested in accurate description of the bending potentials of H-bonded complexes. Dispersion is not isotropic, and its inclusion may be important. However, perhaps of greater importance, due to its stronger sensitivity to angle, is the correlation correction to electrostatics. Both of these terms are included in second-order many-body perturbation theory. 

Evaluation of Second Derivatives Using Second-Order Many-Body Perturbation Theory and Unrestricted Hartree-Fock Reference Functions. 

The applications of many-body perturbation theory in contemporary research in the molecular sciences are manifold and it is certainly not possible to describe more than a mere fraction of the enormous number of publications which have exploited this approach to the molecular structure problem over recent years. Calculations based on second order many-body perturbation theory or MP2 theory are particularly prevalent offering unique advantages in terms of efficiency and accuracy over many other theoretical and computational approaches. Here, we shall briefly describe the use of graphical user interfaces and then concentrate on two recent applications of the many-body perturbation theory which have established new levels of precision. 

All the above mentioned functionals generally provide atomic or molecular properties with a reasonable precision, so that conventional DF methods are claimed to deliver results comparable to those obtained by second-order many body perturbation approaches (MP2). From a purely formal point of view, the reasons for such good performances are not yet evident. 

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