Many-body perturbation theory dependence

Wormer P E S and Hettema H 1992 Many-body perturbation theory of frequency-dependent... 

There are three main methods for calculating electron correlation Configuration Interaction (Cl), Many Body Perturbation Theory (MBPT) and Coupled Cluster (CC). A word of caution before we describe these methods in more details. The Slater determinants are composed of spin-MOs, but since the Hamilton operator is independent of spin, the spin dependence can be factored out. Furthermore, to facilitate notation, it is often assumed that the HF determinant is of the RHF type. Finally, many of the expressions below involve double summations over identical sets of functions. To ensure only the unique terms are included, one of the summation indices must be restricted. Alternatively, both indices can be allowed to run over all values, and the overcounting corrected by a factor of 1/2. Various combinations of these assumptions result in final expressions which differ by factors of 1 /2, 1/4 etc. from those given here. In the present book the MOs are always spin-MOs, and conversion of a restricted summation to an unrestricted is always noted explicitly. 

Wormer PES, Hettema H (1992) Many-body perturbation theory of frequency-dependent polarizabilities andVan derWaals coefficients Application to H20-H20 and A r Nil,. J Chem Phys 97 5592-5606... 

Wormer P E S and Hettema H 1992 Many-body perturbation theory of frequency-dependent polarizabilities and van der Waals coefficients application to H2O. .. H2O and Ar... NH3 J. Chem. Phys. 97 5592... 

Finite Element Methods Applied to Many-body Perturbation Theory. - Over the past ten years, the finite element method, which is a classical tool in classical science and engineering applications, has been developed into a technique for the accurate solution of the atomic243 and molecular244,245 electronic structure problem. The piece-wise definition of the form functions employed in the finite element method prevents the computational linear dependencies which occur in the finite basis set expansion method and, moreover, leads to sparse, band structured matrices for which efficient solvers are available. 

Consequently, DFT is restricted to ground-state properties. For example, band gaps of semiconductors are notoriously underestimated [142] because they are related to the properties of excited states. Nonetheless, DFT-inspired techniques which also deal with excited states have been developed. These either go by the name of time-dependent density-functional theory (TD-DFT), often for molecular properties [147], or are performed in the context of many-body perturbation theory for solids such as Hedin s GW approximation [148]. 

Bokhan, D., Bartlett, R. J. (2006). Adiabatic ab initio time-dependent density-functional theory employing optimized-efifective-potential many-body perturbation theory potentials. Phys. Rev. A 73,022502. 

We elaborate on recent attempts to derive the local and energy-dependent density-functional potential v from the diagrammatic structure of many-body perturbation theory for the exact exchange-correlation energy, without explicit recourse to an extremal principle. The local v can be related to the nonlocal and dynamic self-energy E obtained from perturbation theory. 

Within Green function theory, many-electron effects can be introduced through a non-local and energy-dependent self-energy operator [15]. Since the self-energy is hard to calculate, various approximations are introduced and among the simplest ones is the so-called GW approximation, which is derived from many-body perturbation theory. Although the GW approximation offers in principle a sophisticated account of the electron correlation effects, practical realizations are commonly also based on the LDA method. 

BH5, the intermolecular complex between BH3 and Hg, has been studied theoretically using many-body perturbation theory (MBPT) and the coupled-cluster approximation. The species is found to be unexpectedly stable, ca. 6 kcal/mol more stable than the isolated monomers, but the results of the calculations are greatly dependent on the basis set used. Four isomers were studied and the only stable one is the Cs structure (a) shown in Fig. 2-35, which has the Hg subunit eclipsing one of the B-H bonds. The other structures in Fig. 2-35 are a second Cs structure (b), a Cgv structure (c), and a structure (d) [5]. 

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