Many-body perturbation theory response

Trucks GW, Salter EA, Noga J, Bartlett RJ (1988) Analytic many body perturbation theory MBPT(4) response properties. Chem Phys Lett 150 37 14... 

Linear-response coupled-cluster Many-body perturbation theory of order n Molecular orbital... 

The quantity x is the linear density-density response function of the system. In other branches of physics it has other names, e.g., in the context of many-body perturbation theory it is called the reducible polarization function. Unfortunately, the evaluation of x through perturbation theory is a very demanding task. We can, however, make use of TDDFT to simplify this process. 

In the earlier sections of this chapter we reviewed the many-electron formulation of the symmetry-adapted perturbation theory of two-body interactions. As we saw, all physically important contributions to the potential could be identified and computed separately. We follow the same program for the three-body forces and discuss a triple perturbation theory for interactions in trimers. We show how the pure three-body effects can be separated out and give working equations for the components in terms of molecular integrals and linear and quadratic response functions. These formulas have a clear, partly classical, partly quantum mechanical interpretation. The exchange terms are also classified for the explicit orbital formulas we refer to Ref. (302). 

The interaction energies of clusters of molecules can be decomposed into pair contributions and pairwise-nonadditive contributions. The emphasis of this chapter is on the latter components. Both the historical and current investigations are reviewed. The physical mechanisms responsible for the existence of the many-body forces are described using symmetry-adapted perturbation theory of intermolecular interactions. The role of nonadditive effects in several specific trimers, including some open-shell trimers, is discussed. These effects are also discussed for the condensed phases of argon and water. 

On the other hand, the orbital-dependent treatment of correlation represents a much more serious challenge than that of exchange The systematic derivation of such functionals via standard many-body theory leads to rather complicated expressions. Their rigorous application within the OPM not only requires the evaluation of Coulomb matrix elements between the complete set of KS states, but, in principle, also relies on the knowledge of higher order response functions. In practical calculations, these first-principles functionals necessarily turn out to be rather inefficient, even if they are only treated perturbatively. In addition, the potential resulting from a large class of such functionals is non-physical for finite systems. Both problems are related to the presence of unoccupied states in the functionals which seems inevitable as soon as some variant of standard many-body theory is used for the derivation. 

Based on the Runge-Gross theorem, it is shown that the three-dimensional density of a many body quantum system is sulScient to describe the TD response of the system to an external perturbation, such as electromagnetic field and vibrational motion, R t). This is known as time dependent density functional theory (TDDFT). In the linear response approximation, TDDFT is frequently used to evaluate electronic excitation energies. Here, we use full TDDFT where the density is explicitly propagated in time. Application of the TD (Dirac) vibrational principle to KS energy generates density evolution ... 

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