Electron correlation, many-body theories

The numerical determination of E grr by the use of many-body theory is a formidable task, and estimates of it based on E j and E p serve as important benchmarks for the development of methods for calculating electron correlation effects. The purpose of this work is to obtain improved estimates of Epp by combining the leading-order relativistic and many-body effects which have been omitted in Eq. (1) with experimentally determined values of the total electronic energy, and precise values of Epjp. We then obtain empirical estimates of E grr for the diatomic species N2, CO, BF, and NO using Epip and E p and the definition of E g in Eq. (1). 

To account for the interchannel coupling, or, which is the same, electron correlation in calculations of photoionization parameters, various many-body theories exist. In this paper, following Refs. [20,29,30,33], the focus is on results obtained in the framework of both the nonrelativistic random phase approximation with exchange (RPAE) [55] and its relativistic analogy the relativistic random phase approximation (RRPA) [56]. RPAE makes use of a nonrelativistic HF approximation as the zero-order approximation. RRPA is based upon the relativistic Dirac HF approximation as the zero-order basis, so that relativistic effects are included not as perturbations but explicitly. Both RPAE and RRPA implicitly sum up certain electron-electron perturbations, including the interelectron interaction between electrons from... 

Accurate calculations of relativistic effects in atoms have been done using many-body theory which includes electron-electron correlations. We used a correlation-... 

A general approach to the intramonomer correlation problem is known as the many-electron (or many-body) SAPT method88,141 213-215. In this method the zeroth-order Hamiltonian H0 is decomposed as H0 = F + W, where F = FA + FB is the sum of the Fock operators, FA and FB, of monomer A and B, respectively, and W is the intramonomer correlation operator. The correlation operator can be written as W = WA + WB, where Wx = Hx — Fx, X = A or B. The total Hamiltonian can be now be represented as H = F + V + W. This partitioning of H defines a double perturbation expansion of the wave function and interaction energy. In the SRS theory the wave function is obtained by expanding the parametrized Schrodinger equation as a power series in and A,... 

A system of fundamental theoretical importance in many-body theory is the uniform-density electron gas. After decades of effort, exchange-correlation effects in this special though certainly not trivial system are by now well understood. In particular, sophisticated Monte Carlo simulations have provided very useful information (5) and have been conveniently parametrized by several authors (6). If the exchange-correlation hole function at a given reference point r in an atomic or molecular system is approximated by the hole function of a uniform electron gas with spin-densities given by the local values of p (r) and Pp(C obtain an... 

DFT is the ground-state limit of a more general OFT. The OEL equations of OFT do not necessarily contain local potential functions. Tests of locality fail for the effective exchange potential in the UHF exchange-only model. Dirac s derivation of TDHF theory can readily be extended to a TDOFT that includes electronic correlation. The exchange-only limit of this theory is consistent with TDHF and with the RPA in many-body theory. 

The tendency to retain one-particle features m tne intnnsicaly many-body approach lead to famous Kohn and Sham one-particle equations [2] which pushed the Density Functional Theory towards a form conforming to the spirit of traditional quantum chemistry. By no means, however, became the DFT just a new language and a new formulation of the old concepts in electronic structure description. It is by definition the many-body theory based on many-body property of the system, the electron density in the physical, 3-dimensional space. The immediate consequence is the explicit inclusion of electron correlation into the theory. The entire many-body problem, however, has been transformed to the exchange-correlation functional which is known only up to quite serious approximations. 

From a very general point of view every ion-atom collision system has to be treated as a correlated many-body time-dependent quantum system. To solve this from an ab initio point of view is still impossible. So, one has to rely on various approximations. Nowadays the best method which can be applied to realistic collision systems (which we discuss here) is on the level of the non-selfconsistent time-dependent Hartree-Fock-Slater or, in the relativistic case, the Dirac-Fock-Slater method. Up-to-now no correlation beyond this approximation can be taken into account in the case of 3 or more electrons. (This is in accordance with the definition of correlation given by Lowdin [1] in 1956) In addition no QED contributions, i.e. no correction to the 1/r Coulomb interaction between the electrons, ever have been taken into account, although in very heavy collision systems this effect may become important. This will be discussed in section 5. A short survey of the theory used is followed by our results on impact parameter dependent electron transfer and excitation calculations of ion-atom and ion-solid collisions as well as first results of an ab initio calculation of MO X-rays in such complicated many particle scattering systems. 

Highly-ionized atoms DHF calculations on isoelectronic sequences of few-electron ions serve as the starting point of fundamental studies of physical phenomena, though many-body corrections are now applied routinely using relativistic many-body theory. Relativistic self-consistent field studies are used as the basis of investigations of systematic trends in ionization energies [137-144], radiative transition probabilities [145-148], and quantum electrodynamic corrections [149-151] in few-electron systems. Increased experimental precision in these areas has driven the development of many-body methods to model the electron correlation effects, and the inclusion of Breit interaction in the evaluation of both one-body and many-body corrections. 

An accurate representation of the electronic structure of atoms and molecules requires the incorporation of the effects of electron correlation, and this process imposes severe computational difficulties. It is, therefore, only natural to investigate the use of new and alternative formulations of the problem. Many-body theory methods offer a wide variety of attractive approaches to the treatment of electron correlation, in part because of their great successes in treating problems in quantum field theory, the statistical mechanics of many-body systems, and the electronic properties of solids. 

The pioneering work of Kelly on atoms provided the first comprehensive utilization of many-body theory methods to describe electron correlation in these systems. These studies investigated the use of diagrammatic many-body perturbation theory, an approach that appeared to be quite different from the more traditional wave function methods. However, if a... 

These many-body theories utilize an altogether different operator basis, the many-body basis. These basis operators account for correlation in an approximate way, since they act on the correlation part of the ground state as well as the SCF term. Hence, the many-body basis operators have interesting physical interpretations as primitive ionization or excitation operators. In addition to the excitation operators, the complete many-body basis set for excitation energies includes primitive de-excitation operators, which have no analogs in traditional configuration interaction theory. The many-body basis for ionization processes includes operators that remove electrons from particle orbitals. These operators are also without simple counterparts in Cl theory. The various terms in the expression for photoionization cross sections have been analyzed in light of the physical content of the many-body basis set. 

Given the remarkable progress in many-body theories, accurate descriptions of electron correlation in molecular systems of variable near-degeneracies are still challenging and remain an active area of research. One framework that has provided not only accurate results but also qualitative insight is effective Hamiltonian (EH), based on which various multi-reference (MR) or quasi-degenerate (QD) perturbation theories (PT) have been proposed [ 1-26] in the past (see Refs. [27] and [28] for careful comparisons). Yet, the premises of MRPTs and QDPTs that electron correlation can be separated into static and dynamic components and then that they can respectively be treated variationally and per-turbatively are not always justified. As a consequence, low-order MRPTs and QDPTs usually depend strongly on the... 

Under certain conditions the Brillouin-Wigner pertiubation theory forms the basis for a many-body theory. Whether it can provide a robust multireference many-body theory of electron correlation effects is the subject of current research. 

With eqn (7) the time-dependent Kohn-Sham scheme is an exact many-body theory. But, as in the time-independent case, the exchange-correlation action functional is not known and has to be approximated. The most common approximation is the adiabatic local density approximation (ALDA). Here, the non-local (in time) exchange-correlation kernel, i.e., the action functional, is approximated by a time-independent kernel that is local in time. Thus, it is assumed that the variation of the total electron density in time is slow, and as a consequence it is possible to use a time-independent exchange-correlation potential from a ground-state calculation. Therefore, the functional is written as the integral over time of the exchange-... 

It is well known that Hartree-Fock (HF) theory not only has been proven to be quite suitable for calculations of ground state (GS) properties of electronic systems, but has also served as a starting point to develop many-parti-cle approaches which deal with electronic correlation, like perturbation theory, configuration interaction methods and so on (see e.g., [1]). Therefore, a large number of sophisticated computational approaches have been developed for the description of the ground states based on the HF approximation. One of the most popular computational tools in quantum chemistry for GS calculations is based on the effectiveness of the HF approximation and the computational advantages of the widely used many-body Mpller-Plesset perturbation theory (MPPT) for correlation effects. We designate this scheme as HF + MPPT, here after denoted HF -f- MP2. ... 

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