Many-body effects

Elrod M J and Saykally R J 1994 Many-body effects in intermolecular forces Chem. Rev. 94 1975... 

The SPC/E model approximates many-body effects m liquid water and corresponds to a molecular dipole moment of 2.35 Debye (D) compared to the actual dipole moment of 1.85 D for an isolated water molecule. The model reproduces the diflfiision coefficient and themiodynamics properties at ambient temperatures to within a few per cent, and the critical parameters (see below) are predicted to within 15%. The same model potential has been extended to include the interactions between ions and water by fitting the parameters to the hydration energies of small ion-water clusters. The parameters for the ion-water and water-water interactions in the SPC/E model are given in table A2.3.2. 

Yourshaw I, Zhao Y and Neumark D M 1996 Many-body effects in weakly bound anion and neutral clusters zero... 

Shirley E L 1998 Many-body effects on bandwidths in ionic, noble gas, and molecular solids Phys. Rev. B 58 9579-83... 

The polarisation interaction between a dipole and a polarisable molecule can be affected by the presence of a ond dipole (right) and is therefore a many-body effect. 

The computation of quantum many-body effects requires additional effort compared to classical cases. This holds in particular if strong collective phenomena such as phase transitions are considered. The path integral approach to critical phenomena allows the computation of collective phenomena at constant temperature — a condition which is preferred experimentally. Due to the link of path integrals to the partition function in statistical physics, methods from the latter — such as Monte Carlo simulation techniques — can be used for efficient computation of quantum effects. 

The ionization process can be described as a one-particle event, when only one term dominates in summation (3), yielding a pole strength close unity. In this case, 1 - Fu gives an estimate of the fraction of photoemission intensity dispersed in many-body effects. On the contrary, small pole strengths are indicative (18-20) of a breakdown of the one-particle picture of ionization. 

Rodrigues, G.C., Ourdane, M.A., Bieron, J., Indelicato, P. and Lindroth, E. (2001) Relativistic and many-body effects on total binding energies of cesium ions. Physical Review A, 63, 012510-1-012510-10. 

The electrostatic energy is calculated using the distributed multipolar expansion introduced by Stone [39,40], with the expansion carried out through octopoles. The expansion centers are taken to be the atom centers and the bond midpoints. So, for water, there are five expansion points (three at the atom centers and two at the O-H bond midpoints), while in benzene there are 24 expansion points. The induction or polarization term is represented by the interaction of the induced dipole on one fragment with the static multipolar field on another fragment, expressed in terms of the distributed localized molecular orbital (LMO) dipole polarizabilities. That is, the number of polarizability points is equal to the number of bonds and lone pairs in the molecule. One can opt to include inner shells as well, but this is usually not useful. The induced dipoles are iterated to self-consistency, so some many body effects are included. 

The Si(k) term takes into account amplitude reduction due to many-body effects and includes losses in the photoelectron energy due to electron shake-up (excitation of other electrons in the absorber) or shake-off (ionization of low-binding-energy electrons in the absorber) processes. 

The question of the importance of nonadditive corrections has been largely discussed and a growing body of results shows that many body effects can affect properties (specially for solutions of multivalent ions) in non-negligible ways [93- 104]. 

Many-body effects, 34 214-215 on deep core-level spectra of metals, 34 215 Many-body Hartree-Fock approach, 34 244 Mars-van Krevelen mechanism, 41 211 reaction, 32 120-121 Mass spectrometry, 30 302-304 of C-labeled hydrocarbons, 23 22-25 in detection of surface-generated gas-phase radicals, 35 142-148 apparatus, 35 145... 

Norbomane, hydrogenolysis, 30 64-65 Norbomene, metathesis of, 24 136 Norcamphene, isomerization of, 20 271 Nozieres-De Dominicis many-body effect, 34 247... 

To complete the specification of Jf, it is necessary to introduce time-dependent terms. These are of two types. The first allows for many-body effects which, to a first approximation, correspond to an interaction of the atom with its image in the solid. As a result, the ionization level and the Coulomb repulsion integral for 0> become functions, o(z) and U(z), of the perpendicular distance z of the atom from the surface. The classical electrostatic forms for these functions are... 

Criterion 1 seems to exclude the DET-based methods, because systematic improvements are elusive, and we cannot state, in any precise manner, which many-body effects have been included. Criterion 2 suggests only limited use of... 

Constraint release (CR). This takes place if a confining chain moves out of the way of a given chain and thus opens some freedom for lateral motion. This phenomenon is an intrinsic many-body effect and for monodisperse polymer melts becomes significant mainly in the creep regime. 

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). 

Fock-Breit model, Ej fb and define all other energy corrections to this order of relativistic quantum electrodynamics, as a many-body effects, so that... 

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