Two-body term

The analytic PES function is usually a summation of two- and three-body terms. Spline functions have also been used. Three-body terms are often polynomials. Some of the two-body terms used are Morse functions, Rydberg... 

At present, our modelling approach uses a Lennard-Jones potential for the two-body term... 

Extension to a molecule with more than four atoms or to a solid is straightforward. Usually the two-body terms are much larger than the three-body terms, which in turn are greater than the four-body. For ionic solids, for example, the three-body and four-body terms are often neglected. In contrast, for metals and semiconductors including only two-body terms leads to very poor results (see Sutton (Further reading)). 

Most of statistical-mechanical computer simulations are based upon the assumption of pairwise additivity for the total interaction energy, what means to truncate the right side of equation (48) up to the two-body term. The remaining terms of the series, which are neglected in this approach, are often known as the nonadditive corrections. 

A simpler potential of the form of Eq. (10) has been used by Pearson et al. to model Si and SiC surfaces . The two-body term is of the familiar Lennard-Jones form while the three-body interaction is modeled by an Axilrod-Teller potential . The physical significance of this potential form is restricted to weakly bound systems, although it apparently can be extended to model covalent interactions. 

One formalism which has been extensively used with classical trajectory methods to study gas-phase reactions has been the London-Eyring-Polanyi-Sato (LEPS) method . This is a semiempirical technique for generating potential energy surfaces which incorporates two-body interactions into a valence bond scheme. The combination of interactions for diatomic molecules in this formalism results in a many-body potential which displays correct asymptotic behavior, and which contains barriers for reaction. For the case of a diatomic molecule reacting with a surface, the surface is treated as one body of a three-body reaction, and so the two-body terms are composed of two atom-surface interactions and a gas-phase atom-atom potential. The LEPS formalism then introduces adjustable potential energy barriers into molecule-surface reactions. 

In efforts to improve upon the LEPS scheme outline above, other prescriptions for the single atom-surface interaction have been formulated. The initial studies using the LEPS approach modeled the atom-surface interaction as a two-body term where the parameters used in the function are... 

The first of these two terms cannot be considered a pure two-body term, therefore the A can only be considered as a connected diagram within the context of an antisymmetrized diagrammatical approach. 

Defining the several parts of the correlation energy, some significant terms are collected for the He tetramer studied in Table 9. The results unambiguously show that not only the values follow the differences in their geometrical position, but a transfer-ability property also holds for both the one- and two-body terms, respectively, as well at each level of correlation. 

Table 9 Correlation energy decomposition for the one- and two-body terms in a linear tetramer He-cluster. Values are given in mHartree...

Using SMOs, this expression can be separated into one- and two-body terms... 

The SMO-LMBPT method conveniently uses the transferability of the intracorrelated (one-body) parts of the monomers. This holds, according to our previous results [3-10], at the second (MP2), third (MP3) and fourth (MP4) level of correlation, respectively. The two-body terms (both dispersion and charge-transfer components) have also been already discussed for several systems [3-5]. A transferable property of the two-body interaction energy is valid in the studied He- and Ne-clusters, too [6]. In this work we focus also on the three-body effects which can be calculated in a rather straightforward way using the SMO-LMBPT formalism. 

Neither the DC nor the DCB Hamiltonians are appropriate starting points for accurate many-body calculations. The reason is the admixture of the negative-energy eigenstates of the Dirac Hamiltonian by the two-body terms in an erroneous way [4, 5]. The no-virtual-pair approximation [6, 7] is invoked to correct this problem the negative-energy states are eliminated by the projection operator A" ", leading to the projected Hamiltonians... 

The electron density is expanded in a similar way (with the inclusion of the m = 0 term). We use 7 Fourier coefficients in the expansion of electron density, 6 Fourier coefficients in the expansions of and V (only the first four coefficients turned out to be significantly different from zero), and 8 coefficients (for each of the spin-parallel and spin-antiparallel cases) in the two-body term. 

The molecular dynamics simulation was performed using the MOTECC suite of programs [54] in the context of a microcanonical statistical ensemble. The system considered is a cube, with periodic boundary conditions, which contains 343 water molecules. The molecular dynamic simulation of water performed at ambient conditions revealed good agreement with experimental measurements. The main contribution to the total potential energy comes from the two-body term, while the many-body polarisation term contribution amounts to 23% of the total potential energy. Some of the properties calculated during the simulation are reported in Table 3. 

Since the polarization wave functions pO°10) defining are purely additive, i.e. hpo°i0) = 3> °i0)(2, 3), the two-body term as defined by Eq. (1-209) is equal to as defined by the SRS theory of two-body interactions89. Thus, to extract pure three-body contribution to E one has to subtract the E f term of the two-body SRS theory89. 

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