Three body energies

For 1, the parameters found at the first step are used as the initial set. In the fit of V3 + Vi, for the better reproduction of the three-body energy it was found more effective to add to the E onadd AgN), the EsiAga) for triangles not presented in the Agjv geometry. 

As for the ehface2 model, the three-body energy is partitioned into EHF and corr contributions. Of these, the three-body EHF is conveniently represented by the form... 

The lower part of Table 33.2 shows the SAPT correlation contributions to the three-body energy of the water trimer. These contributions include the electron correlation effects at the level approximately comparable to the supermolecular many-body... 

The results of Table 33.2 suggest that, as expected, the bulk of nonadditive interactions in the water trimer is reproduced quite well already at the SCF level of theory. This observation is further quantified in Fig. 33.2, where the three-body energies computed at the SCF and CCSD(T) levels are compared for ten trimers with maximum 0-0 separations less than 5 A extracted from a snapshot of a Monte Carlo (MC) simulation of liquid water at ambient conditions. Typically, trimers for which the nonadditive... 

Attempts to represent the three-body interactions for water in terms of an analytic function fitted to ab initio results date back to the work of dementi and Corongiu [191] and Niesar et al. [67]. These authors used about 200 three-body energies computed at the Hartree-Fock level and fitted them to parametrize a simple polarization model in which induced dipoles were generated on each molecule by the electrostatic field of other molecules. Thus, the induction effects were distorted in order to describe the exchange effects. The three-body potentials obtained in this way and their many-body polarization extensions have been used in simulations of liquid water. We know now that the two-body potentials used in that work were insufficiently accurate for a meaningful evaluation of the role of three-body effects. 

Conventional three-body energy computations require the integrals for a set of nonnegative integer val-... 

Chua M, Tanner PA (1996) Three-body energy transfer processes of lanthanide ions. J Lumin 66 67 203-207... 

It would be nice to have a simple formula which could replace the tedious calculations involving the above equations. The three-body energy may be approximated by the product of the exponential term bexp(-aRAB) and the electric field produced by C, calculated, e.g., in the middle of the distance Rab between molecules A and B. The goal of the exponential terms is to grasp the idea that the overlap integrals (and their squares) vanish exponentially with distance. The exponent a should depend on molecules A and B as well as on their mutual orientation and reflects the hardness of both molecules. These kind of model formulae have low scientific value but are of practical use. 

Figures 8 and 9 show relaxed triangular plots in mass-unweighted hyperspherical coordinates (all masses are taken equal to unity) for the two lowest A adiabatic sheets of NO2 according to a modified version of the 8x8 DMBE potential energy surface reported in Ref. 124. As in previous work, the parameterization has been done by dressing the nd diatomic curves, using simple three-body energy terms whose parameters have been adjusted by a trial-and-error procedure. The notable features in Figure 8 are the deep minimum of the 1 adiabatic sheet which is...

Figure 17.5 H-H contracted basis from a fit to three-body energies of equilateral H3.

XXZLG interpolant. To avoid contamination of the three-body energies with two-body ones, the two-body EHFACE2U potential curves from DM BE IV have been utilized for the first fit. In fact, the EHFACE2U model has also been adopted for the second fit, but calibrated from the corresponding two-body energies. 

Figure 17.14 A view of the three-body energy for an O atom moving around an equilibrimn OH. Solid (dashed) contours start at 0 (—0.5) mE], at intervals of 10 (0.125) mEi, (distances in bohr). See text.

Recently, both the MK and RVS analyses have been extended to many-body complex systems. This allows the computation of many-body effects on each energy component within the MK of RVS analyses, since rigorously only es is pair-wise additive. In the case of water trimers and tetramers it was found that polarization and charge transfer are the dominant components in the three-body energy terms. The four body term in the water tetramer was found to be negligible. 

The 3-body energy varies from 11.69 to -3.00 kcal mol". This result contrasts with (H20)e for which the three-body energies are negative for the four isomers considered. The positive 3-body terms for some of the isomers of H (H20)5 are a consequence of the impact of the proton on the arrangement of the water molecules in the network. 

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