An attempt to satisfy both needs relies on effective two-body potentials, such as that developed with the polarizable continuum model (PCM) of the solvent, briefly described above (see equations (43)-(48)). [Pg.410]

PCM it is the only method used so far to get effective two body A-B potentials over the whole range of distances R (three-body corrections have been introduced in Ref. [33]). [Pg.455]

As the empirical or semiempirical potentials, those obtained in the supermolecular approach with the PCM, are effective two-body potentials that implicitly include non-additive effects, modeling the solvent molecules as a continuum. [Pg.388]

The potentials discussed above are pairwise or two-body potentials (i.e., potentials describing dimers). Yet, in many cases such potentials are fitted to thermodynamics data for liquids and solids. In such media the pairwise nonadditive effects are usually quite important. Therefore, potentials of this type are called effective two-body potentials since they approximate the many-body effects by an unphysical distortion of the two-body potential relative to the exact two-body potential. As a consequence, the effective two-body potentials perform poorly in predicting pure dimer properties such as dimer spectra or second virial coefficients. In fact, the effective two-body potentials perform poorly also in predicting trimer properties (although the three-body component dominates the nonadditive effects, cf. section III.C). [Pg.155]

In the dense phase the intermolecular potential consists mainly of a two-body term to which small three-body contributions should be added. This problem is poorly documented for molecular systems, and the classic example remains that of argon where an effective two-body Lennard-Jones potential accounts fairly well for the thermodynamic data simply as a result of cancellation of errors. For vibrational energy relaxation one is not directly concerned with the whole intermolecular potential, but rather by its vibrationally dependent part. As mentioned earlier, three-body effects are not usually observable and may be masked by inadequate knowledge of the true potential. Nevertheless one can expect some simply observable solvent effects describable by changes of either the intermolecular or the vibrational potentials. [Pg.323]

On the other hand, empirical or semi-empirical models will be strictly two-body, if only based on data of second virial coefficient of the real gases and of the isolated molecule, or effective two-body potentials, if they keep a two-body form, but also experimental data relevant to the condensed phase are used to construct them. [Pg.382]

The sophistication of these techniques lies somewhere between the methods of molecular mechanics describing the energy by an effective two-body or n-body potential and the full quantiun chemical approach in which the classical molecular dynamics trajectory of the nuclei is followed with a knowledge of the total electron structure of the system [85-87]. The system is divided into a quantum mechanical part (QM) and a molecular mechanical part (MM), so that the Hamiltonian is written as [Pg.139]

What are the most important weaknesses in the above-described parameterizational approach and the use of Equation (4.1) In our opinion, the main ones are the use of an effective two-body potential and the use of only atom-centered charges. [Pg.176]

In (6), e is the dielectric constant of the atomistic water model and Fsr denotes the short range part of the potential which includes effects of dispersion interactions and ion hydration. It could be shown that the effective two-body potential in equation (6) reproduces the osmotic coefficients of aqueous sodium chloride solutions in satisfactory agreement with experiments up to almost 3 M salt [75]. The idea of [Pg.268]

The partial eharges as well as repulsive interactions can be parameterized from quantum chemical calculations. The parameters of the dispersion forces are not true two-body interaction terms but rather are parameters for an effective two-body potential appropriate for a condensed phase environment they are parameterized by comparison with thermodynamic properties such as pVT data, heats of vaporization, or phase behavior. In general one would also need to consider the polarizability of the atoms to account for time dependent partial charges, but we can neglect these effects for the systems we will discuss in the following. [Pg.409]

There are many empirical and semi-empirical pair potentials which describe quite satisfactorily the properties of liquids and solids, see chapter 5 in book The parameters in these potentials are not real parameters of a true two-body interaction, their values depend upon properties of a medium. So these effective two-body potentials include nonadditive interactions through their parameters. The latter can not be directly related to the definite physical [Pg.139]

The form that (p p, the harmonic force constant, takes depends on the nature of the interaction between atoms k and k in the crystal. Although the interactions are, in fact, quite complex, the assumption of effective two-body interactions such as a Born-Mayer potential [Pg.179]

A comparison of results obtained with traditional MD using classical pair potentials and the combined QM/MM treatment has shown however that e.g. the coordination number decreases from 9.2 to 8.3 [230], a trend quite similar to that observed by Floris et al [130] who obtained 9.1 and 8.6 passing from two-body ab initio potential to the effective two-body PCM-based potential. Also it turned out that a minimal basis set (STO-3G) treatment is unable to provide reliable results, in fact the coordination number in this case is ten. Hence, high level QM calculations are required making this approach computationally very expensive. For instance, the run by Tongraar et al. [230] with their most sophisticated QM description could only span 1.6 ps. [Pg.412]

Beyond a certain system size, even DFT methods using conventional basis sets become computationally very intensive. In such situations, one has to take recourse to the use of solid-state physics methods like the pseudopotential plane wave or tight-binding methods [28,29]. As the systems become larger, Monte Carlo (MC) simulations and molecular dynamics simulations based on effective pair potentials (including two-body to multi-body interactions) are carried out. [Pg.967]

Implemented as outlined above, the PCM seems to correctly account for the main non-additive effects for cations in water. Except for cations like NH4 where exchange seems the principal source of non additivity [133], they are basically polarization of water in the electric field of the cation and electron transfer from water to the cation. A second water molecule nearby reduces both these effects, giving a less deep potential well in the effective two-body potential compared to the strictly two-body one. In the PCM picture, a distribution of negative charge on the cavity, due to the polarization of the dielectric continuum induced by the cation, decreases the electric field of the cation and hence both water polarization and electron transfer from water to the cation. [Pg.389]

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