Effective pairs

Sprik M 1993 Effective pair potentials and beyond Computer Simulation in Chemical Physics vol 397 NATO ASI Series C ed M P Allen and D J Tildesley (Dordrecht Kluwer) pp 211-59... 

Figure 4.29 from Computer Simulation in Chemical Physics, edited by Allen M P and D J Tildesley, 1993. Effective Pair Potentials and Beyond, Sprik M, with kind permission from Kluwer Academic Publishers. 

Figure 2.3 Site-site interaetion for water 2.6.2 The Effective Pair Potential...

Notice that Rahman and Stiliinger make use of the concept of an effective pair potential. The potential energy of any substance may always be resolved systematically into pair, triplet, quadruplet,. .. contributions. If we consider N particles each with position vector R, then formally we can write... 

In the case of fluids which consist of simple non-polar particles, such as liquid argon, it is widely believed that Ui is nearly pairwise additive. In other words, the functions for n > 2 are small. Water fails to conform to this simplification, and if we truncate the series after the term, then we have to understand that the potential involved is an effective pair potential which takes into account the higher order-terms. 

For each atom type there are two parameters to be determined, the van der Waals radius and the atom softness, Rq and, It should be noted that since the van der Waals energy is calculated between pairs of atoms, but parameterized against experimental data, the derived parameters represent an effective pair potential, which at least partly includes many-body contributions. 

One of the major ingredient for the understanding of alloy phase stability is the configurational energy. Models have been proposed to represent the configurational energies in terms of effective multisite interactions, in particular effective pair interactions (EPls). 

Table 1 Effective Pair Potentials in mRyd/atom for various distances between the pairs for a 50-50 PdV alloy. KKR-CPA-GPM values are taken from ref(10).

EXPERIMENTAL STUDY OF THE SHORT RANGE ORDER IN THE PT-V SYSTEM EFFECTIVE PAIR INTERACTIONS AS A FUNCTION OF THE CONCENTRATION... 

We define a fee lattice and affect at each site n, a spin or an occupation variable <7 which takes the value +1 or —1 depending on whether site n is occupied by a A or B atom. Within the generalized perturbation method , it has been shown that substitutional binary alloys AcBi-c may be described within a Ising model with effective pair interactions with concentration dependence. Thus, the energy of a configuration c = (<7i,<72,- ) among the 2 accessible configurations for one system can be written... 

Those Warren-Cowley parameters have been determined in situ above the order-disorder transition temperature by diffuse neutron scattering. From these experimentally determined static correlations, the first nine effective pair interactions have been deduced using inverse Monte Carlo simulations. 

Figure 3. Compared effective pair interaction for the two sets Pt V and PtgU in ineV.

Fig. 1. The mixing energies agree rather well with the results of Pasturel et al. and those of Abrikosov et al. . The pair interaction i> (c) is In a very good agreement with the locally relaxed quantity given by Carlsson, and also it is rather similar to the effective pair interaction found by Pasturel et al., although it is smaller approximately by a factor 0.7. The pair interaction u (c) differs from the corresponding quantity reported by Abrikosov et al. , which can be probably attributed to different computational schemes, as we assume neutral spheres, while Abrikosov et al. suppose equal sphere radii. The pair interaction (c) closely follows u (c) for Ni-rich alloys and v (c) for Al-rich alloys, at intermediate concentrations all three quantities...

Figure 1. The effective pair interactions as functions of alloy composition for the alloy system Al-Ni. The results of the CWIS based on the FP-LAPW calculations for 5 ordered structures (full line) and on the TB-LMTO-CPA for 5 disordered alloys (dash line) are compared with the the results of the GPM (dotted line).

EFFECTIVE PAIR INTERACTIONS IN RANDOM ALLOYS BY DIRECT CONFIGURATIONAL AVERAGING... 

The aim of the present paper is to apply the impurity KKR Green s function method to the study of nearest-neighbor effective-pair interaction energies (NN-EPIE s) in low-concentrated fee di.sordered alloys (H = host, X = impurity c < 0.1). It is... 

Fig.3 Sclieinatic representation of initial and final. slates to caJenlate effective pair (X-X) iu-teiactioii energies in a disordered alloy H], .Xc.

Fig.4 Effective pair interaction energies of CuNi, PdV, NiAl as well as the experimental values. The KKR-CPA-GPM result for PdV and the CWM result for NiAl are also shown for comparison.

The aim of the force matching procedure is to obtain the effective pair-force between CG sites using the force data obtained from a detailed atomistic molecular dynamics (MD) trajectory. The current implementation of the force-matching method closely follows the formulation from Refs. [23, 24],... 

At short distances, approximately equal to the excluded volume diameter, effective pair forces obtained from force matching exhibit unphysically large fluctuations. This is largely due to inadequate sampling of configurations at short distances in... 

Favorable coarse-graining results for CCI4 are not surprising because this molecule is spherically symmetric. Planar benzene presents a more stringent test for the force-matching approach. Figure 8-8 shows the effective pair-force and pair-potential for the benzene COM. 

Berendsen HJC, Grigera JR, Straatsma TP (1987) The missing term in effective pair potentials. J Phys Chem 91(24) 6269-6271... 

Thirumalai, D. Hall, R. W. Berne, B. J., A path integral Monte Carlo study of liquid neon and the quantum effective pair potential, J. Chem. Phys. 1984, 81, 2523-2527... 

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