Interatomic pair correlation

The fact that interatomic pair correlation gives dispersion was semi-quantitatively confirmed in a calculation [25] on He2. This Kestner-Sinanoglu work on He2 gave a well depth of 4.32 K = 3.00 cm which is about 2.5 times lower than the presently accepted value. The discrepancy is due to an inadequate AO basis. 

Fig. 6.86. Oxygen-oxygen pair correlation function obtained from molecular dynamic simulations on the adsorbed layer of a Pt(100) surface. Ax and Ay are the projections of the interatomic distances in the x- and indirections, respectively. They reflect the positions of the oxygen atoms on the top site of the platinum lattice, and the pronounced form of the peaks refers to their relatively small displacement. (Reprinted from E. Spohr, G. Toth, and K. Heinzinger, Electrochim. Acta 41 2131, copyright 1996, Fig. 10a, with peimission from Elsevier Science.)...

Recent work improved earlier results and considered the effects of electron correlation and vibrational averaging [278], Especially the effects of intra-atomic correlation, which were seen to be significant for rare-gas pairs, have been studied for H2-He pairs and compared with interatomic electron correlation the contributions due to intra- and interatomic correlation are of opposite sign. Localized SCF orbitals were used again to reduce the basis set superposition error. Special care was taken to assure that the supermolecular wavefunctions separate correctly for R —> oo into a product of correlated H2 wavefunctions, and a correlated as well as polarized He wavefunction. At the Cl level, all atomic and molecular properties (polarizability, quadrupole moment) were found to be in agreement with the accurate values to within 1%. Various extensions of the basis set have resulted in variations of the induced dipole moment of less than 1% [279], Table 4.5 shows the computed dipole components, px, pz, as functions of separation, R, orientation (0°, 90°, 45° relative to the internuclear axis), and three vibrational spacings r, in 10-6 a.u. of dipole strength [279]. 

The strength of the water-metal interaction together with the surface corrugation gives rise to much more drastic changes in water structure than the ones observed in computer simulations of water near smooth nonmetallic surfaces. Structure in the liquid state is usually characterized by pair correlation functions (PCFs). Because of the homogeneity and isotropy of the bulk liquid phase, they become simple radial distribution functions (RDFs), which do only depend on the distance between two atoms. Near an interface, the PCF depends not only on the interatomic distance but also on the position of, say the first, atom relative to the interface and the direction of the interatomic distance vector. Hence, considerable changes in the atom-atom PCFs can be expected close to the surface. 

Fig. 15. Anisotropic oxygen-oxygen pair correlation functions gooip, for the adsorbate molecules (left), the molecules in the second layer (middle), and the molecules in the bulk-like center of the water lamina (right) between Pt(lOO) surfaces, p is the transversal and z the normal part of the interatomic distance.

At the present time, of all EXAFS-like methods of analysis of local atomic structure, the SEES method is the least used. The reason is that the theory of the SEES process is not sufficiently developed. However the standard EXAES procedure of the Fourier transformation has been applied also to SEES spectra. The Fourier transforms of MW SEES spectra of a number of pure 3d metals have been compared with the corresponding Fourier transforms of EELFS and EX-AFS spectra. Besides the EXAFS-like nature of SEES oscillations shown by this comparison, parameters of the local atomic structure of studied surfaces (the interatomic distances and the mean squared atomic deviations from the equilibrium positions [12, 13, 15-17, 21, 23, 24]) have been obtained from an analysis of Fourier transforms of SEES spectra. The results obtained have, at best, a semi-quantitative character, since the Fourier transforms of SEES spectra differ qualitatively from both the bulk crystallographic atomic pair correlation functions and the relevant Fourier transforms of EXAFS and EELFS spectra. 

Interatomic spatial correlations are represented by the radial distribution function, D r), which can be obtained by the X-ray and neutron diffraction methods. From the peak position, the peak area, and the peak width, the interatomic distance, r, the number of atoms within the atom pair, n and the mean-square amplitude of the distance of the atom-pair, a, respectively, can be estimated. 

The total pair correlation functions for the neutron diffraction, MD, and RMC of the all samples are compared in Fig. 4.7. While there is broad similarity between the MD and the neutron data, it is apparent that there are significant interatomic interactions that are not accounted for with the simple Buckingham potentials described in Sect. 4.2. The RMC total structme factors are in very good agreement with the corresponding neutron diffraction structure factors, as shown in Fig. 4.7a. 

The radial distribution function, g(r), is proportional to the density of atoms at the distance R from a certain atom taken for the central atom. The pair correlator is directly comparable to the structural factor obtained from the experiments on the X-ray scattering and it provides only the information on interatomic distances. Figure 6.1 shows the calculated Cu, Ni and Au RDFs in supercooled state in comparison with the experimental data by Waseda [ 14]. It should be noted that there is good correspondence for gold. For copper and nickel the correspondence of the calculated and experimental RDFs is satisfactory. The discrepancy can be explained by the inaccuracy of the used interatomic interaction potentials. Nevertheless, the first RDF peak for all metals under study is very well reproduced, which allows to speak about the adequacy of further analysis of the cluster structure of the melts. Moreover, the discrepancy of the calculated and experimental RDFs allows to clarify the degree of the influence of the accuracy of the interatomic interaction description on the cluster structure by the comparison of the results with those in Refs. [7-9], where the exacter ab-initio methods of simulation were used. 

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