Molecule distances

Solvent Extinction coefficient, a [m ] Thermal conductivity, h[Wm" K ] a/h [W K] Molecule Distance from the bottom of sample cell [pm] AT/AP [KWr j (experimental data)... 

Fig.13 Structure of the Cl3Sn(CH3)(H20)2 complex at the MP2/6 - 31G(d,p) level resulting from the BAC-MP4 calculation for this molecule. Distances are in A...

Thus it seems clear that no direct transitions between essentially repulsive covalent potential surfaces Na + BC and Na + BC are possible. This view is also supported by calculations.68 Under such circumstances an additional ionic potential surface has been postulated,69-70 namely, Na+ + BC, which was supposed to be strongly attractive and to couple with the covalent surfaces. All potentials depend on the molecular distance RM, on the atom-molecule distance Rc during the collision, and on the molecular orientation relative to Rc measured by the angle y. A two-dimensional cut through these surfaces along Rc is shown schematically in Fig. 3 for the... 

Now let us discuss the particular situation of STS experiments [32,33,35, 36]. Here we concentrate mainly on the dependence on the tip-to-molecule distance [33]. When the tip (left lead in our notations) is far from the molecule, the junction is strongly asymmetric rR approximately symmetric rR rR and r] 0.5, and the conductance curve is of the type shown in Fig. 30. We calculated the transformation of the conductance from the asymmetric to symmetric case (Fig. 32). It is one new feature appeared in asymmetric case due to the fact that we started from a finite parameter r] = 0.2 (in the Fig. 31 77 = 0), namely a single peak at negative voltages, which is shifted to smaller voltage in the symmetric junction. The form and behavior of this peak is in agreement with experimental results [33]. 

The dispersion interaction between an atom and a metal surface was first calculated by Lennard-Jones in 1932, who considered the metal as a perfect conductor for static and time-dependent fields, using a point dipole for the molecule [44], Although these results overestimate the dispersion energy, the correct l/d3 dependence was recovered (d is the metal-molecule distance). Later studies [45 17] extended the work of Lennard-Jones to dielectrics with a frequency-dependent dielectric constant [48] (real metals may be approximated in this way) and took into account electromagnetic retardation effects. Limiting ourselves to small molecule-metal distances, the dispersion interaction of a molecule characterized by a frequency-dependent isotropic polarizability a embedded in a dielectric medium with permittivity esol (note that no cavity is built around the molecule) reads ... 

TABLE 4. Basis set dependence of calculated geometries of planar vinylamine (type 116) and related molecules. Distances in A and angles in deg... 

The field enhancements show a clear trend. When the particles are well separated, the wavelength dependence is similar to that obtained for a single particle, with enhancement peaking at 490 nm. As the particles are moved closer together, the peak enhancement increases and red shifts, due to the increased coupling between the particles, as well as the decreased particle-molecule distance. 

The enhanced Raman scattering and fluorescence at close particle-molecule distances show an almost complete quenching of the flucx escence, with a strong... 

If the electric field is caused by an ion, then E = qi/R y where q is the ionic change, i is the unit vector along the ion-molecule direction, and R the ion-molecule distance, which is the E =-l/2aq /R for this ion-induced dipole interaction. The correspondingformulafor dli-pole-induced dipole interaction between two dipolar molecules is... 

Figure 1.—The FXeOS02F molecule (distances in angstrdms and angles in degrees).

Coordinate along the x axis normalized reaction coordinate distance between the centers of reacting molecules distance from the electrode surface Double layer thickness... 

Scheme 5. Comparison of some silanone-aldehyde complexes 10. RHF/6-31G(d,p) calculated energies relative to the uncomplexcd molecules. Distances in pm, energy in kcal/mol.

When attempting to treat ensembles of molecules it is essential to be able to represent the intermolecular interactions, at least beyond some cut-off distance, by pre-determined functions of distance so that high level quantum mechanical calculations do not have to be extended to larger and larger clusters. Masia et a/.88 have addressed the question of how the interaction of a water or carbon tetrachloride molecule interacting with a point charge can be represented. They monitor the molecular dipole as a function of the charge-molecule distance for various orientations of the molecule as calculated by ab initio methods. They find that the most satisfactory method is to represent the molecule by a small number of induced point dipoles with different orientations. In the case of water the ab initio induced dipoles are reproduced at all distances. 

When air is absent in the pores and the pore diameter is substantially greater than the mean free path, X, of the diffusing water molecules (distance traveled between collisions with other molecules), water molecules collide more frequently with each other than with the pore walls and the Poiseuille flow relationship applies. The mean free path can be calculated using Eq. (7), where kb is the Boltzmann constant and a is the collision diameter of the water molecule. However, for pore diameters in the range of membranes that are suitable for OD applications and for a gas-phase pressure attributable to water vapor alone at ambient temperature (approximately 20 mm Hg, 2.7 kPa), the mean free path is significantly greater than the pore diameter. This results in more frequent collisions of the water molecules with the pore walls than with each other, and Knudsen diffusion predominates. 

The field penetration effect is much smaller than structural and nonlocal solvent dielectric effects. Particularly, the increase of Er with increasing electrode-molecule distance is retained, although attenuated. Attenuation can be appreciated as an image delocalization compared to the localized image charge contribution in eqn. (8-8). ... 

CD measurements at 77 °K of a bacteriochlorophyll protein from Chloropseudomonas ethylica indicated exciton splitting near 800 and 600 nm of bacteriochlorophyll a molecules. Distances of 12—15 A between the interacting molecules in a protein subunit were estimated (269). 

Molecule distance according to Pauling s equation according to equation 6.10 Experimental... 

Molecule Distance between molecules in solid state A Dipole moment D Polarizability (cc X IO24) Heat sublimation keals... 

From the analysis of the Auger peak ratio at 1.1 nm (Fig. 1) we obtain that the difference of the screening is mainly related to the first molecular layer at the interface (assuming lying molecules [6] and a molecule-molecule distance of... 

On the other hand, layer dependent screening contributions can be estimated for metal-dielectric interfaces applying a dielectric continuum model according to Aliis(d) A/ 7i(co) = -e2 /(1 (me(f dj [4, 8], where d is the distance from the mirror plane, AEB(d) and AEB(oo) is referred to the distance d and the infinitely thick film, respectively. Here, we assume e 3 and 0.34 nm for the molecule-molecule-distance. The distance of the first layer to the mirror plane of the metal di could be different on a microscopic scale. We apply the van der Waals radius of carbon in organic compounds (analogously to [8]) di = 0.17 nm and for comparison a distinct larger value (0.23 nm). The results are summarized in Table 1 ... 

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