Local dipole moments

In these models, the local dipole moment derivative contribution becomes... 

The net strength of a molecule s Debye interactions is a function of its polarizability and the number and magnitude of its local dipole moments. Since induced dipoles tend to be aligned for maximum attraction, the energy of interaction resulting from Debye forces is very nearly additive. 

Keesom forces are a function of the number and magnitude of a molecule s local dipole moments, but since they are dependent upon the positioning of a molecule with respect to its neighbors, they may not always be strictly additive. Flowever, since the molecules in most crystals are aligned for maximum dipolar interaction, the group interactions are often roughly additive. 

The treatment of the hydration interaction follows the model employed earlier by Schiby and Ruckenstein,7based on the mutual interactions of dipoles. In this model, it is considered that the dipoles of the surface polarize the water molecules of the first layer of water and the polarization propagates from layer to layer. When two surfaces approach each other, the polarized layers will increasingly overlap. As a result, the local dipole moment of the water molecules will be decreased. This increases the free energy of the system and thus generates a repulsive force. 

Substituents bearing electronic lone pairs may also increase the inversion barrier through electron repulsion interactions with the nitrogen lone pair, which are higher in the TS than in the GS. On the other hand, electrostatic dipole-dipole interactions are expected to decrease in the TS where the contribution of the nitrogen lone pair to the local dipole moment vanishes. 

Two other types of descriptor have been included recently to help describe dipolarity and the possibility of multiple ligands. The molecular dipole moment, p, has been found to be insignificant in these TLSER correlations consequently, it was not included in the overall set of descriptors. However, it is possible to define local dipole moments in terms of atomic charges and interatomic distances, Eq. [25]. 

In this account we have attempted to provide a brief overview of the concepts of first-principles methods tailored for the calculation of structures, energetics, and properties of supramolecular assemblies. The presentation of the theory focussed on the most essential building blocks in order to provide a general frame to interrelate the various methods available. Thereafter, we discussed the relation of these methods to experiment and to well-known concepts for the description of typical interaction patterns. Also, new methods tailored for tackling problems specific to supramolecular chemistry have been discussed (like the calculation of local dipole moments in CPMD simulations, the Mode-Tracking protocol for the selective calculation of vibrational frequencies and intensities, or the SEN method for the calculation of hydrogen bond energies). 

Because of its high localized dipole moment, sulfolane is a very good solvent for inorganic salts, and its effect on the acylation activity of Y(9) is ascribed to the formation of a homogeneous catalyst system consisting of dissolved aluminum compound that interacts with BC. Blank experiments and Al NMR analysis of the solution confirm the activity after filtration of the catalyst. These results are not so negative and confirm that a catalytic amount of aluminum species are transferred into solution in sulfolane and catalyzes the quantitative conversion of BC. 

Since oxygen and nitrogen atoms are more electronegative than carbon, their bonds to carbon atoms have an ionic ingredient. That ingredient gives the molecules local dipole moments, whose interaction with the similar dipole moments in neighbouring molecules makes the molecules cohere. 

Fig. 9.6. In plastics of the polyamide type, the skeletal chain acquires local dipole moments at the points where the (NH)-(CO) configuration occurs.

The energy of molecules that contain permanent charges or local dipole moments depends on the interaction of these charges or dipoles with other charges or dipoles in the same molecule or in surrounding molecules. Thus the effects of these electrostatic interactions depend on the conformation of the molecule as well as on the medium. For interactions between ions, the Coulombic potential given by (4) is the dominant terra ... 

Dispersion forces are attractive forces between atoms at close distances. Even molecules with no permanent dipole moment have, due to the movement of their electrons, local dipole moments which induce dipoles in the opposite molecule, leading to fluctuating electrostatic attractions. At a closer distance repulsive forces develop due to an unfavorable overlap of the van der Waals spheres of both molecules. These relationships are typically described by the Lennard Jones potential, with an r attractive term and an r repulsive term (Figure 2) [59, 116]. Dipole-dipole interactions and dispersion forces are much weaker than other electrostatic interactions. Nevertheless, if there is a close contact between both molecules over a relatively large surface area, they may sum up to large values of overall interaction energies. 

Liberies, A. /. Chem. Educ. 1977,54,479 used hybridization parameters to show that lone pairs in sp hybrid orbitals have a greater local dipole moment than do lone pairs in any other hybrids. 

The molecular symmetry is broken by the interaction with the matrix. The slope of the spectral shift versus the electric field mainly depends on A/7, the change of the local dipole moment, which itself depends on the respective orientations of the applied field, the orientation of the molecule, and its local nano-environment. More precisely, the component of A/ along the local electric field relates to the slope dv/d by the equation ... 

To study the influence of an electric field on the diffusion rates, the local dipole moments associated with all important processes must he known. These cannot be obtained from the EAM, so we have calculated them from DFT. Obviously, it is not possible to calculate the changes in the dipole moments for all 544 processes, so we have limited our calculations to the most important processes. KMC offers a convenient way to determine which processes contribute most. In this way, we made a screening of all the processes and selected the basic ones that determine the rates and the fluctuations. We have identified 16 diffusion events that strongly contribute to the fluctuations. All of them were treated with DFT to obtain the local dipole moments at the initial and transition states. A list of the processes considered and the corresponding changes in the dipole moments is given in Table 3.1. 

For PB the dipole moments are located on the vinyl side group aud the cis group. The partial charges, however, are small and that was the reason we did not include Coulomb forces into our MD simulation. Consequently, there can be no correlations due to the local dipole moment occurring in om simulation trajectory. We then have to see, how well our results for the dielectric permittivity agree with the experiments [22]. To this end we reinsert partial charges into the simulated trajectory. We know that we have to find... 

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