Dipoles time-averaged induced

London-van der Waals forces generally are multipole (dipole-dipole or dipole-induced dipole) interactions produced by a correlation between fluctuating induced multipole (principal dipole) moments in two nearly uncharged polar molecules. Even though the time-averaged, induced multipole in each molecule is zero, the correlation between the two induced moments does not average to zero. As a result an attractive interaction between the two is produced at very small molecular distances. 

Here e is the dielectric constant of the gas, F the strength of the applied field, N the number of molecules in unit volumes, n the permanent electric moment of a molecule, and a the coefficient of induced polarization of a molecule cos 9 is the average value of cos 9 for all molecules in the gas, and cos 9 is the time-average of cos 9 for one molecule in a given state of motion, 6 being the angle between the dipole axis and the lines of force of the applied field. 

Figure 6.5 Dynamics of a classical electric dipole induced and driven on resonance by a sequence of two phase-locked ultrashort laser pulses, The driving laser field is shown as gray solid lines in all frames, In addition, the top frames show the induced dipole oscillation as a black dashed line. The instantaneous interaction energy V(t) of the induced dipole in the external driving field is shown in the bottom frames as a black dotted line. Bold black lines display the time average of the interaction energy In Figure 6,5a, the phase relation between both pulses is designed such that the second pulse couples in antiphase to...

A second type of force between water molecules and the metal consists of the dispersion forces. Dispersion forces (or London forces) can be seen classically as follows A time-averaged picture of any atom shows spherical symmetry because the charge due to the electrons orbiting around the nucleus is smoothed out in time. An instantaneous picture of, say, a hydrogen atom, would, however, show a proton here and an electron there—two charges separated by a distance. Hence, every atom has an instantaneous dipole moment of course, the time average of all these dipole moments is zero. This instantaneous dipole will induce an instantaneous dipole in a contiguous atom, and an instantaneous dipole-dipole force will arise. When these... 

Ug expresses the electronic response (induced dipoles), oi is associated with the average orientation induced in the distribution of permanent molecular dipoles, and as denotes the total response. These contributions can in principle be monitored experimentally Immediately following a sudden switch-on of an external field T>, the instantaneous locally averaged induced dipole is zero, however after a time large relative to Xg but small with respect to Xn the polarization becomes Pg = ag D. Equation (1.237) is satisfied only after a time long relative to r . Similarly we can define two dielectric constants, Sg and Sg such that 5 = and Pg = [(sg —... 

Importantly, the induced dipole is also a function of frequency. Therefore, we see that the direction in which the particle moves is not only a function of the properties of the particle and the suspending medium but also the frequency of the applied field. The time-averaged dielectrophoretic force on the dipole is given by ... 

The mechanism by which benzene solvent molecules are able to produce differential solvent shifts in the proton resonances of the same molecule has been widely interpreted in terms of a benzene-solute collision complex. The term collision complex is meant to imply a short-lived orientation of the benzene molecule(s) that has been brought about by dipole-induced dipole, dipole—quadrupole, or other weak chemical association. Any mechanism that is proposed for benzene-induced solvent shifts should take into account the nature, stoicheiometry, strength and time-averaged stereochemical environment of the interaction and we shall deal with each of these points in turn. 

The Polarization of Polar Molecules. Equation (4.7) gives an expression for the electronic polarizability of a spherically symmetric atom or molecule. If a molecule has a freely rotating permanent dipole, which has a time-averaged dipole moment of zero, in the presence of an external field E, there may develop an induced orientational dipole. This would then be related to the orientational polarizability of the molecule. If at some instant, the permanent dipole II of the molecule is at an angle 6 to the applied field, its energy in the field will be given by... 

Some time-averaged electronic properties are summarized in Table 11.1 where they are compared to the gas phase values for the optimized molecular structure. Figure 11.9 displays the time fluctuations of the induced dipole moments for the three molecules along the simulations at the interface. 

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