Varying dipole moment

In spectroscopy one frequently deals with functions of time, f(t), such as the position r(t) of an electric charge, or a time-varying dipole moment, fi(t), which lead to emission of electromagnetic radiation if the second time derivative is not vanishing. The frequency spectrum of the associated emission is obtained by Fourier transform of the function of time. If the absolute value of the function, /(t), is integrable over all times, —co < t < co, one defines the Fourier transform according to... 

D. Quite another approach, as compared with Refs. 7 and 12b was proposed in Refs. 6 and 8 in terms of a semiphenomenological molecular model capable of describing the wideband dielectric and far-infrared spectra of ordinary and heavy water. In the model the total dipole-moment vector was presented as a sum of two components. The absolute value p of the first component is set constant in time the second component, p(f), changes with time harmonically. Such rather formal presentation of a total dipole moment ptot is possibly a simplest step in taking account of the collective effects, since a time-varying dipole moment p(f) arises due to cooperative motion of nearby polar water molecules. 

A time-varying dipole moment emits light. The light scattered from a collection of molecules is simply the sum of the amplitudes of light scattered from each of the individual molecules, i.e., proportional to... 

Strictly speaking, Eq. (1) is only valid for static electric fields. For any field that is time dependent, i.e., E t), the molecular response n(t) will always lag behind somewhat. This is taken into account by assuming that a, fi, and y are complex quantities, and that they relate Eourier components of the time-varying dipole moment to Fourier components of the time-varying electric field. In effect, Eq. (1) needs to be rewritten for the combination of field amplitudes and field frequencies that are of interest. Limiting the following to cubic NLO effects, such an equation will have the following form ... 

The influenee of azobenzene substituents with varying dipole moments has also... 

We have two interaction potential energies between uncharged molecules that vary with distance to the minus sixth power as found in the Lennard-Jones potential. Thus far, none of these interactions accounts for the general attraction between atoms and molecules that are neither charged nor possess a dipole moment. After all, CO and Nj are similarly sized, and have roughly comparable heats of vaporization and hence molecular attraction, although only the former has a dipole moment. 

Since the vibrational eigenstates of the ground electronic state constitute an orthonomial basis set, tire off-diagonal matrix elements in equation (B 1.3.14) will vanish unless the ground state electronic polarizability depends on nuclear coordinates. (This is the Raman analogue of the requirement in infrared spectroscopy that, to observe a transition, the electronic dipole moment in the ground electronic state must properly vary with nuclear displacements from... 

Equation (6.8), to (d /dx)g. Figure 6.1 shows how the magnitude /r of the dipole moment varies with intemuclear distance in a typical heteronuclear diatomic molecule. Obviously, /r 0 when r 0 and the nuclei coalesce. For neutral diatomics, /r 0 when r qg because the molecule dissociates into neutral atoms. Therefore, between r = 0 and r = oo there must be a maximum value of /r. Figure 6.1 has been drawn with this maximum at r < Tg, giving a negative slope d/r/dr at r. If the maximum were at r > Tg there would be a positive slope at r. It is possible that the maximum is at r, in which case d/r/dr = 0 at Tg and the Av = transitions, although allowed, would have zero intensity. 

Equations (6.5) and (6.12) contain terms in x to the second and higher powers. If the expressions for the dipole moment /i and the polarizability a were linear in x, then /i and ot would be said to vary harmonically with x. The effect of higher terms is known as anharmonicity and, because this particular kind of anharmonicity is concerned with electrical properties of a molecule, it is referred to as electrical anharmonicity. One effect of it is to cause the vibrational selection mle Au = 1 in infrared and Raman spectroscopy to be modified to Au = 1, 2, 3,. However, since electrical anharmonicity is usually small, the effect is to make only a very small contribution to the intensities of Av = 2, 3,. .. transitions, which are known as vibrational overtones. 

The dipole moment varies according to the solvent it is ca 5.14 x 10 ° Cm (ca 1.55 D) when pure and ca 6.0 x 10 ° Cm (ca 1.8 D) in a nonpolar solvent, such as benzene or cyclohexane (14,15). In solvents to which it can hydrogen bond, the dipole moment may be much higher. The dipole is directed toward the ring from a positive nitrogen atom, whereas the saturated nonaromatic analogue pyrroHdine [123-75-1] has a dipole moment of 5.24 X 10 ° C-m (1.57 D) and is oppositely directed. Pyrrole and its alkyl derivatives are TT-electron rich and form colored charge-transfer complexes with acceptor molecules, eg, iodine and tetracyanoethylene (16). 

Furthermore, in a series of polyoxyethylene nonylphenol nonionic surfactants, the value of varied linearly with the HLB number of the surfactant. The value of K2 varied linearly with the log of the interfacial tension measured at the surfactant concentration that gives 90% soil removal. Carrying the correlations still further, it was found that from the detergency equation of a single surfactant with three different polar sods, was a function of the sod s dipole moment and a function of the sod s surface tension (81). 

Electron-density calculations for quinazoline (which has no symmetry) vary markedly with the method used. The diagram (6) has the same bases as that given for pyrimidine above it will be observed that the 2- and 4-positions in quinazoline are comparable with the corresponding positions in pyrimidine and that the aromatic carbon atoms (C-5-C-8) in quinazoline are roughly comparable with C-5 in pyrimidine (67MI21300). The dipole moment of quinazoline does not appear to have been measured, but that of 2-methylquinazo-line is 2.2 D. 

This dispersion interaction must be added to the dipole-dipole interactions between molecules, such as HCl, NH3 and H2O which have a permanent dipole, fi. The magnitude of die dipole moment depends on tire differences in electronegativity of the atoms in the molecule. Here again, the energy of interaction varies as (orientation effect). 

---