Dipole moment relaxation

Table 4. Dielectric increments, dipole moments, relaxation times, and calculated axial ratios of certain proteins at 25°.

Cannot distinguish between the intermolecular and intramolecular bond signals. Measurement times are higher than the measured relaxation times Water dipole moment relaxations in the kHz-GHz range... 

A qualitative theoretical interpretation of the experimental findings on the basis of the dipole correlation function has been proposed by Williams and Watts. They assumed that a reference dipole may find itself in a number of different environments and, consequently, the fraction of relaxed by local motions will depend on the particular environment. The environments may, in turn, be changed by micro-Brownian motions. Let the probability of finding the dipole in an environment / be p(l). If the fraction of the mean square dipole moment relaxed by the j -process is = //, then (1 —(5m ) of the mean square dipole moment is left unrelaxed by this... 

The theory predicts two relaxation processes for monodisperse rods a fast one associated with the wobbling of a rod in the cage, and a slow one associated with the overall reorientation of the rod. The fraction of the mean square dipole moments relaxed in the former process should be of the order of 2AQ and the relaxation time should be much shorter than that characteristic of the unrestricted diffusion... 

Wall M C, Stewart B A and Mullin A S 1998 State resolved oollisional relaxation of highly vibrationally exoited pyridine ( ii = 38,000 om ) and CO2 influenoe of a permanent dipole moment J. Chem. Rhys. 108 6185-96... 

The above results indicate that the selcelion rules are relaxed when the geometry modifications taking place upon pholoexcitalion are considered. Although the transition dipole moment between the ground state and the lowest excited state remains small, the luminescence is no longer entirely quenched by the interchain in-... 

Transition dipole moment 88 Transverse relaxation time 31, 32, 33, 44 Twinning 126 Two-phase model 129 Two-term models 149 ----unfolding model 183,185... 

Taylor series 260 torque, correlation functions 28 transfer time, rotational relaxation 51 transitions dipole moment 30 forbidden 30 non-adiabatic 130 translational velocity v 6... 

The transfer of the electron takes place very rapidly compared to nuclear motion, and will only take place when the combination of internal and librational coordinates is such that the curves interact. Thus, the [Fe(H20)6] + species must first distort and/or experience a dipole moment field from the instantaneous positions of the water molecules such that it attains the cross-over point. At this point, the electron may tunnel from the [Fe(H20)6]2+ ion to the metal, leaving behind an [Fe(H20)6]3 + ion with a non-equilibrium geometry, This then relaxes by heat transfer to the solvent to the equilibrium point, q0. 

In contrast with Eq. (5), Eq. (11) gives the frequency behavior in relation to the microscopic properties of the studied medium (polarizability, dipole moment, temperature, frequency of the field, etc). Thus for a given change of relaxation time with temperature we can determine the change with frequency and temperature of the dielectric properties - the real and imaginary parts of the dielectric permittivity. 

The linear response theory [50,51] provides us with an adequate framework in order to study the dynamics of the hydrogen bond because it allows us to account for relaxational mechanisms. If one assumes that the time-dependent electrical field is weak, such that its interaction with the stretching vibration X-H Y may be treated perturbatively to first order, linearly with respect to the electrical field, then the IR spectral density may be obtained by the Fourier transform of the autocorrelation function G(t) of the dipole moment operator of the X-H bond ... 

Another transport property of interfacial water which can be studied by MO techniques is the dipole relaxation time. This property is computed from the dipole moment correlation function, which measures the rate at which dipole moment autocorrelation is lost due to rotational motions in time (63). Larger values for the dipole relaxation time indicate slower rotational motions of the dipole... 

The Forster cycle method is quite simple, which explains why it has been extensively used. One of the important features of this cycle is that it can be used even in cases where the equilibrium is not established within the excited-state lifetime. However, use of the Forster cycle is difficult or questionable when (i) two absorption bands overlap (ii) the electronic levels invert during the excited-state lifetime (usually in a solvent-assisted relaxation process) (iii) the excited acidic and basic forms are of different orbital origins (electronic configuration or state symmetry) and (iv) the changes in dipole moment upon excitation are different for the acidic and basic forms. 

Evolution of fluorescence spectra during the lifetime of the excited state can provide interesting information. Such an evolution occurs when a fluorescent compound is excited and then evolves towards a new configuration whose fluorescent decay is different. A typical example is the solvent relaxation around an excited-state compound whose dipole moment is higher in the excited state than in the ground state (see Chapter 7) the relaxation results in a gradual red-shift of the fluorescence spectrum, and information on the polarity of the microenvironment around a fluorophore is thus obtained (e.g. in biological macromolecules). 

Fig. 7.2. Solvent relaxation around a probe that has a weak dipole moment in the ground state and a large dipole moment in the excited state.

If solvent (or environment) relaxation is complete, equations for the dipole-dipole interaction solvatochromic shifts can be derived within the simple model of spherical-centered dipoles in isotropically polarizable spheres and within the assumption of equal dipole moments in Franck-Condon and relaxed states. The solvatochromic shifts (expressed in wavenumbers) are then given by Eqs (7.3) and (7.4) for absorption and emission, respectively ... 

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