Electro-optical parameters

The calculation of the electro-optical parameters describing Raman intensities is not yet very advanced, because of the paucity of data. Nevertheless, some success was achieved in calculations of the intensity of infrared absorption. The results on trans and gauche bond-rotation in ethylene glycol146 could be taken as a model for carbohydrates. Indeed, similar electro-optical parameters (/aCH, /aOH, /aCC, and /aCO) were calculated. This leads to the expectation that calculations of the intensity of the vibrational spectra of carbohydrates may be accomplished in the near future. In addition, the delicate problem of accounting for molecular interactions in calculating infrared intensities could be approached as it was for v(CCC) and i CO) vibrations in acetone.149 This will allow interpretation of weak, as well as strong, i.r. bands, in order to determine the structural properties of molecules. 

The simplest model consists of two centres, one donor (D) and one acceptor (A), separated by a distance I and contains two electrons. Here we consider this simple system to illustrate some general relations between charge transfer, transition intensities and linear as well as non-linear optical polarizabilities. We will show below that the electro-optic parameters and the molecular polarizabilities may be described in terms of a single parameter, c, that is a measure of the extent of coupling between donor and acceptor. Conceptually, this approach is related to early computations on the behaviour of inorganic intervalence complexes (Robin and Day, 1967 Denning, 1995), Mulliken s model for molecular CT complexes (Mulliken and Pearson, 1969) and a two-form/two-state analysis of push-pull molecules (Blanchard-Desce and Barzoukas, 1998). 

Two types of parameters appear in this expression, m/ represents bond dipole moments, while dm/ / d/ /. represents derivatives of the bond dipole moment with respect to the internal coordinates (bond stretching, angle deformation, out-of-plane deformation, and torsion). These parameters are referred to as electro-optical parameters (eop). All other quantities are derived from the structure or from the normal coordinate calculation. The electro-optical parameters can be derived from measured intensities, like force constants are derived from measured frequencies. Compared to the determination of force constants, the problem in this case is that the number of parameters is much higher. 

The necessary derivations with respect to the small displacements can be performed either numerically, or, more recently, also analytically. These analytical methods have developed very rapidly in the past few years, allowing complete ab initio calculation of the spectra (frequencies and intensities) of medium sized molecules, such as furan, pyrrole, and thiophene (Simandiras et al., 1988) however, with this approach the method has reached its present limit. Similar calculations are obviously possible at the semi-empirical level and can be applied to larger systems. Different comparative studies have shown that the precise calculation of infrared and Raman intensities makes it necessary to consider a large number of excited states (Voisin et al., 1992). The complete quantum chemical calculation of a spectrum will therefore remain an exercise which can only be perfomied for relatively small molecule. For larger systems, the classical electro-optical parameters or polar tensors which are calibrated by quantum chemical methods applied to small molecules, will remain an attractive alternative. For intensity calculations the local density method is also increasing their capabilities and yield accurate results with comparatively reduced computer performance (Dobbs and Dixon, 1994). 

M. Gussoni, in Advances in Infrared and Raman Spectroscopy, R. J. Clark and R. Hester, Eds., Heyden, London, 1979, pp. 61-126. Infrared and Raman Intensities from Electro-Optical Parameters. 

Dynamic and electro-optical properties (related to the variation of the dipole moment with respect to the bond length) of aniline, aminotoluenes and many monohalogenoanilines in CCLt have been studied in order to compare the spectroscopic parameters of the free amino group and of several 1 1 and 1 2 complexes with the proton acceptor CH3CN, THF, DMF, DMSO and FLMPA. The electro-optical parameters of the NH2 group are affected by the type and position of the substituent and by the properties of the proton acceptors139. 

The IR intensity of a normal mode is, from Eq. (79), proportional to (3, /3Q)2. One approach would be to determine experimentally a set of bond moment (electro-optical) parameters from which the (3. /dQ) could be calculated (Person and Zerbi, 1982). For molecules with as low a symmetry as peptides this presents serious difficulties. Our approach has been to use Eq. (76), dii/dQ = 2. (dfi/dSi)Lia, to calculate the dfi/dSi from NMA by ab initio Hartree-Fock methods, and to use the Lia obtained from our empirical force field for the particular polypeptide. 

Our first attempt to apply electro-optics in the investigation of the adsorption of neutral polyacrylamide on kaolinite particles was in 1988 [4,5]. Several electro-optical parameters were used to follow the adsorption of polymer on colloid particles—the amplitude of the electro-optical effect, the critical frequency of relaxation of the low- and high-frequency effects, the electro-optical decay time after the switching off of the electric field. Variations in these parameters with concentration of the added polymer give information on the particle electric polarizability, the thickness of the adsorbed polymer layer, the size of aggregates that appear in the suspension due to flocculation [4-10], etc. 

The first two terms in eq. 12 are known as "electro-optical parameters." If the instantaneous molecular dipole moment is expressed in terms of effective electrical charges, localized on the atoms, M = Iaqa a dipole moment change can then be expressed as a function of... 

Once we have proven the existence of bond alternation, we must prove the existence of p-electron delocalisation (i.e. conjugation). In this case, we use vibrational intensities (see section on Intensity Spectroscopy" above), and compare the data derived from butadiene, the shortest trans-diene. Let us consider the electro-optical parameters which describe the change... 

A full IR spectrum calculation based on the computer data base of molecular parameters (geometry, force constants, electro-optical parameters) can be considered as an effective aid for the IR spectra prediction. At the same time this approach is not so fast as to be applied to a large structural file and in addition the spectrum prediction can not be carried out fully automatically. 

Dielectric constants and refractive indices, as well as electrical conductivities of liquid crystals, are physical parameters that characterize the electronic responses of liquid crystals to externally applied fields (electric, magnetic, or optical). Because of the molecular and energy level stractures of nematic molecules, these responses are highly dependent on the direction and the frequencies of the field. Accordingly, we shall classify om studies of dielectric permittivity and other electro-optical parameters into two distinctive frequency regimes (1) dc and low frequency, and (2) optical frequency. Where the transition from regime (1) to (2) occurs, of course, is governed by the dielectric relaxation processes and the dynamical time constant typically the Debye relaxation frequencies in nematics is on the order of 10 ° Hz. 

Qi are normal comdinates, Rj internal coordinates, and Ljj elements of the normal coordirurte transformation matrix. From expression (3.22) we can see diat electro-optical parameters are die following quantities magnitudes of die bond moments, and... 

Another formidable problem in the above parametric expression of vibraticmal intensities arises from the very large number of parameters appearing in Eqs. (3.23) and (3.27). These exceed by far the number of experimental observables. To arrive at a defined inverse electro-qitic problem, i.e. to evaluate die set of electro-optical parameters from the observed intensities, a considerable number of elmnents of die matrix (dp/dR) have to be necessarily constrained to zero. While this is plqrsically acceptable fin some distant interactimis, the practice shows diat h is necessary to neglect marry close interactions as well. The examples presoited latm in the text illustrate die problem quite clearly. 

Differentiating (3.41) with respect to internal coordinates and usiiig relation (2.4) one arrives at a set of linear equations defining the relation between the exjrerimental dipole moment derivatives dp/dQi and the electro-optical parameters associated with... 

It should be emphasized that the charge-flux effects are implicidy included in electro-optical parameters of the type dpj dRj that appear in the first-order bond moment model [72]. Thus, in standard applications to various molecules it does not seem necessary to extend the original formulation since this would result in further increase in intensity parameters. 

As mentioned, to deal with the considerable gap in number between e q)erimental dipole derivatives and electro-optical parameters, a least squares approach is usually adopted [72], From die available literature it does not become entirely clear how individual parameter values, especially equilibrium bond moments, are derived from the sets of linear equations as defined by Eqs. (3.23) and (3.24). It can be assumed that extended applications to a large number of molecules diat have die same type of structural elements may enable, by multiple testing, to arrive at physically significant electro-optical parameters. In fact, a library of such intraisity parameters has been created and used together with standard transferable force fields to predict die infrared spectra of a number of aliphatic and aromatic hydrocarbons [60-62], Comparisons between calculated and predicted spectra do not, however, appear to be satisfactoiy for many molecules. Thus, the accuracy of both force constants and eop s is under question. On the odier side, the main purpose of these libraries of empirical vibrational parameters... 

In Eqs. (3.51) through (3.53) M is the C-Cl bond moment and p die C-H bond moment. Bond moments are in Debye units, eop s of the type dpj /arj are in units D A while apif/ayi with Yi an angular internal coordinate are in units D rad The total number of electro-optical parameters is 13 while the number of observables that can be used in dieir evaluation is just 7. It is evident that to solve the sets of linear equations some eop s have to be put equal to zero. Another difficult problem is how to decompose p, into particular bond moment values. Even if p and M are assigned particular values [73] a number of different solutions are obtained depending on which electro-optical parameters are ignored. It is, dierefore, of particular importance to discuss in detail the approximations adopted in calculations employing the bond moment model. 

Gussoni and Abbate [151] have derived a general formula relating atomic polar tensors and electro-optical parameters. Eq. (3.27) is an expression of die dipole moment derivatives with respect to symmetry coordinates in terms of electro-optical parameters. 

As an illustration, in Table 5.1 explicit relations between APT and electro-optical parameters for CH3X molecules derived by Gussoni and Abbate [151] are shown. The expressions refer to the local Cartesian systems for X and H atoms defined in Fig. 5.1. 

Atomic polar tensors for X and Hj atoms in methyl halides (CH3X) expressed in terms of electro-optical parameters. 

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