Spectra calculations optical rotations

An interesting method for the estimation of optical purity of sulfoxides, which consists of the combination of chemical methods with NMR spectroscopy, was elaborated by Mislow and Raban (241). The optical purity is usually determined by the conversion of a mixture of enantiomers into a mixture of diastereomers, the ratio of which may be easily determined by NMR spectroscopy. In contrast to this, Mislow and Raban used as starting material for the synthesis of enantiomeric sulfoxides a diastereomeric mixture of pinacolyl p-toluenesulfinates 210. The ratio of the starting sulfinates 210 was 60.5 39.5, as evidenced by the H NMR spectrum. Since the Grignard reaction occurs with full stereospecificity, the ratio of enantiomers of the sulfoxide formed is expected to be almost identical to that of 210. This corresponds to a calculated optical purity of the sulfoxide of 20%. In this way the specific rotations of other alkyl or aryl p-tolyl sulfoxides can conveniently be determined. 

Optical rotation spectroscopy (ORD) can by used in characterizing chiral molecules, like (R)-3-methylcyclopentanone of Fig. 16. This molecule can exist in two conformations, as shown in the figure. Al-Basheer et al studied this molecule experimentally and theoretically in various solvents, including cyclohexane. They calculated the spectra of the two isomers, separately, as shown in Fig. 17. Experimental information on the mole fractions of the two conformers was subsequently used in calculating the spectrum that is shown in Fig. 18, where it is also compared with the experimental results. The agreement between experiment and theory is excellent. 

Optical Rotation.—The c.d. spectrum of (—)-/raw-l,2-di-4-pyridyloxiran (26) has been determined and rotation strengths have been compared with calculated values. The configuration of (—)-(26) was shown as by comparison with (-f)-R-/rfl 5-stilbene oxide. 

The dielectric constant is a natural choice of order parameter to study freezing of dipolar liquids, because of the large change in the orientational polarizability between the liquid and solid phases. The dielectric relaxation time was calculated by fitting the dispersion spectrum of the complex permittivity near resonance to the Debye model of orientational relaxation. In the Debye dispersion relation (equation (3)), ij is the frequency of the applied potential and t is the orientational (rotational) relaxation time of a dipolar molecule. The subscript s refers to static permittivity (low frequency limit, when the dipoles have sufficient time to be in phase with the applied field). The subscript oo refers to the optical permittivity (high frequency limit) and is a measure of the induced component of the permittivity. 

The popularity of the SOS methods in calculations of non-linear optical properties of molecules is due to the so-called few-states approximations. The sum-over-states formalism defines the response of a system in terms of the spectroscopic parameters, like excitations energies and transition moments between various excited states. Depending on the level of approximation, those states may be electronic or vibronic or electronic-vibrational-rotational ones. Under the assumption that there are few states which contribute more than others, the summation over the whole spectrum of the Hamiltonian can be reduced to those states. In a very special case, one may include only one excited state which is assumed to dominate the molecular response through the given order in perturbation expansion. The first applications of two-level model to calculations of j3 date from late 1970s [93, 94]. The two-states model for first-order hyperpolarizability with only one excited state included can be written as ... 

There are few methods suitable for on-line chemical analysis of aerosol particles. Raman spectroscopy offers the possibility of identifying the chemical species in aerosol particles because the spectrum is specific to the molecular. structure of the material, especially to the vibrational and rotational modes of the molecules. Raman spectra have been obtained for individual micron-sized particles placed on surfaces, levitated optically or by an eiectrodynamic balance, or by monodisperse aerosols suspended in a flowing gas. A few measurements have also been made for chemically mixed and poly disperse aerosols. The Raman spectrum of a spherical particle differs from that of the bulk material because of morphology-dependent resonances that re.su It when the Raman scattered photons undergo Mie scattering in the particle. Methods have been developed for calculating the modified spectra (McNulty el al., 1980). 

We calculate the pure rotational part of our spectrum taking into account all the light scattering mechanisms described in Eq. (56). Then the resulting spectrum takes the form of the convolution of the rotational and translational parts [see Eqs. (31) and (32)]. We deal numerically with the rotational and translational spectra and their convolution [15,16,36] by methods described in the previous section for optically isotropic molecules. 

In the rest of this section we discuss our analysis (10,11) of the accurate cumulative reaction probabilities for the halogen-hydrogen halide systems that were published by Schatz (17-19). The CRPs were digitized with an optical scanner, which introduces negligible error. The accurate N°(E) was fit with cubic splines and convoluted using Eq. (20). Our analysis is based on the observation that the calculated CRPs of Schatz for Cl + HC1,1 + HI, and I + DI appeared to have an overall steplike structure reminiscent of that associated with quantized transition states, underlying the narrower features associated with trapped-state resonances and rotational thresholds. Our conclusion that quantized transition states exert broad control of the chemical reactivity for these reactions is not inconsistent with Schatz s description of the narrow trapped-state resonance and rotational threshold features. These different sorts of dynamical features represent different time scales, with the shorter-time (broader) features being more closely related to the traditional concern of chemical kinetics, i.e., reactivity, as discussed below Eq. (23). The relationship of features in the CRP to features in the photoelectron spectrum is not fully worked out yet. 

The two methods give results that are interconvertible hence ord or cd spectra can be selected according to the availability of the appropriate instruments. Yet, one is sometimes preferred over the other when the optical density of the solution in certain areas of the spectrum interferes with the determination of rotation or of dichroism. In both methods the refractive index of the solution should be taken into consideration in the calculation of results, but the ensuing minor correction is often neglected. 

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