Molar rotations

The utilization of optical rotatory dispersion data is complicated by its dispersion mechanism, in which the contributions of all of the electronic transitions in the molecule occur at all wavelengths, as shown in what is called the Drude equation 

ORD data, however, can be obtained for a number of systems of interest where little or no data are possible by circular dichroism, or when the absorption bands cannot be reached due to the high absorbance of a solvent or because the absorption bands of interest are beyond the usual 180-190 nm limit of solution studies. Also, most of the optical rotation data in the literature prior to the mid-1960s are reported in terms of optical rotatory dispersion. Additionally, when correcting the distortions in the CD spectra of biomembranes (see below), it is convenient to have the ORD curve of what is referred to as the pseudoreference state. 

---

McGrath et al. have also thoroughly studied the chiroptical properties of dendrimers such as 40. They compared the optical activities of the series of 1st-, 2nd- and 3rd-generation compounds of type 40, considering the molar rotation per chiral unit ([ ]D/n) [75]. A big difference of the values was found between the generations which could possibly indicate chiral conformations inside the dendrimers, that enhance the optical rotation values per unit when... 

The molar rotation of the dendrimers 49-51 is proportional to the excess of (R,R)- or (S,S)-threitol units. This means that the chiroptical effects of threitol building blocks of opposite chirality cancel out each other. For the homo dendrimers an average positive molar optical rotation value of 146 for each (i, k)-threitol unit was calculated whereas a value of -185 resulted for each... 

Starting with the semiempirical approach of Kauzmann et al. (16), Ruch and Schonhofer developed a theory of chirality functions (17,18). These amount to polynomials over a set of variables that correspond to the identity of substituents at various substitution positions on a particular achiral parent molecule. The values of the variables can be adjusted so that the polynomial evaluates to a good fit to the experimentally measured molar rotations of a homologous series of compounds (2). Thus, properties 1 and 2 are satisfied, but the variables are qualitatively distinct for the same substituent at different positions or different substituents at the same positions, violating property 3. Furthermore, there is a different polynomial for each symmetry class of base molecule. Thus, chirality functions are not continuous functions of atom properties and conformation (property 4). 

Since the optical purity of the starting materials and the molar rotations of the pure optically active products are unknown, it is not possible to assay any partial racemization. In most instances the molar rotation of the products is as large as or larger than the starting material. It is probable that no racemization took place in these reactions, but it is impossible to state this unequivocally without a knowledge of the relationship between the rotatory dispersion curves and visible spectra of the products and starting materials. 

The magnitude of the CD has commonly been calibrated at 290 nm using ( + )-camphor-10-sulfonic acid as a standard. Because of its hygroscopic nature, the water content has led to some confusion. Tsujimura et al. have recommended to use a molar ellipticity of +7.78 x 103 for the compound in an aqueous solution 280). The concentration can be calibrated by the ORD of the same sample, which gave a molar rotation of +4.28 x 103 at 305 nm and of —5.44 x 103 at 270 nm. 

Considering the polymers in which the side chain asymmetric carbon atom is in the y-position with respect to the main chain, a remarkable difference in molar rotation has been found between the monomeric units of the polymers and the model compounds in the case of poly-(S)-5-methyl-l-heptene but not in the case of poly-[(S)-2-methyl-butyl]-vinyl-ether or in the case of poly-(S) l.3-dimethyl-butyl methacrylate. The discrepancy might be related both to conformational and to electronic (113 a) factors. 

In the cases in which remarkable differences exist between the molar rotation of stereoregular polymers and models, the absolute value of the optical activity depends on stereoregularity, being lower in the samples of lower stereoregularity. In these cases the absolute value of the rotatory power decreases by increasing temperature and the temperature coefficients of the molar rotation are at least ten times higher in the polymers than in the model compounds (Table 24). 

Measurements of molar rotation showed that this parameter is almost proportional to the number of chiral binaphthyl units and the molar rotation per binaphthyl unit varies only slightly. On catalysis of the Diels-Alder reaction of cyclopentadiene with 3-[(E)-but-2-enoyl]oxazolidin-2-one the branched catalysts 7 and 8 showed an approximately 25% higher reactivity than the monofunctional catalyst 6 however, the former led to just a slight improvement of ee and endo-selectivity compared to 6. It is thus inappropriate to speak of a dendritic effect on catalysis, although one does indeed exist in relation to the chiroptical properties. 

Anomalous behaviour of the molar rotation depending upon the generation can basically be indicative of the existence of chiral substructures in the dendrimer branches. In many cases such anomalies merely occur as a result of constitutional differences between the chiral building blocks which are exposed to different local environments in the different parts of the dendrimer. CD-spectro-scopic studies can often provide more detailed information about the underlying reasons. 

As shown by the above compilation, comparison of the molar rotations of different dendrimer generations (divided by the number of chiral building blocks in the dendrimer) with those of the corresponding, chiral monomers or appropriate model compounds affords information about the conformational order of the dendrimers. 

The specific rotation [ ]d of the Oth and first generation dendrimers (65 and 67) was recorded at — 59.60 and — 69.70, respectively molar rotation was reported as - 5690 (65) and - 17690 (67), and the molar rotation per tartaric acid unit was determined to be — 1900 (65) and - 1970 (67), respectively. The use of bis(aryl ether) 64 allowed construction of tetrakis(aryl ether) 68, which, when treated with the bistosylate 66, afforded the corresponding dendron to be used for the preparation of the second generation dendrimers subsequent reaction with trisphenol 61 failed to give the desired material presumably due to steric and solubility problems. 

Fig. 1 Top Behavior of the electronic linear chiroptical response in the vicinity of an excitation frequency. Re = real part (e.g., molar rotation [< ]), Im = imaginary part (e.g., molar ellipticity [0]). Without absorption line broadening, the imaginary part is a line-spectrum (5-functions) with corresponding singularities in the real part at coex. A broadened imaginary part is accompanied by a nonsingular anomalous OR dispersion (real part). A Gaussian broadening was used for this figure [37]. Bottom Several excitations. Electronic absorptions shown as a circular dichroism spectrum with well separated bands. The molar rotation exhibits regions of anomalous dispersion in the vicinity of the excitations [34, 36, 37]. See text for further details...

Glycine Change in Molar Rotation (A[4]) as a Function of Solvent-Solute Distance... 

Fig. 25 The sign of the molar rotation (MR) and of the CD of the first three electronic transitions of benzene induced by a point charge of -O.le located 1.3 A above the plane of the ring. The distortions along the edges of the sectors (particularly evident in the center of the ring) are caused by the coarseness of the grid. MR calculated with PBEO/SVP, CD with CC2/SVP. Data to prepare the figure were taken from [155]...

Fig. 32 SOS molar rotation of alanine in the AlaH+1 cationic and zwitterionic AlaZ0 form, as a function of how many states are included in the SOS. Calculations were performed at the B3LYP/ aug-cc-pVDZ level of theory. Data to prepare the figure were taken from [136]...

Fig. 38. The agreement between simulated and experimental CD spectra for the PD complex was very good after a red-shift of 0.25 eV was applied to the excitation energies. Analysis of the computed spectrum showed the intense bands to originate predominately from n-to-n transitions within an extended n framework of the phosp-hole-helicene ligands. Unlike initially expected, the various bands in the CD spectrum cannot be assigned to transitions centered separately on the helicene and phosphole moieties, respectively. The experimentally measured molar rotation of the Pd complex was 23.1 103 deg cm2 dmol 1 2% in dichloromethane. For an analogous Cu complex it was 13.1 103 2%, a staggering 104 deg cm2 dmol 1 lower.

M] or [rh] Molecular rotation, defined as [a] x MW/100. Specific rotation corrected for differences in MW. The symbol [M] and the term molecular rotation are now deemed incorrect, and the term molar rotation denoted by [d ] is preferred. meso- Denotes an internally compensated diastereoisomer of a chiral compound having an even number of chiral centres, e.g., me o-tartaric acid. Formally defined as an achiral member of a set of diastereomers that also contains chiral members, mutarotation Phenomenon shown by some substances, especially sugars, in which the optical activity changes with time. A correct presentation is, e.g., [a]n ° + 20.3 -101.2 (2h)(c, 1.2 in HjO). 

---