The result of a typical VCD measurement includes two vibrational spectra of a sample, the VCD spectrum and its parent infrared absorption spectrum. These can be used together to deduce information about molecular structure. The principal application of VCD is structure elucidation of biologically significant molecules including peptides, polypeptides, proteins, nucleic and amino acids, carbohydrates, natural products and pharmaceutical molecules, as well as chiral molecules of interest to organic or inorganic chemists. It has growing potential as a sensitive, non-invasive diagnostic probe of chiral purity or enantimeric separation that is critically important in the synthesis and manufacture of chiral drugs and pharmaceutical products. As a result, VCD is becoming an important tool for studying different levels of molecular structures.
6.6.2 VCD Theory and Spectral Interpretation VCD is defined simply as the difference in the absorbance of chiral sample between left and right circularly polarized infrared radiation,
where σ is wavenumber (cm-1). If the pathlength and concentration are known, VCD can be expressed in terms of the difference in absorptivity according to the well-known Bouguer-Beer-Lambert Law:
Optionally, the sign and magnitude of VCD is conveniently expressed as the dimensionless anisotropy ratio g, defined as the ratio of the experimental VCD band absorbance to the experimental infrared band absorbance. This ratio g, can be further expressed theoretically as follows:
where μ and m are respectively the electric and magnetic dipole transition moments, given in Cartesian component notation. The repeated Greek subscripts are summed over the coordinate directions x, y and z. VCD arises from the combined effect of linear (electric-dipole) and circular (magnetic-dipole) oscillation of charges during vibrational motion, whereas ordinary infrared absorption is sensitive only to the linear oscillation of charge. The physical process associated with VCD can be illustrated in terms of fundamental transitions between vibrational energy levels of the ground electronic state. VCD is associated with simple one-photon quantum transitions induced by left or right circularly polarized radiation.
VCD spectra can be interpreted on several levels. The simplest is the empirical level, in which VCD features are associated with a region of vibration in a molecule of known absolute configuration. A more sophisticated level of empirical analysis is the statistical approach using, for example, principal components (PC) and factors analysis. In this approach, a set of spectra of samples with known characteristics is used as a training set; these spectra are then reduced to a series of orthogonal PCs of decreasing significance. An unknown spectrum can then be decomposed, or factored, into the set of PCs, and by the relative PV weighting coefficients it can then be correlated with spectra of known structural or conformational features. Beyond empiricism is spectral interpretation by model calculations. The most powerful and successful approach so far to the interpretation of VCD spectra is through ab initio quantum-mechanical calculations. For molecules with well-defined conformational structures, ab initio VCD calculations can be carried out with excellent correspondence to the experimental spectrum. Better results can be obtained through the use of density functional theory when electron correlation is included.
6.6.3 VCD Experiment and Data Process VCD spectra can be measured directly on a polarization modulation-based Nicolet Nexus VCD module. This module is coupled with a Nicolet Nexus dual-channel FT-IR spectrometer. The optical setup of the VCD is identical to that of the VLD as shown in Figure 6.15. The infrared light source from the spectrometer is directed onto the focus lens of the module, passing through a linear polarizer, a PEM-90 operating at 50kHz, and then through the sample under study. A liquid-nitrogen-cooled MCT detector with focus lens assembly is used since it is fast enough to follow the high frequency of polarization modulation. The processing electronics include a dedicated SSD demodulation with a large dynamic range to demodulate the differential signals at the modulation frequency of the PEM (e.g. 50kHz) and two digitizers recording both the raw (non-demodulated) signal from channel A (IDC) and the demodulated signal from channel B (IAC). Prior to spectral presentation, built-in deHaseth phase correction in OMMNIC is used for Fourier transformation.
Since VCD is based on a transmission measurement, Equation (6-16) can then be expressed in terms of transmitted optical intensity for left circularly polarized radiation IL, and right circularly polarized radiation IR,
where v is mirror velocity of the FT-IR interferometer, t is the time constant of the lock-in amplifier or the demodulator used in the experiment, and J1[αM0(σ)] is the first order Bessel function that describes the wavenumber dependent PEM modulation efficiency. Substituting the ratio of Equation (6-21) over Equation (6-20) into Equation (6-19) gives the theoretical expression for the VCD raw spectrum of a sample,
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