Correlation function molecular absorption spectroscopy

Now we can show the explicit relation with experiment. What is usually measured in spectroscopic or scattering experiments is the spectral density function /(to), which is the Fourier transform of some correlation function. For example, the absorption intensity in infrared spectroscopy is given by the Fourier transform of the time-dependent dipole-dipole correlation function <[/x(r), ju,(0)]>. If one expands the observables, i.e., the dipole operator in the case of infrared spectroscopy, as a Taylor series in the molecular displacement coordinates, the absorption or scattering intensity corresponding to the phonon branch r at wave vector q can be written as (Kobashi, 1978)... 

An IR spectrum reflects the Fourier transform of the molecular dipole moment. The absorption coefficient, a(P) measured by IR spectroscopy is given by Eq. (6), where the infrared spectral density is the Fourier transform of the time-correlation function for the dipole moment [11] ... 

A useful and common way of describing the reorientation dynamics of molecules in the condensed phase is to use single molecule reorientation correlation functions. These will be described later when we discuss solute molecular reorientational dynamics. Indirect experimental probes of the reorientation dynamics of molecules in neat bulk liquids include techniques such as IR, Raman, and NMR spectroscopy. More direct probes involve a variety of time-resolved methods such as dielectric relaxation, time-resolved absorption and emission spectroscopy, and the optical Kerr effect. The basic idea of time-resolved spectroscopic techniques is that a short polarized laser pulse removes a subset of molecular orientations from the equifibrium orientational distribution. The relaxation of the perturbed distribution is monitored by the absorption of a second time-delayed pulse or by the time-dependent change in the fluorescence depolarization. 

Fairly good agreement exists between the calculated value of 1682 cm-1 and the experimental value of 1650 cm-1. Based upon the Hooke s law approximation, numerous correlation tables have been generated that allow one to estimate the characteristic absorption frequency of a specific functionality [3], It becomes readily apparent how IR spectroscopy can be used to identify a molecular entity, and subsequently to physically characterize a sample or to perform quantitative analysis. 

Infrared (IR) spectroscopy is probably the quickest and cheapest of the spectroscopic techniques in determining the functional groups of the sample. The samples can be soUds, liquids, or gases and can be measured in solution or as neat liquids mulled with KBr or mineral oil. Comparison of IR spectra of substances of known structure has led to many correlations between wavelength (or frequency) of IR absorption and features of molecular structure. Certain structural features can easily be established. For example, in an organic compound that contains only C, H and O, the oxygen can only be present as C=0,0—H, or C—O—C or a combination of these, such as the ester or carboxylic acid group. 

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