Correlation characteristics of rotational relaxation

If the resolving capacity of the instruments is ideal then vibrational-rotational absorption and Raman spectra make it possible in principle to divide and study separately vibrational and orientational relaxation of molecules in gases and liquids. First one transforms the observed spectrum of infrared absorption FIR and that of Raman scattering FR into spectral functions 

The following correlation functions are found by the Fourier transformation of spectral functions (2.1), (2.3) and (2.4)  

Here a = Spafi is the average value of the polarization tensor of the molecule, / = a —la. being its anisotropy, and fi the dipole moment of the molecule. We assume that the concentration of active molecules in the gas mixture or liquid solution is so small that intermolecular coupling may be neglected. 

Although Ki and Ki are defined by physical quantities of different nature, their time evolution is universally determined by orientational relaxation. This discussion is restricted to linear molecules and vibrations of spherical rotators for which / is a symmetric tensor / = fiki- In this case the following relation holds 

Here u is a unit vector oriented along the rotational symmetry axis, while in a spherical molecule it is an arbitrary vector rigidly connected to the molecular frame. The scalar product u(t) (0) is cos 0(t) in classical theory, where 6(t) is the angle of u reorientation with respect to its initial position. It can be easily seen that both orientational correlation functions are the average values of the corresponding Legendre polynomials  

---