A simple model for the orientational correlation functions of dipolar and induced-dipolar absorptions in liquids

Abstract

The Mori continued fraction approximation to the orientational memory function is used to evaluate the corresponding orientational correlation function C(t) of dipolar and induced-dipolar absorptions in liquids. In the former case the exponential part of C(t) is the Fourier transform of the relaxational Debye absorption, the short time (non-exponential) part of which is the Poley absorption characteristic of dipolar liquids in the far infra-red. In the latter case, the corresponding C(t) is one of both molecular orientation and interaction, having a correlation time typically of much less than 1 ps. This is approximately the inverse width at half peak height of the broad induced-dipolar absorptions which characterise $\text{non}$-dipolar liquids in the far infra-red (1–250 cm⁻¹). This correlation function never becomes exponential, and is damped to zero in approximately the same interval of time as its memory function - meaning that the temporary dipole absorbs only during its short lifetime. The memory function is the correlation function of the random, fluctuating torque forces experienced by any molecule in the system, and is not a pure exponential. Therefore, this model is non-Markovian.