Concept of correlation time, autocorrelation functions, and spectral densities of the tunneling jumps through the potential barrier

Abstract

The concept of the tunneling correlation time according to Schrö dinger is presented. This tunneling jumps and the over the barrier jumps (Arrhenius type) correlation times are applied to calculate the autocorrelation functions and spectral densities of a complex motion. Complex motion means that the relaxation vector performs more than one motion. Two examples of temperature dependencies of a complex motion in a wide temperature regime are given. One example concerns the complex motion consisting of the fast hindered rotation of the methyl group which participates additionally in a slower isotropic motion. The other example concerns the complex motion consisting of the jumps of the proton-proton vector between the two sites in a double hydrogen bond as well as the jumps between other two equilibrium sites (librations of the whole molecule). The latter motion is assumed as slower than the concerted motion of two protons in a double hydrogen bond. In both examples the tunneling jumps are considered as a component of a complex motion. However, only the tunneling jumps of the faster motion are taken into account. Why the tunneling jumps of the slower motion are neglected is explained. The tunneling spectral density dominates only at low temperatures and contributes to the spectral density of the complex motion at intermediate temperatures up to T tun temperature. The sense of T tun temperature is explained. A comparison is made with the other theories of tunneling correlation time. 2012 Wiley Periodicals, Inc. Concepts Magn Reson Part A 40A: 66-79, 2012.

Complex dynamics of 1.3.5-trimethylbenzene-2.4.6-D3 studied by proton spin–lattice NMR relaxation and second moment of NMR line

“…The jumps over the barrier are characterized by Arrhenius correlation time, while the tunnelling jumps can be characterized by the Schrödinger correlation time [16,18]. The correlation time of C 3 jumps over the potential barrier follows the Arrhenius dependence:…”

“…The respective spectral densities of a complex motion consisting of two component stochastic motions, that is over the barrier and tunnelling jumps in triple potential are [16,18] …”

“…The approach assumed in papers [16][17][18] is based on the method of calculation of the total correlation function for a complex motion [15]. The C 3 motion of the methyl group is composed of the jumps over the barrier and through the barrier, taking place with different probabilities.…”

“…The tunnelling jumps through the barrier and jumps over the barrier cause the transport of mass between the same equilibrium sites, but they are based on different correlation times, therefore in the spectral density calculations they have to be treated as components of a complex motion. Following the Woessner theoretical assumptions such equations for the total spectral density of complex motion have been derived [16,18] and have been applied in present paper. The long values of T 1 at lowest temperatures will be explained and correlated with the reduced values of the second moment in this temperature regime.…”

Nuclear spin relaxation in liquids and gases

“…Latanowicz 37 investigated the concepts of correlation time, autocorrelation function and spectral densities in the context of the tunnelling jumps through the potential barrier, superimposed on another type of motion. Two specific case were discussed: hindered methyl rotation combined with isotropic overall reorientation and jumps within a double-well hydrogen bond potential in connection with librations of the whole molecule.…”