Vibrational transitions corresponding time-dependent

Let us assume that a variable A(t) is coupled to the reaction coordinate and that (A) is its mean value. If a measurement of some property P depends on (A), but not on the particular details of the time dependence of A(t), then we will call it a statistical dependence. If the property P depends on particular details of the dynamics of A(t) we will call it a dynamical dependence. Note that in this definition it is not the mode A(t) alone that causes dynamical effects, but it also depends on the timescale of the measured property P. Promoting vibrations (to be discussed in Sections 2-4) are a dynamic effect in this sense, since their dynamics is coupled to the reaction coordinate and have similar timescales. Conformation fluctuations that enhance tunneling (to be discussed in Section 5) are a statistical effect the reaction rate is the sum of transition state theory (TST) rates for barriers corresponding to some configuration, weighted by the probability that the system reaches that configuration. This distinction between dynamic and statistical phenomena in proteins was first made in the classic paper of Agmon and Hopfield.4 We will discuss three kinds of motions ... 

The validity of Eq. (15.11) even at the limit Na Nm means in fact that for harmonic oscillators relaxing in a heat bath there exists a closed equation for the mean energy. This is intimately connected with the linear dependence of transition probabilities on the vibrational quantum number (see Eq. (14.1)) and implies that the energy relaxation rate is independent of the initial distribution of harmonic oscillators over vibrational states. Still another peculiarity of this system is known the initial Boltzmann distribution corresponding to the vibrational temperature Tq =t= T relaxes to the equilibrium distribution via the set of the Boltzmann distributions with time-dependent temperatures. If (E ) is explicitly expressed by a time-dependent temperature, this process is again described by Eq. (15.11). 

Three dipole components occur Pind(< inc)> liind(< inc < vib) and p.i d(o)inc + < vib)> which correspond to Rayleigh, Stokes Raman and anti-Stokes Raman scattering, respectively. The molecular polarizability amoiecuie is a function of the proper molecule. It is a tensor some of its components can vary during the vibration of nuclei around their equilibrium position in the EM field of the electrons. In a quantum mechanical treatment of the polarizabilify and in using a simplified second-order time-dependent theory, the Raman transition between i> and f> stales can be expressed by the tensor element... 

Figure 33 illustrates the schematic set up for a DIRLD spectroscopy experiment. A small-amplitude oscillatory tensile strain is applied to a sample, and the time-dependent fluctuations of IR dichroism signals corresponding to the dynamic reorientations of electric dipole transition moments associated with the molecular vibrations of various constituent chemical groups of the system induced by the applied strain are monitored with a pair of polarized IR beams oriented in directions parallel and perpendicular to the strain direction. Under a small-amplitude dynamic strain, the time-dependent dichroic difference can also be treated as the sum of a quasistatic component AA(v) and a dynamic component AA(v, t) induced by the strain s(t), similar to the stress response described in eqn [25]. 

---