In this exercise we will use the expressions given in section 9.6.3 on page 271 and in
Question:
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(b) Assuming that the molecule is in the fast motion limit, so that J(ω) = 2τc, and taking τc = 20 ps, show that the transition rate constants have the following values (all in units of s-1): W1(1) = 0.0503, W1(2) = 0.0503, W2 = 0.201, W0 = 0.0335. Then, using Eq. 9.19 on page 271, show that Rz (1)= 0.335, Rz(2) = 0.335 and σ12 = 0.168 (all in units of s-l).
(c) Use Eq. 9.20 on page 272 to calculate, Rz(1), Rz(2) and σ12; you should, of course, obtain the same values as you did in the previous part.
(d) Use the expressions in section 9.8.5 on page 296 to determine Rxy(1) and R(2)xy ; you should find that both have the value 0.335 s-1.
(e) Comment on the values you have calculated, and the comparison between them.
(f) The next task is to repeat all of these calculations for a correlation time of 500 ps, and for a magnetic field strength of 11.74 T (a proton Larmor frequency of 500 MHz). Such a correlation time places the motion well outside the fast motion limit, so you will need to compute the reduced spectral densities explicitly for each frequency. First, show that the proton Larmor frequency is 3.140 x I09 rad s-1, and the use this to show that J(ω0) = 2.88 x 10-10 s, j(2ω0) = 9.20 x 10-11 s and j(0) = 1.00 x 10-9 s. To compute j(ω), co must be in rad s-1. Use these values for the reduced spectral density, along with the value of b2 computed earlier, to show that Rz(1) = 2.025, Rz(2) = 2.025 and σ12 = -0.375, Rxy(1) = 3.41 and Rxy(2)= 3.41, all in units of s-l.
(g) Comment on the values you have obtained for the longer correlation time, and compare them with those obtained in the extreme narrowing limit.
Step by Step Answer:
a The expression for b is from section 963 on page 271 b The expressions for the transition rate con...View the full answer
