Bandwidths

Abstract

The shapes of vibrational bands in solution can provide detailed information about the dynamics of the system. The band shape and the dynamics are related by the Fourier transform relation between frequency and time. The shape is dependent on whether the band is homogeneously or inhomogeneously broadened. Modern vibrational “echo” experiments can distinguish between the two. Most theories of band broadening assume homogeneous broadening. Various dephasing mechanisms contribute to the homogeneous band shape, and the “echo” experiments can unravel – with some surprising results – these contributions. Under appropriate circumstances, dynamic nuclear magnetic resonance (NMR) can provide detailed information about the rate of chemical exchange processes on a “slow” timescale. Under more restrictive conditions, the change in vibrational band shape with temperature can provide the same information but on a “very fast” timescale.

A Hyphenated Approach Combining Pressure-Decay and In Situ FT-NIR Spectroscopy to Monitor Penetrant Sorption and Concurrent Swelling in Polymers

“…The NIR spectrum of condensed CO 2 , isolated by difference spectroscopy, displays three sharp peaks at 5073, 4954, and 4824 cm –1 , corresponding to the Fermi triad with frustrated rotovibrational transitions. The three lineshapes are coincident and, according to the general theory of vibrational line profiles, , can be described by the sum of a Gaussian and a Lorentzian component both centered at the peak maximum. The appropriateness of the theoretical model to simulate the 4954 cm –1 band shape is demonstrated in Figure , which also confirms that the proposed data analysis isolates correctly the signal of interest.…”

Infrared Dynamics of Iron Carbonyl Diene Complexes

“…They objected to the transfer of Bloch equation use from NMR to IR exchange processes. For Bloch equations to be applicable, they state, “The transfer between the two sites must be fast enough to cause no change in the phase of the density matrix elements during the transfer.” This means that as the group moves from site to site, such as by a rotation, the time taken for this motion (i.e., the transit time) must be very short when compared with the reciprocal of the spread of frequencies that characterize the reaction . In the case of NMR, we can imagine two peaks separated by 10 Hz; the time scale is 1/10 s. With a transit time of, say, 10 –12 s, the requirement is satisfied.…”

Ultrafast Wiggling and Jiggling: Ir2(1,8-diisocyanomenthane)42+

“…(Homogeneous IR bandwidth Γ (in cm –1 ) = 1/π cT 2 , and 1/ T 2 = 1/2 T 1 + 1/ T 2 * + Γ or , where c is the speed of light, T 1 is the population lifetime of the v = 1 ν­(CN) level, T 2 * is the pure dephasing time, and Γ or is a contribution from orientational effects. ) − The homogeneous (Lorentzian) excited-state IR band shape and its large width essentially exclude the possibility that pure dephasing is the predominant broadening mechanism because unrealistically large (>100 cm –1 ) fast frequency fluctuations would be required. Hence, we found it necessary to consider all three contributing terms, T 1 , T 2 *, and Γ or .…”