minor empirical modifications provide a reasonable way to do this
3.6 Conclusions and Outlook
Figure 3.30:(facing page) Difference spectra of key absorption bands calculated based on an-harmonic constantsxij. Canonical ensembles of the indicated temperatures were assumed and phenomenological line shape functions fitted to the observed spec-tra were used. The geometry of ON O N3
H
is given in Appendix B. Selected experimental data ( ) are shown for comparison. The dashed spectra shown for the amide band were obtained by successively setting the “temperature” of the modes belonging to the listed groups to a room temperature value of 296 K; e.g. in the spectrum titled “+ Delocalized modes at RT”, all but the azulene modes are at room temperature.
Additionally setting the neighboring ethyleneoxy group to room temperature has a visible, but small effect, which is – surprisingly – larger than that of adding the ethy-lene group (i.e. setting the entire polyethyethy-lene glycol chain and azide group to room temperature). “Cooling” the amide group itself yields a stronger response due to the larger anharmonic constants, while the methylene group has an effect on the amide mode similar to the ethyleneoxy group. The largest effect was achieved by decreasing the temperature of the modes classified as delocalized, which is owed to their large number and – on average – low frequencies. The “cooling” of all of these groups trig-gers a blue shift of the amide absorption, which results in a substantial shift of the positive signal to higher frequencies, but a much smaller one of the bleach.
This is the opposite of the experimental result in two respects: a red shift for pre-sumably less randomized situations and a larger shift upon randomization for the bleach than for the positive part of the signal was observed in the experiment, while the model suggests a blue shift upon partially cooling the system and the shift is large for the positive part of the signal, while it is hardly visible for the bleach. These pro-cesses are thus either more subtle than assumed or the premises of the modeling are wrong.
3.6 Conclusions and Outlook
In this section, the findings of this study shall be summarized with regard to the energy loss of the azulene unit, energy transfer along molecular chain structures, IR bands as sensors for vibrational energy, and the description of IVR processes. The finding of earlier studies[7, 69, 75, 80, 81] that the loss of energy from the azulene unit tends to sat-urate with increasing chain length, has generally been confirmed. However, instead of the earlier assessment that energy loss rates for chains with more than four bonds
Chapter 3. Intramolecular vibrational energy transport
is “essentially constant”[7], the data of this study rather supports an ongoing asymp-totic decline even for longer chains. While the earlier conclusion was essentially based on only two data points and supporting MD simulations, the result of the newer ex-periments does not strictly contradict it, considering that the molecular systems and experimental techniques employed differed substantially.
With regard to the signal arrival time at the terminal group of the chain, results obtained simultaneously by the Rubtsov group[8, 63] were confirmed as well. Signal arrival times were found to be proportional to chain length and in good quantitative agreement, leading to the conclusion that energy transfer proceeds ballistically. The presented results differ in two respects from the Rubtsov group’s findings: First, there is a hint at a fall-off behavior from proportionality for very short chains, as found in earlier studies[7] and MD simulations[69]. However, an insufficient number of chains and insufficiently short chains were investigated in this study to substantiate this hint.
Second, polyethylene glycol based chains were found to exhibit systematically larger signal arrival times than found by Linet al.[8, 63]by a constant offset. Most likely, this is due to the transfer of vibrational energy from the modes of the azulene moiety to the chain being statistically unfavorable compared to the transfer from a single oscillator as in their experiments. At the same time, values for alkyl-based chains exhibited the same increase of arrival time with chain length, but were at the lower limit of the values reported by Linet al.and thus offset from the polyethylene glycol-based chains by a nearly constant amount. Earlier studies[7, 75, 81] concluded that this was due to a disturbance of strongly delocalized normal modes by hetero atoms in the chain.
Closer inspection of the spectral response of the bands used for monitoring en-ergy flow revealed that the assumption of nearly canonical enen-ergy distribution seems to hold well only for the azulene ring distortion mode. Amide I, azide asymmetric stretching, and carbonyl bands, on the other hand, show surprisingly little shift of the absorptions of the vibrationally excited molecules, indicating that a statistical distri-bution of energy in the vicinity of these modes is probably not reached, but instead transfer of energy of a limited number of some excited modes to the solvent prevails.
The absorption of the amide I mode exhibits a particularly interesting shift after pass-ing the maximum of its signal, which could not be explained on the basis of the shifts induced by anharmonic coupling to other groups of the respective molecules. It is conceivable that a closer inspection of individual modes instead of groups of modes is necessary, but the signal generally underscores the aptitude of the amide linker group to reflect the progress of IVR.
A simple diffusive-like model of energy transport has been discussed. Its
deficien-3.6. Conclusions and Outlook cies in describing the temporal profile of the experimental signals can well be explained by the difficulty to make sound assumptions about the nature of the transport. The fast rate of energy transport found, again, suggests it is not of diffusive, but rather of bal-listic nature, as they are similar to the value of 450 m/s reported earlier[8]. The fact that energy transport in alkyl chains on gold surfaces is more than twice as fast (950 m/s[68]) might be owed to a greater degree of order in these systems.
Future research should focus on establishing a mode-based treatment of both the process of IVR in medium-sized and large molecules and its monitoring by IR spec-troscopy. The approach taken here to analyze the spectral response of the different marker bands seems promising but requires improvement in several respects. First, anharmonic constants need to be determined reliably including a possible conforma-tional distribution. It seems desirable to limit conformaconforma-tional flexibility in order to reduce uncertainties, and it is certainly necessary to study the dependence of the an-harmonic constants on method and basis set. Second, a better understanding of the energy distribution is required. Simulations of the energy redistribution dynamics can help to determine how the energy distribution most likely differs from a canonical one.
Recent progress has been achieved in this regard based on Marcus’ electron transfer theory.[100] Third, experimental investigation of the anharmonic interactions between vibrational modes, as well as better-defined techniques of excitation, for instance of in-dividual vibrational modes, are needed. Recent studies using 2DIR spectroscopy have made progress in both of these directions.[66, 101]
Chapter 3. Intramolecular vibrational energy transport
Chapter 4
Interactions in weakly bound noble gas–halide clusters
In an effort to enhance the understanding of IVR in the azulene compounds which were investigated experimentally for this work, a computer program was designed to allow for the easy implementation of arbitrarily complex potential energy functions.
The program is documented in section D.3. It was intended to be also employed in the analysis of instantaneous normal modes of the azulene derivatives described in the previous chapter, because the use of more complex potentials, such as the ones devel-oped by Steele[161–163], in molecular dynamics programs is often not straightforward.
These efforts remained unfinished.