The azulene ring distortion mode

Spectral evolution

Figure 3.10 shows a number of transient spectra of the azulene ring distortion mode obtained in CH2Cl2. It should be noted that while a good baseline correction could be performed for the higher frequency edge of the spectra, the lower frequency detection range does not provide any points or intervals that would allow for the application of the customarily used procedures described in section 1.3. This is due to overlapping of the bleach of the amide II mode starting around 1540 cm⁻¹with the absorption of the vibrationally hot azulene mode. Accordingly, spectral information in said region has to be considered somewhat less reliable than in the higher frequency region.

The earliest spectrum indicates complete change in absorption characteristics of

Chapter 3. Intramolecular vibrational energy transport

1520 1530 1540 1550 1560 1570 1580 1590 1600

−1

−0.8

−0.6

−0.4

−0.2 0 0.2

˜ ν/cm⁻¹

∆A/mOD

FTIR 1.2 ps

2.6 ps 5.2 ps 8.2 ps 11.1 ps 16.8 ps 26.6 ps 43.0 ps 102.0 ps

Figure 3.10:Transient difference spectra of the azulene ring distortion absorption of

O

N O O N3

H

in CH₂Cl₂after excitation at 610 nm.

the excited species previously causing the original absorption of the ring distortion mode, as is obvious by its near-identity with the stationary spectrum. Assuming a great frequency shift upon electronic excitation, a partial explanation may be due to the ongoing relaxation from theS1state^[83–85], which was reported to be bi-exponential with the slower component having a time constant of about one picosecond for pure azulene in cyclohexane^[85]. Much of the population which was initially excited elec-tronically, however, appears to be highly excited vibrationally after its return to the electronic ground state, as indicated by a tremendous red-shift ranging far into the ab-sorption of the amide II mode. The room temperature abab-sorption of the latter is itself bleached due to harmonic energy flow (see subsection 3.1.3) and anharmonic coupling to excited modes (see subsection 3.3.1). It is not quite clear, if the small shoulder at 1590 cm⁻¹ is due to impurities. In either case, there is practically no blue-shifted ab-sorption of the azulene ring distortion mode, hinting at all anharmonic constants being

3.3. Investigation via UV pump IR probe spectroscopy less than zero for this mode.

As energy transfer beyond harmonic energy flow within the molecule itself and to a lesser degree also to the solvent progresses, the bleach of the amide II mode appears to increase. In part, however, this is certainly owed to the cooling of the azulene unit and the consequent return of the absorption of the ring distortion mode to its original position, rather than energy transfer to the amide unit. In the last spectrum, nearly full recovery of the room temperature vibrational population seems to be achieved.

The very small residual signal reflects an overall heating of the sample solution by the release of energy from the excited solute to the solvent. This has been shown to amount to less than a Kelvin under similar conditions. The magnitude of the residual signal compared to the direct excitation is owed to the greater number of participating molecules: all within the focus of the probe laser versus only a small fraction of those in the pump lasers focus in the case of direct excitation.[1, 72, 78]

Temporal evolution

Kinetic traces were obtained by picking the minimum signal value (within a suitable spectral window containing the azulene ring distortion mode) at each delay. In order to compare the different velocities of vibrational cooling, an asymmetric sigmoidal

“growth and saturation” function first described by Gompertz^[120]of the form f(t) = A exp

−exp γ(t0−t)+c (3.6)

was used. This function provides sufficiently many parameters to fit the data reason-ably well in an empirical manner. It is, of course, not intended to be understood to have any theoretical justification by the actual microscopic processes taking place in IVR and VER, but rather serves as a phenomenological description.

Naturally, picking the minimum value will result in negative values due to noise even after the actual signal has vanished. Accordingly, the offsetcwas subtracted from both the data and the fit result. While this also eliminates the temperature rise, as dis-cussed in section 3.3.2, the latter is fairly small and nearly of the same magnitude as the noise of the signal. This makes a better treatment, i.e. the separation of the temper-ature rise from the IVR signal, infeasible. Furthermore, both fit and experimental trace were normalized using the amplitude of the fitA. The result of applying this protocol to all the data obtained is shown in Figure 3.11.

Note should be made that there is no immediate quantitative relationship between

Chapter 3. Intramolecular vibrational energy transport

Figure 3.11:Kinetic traces of the azulene ring distortion mode. Measured in CH2Cl2 using an excitation wavelength of 610 nm.

3.3. Investigation via UV pump IR probe spectroscopy the minimum signal value on the one hand, and the average energy content or tem-perature or any other physically relevant quantification of the energy content of the observed molecule on the other (cf. subsection 3.3.1). However, as the initial state is well-defined by the preparation and identical for all substances – namely the excita-tion and subsequent internal conversion of the azulene moiety – any fixed fracexcita-tion of the magnitude of the respective initial signal is suited for quantifying the progress of vibrational cooling. Due to the same original value, i.e. the value at t = 0, this frac-tion will also represent the same energy content in all the species, provided that the observed mode is not coupled strongly to any modes not common to all substances (i.e. localized outside the azulene moiety) and that IVR leads to randomization on a sufficiently fast timescale.

With an exponential rate law for the loss of energy to the solvent^{[121, 122]}, this frac-tion value is directly proporfrac-tional to the time constant of VETτ_VET. The chosen func-tion Equafunc-tion 3.6 makes it fairly simple to extract the half-step valuet1/2 defined by the following equation:

f(t1/2) = ^A 2 +c

or simply by reading off the abscissa value corresponding to an ordinate value of one half in the normalized and offset-corrected graph.

Comparison of substances

The value of t1/2 = (44.0 ± 1.5) ps for azulene is substantially larger than those re-ported for the cooling constant of azulene in comparable solvents (e.g. 14.6 ps in ace-tonitrile) when pumped between 580 and 600 nm^[121]. The value given by Schultz et al. of (19 ± 3) ps for azulene in CH2Cl2[122], on the other hand, was not calibrated to reflect energy loss, but rather decay of spectral signal at 740 nm after pumping at 590 nm. Certainly, however, thet1/2values are larger than the characteristic decay time, meaning that they indicate a point at which the energy content of the azulene unit has arrived at substantially less than 1/eof its initial value.

As vibrational ground state recovery is measured here, the explanation of the wavelength dependence of relaxation times^{[122, 123]} holds here as well: a decrease in temperature affects the occupation of high energy vibrational states more strongly than that of states lower in energy. Here this does of course include states coupling to the observed mode. The spectra presented in Figure 3.10 illustrate this effect, alongside

Chapter 3. Intramolecular vibrational energy transport

0 3 7 9 11 12 15 24

10 15 20 25 30 35 40 45

O N H O O

N

H O O

N O O O N3

H

O

NOOOOOON3

H

O

N O O N3

H O

N O N3

H O

Number of bonds t1/2/ps

Figure 3.12:Comparison of the t1/2 value of the azulene distortion mode for all substances investigated. All measurements were conducted in CH₂Cl₂ using a pump-wavelength of 610 nm. represent values extrapolated using the value of azulene and assuming proportionality oft⁻_1/2¹to the number of vibrational degrees of free-domn_vib.

with the initial lag time of the kinetic traces of Figure 3.11.

In Figure 3.12, the t1/2values for all the substances investigated are compared. As was already evident from Figure 3.11, longer aliphatic residues tend to speed up the loss of energy to the solvent. In a very naive picture, neglecting possible resonances of solvent and solute vibrations as well as the nature of the energy distribution among the vibrational degrees of freedom of the solute, one might assume this energy transfer to be more or less proportional to the number of vibrational degrees of freedom n_vib. More sophisticated descriptions might include the size of the “surface” of the molecule exposed to the solvent and thereby the probability of collisions with the solvent. This, however, would either require additional assumptions on the specific conformation of the molecule – or rather distribution of conformations in many cases – while not promising substantially improved insight at the same time.¹

Assuming that energy transfer to the solvent is described best by the number of

1A very simple-minded approach assuming that a cylindrical shape of the molecule and thus t1/2 ∝ (a+`)<sup>−1</sup>, where` is the approximate length and ais the approximate diameter of that cylin-der (assuming the molecule is not coiled or folded), leads to rather poor results.

3.3. Investigation via UV pump IR probe spectroscopy vibrational degrees of freedom of the solute rather than the number of collisions with the solvent, and further asserting thatt1/2is a good quantification of that process as laid out in section 3.3.2, the value oft1/2of azulene can be used to predict those of the other substances. In Figure 3.12, the results are depicted by . While the agreement with the first three experimental data points is remarkable, it is simultaneously obvious that, while the asymptote of the prediction is zero forn_vib →∞, the real asymptote appears to be around 14 ps.

This divergence may well be interpreted to reflect – beyond the shortcomings of the naive assumptions – the inability of a number of oscillators to transfer energy to the solvent as they are initially not excited. Ultimately, this is the signature of the initial energy distribution following the internal conversion of the azulene moiety as well as of the ensuing competition between IVR and VET.

It has been found by the Schwarzer group[7, 69, 75, 81, 82] that energy transfer from a vibrationally excited azulene moiety to an anthracene unit via an aliphatic chain incurs congestion along the first four atoms of the chain. The present results confirm these findings, as for longer chains than ^O the values oft1/2 are almost at the apparent value of the asymptote. This implies that IVR up to about four or five bonds from the azulene moiety is very fast – and energy can be transferred to the solvent by those atoms practically at the same rate as by the azulene moiety itself – but then slows and is finally in competition with VET.