A donor-acceptor pair for the real time study of vibrational energy transfer in proteins
3.3 Investigation via UV pump IR probe spectroscopy
3.3.4 The azide asymmetric stretching mode and the carbonyl mode
Spectral evolution of the azide asymmetric stretching mode
In four substances used for this study, an azide group was employed as a sensor to monitor the progress of IVR along a polyethylene glycol type chain. With regard to the frequencies of the three main azide modes, symmetric stretching (ν1), bend-ing (ν2), and asymmetric stretching (ν3), the vibrational spectrum of aliphatic azides generally resembles more that of the azide anion than that of the corresponding radi-cal[103, 125, 126]. The absorptions of the symmetric stretching and the bending vibration lie in the fingerprint range[103, 126]. This fact makes them unsuitable for IVR monitoring using difference IR spectroscopy, because this region is opaque as a result of solvent absorptions and congested by various other absorptions in theN-(azido-oligo ethylene glycol)-2-(1-azulenyl)-acetamides. Further, the intensity of the of the ν2 mode is pre-dicted to be very small[103]and would fall outside the spectrally available range of the apparatus used.
With the solvent chosen for this study, CH2Cl2, the asymmetric stretching vibration remains observable. Accordingly, it presents a natural choice for IVR monitoring. The data obtained for all of theN-(azido-oligo ethylene glycol)-2-(1-azulenyl)-acetamides differ mainly in their temporal and much less in their spectral characteristics. There-fore, only one compound, namely O
N O O N3
H
, shall be discussed here as an example.
Difference spectra recorded at various times are shown in Figure 3.15. Obviously, these spectra depict the superposition of red-shifted absorption (positive signal) and a bleached room temperature spectrum (negative signal), the latter with a peak around 2108 cm−1(cf. subsection 3.2.1). Starting with a non-zero signal, the maximum of both positive and negative signals is reached after a little more than seven picoseconds for this compound, followed by a much slower decay, leaving only little residual heat after one hundred picoseconds, which reflects a general rise in temperature of the sample solution (see section 3.3.2).
Chapter 3. Intramolecular vibrational energy transport
2020 2040 2060 2080 2100 2120 2140 2160 2180
−1
−0.8
−0.6
−0.4
−0.2 0 0.2 0.4 0.6
˜ ν/cm−1
∆A/mOD
FTIR 1.8 ps
4.0 ps 7.3 ps 10.2 ps 14.0 ps 21.3 ps 29.2 ps 100.9 ps
Figure 3.15:Transient difference spectra of the azide absorption of O
N O O N3
H
in CH2Cl2after excitation at 610 nm.
As in the case of the amide I mode (section 3.3.3), the overall integral of the signal is less than zero, indicating some decline in oscillator strength upon excitation of an-harmonically coupled modes. Contrary to the amide I and azulene modes, however, the transient spectra of the asymmetric azide absorption deviate considerably from the stationary spectrum, which could be explained by an appreciable number of anhar-monic coupling constants bearing positive sign. Also, there is no significant shift of the bleach as the signal evolves and thus no marked difference of the signatures of IVR and post-IVR energy distributions as in the case of the amide I mode. Finally, the signal at short delay times due to harmonic energy flow is, as expected, much smaller than in the case of the amide I mode.
It is noteworthy that the peak positions of both the bleach and the red-shifted posi-tive signal do not change significantly throughout the IVR and ensuing VER processes.
This differs substantially from what was observed for the azulene ring distortion mode
3.3. Investigation via UV pump IR probe spectroscopy and from what one would normally expect in a medium-sized molecule with a certain distribution of anharmonicity constants to occur (see, e.g. Figure 2.5): the gradual shift of the absorption as the internal energy of the molecule increases or decreases.
This can tentatively be interpreted as a limited number of specific modes (or even in-dividual vibrational states) coupling to the asymmetric azide mode at their respective anharmonicity constants. The signal of the azide mode itself would then reflect the population of these modes (states). As no shift of its spectral signal occurs, it would have to be inferred that energy is released to the solvent directly from these modes (or states) rather than redistributed within the molecule.
From the calculated anharmonic constants of the azide asymmetric stretching mode (subsection 3.5.5) it appears that it reflects only upon a very limited part of the molecule, i.e. essentially almost exclusively the azide group itself. Thus, it would not be a good reporter for IVR taking place throughout the remainder of the molecule, and the latter should not be ruled out based on the spectrum of the azide mode alone.
Spectral evolution of azulene ring distortion, amide I, and carbonyl mode of N-(oxo-alkyl)-2-(1-azulenyl)-acetamides
The characteristic absorptions evaluated for the N-(oxo-alkyl)-2-(1-azulenyl)-acetam-ides used in this work largely resemble those of the N-(azido-oligo ethylene gly-col)-2-(1-azulenyl)-acetamides, as exemplified in Figure 3.16 for
O N H O
. Much of what has been said regarding the asymmetric azide mode (section 3.3.4) ap-plies to the carbonyl mode as well: The initial signal due to harmonic energy flow is much smaller than for the amide I mode and there is no appreciable shift of the maximum negative signal that would allow to discern different stages of progress of IVR. Interpretation of such features on the low frequency edge of the absorption is questionable due to the overlapping bleach of the amide I absorption. As with the asymmetric azide absorption, some of the anharmonic constants seem to be greater than zero, since the high frequency portion of the bleach does not match the stationary spectrum. With regard to the integral of the difference signal, it seems that of all the absorptions considered, the electrically harmonic approximation is best fulfilled for the carbonyl absorption, considering that parts of the positive signal reach over into – and are consequently masked by – the negative signal of the amide I mode.
The features previously discussed of the azulene ring distortion mode and the amide modes are consistently found in N-(oxo-alkyl)-2-(1-azulenyl)-acetamides as
Chapter 3. Intramolecular vibrational energy transport
1520 1540 1560 1580 1600 1620 1640 1660 1680 1700 1720
−1.2
−1
−0.8
−0.6
−0.4
−0.2 0 0.2 0.4
˜ ν/cm−1
∆A/mOD
FTIR 1.0 ps 2.9 ps 5.4 ps 8.3 ps 15.0 ps
Figure 3.16:Transient difference spectra of
O N H O
in CH2Cl2 after excitation at 610 nm. The low frequency edge is somewhat unreliable as alignment of indi-vidual spectra was hampered by overlapping absorptions.
well. It is evident that the bleaches of the azulene ring distortion mode and also of the amide II mode are much stronger than those of the amide I and carbonyl modes, when comparing them to their respective stationary absorptions. To some extent this may be explained by “spatial overlap”[8, 98] with the site of excitation, i.e. the azu-lene moiety. However, electrical and mechanical anharmonicities would probably also lead to differing signal intensities in a thermalized ensemble, which would have to be considered as well. Finally, as hinted at above, the mismatch of the high frequency edge of the bleach of the amide I absorption can mostly be attributed to the redshift of the carbonyl absorptions, thus upholding the earlier assessment that most anhar-monic constants are less than zero for the amide I mode. Considering this overlap of both signals, it is not obvious whether the absorption of the mode shifts continuously upon excitation, as the azulene ring distortion mode, or remains fixed, as the azide
3.3. Investigation via UV pump IR probe spectroscopy
1540 1560 1580 1600 1620 1640 1660 1680 1700 1720 1740
−1.4
−1.2
−1
−0.8
−0.6
−0.4
−0.2 0 0.2 0.4
˜ ν/cm−1
∆A/mOD
FTIR 0.9 ps 1.9 ps 2.5 ps 5.0 ps 9.0 ps 13.3 ps 20.4 ps 28.3 ps 40.4 ps
Figure 3.17:Transient difference spectra of O in CH2Cl2after excitation at 610 nm.
asymmetric stretching mode.
The transient spectra of O shown in Figure 3.17 are not as ambiguous, on the other hand, and a shift in the positive peak – and thus of the “hot” absorption spectrum – of the carbonyl mode at 1714 cm−1 (FTIR) as well as in the bleach is clearly visible.
For this substance, however, the carbonyl group is separated from the azulene moiety by far fewer bonds than in all N-(oxo-alkyl)-2-(1-azulenyl)-acetamides. Accordingly, the tentative explanation for the lack of a gradual shift put forth in section 3.3.4 for the azide asymmetric stretching vibration – a transfer of certain low-frequency modes directly to the solvent rather than to other intramolecular modes – might not hold here, as the short chain here possesses far fewer modes which might couple to the solvent.
Additionally, the close proximity of the carbonyl group to the azulene moiety will lead to some appreciable coupling between the carbonyl mode and modes of the azulene moiety. The carbonyl mode would then reflect the gradual loss of energy from the
Chapter 3. Intramolecular vibrational energy transport
azulene moiety rather than the population of a privileged channel of energy loss to the solvent.
Temporal evolution
In processing the data of the sensor mode in the respective molecule, i.e. the carbonyl – or asymmetric azide mode, the protocol described for the amide I mode in section 3.3.3 was adhered to analogously. The results are shown in Figure 3.18.
The positions of the respective maximum signals correlate well with the chain lengths of the molecules. As already established[7, 75, 81], IVR is slower in chains con-taining heteroatoms than in those of equal length concon-taining only methylene groups.
Additionally, in shorter chains an (extrapolated) non-vanishing value shortly after t = 0 is an indication of harmonic energy flow[7, 75, 81]. The resolution of the data does not allow to resolve harmonic energy flow and possibly separate it from direct anhar-monic coupling. For molecules with longer chains this effect subsides and is eventually replaced by a delay interval which precedes the rise of the signal.
The decaying flank of the bi-exponential described by τ2 is fairly similar in all substances, thus indicating similar velocities of VET to the solvent. Comparing this to the results obtained for the azulene ring distortion mode in section 3.3.2, it must be concluded that the signal of the azulene mode reflects energy release not only to the solvent, but also to the attached substituent. Thus the increase in energy loss from the azulene moiety with increasing chain length would be due to a larger heat capacity of the attached chain.
Comparison of substances
Values of tmax for all substances are shown in Figure 3.19 alongside a range of fitted linear functions reported by the Rubtsov group[63]. BothN-(azido-oligo ethylene gly-col)-2-(1-azulenyl)-acetamides andN-(oxo-alkyl)-2-(1-azulenyl)-acetamides agree well with the slope of Rubtsov’s values, which were obtained for polyethylene glycol oligomers in CCl4[8] and also with a value of 0.4 ps per methylene group reported by Wang and coworkers[127]. For N-(azido-oligo ethylene glycol)-2-(1-azulenyl)-acetam-ides, the ordinate intersect seems to be larger than Rubtsov’s value, however, which is most likely an indicator of slower IVR from the azulene moiety to the chain. The Rubtsov group used IR excitation of the asymmetric stretching vibration of an azide group to deposit energy in their system and reported a mere 1.2 ps for the lifetime of
3.3. Investigation via UV pump IR probe spectroscopy
Figure 3.18:Kinetic traces of the carbonyl and asymmetric azide mode. Measured in CH2Cl2 using an excitation wavelength of 610 nm. τ1andτ2are the time constants of the bi-exponential fit function.
†Variable fixed to average value obtained from other substances in order to better localize least squares minimum.
Chapter 3. Intramolecular vibrational energy transport
3 7 9 11 12 15 24
0 2.5 5 7.5 10 12.5 15 17.5
O N H O
O N H O
O N H O O
N O O O N3
H
O
N O O O O O O N3
H
O
N O O N3
H
O
N O N3
H
O
Number of bonds tmax/psorτIVR/ps
Figure 3.19:Comparison of thetmaxof the azide asymmetric stretching – and carbonyl modes for all substances investigated. All measurements were conducted in CH2Cl2 us-ing a pump-wavelength of 610 nm. The gray, shaded area represents all fits re-ported by Linet al.[8] for polyethylene glycol oligomers in CCl4, including the re-spective error bars, assuming a bond length of 1.5 Å. are the theoretical values of τIVRfor anthracene taken from [69].
the excitation[8].
Slower IVR in chains containing heteroatoms than in those composed solely of methylene groups has been observed before[7, 75, 81] and attributed mainly to changes in the potential energy surface rather than the greater mass of the heteroatoms as com-pared to carbon[75, 81, 128]. From Figure 3.19 it appears that this effect is predominantly a constant difference due to the nature of the system and increases only slightly as chain length and number of hetero atoms are increased (cf. section 3.4.2).
The results do not support the assessment that IVR times are independent of chain length in larger chains[7, 75, 81]. Rather – and in accord with the Rubtsov group’s find-ings – IVR times appear to be proportional to chain length.[8, 63]
In the light of the Schwarzer group’s earlier results for even shorter chains[7, 75], it seems reconcilable with the present data, that a fall-off behavior exists for the
depen-3.3. Investigation via UV pump IR probe spectroscopy dence of IVR time on chain length for very short chains. The effect was also supported by the Schwarzer group’s later theoretical work[69], from which some data are also shown in Figure 3.19, and, while yielding IVR values roughly twice as large as the ex-perimental ones [sic], it shows both the fall-off behavior and an approximately linear trend for longer chains. A comparison with the present data is difficult, since IVR times were mostly obtained as the fast component of the bi-exponential of the energy con-tent of the azulene moiety, rather than arrival times or tmax values of a sensor group in the theoretical work. Further, the chains used here were not sufficiently short to show a marked fall-off. With the results of section 3.3.2, the use of the azulene moiety as a reporter for IVR seems dangerous as IVR and VET may become difficult to dis-tinguish for longer chains. This does, however, not refute the IVR time constants of earlier works[7, 75] as they were well separable from VET.
In Figure 3.20, maximum signals of the respective sensor absorptions are com-pared. It should be noted that while this data is normalized with respect to the maxi-mum amide signal amplitude of the respective substance – as the amide band is fairly insensitive to the remaining chain – it was not accounted for differing absorption co-efficients of azide and carbonyl marker bands (see section 3.2). There is no immediate quantitative relationship between the bleach of an absorption and the intensity of that same absorption in a stationary spectrum, if it overlaps with its red-shifted absorption, as in this case. First, this is particularly true comparing the azide and carbonyl modes, as these will probably differ in their sensitivity to temperature[8]. Second, even within a group of substances normalization to the stationary spectrum is not sound, as the vibrational energy and virtual temperature of a molecule at the point in time when the bleach of the sensor reaches its maximum depends on chain length: the longer the chain, the later this point will be reached, the more energy will have been lost to the solvent, apart from that the heat capacity of the molecule will be greater. Hence the maximum signal corresponds to entirely different energetic situations (total amount of vibrational energy as well as its distribution over more or fewer degrees of freedom) in the various molecules.
Lin et al.[8] used a single exponential to describe the decay of the maximum of the signal of the sensor with chain length. Based on the dependence on chain length determined by them and the first data point in each series of substances, fairly simi-lar predictions for both groups of substances are shown in Figure 3.20. Although the number of data points is somewhat scarce, two systematic differences can be inferred:
The experimental points suggest a greater rate of decline than the exponential and they seem to reach a non-zero asymptote. The most probable explanation for both aspects
Chapter 3. Intramolecular vibrational energy transport
7 9 11 12 15 24
0.2 0.4 0.6 0.8 1
O N H O O
N H O O
N H O
O
N O N3
H
O
N O O
O N3 H
O
N O O N3
H
O
N O O
O O
O O N3
H
Number of bonds
Max.sensorbleach Max.amideIbleach
Figure 3.20:Maximum sensor mode signals relative to the maximum amide I mode signal. No normalization was performed to account for the differing intensities of the sensor absorptions (see text). Lines represent exponential decays according to Linet al.[8], using a characteristic decay length of 15.7 Å, assuming bond lengths of 1.5 Å, and scaled to the value of the smallest molecule in each set.
is the difference in excitation methods. While in Linet al.’s case IR excitation was used and hence the initial bleach of the sensor band reflects directly its coupling to the ex-cited mode, here excitation of an electronic state and successive internal conversion were employed, which invariably leads to the excitation of a multitude of modes[124]. This multitude will include both strongly localized normal modes and modes delo-calized over the entire molecule. While the anharmonic coupling of the former to the sensor mode ought to decay quickly with distance, the latter may be varying little in their coupling to the sensor mode[129]. Accordingly, the delocalized modes probably cause the apparent plateau or a second, much slower decline.