Wachsmann-Hogiu, Sebastian: Vibronic coupling and ultrafast electron transfer studied by picosecond time-resolved resonance Raman and CARS spectroscopy


Chapter 5. Mode specific vibrational kinetics after intramolecular electron transfer in Betaine-30

5.1 Motivation

Betaine-30 (B-30) is a molecule undergoing ultrafast intramolecular electron transfer in condensed phase [1, 2]. In the electronic ground state, B-30 has a high dipole moment which is substantially reduced upon electronic excitation to the first excited singlet state. The absorption to this state exhibits a charge transfer character. Relaxation of the first excited singlet state involves back-electron transfer (back-ET) restoring the charge distribution of the ground state.

According to time-resolved absorption measurements of Barbara and co-workers [2-5], the back-ET times of B-30 vary from 0.6 ps up to about 100 ps depending on the temperature and the solvent. It has been observed that in rapidly relaxing solvents -like acetonitrile, propylene carbonate (PC) etc.- the back-ET time tauback-ET is close to the solvation times taus. These conditions are rationalized as „solvent controlled regime“, where solvent reorientation during the excited state lifetime of the solute strongly accelerates back-ET by lowering the excited state potential energy surface (see also paragraph 2.2.3). In solvents with slower taus (e.g. glycerol triacetine (GTA), alcohols etc.) the back-ET transfer time is shorter than the solvent response, and hence back-ET occurs under the condition of a „frozen“ solvent shell.

According to classical Marcus theory of ET [6], the fastest rates of back-ET are expected near the turning point between the „inverted“ and „normal“ regime, where the free energy of activation of the reaction approaches zero. For B-30, it has been shown that the back-ET occurs in the inverted regime [1, 2], i.e., the DeltaG0 energy gap between the excited and ground state is larger than the solvent reorganization energy lambda (see Fig. 2.3). For a theoretical description of ET rates, the model of Marcus and Sumi [7] has been used, where the action of a low frequency mode together with a classical solvent degree of freedom is considered (see paragraph 2.3.5). For B-30, however, this model predicts much lower back-ET rates than observed experimentally [4]. Jortner and Bixon have shown that additional intramolecular high frequency modes, which are treated quantum-mechanically, have to be taken into account for calculating these rates more accurately [8,9]. The back-ET rate is then given as a sum of rates from all occupied levels of the reactant state to all vibrational levels of the product state [9] (see also Fig. 1.2). Combining these two approaches in a hybrid model, Barbara et al. were able to reproduce the back-ET kinetics in a wide range of different environments [4].

Nonequilibrium vibrational excitations should occur for intramolecular vibrational modes which are involved in back-ET, i.e., are part of the reaction coordinate. For back-ET times faster or at least comparable to the time scale of intramolecular redistribution of vibrational energy (IVR), one expects pronounced excess populations of these modes via back-ET. The excess populations decay by IVR and by simultaneous or subsequent flow of energy to the surrounding solvent (i.e. vibrational cooling). B-30 represents an interesting model system for such studies as the ET time varies substantially with the


solvent. As a result, vibrational dynamics can be studied both for solvent controlled ET, as well as for ET controlled by intramolecular couplings.

It has to be noted that IVR includes (i) intra-mode energy transfer along the ladder of excited levels in a certain mode as well as (ii) inter-mode vibrational energy transfer (see also paragraph 5.2). Early picosecond pump-probe absorption spectroscopy suggested that IVR in large molecules is completed on a subpicosecond time scale [10]. Subsequent vibrational cooling of the vibrational-thermalized solute molecule to the solvent proceeds within some tens of picoseconds. In contrast, more recent absorption measurements with improved time resolution and sensitivity indicated non-thermal distributions up to several picoseconds [11,12]. However, this type of experiment does not allow to gain information about the selective population of vibrational modes, because of the usually broad and structureless absorption bands of large molecules in solution.

Time-resolved vibrational spectroscopy represents a technique directly addressing the dynamics of nonequilibrium vibrational populations. Nonlinear changes of vibrational absorption on the v=0 to v=1 transition and/or on the anharmonically shifted v=1 to v=2 transition give insight into the mode specific population dynamics. Using this technique, intra-mode vibrational relaxation of the C O stretching vibration after back-ET in the [Co(Cp)2+/Co(CO)4-] ion pair has been observed [13]. In a different approach, vibrational populations of Raman active modes are monitored by anti-Stokes Raman spectroscopy [14-18]. Here, the anti-Stokes Raman signals originate exclusively from excited vibrational levels, in most cases from the population of the v=1 level.

So far, there are very limited information on the vibrational dynamics of B-30. Resonance Raman spectroscopy provides insight into the dynamics of modes which are strongly involved in the intramolecular vibronic coupling, i.e., the group of modes which is expected to contribute predominantly to back-ET.

In this thesis, a detailed study of vibrational dynamics during and after back-ET in B-30 is presented, both for the „solvent controlled regime“ as well as under conditions of a „frozen“ solvent. Modes with strong origin shifts of the excited state potential are identified by resonance Raman spectra in the charge transfer absorption band. From time-resolved anti-Stokes Raman spectra vibrational excess populations have been determined and - as soon as thermal equilibrium between Raman active modes has been established - vibrational temperatures. The results indicate selective excitation of Raman active modes within the first few picoseconds. Differences in the excitation behavior of several modes are clearly pronounced for fast relaxing solvents. Thermal equilibrium between the Raman-active modes is established within 10 to 15 ps after back-ET. It results in higher vibrational temperatures in slowly relaxing compared to fast relaxing solvents.


5.2 Absorption spectra and photophysics of the molecule

The molecular structure of B-30 in the electronic ground state is presented in Fig. 5.1. The different dipole moments of the molecule in polar and nonpolar solvents, and the changes of the dipole moments after absorbing of one photon with hny energy, are shown schematically. The back-ET is marked by b-ET. The charge transfer reaction of B-30 as illustrated in Fig. 5.1 is „direct“, i.e., excitation within the CT band is directly accompanied by the transition from a strongly charge separated ground state to a more neutral first excited singlet (Franck-Condon) state. Dipole moments in the electronic ground state and in the S1 state of 16 D and 6 D, respectively, have been determined experimentally [19].

Fig.5.1: Molecular structure of B-30

Absorption spectra of B-30 in different solvents (in GTA, PC and Ethanol (ETH)) are plotted in Fig. 5.2.

Fig. 5.2: Absorption spectra of Betaine-30 in Glycerol triacetate (GTA), Propylene Carbonate (PC) and Ethanol (ETH). In the insert is marked the change in the position of the potential surfaces of the ground state (S0) and first excited singlet state (S1).


The position of the broad band between 500 nm and 700 nm is solvent dependent, indicating the strong charge transfer character of the lowest electronic transition (CT band). This behavior has been used to define the empirical ET30 polarity scale [20]. The position of the strong band around 300 nm is not solvent dependent and is assigned to a transition to a locally excited (LE) electronic state. In the insert, the change in the position of the potential surfaces of the ground and first excited singlet state is shown. Because the dipole moment in the ground state is about three times the dipole moment in the excited state, the potential surface of the ground state is more sensitive to the changes of the environment polarity.

Fig. 5.3: Fit of the CT absorption band of B-30 dissolved in ETH, PC and GTA. Dot line: experimental curve; solid line: fit with Eq. 5.1. The parameters obtained from the fit are seen in the inserts.

The static CT absorption band has been fitted to a line shape model by using the same formalism described in paragraph 2.3.5, which includes one classical (lambdas) and one high-frequency (lambdaq) degree of freedom. The form of the absorption line shape is therefore a sum of Gaussians in a Franck-Condon distribution, as follows:



where is related to the origin shift parameter z, k is positive and integer and represents the vibronic quantum number, is the total classical reorganization energy, the free energy of reaction, and is the frequency of the quantum vibrational mode, which was chosen as 1603 cm-1, i.e., equal to the highest frequency mode observed in the Raman spectrum. The parameters obtained from the fit of the CT absorption band of B-30 dissolved in ETH, PC and GTA are given in the inserts of the Fig. 5.3. Obviously, the asymmetry of the absorption band is due to the Franck-Condon progression. The high-frequency region in Fig. 5.3 is dominated by the absorption to a higher electronic state.

In Fig. 5.4. the photophysical processes occurring in B-30 after photoexcitation are shown schematically.

Fig. 5.4: Photophysics of B-30: (1) direct excitation in the CT band, (2) reorganization in the excited state, (3) back-ET and (4) vibrational relaxation.

The very fast excitation in the CT band (step 1) is followed by solvation in the excited singlet state (step 2). The time duration taus of this process is solvent specific and depends strongly on the temperature. At room temperature, taus lies between 0.5 ps for acetonitrile to few hundred of ps for GTA. If taus is fast (0.5 ps to 3 ps), the reorganization in the excited singlet state strongly accelerates the back-ET by lowering the excited state potential energy surface. In this case (where is the duration of the back-ET in the step 3), and the terminology „solvent controlled regime“ is usually used. For slowly relaxing solvents (taus>3 ps) a smaller amount of energy is expected to be


transferred to the solvent, and the terminology used in this case is „vibrational controlled regime“.

During back-ET, it is assumed that the excess energy is deposited into highly excited vibrational modes of the electronic ground state. Step 4 represents schematically the intra- and inter-mode (not shown in the Fig. 5.4) vibrational relaxation in the electronic ground state (IVR).

5.3 Stationary vibrational spectra and ab initio calculations of geometry and vibrational spectra.

Before going to deal with the Raman pump-probe experiment, information concerning molecular structure of B-30 will be gained by a combined study of the stationary Raman and infrared spectra with ab initio calculations.

In particular, the influence of the solvents and excitation wavelengths on the Stokes-Raman spectra will be presented. In addition, the calculated vibrational frequencies in the electronic ground state allow an assignment most of the observed vibrations. The reasonable agreement between calculated and observed vibrational spectra indicate that the optimized molecular structures used in this calculations are close to reality. From the calculated geometry of the molecule in the electronic ground and excited state, statements regarding the vibrational modes involved in the geometry change will be made.

5.3.1 Stationary Stokes-Raman and infrared spectra

In Fig. 5.5 (a) and (b), resonance Stokes Raman spectra of B-30 dissolved in GTA are plotted for excitation at 606 nm and 303 nm, respectively (sample concentration 2×10-3 M). Solvent Raman lines are indicated by (*), and contributions from spectrally unresolved solvent and solute lines are marked by (+). Closely positioned Raman lines are better resolved with 606 nm excitation due to the smaller bandwidth of the pulses, compared to 303 nm excitation. Most of the strong Raman bands occur under both excitation conditions. There are, however, significant changes of relative intensities in the Raman spectrum under excitation in the CT and in the LE band. The resonance Raman spectrum of the CT band shows some additional bands, which are weak or even not present with 303 nm excitation.


Fig. 5.5: Stationary Resonance Raman spectra of B-30 dissolved in GTA recorded by excitation in the charge transfer band (top) and in the locally excited band (bottom). Solvent lines are marked with *, and contributions from both solvent and solute lines with +.

Due to the limited performance of the polychromator without Notch filter, the low frequency region (ny<400 cm-1) could not be recorded with a sufficient signal to noise ratio at 303 nm excitation.

Fig. 5.6: Stokes-Raman spectra of B-30 dissolved in methanol (solid line) and in PC (dashed line).

The Stokes-Raman spectra recorded by excitation with 606 nm laser light are very similar for B-30 dissolved in PC and GTA. There is a difference in the 1250-1320 cm-1


spectral region for B-30 dissolved in ETH or methanol, as seen in Fig. 5.6, probably due to the formation of H-bonds between solute and solvent [21, 22].

In Fig. 5.7 Raman spectra of B-30 dissolved in PC (2×10-2 M) are presented, recorded with 1064 nm by Brzezinka -see [23]- (lower panel) and with 600 nm excitation (upper panel), respectively.

Fig. 5.7: Raman spectra of B-30 obtained after excitation in the CT band (600 nm) and off-resonance (1064 nm).

Raman spectra recorded with 600 nm excitation are resonance enhanced compared to excitation at 1064 nm by a factor of about 10. For off-resonance conditions, the solvent contribution has been subtracted from the original spectrum, whereas under electronic resonance the relative contribution of solvent Raman lines is negligible. The Raman spectrum recorded at 600 nm is in good agreement with the spectrum reported by McHale et al. recorded under similar excitation conditions (i.e., in the resonance with the

CT transition) [21, 22]. In these papers, it has been reported that due to electronic resonance conditions, the depolarization ratios of all vibrations are close to rho=0.3. In addition to the published vibrational frequencies (see [21, 22]), we found a rather strong low frequency line at 133 cm-1. As will be discussed later, this mode is assigned to a torsional motion, which is assumed to play an important role in the ET reaction.

The Raman spectrum recorded at 1064 nm excitation shows the same vibrational pattern as the spectrum obtained with 600 nm excitation. However, we detect different relative intensities for some distinct Raman lines. For example, the Raman lines at 1622 cm-1 and 1419 cm-1 gain in their relative intensities under resonance excitation. Vice versa, we observe a strong line at 999 cm-1 with 1064 nm excitation which is rather weak


under resonance excitation at 600 nm. Whether a Raman band gains or looses in relative intensity in changing the electronic resonance conditions depends on whether or not the normal mode is localized (spatially) in the same part as the electronic transition. The conclusions that can be derived will be discussed in paragraph 5.3.4.

The corresponding infrared spectrum of B-30 embedded in KBr (top) measured with a FTIR device together with a Raman spectrum of B-30 in PC (bottom) is presented in Fig. 5.8.

Fig. 5.8: Infrared spectrum of B-30 embedded in KBr (top) and Raman spectrum of B-30 dissolved in PC (bottom) for comparison.

5.3.2 Molecule geometry in ground and excited electronic state

Ground state geometry optimization and vibrational analysis of the complete B-30 molecule has been made by Dreyer [23]. He used the HF/3-21G (Hartree-Fock) method implemented in the program package GAUSSIAN98 [24]. For excited state calculations, the full structure was reduced to a model system solely consisting of the phenoxide and pyridinium rings and calculated with CI-singles/6-31G(d). For comparison, the ground state model structure was optimized at the HF/6-31D(d) level as well. All reported frequencies were scaled by a factor of 0.91 [25,26]. The obtained ground state geometry is shown in Fig. 5.9.

The most important geometry parameters are collected in Table 5.1. Bond angles are only given for the two cases in which the values deviate considerably from 120°. The numbering of atoms and notation of phenyl rings are shown in Fig. 5.9. The molecular structure is C2 symmetric with a twisted chain of the phenoxide, pyridinium and phenyl ring C.


Fig. 5.9: Molecular structure of betaine-30 (B-30): see the numbering of atoms and naming of outer phenyl rings.

The most relevant geometry changes upon excitation to the first excited state are depicted in Figure 5.10.

Fig. 5.10: Geometry change of B-30 after excitation in the CT band

The phenoxide and pyridinium rings are moved from a twisted conformation into a perpendicular position. This has also been observed by Lobaugh and Rossky [27] and was earlier considered by Bartkowiak and Lipinski [28]. In addition, the pyridinium ring tilts and the nitrogen atom becomes pyramidalized by lambda = 167.8°. These two geometrical changes can be induced by the torsional and N-inversion vibrational modes, which were identified in the Raman spectrum at 133 and 291 cm-1 (see paragraph 5.3.3). The dipole moment is reduced from 15 D (18 D for the complete molecule) in the ground state to 3 D in the excited state, in reasonable agreement with experimental values of 16 D in the ground state and 6 D in the S1 state [19]. The electronic wave function mainly corresponds to a HOMO-LUMO pirarrpi* transition. The HOMO is localized in the phenoxide ring, whereas the LUMO is distributed over both rings.


The calculated bond length changes from the ground to the excited state allow to make the prediction that bands which dominantly contain C-O (Raman: 1582 cm-1, IR: 1553 cm-1) or C-N stretching (Raman: 1209 cm-1) contributions are expected to shift to higher wavenumbers in the excited state because of the increased bond order.

The calculated B-30 geometry can be roughly evaluated with respect to the crystal structure of 2,6-diphenyl-4-(4-bromophenyl)-N-(p-oxy-m,m'-diphenyl)-phenyl-pyridinium-betaine-monoethanolate, a B-30 structure with bromine attached at C13 and crystallized with an ethanol molecule, which distorts the crystal structure from C2 symmetry [28]. The twist angle theta between the phenoxide and the pyridinium ring is calculated to 68° in the electronic ground state, which is very close to the crystal structure value of 65° [29]. Earlier semiempirical PPP [27] and AM1 [28, 30] calculations resulted in values of 52°, 60° and 48°, respectively. Phenyl ring C is twisted by chi = 45° with respect to the pyridinium ring, which is in the same order of magnitude as the sample range of chi values reported by Lobaugh and Rossky [27]. The experimental value measured under conditions of a frozen molecule is only 18° [29]. The twist angle of the A/A' and B/B' phenyl rings amount to xi = 34° and phis = 54°, respectively, again in qualitative agreement with results of Lobaugh and Rossky [26]. Standard bond lengths

Table 5.1: Optimized geometry parameters for the complete B-30 molecule and the model structure. The dipole moments are given in D, bond lengths in pm, bond and dihedral angles in degrees.
a The model structure comprises the phenoxide and pyridinium rings (cf. Fig. 5.9).
b Experimental crystal structure of B-30 substituted with bromine at C13 and crystalized with ethanol hydrogen-bonded to O1 [28].
c Both rings are orthogonal to each other, the N-pyramidalization causes the deviation from 90°.


S0 (full)

S0 (model) a

S1 (model)

experiment. b











µ (dipole moment)





















































































C5-N6-C9 (lambda)










C4-C5-N6-C7 (theta)



98 c


C8-C9-C10-C11 (chi)






C14-C15-C3-C2 (xi)





C16-C17-C7-N6 (phis)





for C-O single and double bonds are 135 pm [C(sp2)-O] and 121 pm [C=O] [31]. Thus, the calculated C2-O1 bond length of 125.1 pm corresponds to a significant degree of double bond character. Accordingly, the adjacent C2-C3,3' bonds are noticeably stretched in comparison to aromatic C-C bonds in benzene, and thus the phenoxide ring structure exhibits some degree of quinoidal character. All other phenyl ring structures are nearly uniform. This is in qualitative agreement with experimental values, although the quinoidal character is somewhat less pronounced [29]. However, the experimental C2-O1 bond length of 129.1 pm is elongated because of hydrogen bonding in the crystal structure, which also affects the quinoidal pattern. For the uncomplexed molecule the C2-O1 bond length can be expected to be much closer to the calculated value of 125.1 pm. The C5-N6 bond length of 146.7 pm between the phenoxide and the pyridinium ring is even somewhat longer than a standard [C(sp2)-N(sp2)] bond length of 140 pm [31], probably induced by the repulsion between the outer phenyl rings A and B. This long C5-N6 bond suggests that there is no significant degree of conjugation between the rings, in accordance with the large twist angle theta being far away from the coplanar conformation, which would maximize conjugation. Similar considerations hold for all other bonds between rings.

5.3.3 Assignment of the Raman vibrations

Experimental Raman frequencies obtained in PC (Fig. 5.7) and the corresponding experimental infrared frequencies measured in KBr (Fig. 5.8), together with the calculated vibrational frequencies at the ab-initio Hartree-Fock level (HF/3-21G) made by Dreyer [23], relative intensities, depolarization ratios and assignments, are collected in Table 5.2. The good agreement of experimental and calculated patterns allows to assign the majority of observed Raman and infrared bands.

The high-frequency Raman bands at 1622 and 1601 cm-1 (Fig. 5.7) originate from aromatic stretching modes of the pyridinium ring combined with aromatic stretching modes of the outer phenyl rings. In contrast, the mode at 1582 cm-1 corresponds to an aromatic stretching mode of the phenoxide ring and thus, exhibits C-O as well as C-N (PhO-Pyr) bond stretching character. The similarity of the frequencies with those measured in the infrared spectrum (Fig. 5.8) suggests that the three high frequency infrared bands are the same as the corresponding Raman bands.

A band being dominated by the C-O stretching motion is only observed in the infrared spectrum at 1553 cm-1. In agreement with the calculated C2-O1 bond length of 125.1 pm, this frequency reveals partial double bond character. The region between 1350 and 1550 cm-1 contains several intense Raman and infrared band, which are mainly characterized by aromatic ring stretching motions. The most intense Raman band measured in polypropylene carbonate with excitation at 1064 nm occurs at 1355 nm and can be attributed to a stretching mode of the pyridinium ring combined with stretching modes of outer phenyl rings B and C against the pyridinium ring. The band at 1290 cm-1 corresponds to stretching modes of the phenoxide ring together with stretching modes of the adjacent phenyl rings A and the nitrogen from the pyridinium ring. The infrared bands


Table 5.2: Experimental Raman (in propylene carbonate, 1064 nm excitation) and infrared (in KBr) frequencies, calculated (HF/3-21G) vibrational frequencies (in cm-1), experimental and calculated depolarization ratios rho and assignments.
Abbreviations: Pyr = pyridinium ring; PhO = phenoxide ring; PhA,B,C = outer phenyl rings (cf. Figure 5.9); C-N = PhO-Pyr; ny = stretching; delta = in-plane deformation; gamma = out-of-plane deformation; tau = torsion.
According to calculation the ground state molecule possess C2-symmetry. Modes belonging to the B-species are designated (B), the other belong to A-species.


















ny(Pyr) + ny(PhB,C)







ny(Pyr) + ny(PhA,B,C)







- ny(PhO) + ny(C-O) + ny(C-N)







ny(C-O) - ny(C-N) + ny(PhO)





1541 (B)







1501 (B)














1444 (B)


ny(PhO) + ny(PhA)







ny(Pyr) + ny(PhB,C)







ny(Pyr-PhB) + ny(C-N)







ny(Pyr) + ny(Pyr-PhB,C)





1290 (B)


delta(CH, PhO) + delta(CH,Pyr)





1280 (B)


delta(CH, PhO) - delta(CH,Pyr)







ny(PhO) + ny(PhO-PhA) + ny(C-N)







delta(CH,PhO) + delta(CH,Pyr)







delta(CH,PhO) - delta(CH,Pyr)







ny(Pyr-PhC) + ny(Pyr-PhB)







ny(C-N) + delta(CH, PhO) + delta(CH, PhA,C)







breathing(PhA,B,C) + gamma(CH, PhO)







gamma(CH, PhO) + gamma(CH, PhO) + gamma(CH, PhA)







breathing(PhB,C) + gamma(CH, Pyr)














delta(PhO) + delta(Pyr) + gamma(CH, PhB)


























361 (B)


N-inversion + wagging(PhA,B)




























gamma(Pyr) + translation (Pyr-PhC)














translation (Pyr-PhB,C)







tau (PhO-Pyr)







tau (PhO-Pyr-PhC)


at 1287 and 1271 cm-1 are attributed to out-of-plane C-H deformation modes. The C5-N6 stretching motion dominantly contributes to the Raman band located at 1209 cm-1. The sharp band at 999 cm-1 corresponds to breathing modes of the outer phenyl rings in combination with C-H out-of-plane deformation modes. The infrared band at 889 cm-1 has been assigned to an out-of-plane deformation mode of the C-O bond.

Four Raman bands are measured in the low frequency range below 400 cm-1. At 341, 291 and 235 cm-1 a pattern of three bands with comparable intensities is observed. The central peak is attributed to the inversion of the pyridinium nitrogen atom, whereas the upper one corresponds to an out-of-plane deformation mode of the phenoxide ring and the lower one to a translation of the phenyl rings B and C against the pyridinium ring. The broad band at 133 cm-1 can be assigned to torsional motions of the three rings in the chain. Two different normal modes in this frequency region are calculated. The one at 130 cm-1 corresponds to the torsional motion of the phenoxide and pyridinium rings, which is described by a variation of the dihedral angle theta. The second calculated peak at 116 cm-1 is characterized as torsional motion of the pyridinium ring against the phenoxide ring and phenyl ring C, which is specified by changing the dihedral angles theta and chi.

The N-inversion and the torsional modes of the skeleton are very important molecular motions, which mediate the rearrangement in the first excited state as deduced from computational results.

5.3.4 Discussion of the dispersion effects

Next, the dispersion effects described in paragraph 5.3.1 will be discussed. The majority of the intense Raman bands in the range 1650 to 1200 cm-1 originate from modes localized in the phenoxide-pyridinium core of B-30 (see paragraph 5.3.3). They will experience high resonance enhancement under resonant excitation. Normal modes which dominantly originate from vibrational motions of the outer phenyl rings (like the band at 999 cm-1, which is assigned to breathing motions of the outer phenyl rings), decrease in relative intensity under resonant excitation compared to non-resonant excitation. In the low wavenumber region, we observe a strong enhancement for the mode at 291 cm-1, which contains a large contribution from the wagging motion of the central C-N bond in accordance with the calculated geometrical changes (see paragraph 5.3.3). In contrast, the dispersion effect for the torsional mode at 133 cm-1 is not so pronounced, although the band exhibits a very large origin shift (and consequently very high Franck-Condon factor), as deduced from its very high Raman intensity. The resonance Raman intensity is sensitive to geometrical changes between the electronic ground state and the corresponding Franck-Condon region of the excited electronic state, i.e., to geometrical changes occurring within the first tens of femtoseconds. As calculated by Lobaugh and Rossky by molecular dynamic simulations in acetonitrile [27], torsional relaxation of the central dihedral angle theta is supposed to occur on a time scale of several picoseconds. In other words, the vibration at 133 cm-1 will experience less resonance enhancement than the high frequency vibrations due to its slow torsional motion.

5.3.5 Overtones and combination tones


In addition to the fundamental frequencies, a manifold of overtones and combination tones can be observed by excitation of a B-30 solution (2x10-2M) in UV at 303 nm. These spectra gives an indication about the anharmonicity of the potential energy surface

Fig. 5.11: Overtones and combination tones observed in B-30 dissolved in PC measured by 303 nm excitation.

in the ground state, and about the amounts of the anharmonic frequency shifts that should be observed in the case of intra-mode vibrational relaxation from the high-excited vibrational levels to the vibrational ground state. A typical Raman spectrum including the overtone region is shown in Fig. 5.11.

Besides the first and second overtone of the 1603 cm-1 vibration at 3196 cm-1 and 4790 cm-1, respectively, combination tones of other frequencies with the 1603 cm-1 frequency can be observed. An anharmonical shift of approximately 12 and 19 cm-1 can be deduced for the first and second excited vibrational level of the 1603 cm-1 vibration, respectively.

5.4 Transient spectra and a view into the mechanism of back-ET

Detailed information about the mechanism of the intramolecular back-ET in B-30 can be further obtained by investigating the time evolution of the vibrational modes after back-ET by anti-Stokes Raman spectroscopy. It reflects the population change of particular modes and can be used to monitor the specific participation of vibrational modes in the ET. A detailed study of the transient anti-Stokes Raman spectra will be presented under the conditions of ’solvent controlled‘ and ’vibrational controlled‘


regime. The spectra are measured in the electronic ground singlet state after the back-ET. Transient Stokes-Raman spectra in the excited singlet state will also be presented.

5.4.1 Kinetics of the anti-Stokes Raman modes in slowly and fast relaxing solvents

The sample (concentration 3x10-3M) was excited via the charge transfer transition by pulses at 606 nm (30-100 µJ energy/ pulse), while the probe pulses at 303 nm (2-10 µJ energy/pulse) were resonant with the transition to the locally excited state of the B-30 molecule. This scheme is illustrated in Fig. 5.12. The probe pulse was polarized linearly at magic angle (54.7o) relative to the pump, in order to avoid temporal changes of the anti-Stokes Raman intensities due to molecular reorientation. Probing the very weak anti-Stokes Raman spectra in the UV spectral region is advantageous because the scattering signal increases with a ny4 dependence (where ny is the excitation frequency), and because of the lack of fluorescence.

Fig. 5.12: Schema for excitation and probing of anti-Stokes Raman mode in B-30.

Time resolved anti-Stokes Raman spectra were obtained by subtraction of the spectra recorded with pump pulses at a negative delay of 50 ps with respect to the probe pulse from the corresponding spectra measured at positive delays. Thus, stray light due to the pump pulse does not contribute to the signal and the observed signals are due to the vibrational excess population only produced by back-ET in the electronic ground state. A typical accumulation time for each spectrum at a fixed delay was 200 s and up to ten of such spectra were averaged to obtain a sufficiently high signal to noise ratio. Integrated Raman intensities were determined - after subtraction of a base line - by fitting the Raman bands by Voigt line shapes.

Time-resolved anti-Stokes Raman spectra were measured for B-30 dissolved in PC, GTA and ETH. The solvation time of PC at room temperature is very fast (about 1 ps), and the measured back-ET of B-30 in PC equals the solvation time [4]. This is a typical case of ’solvent controlled‘ back-ET, where a considerable amount of energy is transferred to the solvent during the back-ET process. Despite the clearly longer solvation time of GTA (about 100 ps) and ETH (about 15 ps) at room temperature, the measured back-ET is only slightly longer (3.6 ps in GTA and 5.6 ps in ETH) [3-5]. These are typical cases of ’vibrational controlled‘ back-ET, where energy transfer to the solvent plays a minor role.


In Fig. 5.13 are presented the spectra recorded for a solution of B-30 dissolved in PC (left side) with an accumulation time of 30 min. for each spectrum, and GTA (right side) with an accumulation time of 90 min. for each spectrum, for different delays between excitation and probing. All strong Raman lines of the Stokes Raman spectrum with 303 nm excitation (Fig. 5.5) can be identified in the anti-Stokes Raman spectrum as well. Moreover, it is easy to observe a build-up of the anti-Stokes Raman intensities first in the high-frequency region within a few picoseconds and their subsequent decay that is slightly slower than the rise and accompanied by a redistribution of the relative intensities. The rise times are significantly slower for B-30 dissolved in GTA than in PC.

At early times, the mode with the highest frequency (1603 cm-1) is dominant, at later times (t > 10 ps) the Raman bands with lower frequencies (1360 cm-1, 1200/1245 cm-1, 1013 cm-1, 650 cm-1 and 435 cm-1) increase in relative intensity. Within our experimental accuracy of ±15 cm-1, the spectral positions of the Raman bands are independent of time delay.

Fig.5.13: Transient anti-Stokes Raman spectra of B-30 dissolved in PC (left) and GTA (right).

In Fig. 5.14, the time evolution of the Raman intensities of the modes at 1603 cm-1, 1360 cm-1 and 1200/1245 cm-1 are presented for B-30 dissolved in PC (left side), GTA (middle) and ETH (right side). In the upper panel of Fig. 5.14 the time-resolved small signal amplification of Sulforhodamine 101 (see also Fig. 3.10) which is used for determining the time resolution in the experiment and the zero-delay point is shown as well in addition.

Rise and decay of the anti-Stokes Raman intensities reflect the population dynamics of the corresponding excited vibrational levels. To quantify the different rise and decay times, the population dynamics of the vibrational level i, ni, is modeled in a three level scheme. Within this simplest possible approximation, vibrational population ni is fed


into the level i from an initially excited level p of population np(0) with a time constant t1, while the population of the ith level decays to a further level with a time constant t2.

Fig. 5.14: Kinetics of the vibrational modes at 1603, 1360 and 1200/1245 cm-1 measured for B-30 dissolved in PC (left), GTA (middle) and in ETH (right), respectively.

The population kinetics is thus described as follows:


This time behavior is convoluted with the cross correlation function of the pump and probe pulses. The solid lines in Fig. 5.14 give the results of the fit using this model.

In most cases, this approach reproduces the experimental results quite well. The Raman signals show a non-instantaneous intensity rise with the delay between pump and probe pulses, which is different for different modes and solvents. Mode selectivity, i.e., differences in rise times of the different vibrational modes, is most pronounced for B-30 in PC. The mode with the highest vibrational frequency at 1603 cm-1 exhibits the fastest rise time of t1le1 ps, i.e. within the time resolution of the experiment, whereas a rise time of t1=3 ps is determined for the vibration at 1360 cm-1. The intensity of the Raman band at 1200/1245 cm-1 increases even more delayed, but does not follow a simple single exponential kinetics. All vibrational modes - within experimental uncertainties - decay single exponentially with a time constant of t2=5 ps. For B-30 dissolved in GTA and in ETH (Fig. 5.14), the temporal rises of the anti-Stokes Raman intensities are slower than in PC solution. Furthermore, mode selectivity is less pronounced in GTA solution than for B-30 in PC and nearly disappears for B-30 in ETH. The decay of anti-Stokes Raman


intensities is somewhat slower in GTA and ETH solutions, compared to B-30 dissolved in PC.

The time constants (rise time: t1, decay time: t2) determined for the vibrations at 1603 cm-1, 1360 cm-1 and 1200/1245 cm-1 for B-30 dissolved in PC, GTA and in ETH are summarized in Table 5.3. Back-ET times determined from transient absorption measurements (5) are given for comparison in the first column of Table 5.3.

Table 5.3: Rise and decay times of anti-Stokes Raman kinetic curves measured for B-30 dissolved in propylene carbonate (PC), glycerol triacetin (GTA) and ethanol (ETH). They were approximated by an expression with two monoexponential terms (rise time t1, decay time t2). Back-ET times [3, 5] (tauback-ET) are given in parentheses.

Vibrational frequency

1603 cm-1

1360 cm-1



t1, (tauback-ET) [ps]












1.0±0.3, (1.1)







3.8±0.8, (3.5)







5.6±1.2, (6.1)






5.4.2 Selective excitation of the vibrations and IVR after back-ET

The spectra in Fig. 5.5 show a change of the Raman intensities when changing the conditions of resonant Raman enhancement, i.e., when moving from 600 nm (CT band) to 300 nm (LE transition). This behavior reflects the different origin shifts of the vibrational potentials in the CT and LE states of B-30. Despite the differences in the Raman spectra, most of the bands that are strong in the CT resonance Raman spectrum show high intensities in the LE Raman spectrum. Consequently, it is possible to monitor the vibrational kinetics of the majority of modes involved in ET by recording the time-resolved anti-Stokes Raman spectra in resonance with the LE transition (except for the rather intense vibrations at 1290 cm-1 and 1419 cm-1 and the vibrations below 400 cm-1).

The rate of intramolecular electron transfer is frequently approximated by Fermi‘s Golden Rule (FGR) (see paragraph 2.3.5):


Vel is the electronic coupling constant for the two diabatic electronic states and F contains a sum taken over the FC factors of the modes active in electron transfer. Each of them is multiplied by an effective energy conservation factor. On the basis of FGR, Wynne et. al. [32,33] derived a formula giving the transfer probability for the vibrational mode j (frequency omegaj) from the zero level in the donor (CT) state to the nth level in the acceptor state:



Here, Nj is a normalization factor, k the Boltzmann constant, lambdaS the solvent reorganization energy, <SPAN CLASS=@ITALIC@>G</SPAN><sup>0</sup> the energy gap between the reactant and product state and gj(t) is the line shape function.

Assuming equal mode frequencies in the CT and electronic ground states, the coupling strength of each mode j is given by its respective FC overlap :

= (5.5)

with the origin shift parameter zj = , which can be derived from the Raman spectrum with the relation: z2 I/omegaj, where I is the intensity of the Raman mode omegaj, mj and q0j are the effective mass and origin shift of the jth mode with frequency omegaj. From Eq. (5.4) and Eq. (5.5) it follows that applying comparable origin shift parameters of most transfer active modes (close to zj le 1 as determined for B-30 [21,22]), the transfer is most favorable into those modes which bridge the gap with a minimum of quanta n. For a large energy gap and similar zj le 1, i.e., the situation in B-30, the probability for back-ET mediated by high frequency modes should be higher than by low frequency modes. In agreement with this argument, the time-resolved data show pronounced vibrational excess populations of high-frequency modes, in particular of the mode at 1603 cm-1.

In accordance with the predictions derived from FGR, the time-resolved data for B-30 in PC show different rise times of three prominent modes in the transient Raman spectra (see Fig. 5.14). A rise time of the 1603 cm-1 band in the PC solution close to the back-ET time of 1 ps indicates that this mode is excited predominantly by back-ET, whereas low frequency vibrations are less effective in accepting energy. However, from the almost equal decay times of the three modes it can be concluded that excitation of the modes at 1360 cm-1 and 1200/1245 cm-1 via energy transfer from the 1603 cm-1 mode is not effective. In contrast, those modes are partly excited by transfer via indirect channels of internal vibrational redistribution. The presented experimental data do not allow to determine other pathways of IVR which may represent such indirect channels.

A comment should be made on the role of low-frequency modes for back-ET. Low frequency vibrations can be involved in back-ET provided that their FC factors are large enough. In a variety of electron transfer systems, coherent wave packet propagations with frequencies on the order of 150 cm-1 have been observed. Molecular dynamics simulations for B-30 predict that the torsional motion between the phenoxide and the phenolate ring tunes the gap between the electronic ground and the CT state and thus promotes back-ET [27]. The vibration at 133 cm-1 has been identified as a torsional mode (Table 5.2). It exhibits about half the intensity of the mode at 1603 cm-1. It has been suggested that the corresponding torsional motion of B-30 promotes back-ET [27]. Taking into account that the origin shift parameter can be approximated by z2 I/omega (I: intensity of the band), it is obvious that z2 is considerably higher for this low frequency mode than for modes in the high frequency region. These considerations suggest that the 133 cm-1 torsional mode is part of the reaction coordinate. Further time-resolved studies are required to clarify this point experimentally.

Less pronounced differences in the rise times of the different vibrational bands are expected for the case that back-ET times are comparable to the time scale of IVR. This is the case for B-30 in GTA and ETH (see Table 5.3). Here, IVR processes strongly


influence the observed rise times for all modes. Thus, these data clearly demonstrate the transition from a mode-specific behavior of B-30 in PC to IVR-dominated vibrational dynamics of B-30 in ETH.

5.4.3 Nonequilibrium vibrational populations of B-30 after back-ET

The data collected in Table 5.3 demonstrate that the measured rise times of the anti-Stokes Raman line at 1603 cm-1 agree with the respective decay time of the first excited electronic state tauback-ET in different solvents. The rise times of the other vibrations are longer or comparable with t1 of the 1603 cm-1 vibration. The anti-Stokes Raman frequencies coincide with the corresponding Stokes Raman frequencies measured at low intensities and do not change with delay. Consequently, the observed anti-Stokes Raman lines are due to population of excited vibrational levels of the electronic ground state. Furthermore, there are no apparent anharmonic shifts of the Raman line at 1603 cm-1 with delay time. This indicates that the anti-Stokes Raman signal originates mainly from the v=1 level of that mode, possibly with a small additional contribution from the v=2 and v=3 states. As high-lying levels of this mode are directly populated by the back-ET, the rise of nonequilibrium population in low-lying levels is determined by the electron transfer time and the intra-mode relaxation time. The experimental data show that the rise time of the Raman signal is identical to tauback-ET , pointing to a fast subpicosecond intra-mode relaxation.

Assuming equal scattering cross sections for the Stokes and anti-Stokes Raman signals18, it is possible to make a rough estimation of the peak value of the population of the excited vibrational levels. A value of about 3% compared to the ground state population of the 1603 cm-1 mode can be obtained. However, despite the broad spectral width of the absorption near 300 nm of about 4700 cm-1, different Raman excitation profiles for Stokes and anti-Stokes Raman scattering are to be expected [16, 18, 34, 35]. It is more realistic to assume that the ratios of cross sections between the vibrations in the Stokes Raman spectrum are nearly equal to the ratios between the same vibrations in the anti-Stokes Raman spectrum. Furthermore, following assumption has been made: the contributions from higher excited vibrational levels (v>1) to the anti-Stokes Raman scattering can either be neglected or contribute with approximately the same cross section as the v=1 vibrational level. Consequently, the "relative vibrational excess populations" have been derived by dividing the anti-Stokes Raman intensities with the corresponding relative Raman cross sections which, in turn, have been calculated from the Stokes Raman intensities recorded at 300 nm (see Table 5.2).

In Fig. 5.14 the relative vibrational populations at different delay times are shown for B-30 in PC and GTA. It is obvious for all solvents that the vibrational populations deviate substantially from thermal equilibrium within the first few picoseconds. For delay times of 1.5 ps, 3 ps and - for B-30 in GTA - 7.5 ps, one finds smaller populations of low-frequency than of high frequency modes, in contrast to equilibrium (Bose-Einstein) statistics. For example, the population of the mode at 1360 cm-1 exceeds the 1200/1245 cm-1 population. This finding reflects the incomplete randomization of vibrational energy among the Raman active modes, pointing to a relatively slow intramolecular thermalization of the vibrational system on a picosecond time scale. At delay times longer than about 10 ps, the vibrational populations are close to equilibrium statistics, which is characterized by a vibrational temperature of the subgroup of these vibrations.


However, the procedure for determining the vibrational temperature has to be very carefully analyzed, since higher excited vibrational levels in the ladder of a certain mode can contribute to the anti-Stokes Raman signal. For off-resonant excitation conditions the Raman signal increases linearly with the quantum number of the vibrational level [36]. In contrast, for resonance Raman excitation conditions a shift of the maxima of REP to longer wavelengths for excited vibrational levels and a decrease of the corresponding anti-Stokes Raman efficiency has been calculated for canthaxanthin [16]. Consequently, a decrease of the anti-Stokes Raman signal with increasing level number for excitation near the maximum of the absorption band seems to be more likely for the experimental conditions used here.

To evaluate how the estimated temperature deviates for different models, the distributions of excess populations shown in Fig. 5.15 has been approximated under three different assumptions. These are: the anti-Stokes Raman signal

  1. grows linearly with the level number, i.e., where is the Raman cross-section of the vibrational level i, and is the Raman cross-section of the ground state vibrational level
  2. is independent of the level number, i.e., and
  3. originates from the lowest excited vibrational level only, i.e., for

In order to fit the experimental points in Fig. 5.15, the anti-Stokes difference signal Mj for one mode omegaj normalized to the corresponding Stokes signal ISj have been derived (see Appendix 1) for the three cases:

(i) = (5.6)

with the thermal population distribution:


Here, Tr and Te(t) are the vibrational temperatures before and after excitation by the pump pulse, respectively. Tr is the room temperature considered 300K, and Te(t) is a parameter which will be obtained form the fit of the experimental points with Eq. (5.6).

(ii) (5.8)

(iii) (5.9)

For B-30 in PC solution after 9 ps delay time, the assumptions (i) and (ii) result in different temperatures of 740 K and 595 K, respectively. The four modes 440, 1200/1245, 1360 and 1603 cm-1 can not be approximated reasonably assuming (iii), but they can be fitted excluding the vibration at 440 cm-1. In the latter case, the fit with (ii) and (iii) results in the same temperature, with an uncertainty of 60 K. The minor influence on the result, despite the completely different assumptions, can be understood by taking into account that - for the temperature range under consideration - the populations of excited levels of the high frequency modes are below 15%. In contrast, for the 440 cm-1 vibration the contributions from higher excited levels are significant.


Changes in the Raman cross sections comparing excited vibrational levels should play a minor role for low frequency modes and consequently, (iii) can not be applied.

Fig. 5.15: Relative vibrational populations of the excited vibrational levels different vibration determined at different delays. Left: B-30 dissolved in PC; right: B-30 dissolved in GTA. Vibrational temperatures for relative vibrational populations, which have been fitted by Eq. (5.8), are given in the insert.

Because the temperatures Te derived from (ii) represent a lower limit in comparison to (i), it is instructive to estimate and to compare temperatures Te at thermal equilibrium based on assumption (ii). The temperature values Te obtained at different delays are given in the inserts of Fig. 5.15. The measurements with B-30 in ETH give temperature


values slightly higher than in the GTA solution. Vibrational temperatures Te in ETH solution are 830, 730 and 530 K at 15, 18 and 22.5 ps, respectively.

For a comparison of the temperatures Te derived for the subgroup of Raman active modes with the equilibrium temperature Tequ which would be achieved in case of random distribution over all vibrational modes (degrees of freedom) of the molecule, the temperature Tequ has been derived applying the expression:


cm-1 is the photon energy of the pump pulse, is the room temperature (300 K), has the same form as in Eq. (5.7) and N=71 is the number of atoms in the molecule. An equilibrium temperature of Tequ= 520 K has been obtained. Tequ represents the maximum temperature at thermal equilibrium within the complete molecule as it neglects any flow of energy to the solvent shell. Nevertheless, Te determined for early delay times in different solvents is always higher than Tequ. This suggests that (a) back-ET transfers most of the excess energy to the Raman active modes involved in the reaction, and (b) thermalization within the vibrational manifold of B-30 is incomplete even 10 to 15 ps after photoexcitation.

It is interesting to note that the measured excess of the temperature Te above the calculated equilibrium temperature Tequ is larger for B-30 in GTA and ETH than in PC. This can be rationalized by taking into account that in the solvent controlled regime a considerable part of the absorbed energy is deposited into the solvent directly. For B-30, solvent reorganization energies between 3000 cm-1 and 6000 cm-1 have been estimated (see paragraph 5.2 and [4, 21, 22]). In contrast, if the solvation time exceeds the back-ET time, a larger fraction of the initial excitation energy is randomized within the solute before dissipation to the surrounding becomes efficient. Consequently, lower vibrational temperatures in the PC compared to the GTA and ETH solutions are to be expected. The experimental results are therefore in accordance with the theoretical models of intermolecular energy transfer during back-ET in the solvent controlled regime and under conditions of a "frozen" solvent.

5.4.4 Transient Stokes-Raman spectra in the first excited electronic singlet state

In order to gain more information about the change of the molecular structure during the ET process, a study of the Raman spectra in the first excited singlet state has been made. The excitation and probing scheme used is shown in Fig. 5.16.

The pump-probe transient spectra contain implicit information about the geometrical changes that occurs in the first excited singlet state, and follow up the relaxation to the ground state. Moreover, they can give an indication about the dynamics of H-bonds, if they are present.


Fig.5.16: Schema for excitation and probing of Stokes Raman scattering in the excited singlet state of B-30.

Stokes-Raman spectra were measured for B-30 dissolved in dimethylsulfoxide and pentanol. These solvents are advantageous because of comparatively longer excited state lifetimes and good solubility of B-30. Pentanol forms H-bonds with B-30 as indicated by the appearance of the strong Raman band at 1300 cm-1 (see Fig. 5.17.a and the discussion of Fig. 5.6).

For the measurement of Raman spectra in the first excited electronic state, 600 nm laser light was used for excitation (maximum of the CT absorption band is 580 nm in pentanol and 620 nm in dimethylsulfoxide). The probe laser wavelength at 364 nm was generated by frequency doubling of the radiation at 728 nm, which, in turn, has been obtained by Raman shifting (SRS) of the 600 nm laser wavelength in high pressure methane. In this way, the resonance Raman enhancement due to transient absorption near 400 nm has been used.

The following procedure was applied in order to subtract the contribution of the molecules in the ground state to the spectra in the excited electronic state:

(i) a Stokes-Raman spectrum was recorded by excitation with the probe laser light at 364 nm, with a negative delay (-50 ps) between the pump and probe (i.e., the probe pulse hits the sample 50 ps before the pump pulse). A ground state Raman spectrum of B-30 was obtained in this way, as shown in Fig. 5.17.a for B-30 dissolved in pentanol;

(ii) a spectrum at a positive delay between the pump and probe pulses was measured;

(iii) the spectrum measured at point (i) was subtracted from the spectrum (ii).

Fig. 5.18 shows the kinetic of the intensity of the Raman band at 1000 cm-1 recorded at different delays between the pump and probe pulses. Other bands show the same dependency. In this experiment, a cross-correlation time between the pump and probe pulses of about 6 ps has been determined (under the assumption of gaussian pulses) by measuring the Kerr signal generated in CS2 (open squares in Fig. 5.18). In a two-level model, a decay time of 10.8 ps of the Raman intensity has been determined from the fit of the experimental points. This decay time is very similar with the excited state lifetime measured by Barbara et al. (11 ps) in a transient absorption experiment, giving evidence that the observed spectra originate from the excited electronic state of B-30.


Fig. 5.17: Stokes-Raman spectrum of B-30 in pentanol in the electronic ground state with 364 nm excitation (a) and in the first excited electronic state by pump with 600 nm and probe with 364 nm (b). For comparison, a Raman spectrum of neat pentanol is shown, by excitation with 364 nm laser light (c).

The spectrum measured at 6 ps delay is presented in Fig. 5.17.b. The neat solvent spectrum is shown for comparison in Fig. 5.17.c.

Positive and negative components in the spectrum in Fig. 5.17.b are due to the contributions of Raman vibrations in the excited state and to depletion of the electronic ground state, respectively. Considerable frequency shifts of some Raman vibration in the excited state compared to the ground state are observed.


Fig. 5.18: Kinetic of the Stokes-Raman spectra in the first excited electronic state of B-30 dissolved in pentanol (solid squares) and cross-correlation between pump and probe beams (open squares). The solid lines are the fits of the experimental points.

The S1 Raman pattern of B-30 does not show significant differences when dissolved in GTA or dimethylsulfoxide compared to the spectra recorded in pentanol (in contrast to the S0 Raman pattern, where differences at 1300 cm-1 are observed for protic and aprotic solvents as shown in Fig. 5.6). As pentanol forms H-bonds in the electronic ground state, H-bond breaking after photoexcitation and subsequent formation of these bonds after back-ET may occur. For a discussion of these processes, the experimental results are summarized here:

(a) different patterns of Stokes-Raman spectra of B-30 dissolved in protic and aprotic solvents measured in S0;

(b) similar patterns of Stokes-Raman spectra of B-30 dissolved in protic and aprotic solvents measured in S1;

(c) no changes in the pattern of the S0 Stokes-Raman spectra of B-30 dissolved in pentanol measured before and after back-ET, i. e., at negative (-20 ps) and positive (>10 ps) delay times.

Points (a) and (b) implies two possible explanations:

  1. there is no H-bond in the excited electronic state, i.e., the H-bond which are seen in S0 in protic solvents breaks during (or after) ET.
  2. there are H-bonds in S1, but the respective vibrations are not Raman active.

In both cases there will be no differences in the spectra in S1. However, if the bonds break, and either breaking in S1 or formation in S0 is long compared to the generation of S1 (ET) or formation of S0 population (back-ET), changes should be observable. Point (c) shows that this is not the case.


5.5 Conclusions

In conclusion, it has been shown that stationary, as well as time-resolved Stokes- and anti-Stokes Raman scattering, combined with ab-initio calculations is a powerful method to gain information about the role of vibrational modes in the process of ultrafast intramolecular ET.

As we are able to assign the observed vibrational (Raman and IR) spectra to the vibrational pattern calculated by HF methods, this gives strong support that the optimized geometries used in this calculations are close to the geometry of the real molecule. Additionally, very high FC-factors of the Raman line assigned to the torsional motion, and the pronounced dispersion effect of the line assigned to a N-inversion motion, indicate that strong geometrical changes accompanies the ET reaction. Furthermore, strong change of the C=N bond length has to be expected during ET.

Time-resolved anti-Stokes resonance Raman measurements give evidence that the vibrational modes which accept the main amount of excess energy due to back-ET can be predicted from the stationary resonance Raman spectra measured in the CT absorption band. In other words, our results are at least qualitatively in accordance with the calculations derived from FGR, that predicts that high frequency modes with strong FC factors are the main accepting modes.

In agreement with this predictions, our time-resolved anti-Stokes resonance Raman measurements show that the rise time of the vibrational population of the mode with highest frequency at 1600 cm-1 is near to the corresponding b-ET in different solvents. Modes with lower frequencies appear more or less delayed in comparison to the high frequency mode.

Our measurements also demonstrate the interplay of direct vibrational excitation and intramolecular vibrational redistribution in the electronic ground state, occurring after back-ET. In fast relaxing solvents, i.e., in the case of fast back-ET, we clearly observe mode specific rise times due to dominance of direct excitation of high frequency modes. In contrast, in slow relaxing solvents, i.e., in the case of slow back-ET, the selectivity diminishes, probably due to dominant IVR processes.

Furthermore, this study also give information concerning the process of IVR. We observe strong non equilibrium populations in the first picoseconds for all Raman modes which are assumed to accept the main amount of excess energy. About 10 ps after excitation (depending on the solvent), a Boltzmann distribution between these modes has been established, and determination of the temperature of this subgroup of vibrations becomes appropriate. A value of about 10 ps for thermalization is in contrast to earlier measurements [10] and supports recent measurements.

These investigations also show that the temperature observed in the subgroup of vibrations exceeds the vibrational temperature that could be achieved in the molecule if the whole excess energy available in the back-ET process were distributed thermally over all internal degrees of freedom of an isolated molecule, even 10-15 ps after photoexcitation. This indicate that even at this time, thermalization in the whole molecule is not complete. Different temperatures observed in slowly and fast relaxing solvents can be attributed to different pathways of vibrational relaxation in the excited electronic state under condition of „solvent“ and „vibrational“ controlled regime, respectively.


Although far from being complete, we have obtained essentially new information about excitation and vibrational energy redistribution in a complex molecule undergoing ultrafast intramolecular ET. This study demonstrates that anti-Stokes resonance Raman scattering is a valuable tool for the study of the ET mechanism in condensed matter. Extending time-resolution and sensitivity, even more information can be expected.


5.6 References

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[Front page] [Acknowledgements] [1] [2] [3] [4] [5] [6] [7] [8] [Vita] [Declaration]

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