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

43

Chapter 4. Vibronic coupling in the first excited singlet state of DPH

4.1 Motivation

Diphenylpolyenes belong to the class of polyenes, and they are very interesting as they can serve as models for retinoids and carotenoids. The physiological function of these pigments is triggered by its photoexcitation and include isomerization and energy transfer. Efficient utilization of a limited number of photons, as well as dissipation of excess energy delivered by photons, are here of primary importance. Coupling between the electron and nuclear motions is the main mechanism which assure the functionality of these molecules.

In particular, diphenylhexatriene (DPH) is one of the most widely used fluorescent probes in studies of biological membranes [1]. A high fluorescence quantum yield in hydrophobic environments, but negligible fluorescence in water, as well as a lifetime of the excited state dependent of the environmental properties, makes this molecule very attractive for studies regarding the membrane‘s role in the cell life.

Another interesting property of diphenylpolyenes is their high third order optical nonlinearity gamma in the electronic ground state, which can be further increased after electronic excitation [2-4]. These properties, and the very fast response time of the nonlinearities (which are related to the delocalization of the pi-electron systems in the molecules), make them interesting from technological point of view.

Another interesting feature of diphenylpolyenes, related to their functionality, is the reversal of the 11Bu and 21Ag levels as the lowest excited singlet state with increasing chain lengths and an increasing gap between the two states for longer polyenes [5,6] (Fig. 4.1). In trans-stilbene (TS), the primarily excited 11Bu state also represents the lowest excited singlet state. In DPH, however, the 21Ag state is located slightly below the 11Bu state [7] with a small gap depending mainly on solvent polarizability [7,8]. In DPO, the 21Ag - 11Bu gap amounts to approximately 2000 cm-1 [7,9]. It grows with increase of the polyene chain length. The optical transition between the 11Ag and the 21Ag electronic states is forbidden (see Paragraph 2.1.3). Consequently, photoexcitation of the 21Ag state is possible only via 11Ag - 11Bu excitation, which is optically allowed.

Fig. 4.1: Molecular structure and ordering of the three lowest electronic levels in trans-stilbene (TS), diphenylhexatriene (DPH) and diphenyloctatriene (DPO).


44

Since for about twenty years it is known that the totally symmetric C=C stretching vibration of the polyenic chain strongly couples the 11Ag and 21Ag electronic states [7-12], which represent - for polyenes longer than butadiene- the S0 and S1 states, respectively. Vibronic coupling causes the vibrational frequency of this vibration in the S0 state to be shifted down and in the S1 state to be shifted up by an amount of ca. 100 cm-1. These anomalously strong shifts beyond the range of the C=C stretching frequencies can be described without assuming any changes of the corresponding bond orders, and are explained by vibronic coupling between the two electronic states [11].

Recently, it has been shown quantitatively that the radiationless 21Ag - 11Ag transfer rate in beta-carotene is directly related to the vibronic coupling strengths of the C=C stretching mode to the electronic transition, i.e. vibronic coupling plays a dominant role in 21Ag - 11Ag internal conversion [12]. Internal conversion between the primarily optically pumped 11Bu (S2) level to the 21Ag (S1) level is even faster than the 21Ag - 11Ag transfer, occurring on a femtosecond time scale [13]. The mechanisms involved in this fast transfer are not fully understood [14]. The energy gap between 11Bu and 21Ag is much smaller than that between 21Ag and 11Ag favoring vibronic coupling effects. However, in symmetric polyenes, coupling of these two excited states by an ag mode, e. g., by the totally symmetric C=C stretching mode, should not be effective because of symmetry reasons. In contrast, it has been shown that in diphenylbutadiene investigated in gas phase, the optically forbidden transition between 11Ag and 21Ag gains oscillator strength from the allowed 11Ag - 11Bu transition via 11Bu - 21Ag vibronic coupling by a low frequency bu mode [15]. Consequently, asymmetric low frequency modes should be taken into account for 11Bu - 21Ag vibronic coupling in other polyenes, too. On the other hand, 11Bu - 21Ag vibronic coupling effects by the totally symmetric C=C stretching vibration of the chain have been observed in the first excited state of asymmetric polyenes, as well as in beta-carotene [16]. For this molecule, which is assumed to belong to the C2h symmetry group in the ground state, it has been argued that in the first excited singlet state, symmetry distortions may occur. Therefore, the observed coupling effects were explained as a result of deviation from the symmetry.

Because of their chemical stability, diphenylpolyenes are very suitable as models for studying vibronic coupling [17, 18]. Like in other (not too short) polyenes, the optically accessible 11Bu state (S2) is located above the 21Ag electronic state (S1), and the gap becomes closer with decreasing chain lengths [19]. It almost disappears in the case of DPH. Furthermore, this low gap can be tuned significantly in changing the polarizability of the solvent [20]. The latter effect occurs because the S2 state is more polarizable than the S1 state and changes its energy from one solvent to another, but S1 does not. Because the energy gap between the two electronic states is one of the factors determining the strength of the vibronic coupling, the S1-S2 coupling should be influenced by changing solvents, while the S0-S1 coupling should remain nearly unchanged.

In DPH the trans-cis-trans (tct)- and cis-trans-trans (ctt)-photoisomers have been isolated as primary photoproducts [21], and it has been reported that the yield for isomerization increases in polar solvents [22]. As a consequence, the excited-state geometries determining the pathways of photoisomerization should be affected significantly by solvent polarity.


45

The excited singlet states of DPH populated after photoexcitation have been mainly investigated by time-resolved fluorescence [23,24] and transient absorption spectroscopy [25-27]. However, both the assignments of the transient absorption bands, as well as the kinetics towards an excited-state equilibrium mixture, are still the subject of controversy. It is very difficult to obtain any structural information from the broad and structureless bands of the excited-state absorption of DPH. Alternatively, vibrational spectroscopy is suitable for determining the structure of the probed state.

We use time-resolved resonance CARS and polarization CARS for the study of the excited electronic states of DPH, in order to:

  1. get structural information about the excited states in different environments. This is achieved by combining our experimental results with a normal coordinate analysis on a semi-empirical PM3 level;
  2. determine the time duration until equilibrium between the excited electronic states has been established;
  3. get information about the mixing character between the two excited electronic states.

4.2 Photophysics of DPH

The molecular structure of DPH, together with the excitation and probe scheme, is depicted in Fig. 4.2. The molecule is a linear polyene with three double bonds and two terminal phenyl rings, and belongs to the C2h point symmetry group. The delocalization of the pi-electron system along the chain gives rise to a large value of the second-order hyperpolarizability gamma. On the other hand, the existence of an inversion center determines the zero-value (in the dipole approximation) of the hyperpolarizability beta. The lowest band in the absorption spectrum (Fig. 4.3) is due to the S0-S2 transition near 350 nm. That means in molecular orbital language the promotion of a single electron from the highest occupied molecular orbital (HOMO) to the lowest unoccupied molecular orbital (LUMO). The existence of an 21Ag state below the 11Bu state has been established by many high resolution one- and two-photon spectroscopic studies on samples at low temperature [7]. For room temperature solutions, the 11Bu state is only slightly higher in energy than the dipole forbidden 21Ag state, and should be thermally repopulated. This is the reason for observing a weak fluorescence emission from the 11Bu state. Deactivation of the optically active 11Bu state to the lowest excited 21Ag state occurs on a 500 fs time scale, as being determined by the changed transient absorption signal near 650 nm [28] (see also Fig. 4.2). The assignment of this transient absorption around 650 nm to excited state electronic transitions is not fully elucidated. Assignments to both the 21Ag - n1Bu as well as the 11Bu - n1Ag transitions have been reported [25, 28], and it has been argued that the lowest excited singlet has some Bu character as well [22]. The gap between the two excited states is about 1000 cm-1 [29] and can be varied by about 500 cm-1 in choosing solvents with different polarizability alpha [20]. The lifetime of the lowest excited


46

electronic state has been measured by time-resolved fluorescence spectroscopy, showing a single exponential decay with tau = 13.1 ns in cyclohexane solution [1].

In Fig. 4.2, the wavelength for photoexcitation (lambdaUV) and the frequencies for CARS probing (omega1,omega2,omega3) near the transient absorption around 650 nm are shown schematically. CARS probing is carried out at the transient absorption band, to obtain selective resonance enhancement for the detection of vibrations originating from the excited electronic state.

Fig. 4.2: Molecular structure of diphenylhexatriene (DPH). Photoexcitation to the 11Bu state by a pulse at lambdaUV=350 nm and CARS probing of a vibrational resonance of the excited electronic state are illustrated. The relaxation from the 11Bu to the 21Ag state occurs in about 500 fs. For simplicity, the excited state absorption is indicated as a 21Ag - n1Bu transition only.

Fig. 4.3: Absorption spectrum of DPH dissolved in cyclohexane (10-3 M). The excitation wavelength is marked with an arrow.

In Fig. 4.3 is shown a typical absorption spectrum of DPH dissolved in cyclohexane at a concentration of 10-3 M.


47

4.3 Results

4.3.1 Raman spectra in ground state and time-resolved CARS spectra in excited states

The resonance CARS spectra presented here are obtained with the experimental set-up described in paragraph 3.2.2.

An excited-state CARS spectrum of DPH dissolved in cyclohexane (concentration 10-3 M) in the frequency range of 1000-1900 cm-1, obtained with excitation at ?1 =710 nm, is shown in Fig. 4.4.a. The spectrum was recorded with a temporal pulse width of 8 ps and a time delay between excitation at 355 nm and CARS probing of 20 ps. The vibrational resonances of the excited DPH (Fig. 4.4.a) are indicated by arrows. They show pronounced dips, with an additional slight dispersion-like contribution of the shape occurring within the electronic four-wave mixing background. In contrast to the DPH ground state spectrum, where only a few intense Raman lines are located near 1200 and 1600 cm-1, a much greater variety of vibrational resonances can be observed, which are of comparable intensities (see Fig. 4.4.b). These resonances cover the whole frequency region. Obviously, in the range 1050 cm-1 - 2000 cm-1 the excited state CARS spectrum exhibits a completely changed pattern compared to the electronic ground state, indicating a changed geometry. It is interesting to observe that compared to the frequencies of the C=C stretching region around 1600 cm-1 in the electronic ground state, there are strong vibrational resonances which are either down shifted (probably as a result of a decreased C=C bond order in the excited state) or unusually upshifted (as a result of dominating S0-S1 vibronic coupling) in their vibrational frequencies. It should be noted that the solvent CARS line shapes of the solution are also affected by UV pumping, occurring on a strongly enhanced four-wave mixing background. The most surprising experimental result is, however, the observation of two "high-frequency modes" at 1620 and 1780 cm-1 marked with thick arrows in Fig. 4.4.a. These lines are extremely frequency broadened. Vibrational frequencies, intensities and line widths of the excited-state spectrum were obtained by a fitting procedure [30]. The fit was carried out in three steps:

  1. First, the CARS spectrum of the DPH solution without UV excitation was fitted.
  2. From a fit of rather isolated solvent CARS lines, which change their shapes and their CARS line/background intensity ratio after UV excitation, the excited-state electronic hyperpolarizability of DPH has been determined.
  3. Taking into account the electronic hyperpolarizability of DPH, as determined before, the CARS line shapes of excited-state DPH were fitted to get their frequencies and intensities.

48

Fig. 4.4: Excited state resonance CARS spectrum (a) of DPH dissolved in cyclohexane (10-3 M) recorded in the frequency range 1050-2000 cm-1, and the Raman spectrum of the electronic ground state (b)-solid line, together with the CARS intensities determined from fit shown for comparison in (b)-column bars.

By applying this procedure, it is possible to obtain with a good accuracy [±5 cm-1] the spectral parameters of the narrow CARS resonances, marked with thin arrows in the CARS spectrum in Fig. 4.4.a. However, fitting of the broad CARS resonances above 1600 cm-1 contains considerable uncertainty. This fact is due to spectral drifts of the four-wave mixing background after excitation with respect


49

to the reference spectrum, resulting in artificial changes of the shapes of the broad dips.

Fitted CARS frequencies and relative cross-sections determined in cyclohexane solutions in the frequency range of 950-2000 cm-1 are summarized in Table 4.2 (see paragraph 4.4.1.), and represented as column bars in Fig. 4.4.b. The corresponding spontaneous Raman data of the electronic ground state of DPH dissolved in carbon tetrachloride are given for comparison in Fig. 4.4.b. Relative Raman cross-sections are also calculated as Iraman/gammaR for the Raman bands (gammaR is here the half-width of the Raman line and R means Raman resonance) and \|[boxv ]\|gammaR \|[boxv ]\|/ gammaR for the CARS bands (gammaR is the third-order hyperpolarizability of the CARS band) - see also 3.1.2.

Fig. 4.5: Resonance Raman spectrum of DPH in the low-frequency range (lambdaexcit=334.5 nm), corrected for 0K with the Bose-Einstein formula. For comparison, the spectrum of the neat solvent is given. The solvent lines are marked by (*), the DPH Raman line which serves for normalizing to the solvent line is marked with a thin arrow and the DPH Raman line of interest is marked with a thick arrow.

In Fig. 4.5 the corrected resonance Raman spectrum of DPH dissolved in cyclohexane is presented, together with the Raman spectrum of neat cyclohexane. The spectra measured in the low frequency range 10-400 cm-1 were recorded using the 334.5 nm line of an Ar2+ laser for excitation. They were corrected by dividing them through the Bose-Einstein factor , in order to determine the contribution to the Raman spectrum at 0 K. Here, is the thermal population of the -th vibrational mode, and is described by , with and kB the Boltzmann constant. This correction takes into account that at room temperature, for low frequency vibrations, higher vibrational levels i are populated and contribute to the Raman signal due to their high Raman cross-sections , where sigma0 is the Raman cross-section for the lowest vibrational level.


50

The solvent has only a single broad peak at 29 cm-1 in the low frequency range. DPH gives the dominant contribution in this region with a broad low-frequency mode at 35 cm-1. Additional narrower lines below 300 cm-1 are observed at 64, 97, 135, 187 and 257 cm-1.

4.3.2 Depolarization ratios of the Raman vibrations

In order to identify the symmetry of the observed vibrations in the excited state of DPH, the depolarization ratios of the respective vibrations were determined by a polarization CARS scheme described in paragraph 3.1.3.2. The excitation has been done with circularly polarized light at 355 nm, and the CARS spectra were recorded 50 ps after excitation. The polarization CARS experiment was carried out with an angle =71.50 between the planes of polarizations of the two incident laser beams by rotating the transmission plane of the analyser A (see Fig.3.4). The depolarization ratios were calculated, as described in paragraph 3.1.3.2, by finding the angle where the CARS signal for the respective Raman resonance vanishes.

CARS spectra of pure cyclohexane (left hand side) and of the DPH solution (5x10-4 M), recorded 50 ps after excitation with the 355 nm excitation pulse (right hand side), are shown in Fig. 4.6. Raman resonances are indicated by dashed lines. The spectra a, A, d, D of Fig. 4.6 have been obtained with =0o and =90o, respectively. Due to cross terms between lambdaR and lambdaNR in Eq. (3.15), the strong cyclohexane vibration at 1447 cm-1 occurs in both spectra as a dispersion-like shaped peak within the four-wave mixing background. In contrast, the excited state CARS lines of DPH occur as slightly asymmetric dips, which are due to the close resonance with the excited state transition around 650 nm generating a complex value for lambdaR. At =35o, it can be seen that the lineshape of the cyclohexane vibration becomes again dispersion-like, but with an opposite sign than for =0o and =90o. This feature arises because the projections lambdaR and lambdaNR at =35o (see Figs. 3.4 and 4.6.b) point to opposite directions, resulting in negative sign of the respective cross terms in equation (3.14) compared to the positive sign obtained for =0o or =90o, where lambdaR and lambdaNR point to the same direction. Furthermore, the positions of peaks and minima of the excited state vibrational resonances are nearly exchanged. The strengths of the Raman resonances show a pronounced minimum at the angle =25o, resulting in depolarization ratios ~ 0.72 for these lines. For the solvent line at 1447 cm-1 the measured depolarization ratio of 0.7 is in accordance with the data reported in the literature [31]. The small peak in Fig. 4.6.c is probably due to a weak shoulder of the cyclohexane Raman line being observed in the spontaneous Raman spectrum which may be polarized differently from the main peak. Residual structures in the spectrum in Fig. 4.6.C are caused by a weak induced birefringence in the sample. Drifts in the base line are mainly due to imperfect reference spectra. Similar depolarization ratios values of about 0.72 in the excited state of DPH were obtained in the whole frequency range under investigation (1000-1900 cm-1) and are summarized in Table 4.1.

It is useful to compare these values with the corresponding values in the ground state. The determination of the depolarization ratios of the Raman vibrations in the ground state have been done for DPH dissolved in acetone (because of better solubility -


51

concentration 1*10-2 M) by excitation with the linear polarized light of an argon laser at 458.08 nm. The emitted Raman signal was measured in a rectangular geometry in the directions parallel and perpendicular to the direction of the polarization of the laser light, and the depolarization ratios were calculated according to rho= I((/ I\|[bottom]\|. The results are shown in Table 4.1.

As can be seen in Table 4.1, the vibrations in the excited states are considerably less polarized than the corresponding vibrations in the electronic ground state. A depolarization ratio below 0.75 for all the observed Raman resonances in the excited state as well as for the Raman lines in the electronic ground state indicates that the modes should be of predominant ag symmetry in the frequency range under consideration.

Fig.4.6: Polarization CARS spectra of cyclohexane (spectra a, b, c, d) and excited state polarization CARS spectra of DPH dissolved in cyclohexane in a concentration of 5x10-4 M (spectra A, B, C, D). The spectra of DPH have been recorded at 50 ps time delay after excitation at 355 nm with circularly polarized light. The CARS spectra were measured with an angle =71.5o between the planes of polarizations of the laser beams of the frequencies (2 and (1 respectively. Spectra were recorded with different transmission planes \|[PSgr ]\| of the analyzer.


52

Table 4.1: Depolarization ratios of the electronic ground state and of the first excited state of DPH. Spectra of the electronic ground state and depolarization ratios were obtained from DPH dissolved in acetone (1*10-2M) and measured at an excitation wavelength of 458.08nm. CARS frequencies of the first excited singlet state of DPH (5*10-4 M in cyclohexane) were recorded with 50 ps time delay after photochemical excitation at 355nm. For CARS generation we used an excitation wave length lambda1=710nm. Depolarization ratios rhoR of the excited electronic state were obtained in determining the planes of polarization: \|[PSgr ]\|=900-betaR for suppression of the CARS lines.

Electronic ground state

 

First excited singlet state

 

omegaR (cm-1)

(R

omegaR (cm-1)

(R

 

 

1795

0.7±0.07

 

 

1620

0.72±0.05

1607 0.325±0.015

 

 

1595 0.325±0.015

 

 

1588 0.39±0.02

 

 

1570 0.39±0.02

 

 

 

 

1542

0.71±0.05

 

 

1495

0.73±0.05

 

 

1420

0.70±0.06

 

 

1330

0.72±0.06

 

 

1310

0.72±0.05

 

 

1290

0.73±0.07

1253 0.39±0.02

 

 

 

 

1245

0.70±0.05

 

 

1192

0.72±0.06

1178 0.455±0.02

 

 

 

 

1172

0.74±0.07

1157 0.52±0.02

 

 

 

 

1158

0.72±0.07

1144 0.39±0.02

 

 

 

 

1143

0.68±0.09

4.3.3

4.3.3 Background free CARS measurements

4.3.3.1 Background free CARS measurements of DPH in octane

Because the exact characterization of the Raman resonances from the fit of the very broad CARS shapes is subject of some uncertainties, the polarization CARS scheme (see paragraph 3.1.3.2) has been used as an additional method to confirm the position of the two very broad CARS bands of DPH. The spectra obtained for DPH dissolved in octane without and with background suppression are presented in Fig. 4.7.a and 4.7.b, respectively. Background free CARS spectra are obtained with the plane of the analyzer A perpendicular to the polarization plane of the nonresonant background PNR (see Fig. 3.4). The strong asymmetric CARS bands (4.7.a) transforms under these conditions in almost symmetric maxima (4.7.b), which give the real vibrational frequencies like in a spontaneous Raman experiment.


53

Fig. 4.7: Resonance CARS spectra of DPH in octane (5x10-4 M) measured under normal conditions (a) and with the background-free technique (b).

4.3.3.2 CARS measurements of DPH in different solvents

The solvent influence on the frequency of the observed Raman resonances was further studied. Six solvents (methanol, acetone, hexane, octane, cyclohexane and dimethylsulfoxide) were chosen, which differ in their polarities, viscosities, and polarizabilities. Moreover, a mixture of glycerol and methanol was prepared in the volume proportions glycerol/methanol 10%, 20%, 30% and 40%. The polarity induces a change in the dipole moment of the molecule, the viscosity makes the molecule more rigid, and the polarizability changes the energy gap between the first and second excited states.

The analysis of the spectra shows that only minor changes of the excited state frequencies (less than 10 cm-1) and of the relative intensities were observed in the frequency range 1000-1550 cm-1 for various solvents. However, the two broad Raman resonances above 1600 cm-1 undergo considerable changes. Fig. 4.8 depicts the background free excited state spectra of DPH dissolved in dimethylsulfoxide and in methanol, respectively, in the frequency range 1550-1900 cm-1. They show strong shifts of these broad bands.


54

Fig. 4.8: Background-free CARS spectra of DPH after photochemical excitation obtained in the frequency range 1550-1900 cm-1. Dashed line: DPH (5x10-4 M/l) dissolved in methanol; solid line: DPH (5x10-4 M/l) dissolved in dimethylsulfoxide.

A detailed analysis carried out in the six solvents mentioned before shows a clear correlation of these shifts with the solvent polarizability (Fig. 4.9) and no correlation with the solvent polarity or viscosity (Fig. 4.10).

In contrast to the shifts observed for the two vibrations in the excited singlet state, we did not observe any solvent dependent shifts of the Raman frequencies of DPH in the electronic ground state. Additionally, the vibration at 1754 cm-1 of the excited singlet state of DPO - the analog of the 1780 cm-1 band in DPH - does not show any significant frequency shift in changing the solvent. The main difference between DPO and DPH is the higher gap between the first and second excited states (about 2000 cm-1) in DPO. Therefore, the shifts observed in DPH gives an indication that specific effects should occur.


55

Fig.4.9: Dependences of the two high-frequency vibrations above 1600 cm-1 of the excited electronic state of DPH on polarizability of neat solvents (°) and of mixture of glycerol and methanol (·). The solvents used are: (1) methanol, (2) acetone, (3) hexane, (4) octane, (5) cyclohexane, (6) dimethylsulfoxide, G/M 10=10 vol% glycerol in methanol, G/M 20=20 vol% glycerol in methanol, etc.

Fig.4.10: Dependences of the two high-frequency vibrations above 1600 cm-1 of the excited electronic state of DPH on solvent polarity (a) and viscosity (b). The solvents used are: (1) methanol, (2) acetone, (3) hexane, (4) octane, (5) cyclohexane, (6) dimethylsulfoxide.


56

4.3.4 Kinetics of the CARS spectra

In order to gain further information about the origin of the Raman bands in the excited singlet states of DPH, we measured the time evolution of the intensities of these bands.

Fast kinetic measurements are shown in Fig. 4.11. The CARS spectra of DPH dissolved in cyclohexane (concentration 1*10-3 M) were obtained with different time delays between the pump laser at 363 nm and the CARS probe at 726 nm. In this experiment, pulses of 2 ps duration have been used. From the spectra, it can be clearly seen that:

  1. The CARS dips grow immediately after excitation, i.e., limited by our instrumental response.
  2. The relative intensity of the vibrational resonances does not change with the delay.
  3. The spectra remain unchanged for long delays up to 200 ps.

These facts indicate that the Raman bands belong to the same electronic state, which should be the optically allowed 11Bu and the long living (about 13 ns) 21Ag electronic states. This is another indication of mixing between the two excited states.

Fig.4.11: Excited-state resonance CARS spectra of DPH dissolved in cyclohexane (10-3 M) recorded at 726 nm to different delays after UV (363 nm) excitation.


57

4.4 Discussion

4.4.1 Molecular geometry and assignment of the Raman frequencies in the ground and excited states

MNDO-Configuration Interaction (CI) semi-empirical calculations done by Pfeiffer et al. [33] with the MOPAC93 package [36] indicate a plane molecular geometry in the ground state, due to pi-electron delocalization. This affirmation is supported by other authors [32]. The planarity at nearly C2h symmetry seems to be preserved during the transition in the first and second excited singlet states [33]. Within this symmetry, intense Raman lines are expected to occur only for modes belonging to the Ag species (see paragraph 2.1.1.3). In the spectral range of interest (850-1650 cm-1), these are in-plane stretching vibrations of the C-C skeleton (ny-modes), in-plane deformations of the CH bonds (delta-modes) and modes related to the breathing vibration alpha-A1g mode of the benzene ring (at 991 cm-1 in isolated benzene). The strongest Raman lines in the ground-state spectrum of DPH nearly coincide with frequencies of hexatriene, which were assigned by Langkilde et al. [34]. Analysis of the potential energy distribution (PED), derived from normal mode calculation for DPH [33], shows that most of the modes between 880 and 1607 cm-1 are highly localized in either the chain- or benzene subsystems. Only three modes of the Ag species between 1200 and 1350 cm-1 exhibit a mixture between chain- and ring-stretching modes. The benzene modes characterized by their species under D6h symmetry are degenerate modes which are split according to the attachment of benzene to the polyenic chain [35]. The modes related to the hexatriene segment are named by numbering of the Ag modes for this molecule. The assignment given in the right column of Table 4.3 for the ground-state vibrations is based on the calculations done by Pfeiffer et al. [33].

Table 4.2. Comparison of Raman spectra of DPH dissolved in cyclohexane electronic ground state with transient resonance CARS spectra originating from the first excited singlet state. An assignment related to Raman spectra of hexatriene (hx) and benzene (bz) is presented.

CARS, excited state

 

Raman, ground state

 

Assignment related to Raman spectra of hexatriene (hx) [34] and benzene (bz) [35]

ny (cm-1)

\|[boxv ]\|gammaR\|[boxv ]\|/gammaR (au)

ny (cm-1)

Iraman/gammaR (au)

 

 

 

880

2

bz.alpha_A1g

970

13

 

 

 

 

 

999

11

hx.ny11

1080

30

 

 

 

1131

73

 

 

 

1143

57

1144

31

hx.ny10

 

 

1157

22

bz.delta_E2g

1160

57

 

 

 

1185

60

1178

21

bz.delta_E2g

1240

57

 

 

 


58

 

 

1253

22

hx.nyg, ny9

 

 

1295

3

bz.ny_B2u

1322

55

 

 

 

 

 

1331

4

bz.ny_B2u

1410

45

 

 

 

 

 

1446

15

bz.ny_E1u

 

 

1496

6

bz.ny_E1u

1490

100

 

 

 

1542

98

 

 

 

 

 

1570

19

bz.ny_E2g

 

 

1588

77

hx.ny6

 

 

1595

100

hx.ny5

 

 

1607

38

bz.ny_E2g

1620

60

 

 

 

1795

17

 

 

 

4.4.2 Bond order equalization in the first and second excited state

The semi-empirical calculations done by Pfeiffer et al. [33] give also information about the bond orders of the skeletal bonds, i.e., about the geometry of the molecule in both ground and excited singlet states. This subject will be discussed in the following.

In order to reproduce the correct term ordering of the 21Ag and 11Bu excited states, it is necessary to include double excitation in the CI calculation. The calculation can be confined to the two highest occupied levels of the ground state configuration, and to the two following lowest unoccupied molecular orbitals. These four molecular orbitals are practically determined by the pi-electron system of the hexatriene backbone. They belong (with increasing energy) to the bu, ag , bu and ag symmetry species, respectively. Compared to the closed-shell configuration for the 11Ag state, the second excited singlet of 11Bu type is nearly perfectly a configuration with singly excited HOMO rarr LUMO transition. The first excited singlet of 21Ag type can be described as a combination of two singly excited configurations HOMO rarr LUMO+1, HOMO-1 rarr LUMO and one doubly excited closed-shell structure (HOMO, HOMO rarr LUMO, LUMO). Applying the PM3-Hamiltonian and the CI option OPEN (4,4) Pfeiffer et al. [33] obtained a gap between the 11Bu and the 21Ag state of about 2000 cm-1 (that is nearly the same as obtained from experiment [6, 7]), and a correct ordering of the two excited states.

The calculated geometry gives strong changes of bond lengths in the pi-chain for the two states in comparison to the ground state condition, as shown in Fig. 4.12.


59

Fig. 4.12: Calculated bond length of DPH along the pi-chain. (a)-electronic ground state; (b) local minima of the 21Ag and 11Bu excited electronic states. The arrow between these two states indicate mixing.

The ground state geometry of DPH exhibits a pronounced alternation of Ci-Ci+1 bond lengths between neighboring bonds in the chain, which is typical for a polyenic structure. The Bond Length Alternation (BLA) given by BLA= , with ri the bond lengths, becomes BLA 0.08. Both excited states show decreased bond orders of double bonds. However, in contrast to the 11Bu state, where the bonds tend to equalize (BLA=0.02), in the 21Ag state two bonds are found as pronounced double bonds, but with a reversal of the former double- and single-bond positions.

According to Pfeiffer‘s calculations [33], one can expect upshifts of some tens of wavenumbers of the vibrational frequencies of the chain normal modes containing a high degree of single-bond C-C stretching motions (about 1150-1300 cm-1 in the electronic ground state), while those vibrations which are strongly localized in the phenyl rings exhibit only small shifts of some wavenumbers. In the C=C double-bond stretching region of the chain (about 1600 cm-1 in the electronic ground state), considerable down shifts of some tens of wavenumbers are calculated. These trends hold for the 21Ag and 11Bu states as well. Quantitatively, the calculated down shifts in the double-bond region are stronger for the 21Ag than for the 11Bu state. The exception from those "well behaving modes", which shift down if the bond order of the double bonds is decreased, is one totally symmetric double-bond stretching vibration. For this vibration, upshifts of 211 and 84 cm-1 were calculated for the 21Ag and 11Bu excited states, respectively [33].


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4.4.3 Origin of the Raman resonances

Now it is important to discuss the origin of the excited-state CARS spectra. Under off-resonance excitation conditions and for DPH concentrations below 10-3 M/l, CARS lines from DPH molecules in the electronic ground state can hardly be observed. The lower concentrations of molecules in the excited states can only be detected by resonance CARS spectroscopy. This is due to the signal enhancement which is achieved by using a transient electronic resonance of the excited state. The appearance of CARS lines of the excited DPH as dips further confirm resonance enhancement due to the absorption band of the excited electronic state near 650 nm.

If the assignment of the 650 nm transient absorption as a pure 21Ag - n1Bu electronic transition [25-27] were correct, then the CARS spectra should originate from the 21Ag state. Consequently, one upshifted frequency should be observed, due to the 11Ag-21Ag vibronic coupling. However, two CARS resonances are observed upshifted to 1620 and 1760 cm -1 in the excited DPH molecules dissolved in cyclohexane. These frequencies nearly coincide with calculations predicting two upshifted totally symmetric C-C double-bond vibration, one for the 11Bu and the other one for the 21Ag electronic state [33].

Furthermore, vibrational resonances detected in the fluorescence excitation spectra of long-chain polyenes observed in the range of 1750-1800 cm are due to the 21Ag electronic state [10]. It is known that this strong upshift occurs because of 11Ag -21Ag vibronic coupling [10, 11]. The excited-state CARS spectra of DPO shows only one rather sharp vibrational resonance at 1755 cm-1 in that region [17], which nearly coincides with one excited-state vibration of DPH at 1780 cm-1. On the other hand, the excited-state Raman spectrum of DPB has been attributed to the 11Bu or to a mixed electronic state [18]. In this molecule only one very broad line at 1650 cm-1 has been observed corresponding to a frequency at 1620 cm-1 calculated for the 11Bu state [37]. This resonance coincides with the other up-shifted vibration of the excited DPH. Thus, one can conclude that the observed vibrations in DPH belong to the 11Bu and to the 21Ag electronic states.

In the next step, it has to be distinguished between a 11Bu - 21Ag thermalized mixture [7] and an excited singlet of mixed 11Bu and 21Ag character. Assuming two separate excited electronic states after primary population of the 11Bu state, fast energy transfer to the 21Ag or to the mixed state is expected. The transfer time (500 fs [28]) is faster than our time resolution. However, the transfer from the hot but thermalized excited electronic states to the solvent cage should occur on a 10 ps time scale [38, 39]. Assuming a gap of 1000 cm-1 between the excited states in the cyclohexane solution, a thermal population of the 11Bu state at room temperature below 0.1% of that of the 21Ag population should result [27]. Consequently, the initially populated 11Bu state should dramatically drop to a value far below the detection limit for the vibration belonging to the 11Bu state after about 10 ps (which is a usual thermalization time in liquids). In contrast, the time-resolved vibrational spectra show that the relative strength of the vibrational resonances attributed to the Ag and Bu electronic states are independent on the delay and that only one excited state is populated. The growth in the population of this electronic state is finished at least after 1-2 ps, which is in accordance with the result of Atom Yee [28]. Furthermore, in changing the solvent and hence the gap between the 21Ag and 11Bu electronic states, a strong alteration of the relative strength of vibrations belonging to different electronic states has to be expected, according to a changed Boltzmann equilibrium. In contrast, the main effect is the frequency decrease of the two broad Raman resonances with increasing solvent polarizability (Fig. 4.9). Because the gap


61

21Ag - 11Bu narrows with increasing polarizability of the solvent, the dependence in Fig. 4.9 gives evidence of a mixed 21Ag - 11Bu excited state.

This will be discussed in the following paragraph.

4.4.4 Mechanisms of vibronic coupling

In his book about vibronic coupling mechanisms [40], Bersuker has shown that the adiabatic approximation can be applied only if , where the term on the left side is the energy quantum of vibrations in the electronic state under consideration (k or m) and and represents the electronic energy levels m or k. Because the gap between the first and second excited state of DPH is about 1000 cm-1, it is obvious that the adiabatic approximation cannot be applied and vibronic coupling effects have to be considered.

For a discussion of the vibronic coupling mechanism, the major experimental findings are reviewed here. First, two unusually upshifted bands have been observed in DPH with frequencies higher then 1600 cm-1. The second interesting aspect is the decrease of their frequency with increasing solvent polarizability, i.e., with decreasing the 21Ag - 11Bu gap. If the molecule keeps a planar configuration, and the C2h symmetry is maintained in the excited state, coupling between the 21Ag and 11Bu states by the ag mode is symmetry forbidden, as discussed in paragraph 2.1.1.3. In the following, two mechanisms of vibronic coupling will be discussed, which are able to explain the appearance of the two upshifted vibrational frequencies, as well as their solvent dependence. These are: (i) distorsion of symmetry by two rotamers and (ii) vibronic coupling by a bu-type vibrational mode influencing the potential of the high-frequency ag mode.

4.4.4.1 (i) Coexistence of two species in the 21Ag state

In the following, the possibility of molecular symmetry distortion and its influence on vibrational spectra will be discussed. In this model, the two vibrational frequencies of the same vibrational mode originate from two different species (for example two rotamers) in the 21Ag state, both deviating from C2h symmetry (due to the twisting of the backbone). In this case, vibronic coupling by an ag mode is not strictly forbidden [16] and conformational dependent coupling constants of the two rotamers can generate two frequencies belonging to the same C=C stretching motion. Because of the very small gap, even with rather small coupling constants, vibronic coupling can be quite effective. Both vibrational frequencies are expected to shift down with decreasing gap between the two excited electronic states, as they belong to the lower of the two excited singlet states, i.e., to the 21Ag state. Frequency broadening can be caused by conformational distributions around the two equilibrium geometries. Other vibrational modes which do not couple the two excited electronic states are not expected either to be shifted in solvents of different polarizabilities, nor unusually frequency broadened due to conformational distributions.

However, according to the electronic structure calculations (MOPAC93 [36]) presented in the paragraph 4.4.2, and because of the pronounced pi-electron delocalization, DPH is planar in the electronic ground, as well in both excited electronic states, maintaining C2h symmetry. Furthermore, the existence of two different species seems to be unlikely


62

because the observed kinetics (rise of the CARS lines originating from S1 and fluorescence decay [1]) give no hints for two separate species in the excited state.

4.4.4.2 (ii) Model of vibronic coupling with an asymmetric low-frequency mode

In the following, a model of vibronic coupling will be presented, which is based on the pseudo Jahn-Teller effect. This model was developed by Pfeiffer et al. [33]. It can reproduce the potentials of the high frequency ag mode, resulting in two upshifted frequencies.

4.4.4.2.1 Determination of the modes responsible for vibronic coupling

Symmetry considerations require that vibronic coupling between the 21Ag and 11Bu states is mediated by vibrational modes of bu type only. For the 11Ag -21Ag coupling, only ag -type modes are admitted, and it can be expected that the modes with the largest origin shift, i.e., with the strongest Raman activity will contribute substantially. The equilibrium geometries of the 21Ag and 11Bu states differ markedly from that of the ground state. By decomposing the nuclear displacements in normal coordinates the dominantly contributing modes can be identified. Atomic positions are calculated optimizing the geometry for the respective electronic state on the quantum chemical level characterized in section 4.4.1. By taking the normal coordinates calculated for the ground state, the relative intensities of the excited states in-plane modes are given in Fig. 4.13. The modes are numbered by increasing wavenumbers. For both final geometries, Fig. 4.13 shows that in the low frequency region there is a dominating contribution from just one low-frequency bu mode calculated at 40 cm-1 in the ground state. The same normal mode appears in both excited states with slightly shifted frequency at 42 cm-1 in the 1Bu and 49 cm-1 in the 2Ag state. In the high frequency region there is one dominant contribution from the high-frequency totally symmetric C=C ag stretching mode. The corresponding normal coordinate represents a vibration with antiphased elongation in all neighboring C-C bonds of the polyenic chain. This mode is known to give the largest origin shift value along the pi-chain and generally results in the strongest bands in the resonance Raman spectra of the polyenes. Both low- and high-frequency modes are marked with arrows, and their geometry is shown in the upper part of Fig. 4.13. The bu mode is the zero-node string mode of the polyenic chain. The applied semiempirical calculation of vibrational frequencies reproduces the experimental frequencies in the low-frequency range with an accuracy better than 10%. Therefore, the broad intense band observed at 35 cm-1 in the ground state spectrum (Fig. 4.5) is proposed as the candidate for the bu coupling mode.


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Fig. 4.13: Decomposition of geometrical displacements in the two lowest excited singlet states according to normal coordinates of in-plane modes. Modes number 3 and 78 are those taken as involved in the vibronic coupling.

4.4.4.2.2 Pseudo-Jahn-Teller effect in the excited states of DPH

Based on the calculations presented in the preceding paragraph, a 3-state model has been chosen to describe vibronic coupling in the case of DPH, with two active coupling modes (normal coordinates Q1 for the a mode at 1595 cm-1 , Q2 for the bu mode at 40 cm-1). It is the generalization of the two-state, one-mode model of coupling between 11Ag and 21Ag states, which was developed to reproduce the upshift of the 1600cm-1 mode in the excited state relative to its ground state frequency [11]. Within the three-state model, the effective two-dimensional potential energy surface E(Q1, Q2) has been estimated by diagonalization of the diabatic Hamiltonian

(4.1)

The indices denote the electronic singlet states involved (index 0 for the 11Ag ground state, 1 and 2 for the excited 21Ag and 11Bu states, respectively). The vibronic coupling constant (01 is set equal to the value derived by Orlandi and Zerbetto for hexatriene [41] (|alpha01|=1.65 eV A-1 amu -1/2). The estimates within the Pariser-Parr-Pople (PPP) method give for alpha12 a value approximately one order of magnitude lower than that, and it is set to 0.2 eV A-1 amu-1/2. Within this approximation, there is no vibronic coupling between the 11Ag -11Bu states through the bu mode. The harmonic approximation is chosen for the diabatic potentials. Thus, the potentials in the two (uncoupled) excited singlet states can be written as:

(4.2)

(4.3)


64

where and are the elongations of the ag mode and of the bu mode, respectively, and are the positions of the diabatic minima of the corresponding potentials (mass normalized origin shifts), and Delta12 is the gap between the two minima. Vibronic coupling between the states is performed by a linear coupling ansatz <SPAN CLASS=@ITALIC@>.</SPAN>

Coupling results in the two dimensional potential.

(4.4)

Under these conditions a double well potential along the Q1 coordinate in the first excited singlet state is generated by a pseudo-Jahn-Teller mechanism. It arises from coupling of both potentials (Eqs. 4.2 and 4.3) in assuming a sufficiently large shift between the minima . For an estimated value of d = 0.18 Å, two minima arise in the potential of the lowest excited singlet state.

In Fig. 4.14.a and 4.14.b is shown the double minimum potential of the two vibronically coupled states for the totally symmetric C=C stretching mode. As a result, the same vibrational mode give rise to two vibrational frequencies, one in the potential minimum of the 21Ag excited state, and the other one in the potential minimum of the 11Bu excited


65

Fig. 4.14: (a) Effective potential for the totally symmetric C=C stretching coordinate around 1700 cm-1 in the two vibronically coupled states. In the 21Ag state the pseudo-Jahn-Teller effect leads to a double-well potential; (b) Enlarged segment of the range of avoided level crossing between the 11Bu and 21Ag singlet states. The dashed line represents the potential curve for a smaller gap. Horizontal lines indicate the energy positions for the lowest vibrational levels in the respective diabatic potentials (left 11Bu - section, right 21Ag - section). The assumed Raman transitions are indicated; (c) Contour diagram of the effective 2-d vibrational potential for the first excited singlet state of DPH resulting from strong vibronic coupling (the cut at Q2= Q20/2 represents the lower potential in (b).

state. From the curvature of these minima, the two frequencies of the quasi bound vibrational levels around the and minima have been determined. Fig. 4.14.c shows also a contour diagram of the effective 2-d vibrational potential for the excited singlet states of DPH resulting from strong vibronic coupling.

The observed dependence of vibrational frequencies on the solvent polarizability can be explained by the following considerations. In transparent solvents, the effective vibronic coupling between the excited states in the first approximation varies with the Lorenz-Lorentz molar refraction according to the relation:

(4.5)


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Fig.4.15: Dependences of the two high-frequency vibrations above 1600 cm-1 of the excited electronic state of DPH on the polarizability of neat solvents (ç) and of mixture of glycerol and methanol (æ). The solvents used are: (1) methanol, (2) acetone, (3) hexane, (4) octane, (5) cyclohexane, (6) dimethylsulfoxide, G/M 10=10 vol% glycerol in methanol, G/M 20=20 vol% glycerol in methanol, etc. Straight lines represent calculated frequency dependences on the vibronic coupling strength of the bu-mode between the excited electronic states.

The equation is derived applying Hudson‘s rule [20] for the dependence of the effective coupling element on the solvent refractive indices n. Here, beta is a positively valued parameter related to the transition dipole and polarizability properties of the solute molecule. Applying Eq. (4.5) in combination with Eq. (4.4), the observed frequency shifts versus solvent polarizability are reproduced qualitatively, as shown in Fig. 4.15. The two minima arise from the originally diabatic potentials of the 21Ag and of the 11Bu potentials. This also explains the close correspondence of the two vibrational frequencies measured in DPH either to the excited state frequency observed in DPO at 1755cm-1 (assigned to the 21Ag state [17]) or to the band in DPB at 1620cm-1 measured after electronic excitation which has been assigned to the 11Bu or to a mixed 11Bu/21Ag state [18]. This double minimum appears in the case of DPH through vibronic coupling by the bu mode under the condition of nearly zero gap between the two lowest excited singlet states. Based on this model, the anomalous character of the two bands in the C=C stretching range with respect to solvent shift and high spectral broadening were inter-preted as a pseudo Jahn-Teller-like vibronic coupling in the excited state of DPH [33].


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4.4.4.2.3 Frequency broadening by vibrational coupling under the condition of the pseudo-Jahn-Teller effect

Within the proposed model, there is a simple explanation for the broadening of the two high-frequency stretching bands. It results from the excited state dynamics proceeding predominantly within the two-dimensional subspace of molecular vibrational coordinates, as given by the contour-diagram in Fig. 4.14.c. Fig. 4.14.a and 4.14.b give the cut through the potential at Q2=Q20/2 with a double well along the Q1 coordinate. Vibronic coupling of the 21Ag and 11Bu states by the low-frequency bu mode, according to the coupling scheme of Eq. 4.1, results in an anharmonic coupling between the Q1 and the Q2 coordinates. The periodic variation of the Q1 potential during the oscillation in the Q2 mode modifies the Q1 curvature and leads to a broadening of the bands for the high-frequency oscillation. The lowering of the saddle point at maximum elongation of the Q2 mode may lead to a cross over of the primarily excited wavepacket from one valley of the Q1 potential to the other, and thus, periodically varying the probability of finding the molecule at each region of the potential.

The modulation of the Q1 potential with the cycle of the low-frequency oscillation yields a Fourier transform representing a spectral broadening Deltaomega? ap omega2. ??As spectral broadening and solvent effects for vibrational modes are absent for all other modes, one can assume that the essential coupling in the excited state could be confined to the two coordinates Q1 and Q2 . The other modes shall be described by independent normal coordinates.

4.5 Conclusions

In conclusion, two up-shifted and extremely broad Raman resonances have been observed in the excited state of DPH, with frequencies higher than 1600 cm-1. The measured frequencies in different solvents show a clear dependence on solvent polarizability, but no dependence on viscosity or polarity of the solvent. These effects are not observed in related diphenylpolyenes, like DPO or diphenylbutadiene.

Moreover, it has been shown that there is no difference in the kinetics of the observed modes.

The two broad Raman resonances are assigned to the totally symmetric C=C stretching vibration, based on semiempirical calculations and similarity of the frequencies with the frequency of this mode in related polyenes (DPO and diphenylbutadiene). The same considerations suggest that the up-shift of the frequencies is due to S0-S1 vibronic coupling.

From the observed polarizability dependence of the frequencies of the C=C stretching mode, which is essentially a dependence on the gap between the S1 and S2 excited singlet states, and from the kinetics measurements, one gets evidence of S1-S2 vibronic coupling.


68

These findings are rather unusual, as it is believed that, because of symmetry reasons, such effects should not occur. Two explanations for the experimental findings are presented:

1. Simultaneous existence of two rotamers in the first excited singlet state. In this case, small distorsions of the symmetry are reflected in the vibrational spectra, due to their influence on the vibronic coupling effects, which are further influencing the vibrational spectra.

2. Distorsion of the potential of the totally symmetric C=C mode by a low frequency bu mode. According to this model, coupling of the two excited singlet states by a low frequency asymmetric mode generates a double minimum for the C=C stretching coordinate in the lowest excited singlet state. Consequently, the two frequencies originate from this mode. Furthermore, anharmonic coupling between the two modes (high- and low-frequency) leads to strong frequency broadening of the C=C stretching bands.

Because these effects appear under the condition of nearly degenerate excited singlet states, this explanation was identified with a pseudo-Jahn-Teller model.

Under the viewpoint that vibronic coupling is believed to control the S2-S1 relaxation, our investigations should contribute to an understanding of the S2-S1 dynamics occurring on a fs time-scale.


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