J. Phys. Chem. 1993,97, 1758-1164
1758
ARTICLES Local Anisotropy and Structural and Phonon Dynamics of Mn04- in Glassy and Liquid LiC14Hz0 by Ultrafast Transient Hole Burning Jongwan Yu and Mark Berg' Department of Chemistry and Biochemistry, University of Texas at Austin, Austin, Texas 78712 Received: November 12, 1992
The division of solvent dynamics into phonon and structural components recently found in organic systems is also found for the d - d transition of Mn04- dissolved in the highly ionic solvent LiCMH20. An analysis of the polarization dependence of the transient hole burning spectra is developed, yielding the local structural anisotropy of the solvent. Anisotropic interactions are found to be similar in importance to isotropic interactions.
I. Introduction The distribution of solvent-solute interaction strengths in solution is evident in the breadth of the absorption spectra of solutes in liquidsand glasses. The molecular motion of the solvent modulates these interactions, causing the electronic state energy of an individual solute to vary in time. Recent transient hole burning (THB) measurements have shown that the dynamics of the electronic state energy are decomposable into two major components.'-' One component has a temperature-independent subpicosecond relaxation time, even below the glass transition, and has been identified as a phonon-modulated interaction. The other component, denoted as a structural interaction, is static below the glass transition, but has a relaxation time which rapidly decreases to the picosecond timescale with increasing temperature. Although there are many important details of the structural relaxation which are not yet established, the existence of such a relaxation is not surprising. Solvation theories from classical continuum theories4to more recent molecular theories5 predict solvation rates which are governed by structural features, i.e. the relaxation times are linked to the solvent viscosity. The role of very fast collision- or phonon-like motions was assumed to be minor. The fact that an additional ultrafast process could play a major role in solvation was identified in THB mea~urementd-~ and computer simulations,6'6 and also has been supported by photon ech0'~-1~ and time-resolved Stokes shift experiments.20 At lower temperatures, the phonon and structural components relax on distinctly different rates. Transient hole burning measurements in low temperature organic systems have used this fact to measure the magnitude of each component over wide temperature r a n g e ~ . ~InJ particular, the continuity between the ultrafast relaxation processesin the liquid and phonon-modulated interactions in the glass was used to identify the fast component in the liquid as a phonon-like process. This paper seeks to determine the generality of these features by examining a very different type of solution. Experiments are performed on a d - d transition of Mn04-in the highly ionic and inorganic solvent LiCb6H20. This system is a distinct contrast to the n - w + transition of dimethyl-s-tetrazine in organic solvents which have been reported previously.2J In addition, the triply degenerate excited state of MnOd- permits a new type of information to be extracted from THB. This paper analyses transient hole burning in the case of degenerate excited states to show that the anisotropy of the local structure can be extracted from spectra taken at different polarizations. Transient hole burning21-2' is a time-resolved spectroscopy 0022-3654/93/2091- 1158$04.00/0
which we have applied to the dynamics of solvent/electronic state interactions.'-' In the ground state, the solutes exist in a variety of local solvent configurations, leading to a distribution of absorption frequencies. An initial light pulse is used to bleach the subset of solute molecules which are in solvent configurations which bring them into resonance with the pulse. A deficit in absorption strength, or a spectral hole, is left at the frequency of the initial light pulse. The hole shape is measured by a delayed probe light pulse. With increasing time, the movement of the solvent mlecules randomizes the frequencies of the solutes, causing the spectral hole to broaden. If significant solvent motion occurs during the initial light pulse, the earliest observable hole will be broader than the frequency width of the bleaching light pulse; its width will reflect the extent of relaxation which has occurred during the pulse duration. At long times when the solvent has reestablished equilibrium, the hole will broaden to the width of the absorption spectrum. In a glass, equilibrium is never reestablished, and permanent hole burning is possibleOz4 This description is adequate for solutes with nondegenerate states. The additional features relevant to a degenerate excited state are shown in Figure 1. If bleaching and probing occur to the same excited state (diagonal probe), there is no difference in the analysis. To the extent that the solvent perturbation is isotropic, the different excited states will be perturbed in unison (Figure 1A). In this case, observing the hole on a transition different from the bleaching transition (off-diagonalprobe) gives the same width as observing the hole on the bleaching transition. On the other hand, if the solvent perturbation has a lower symmetry than the solute, the excited states will be split. Since the amount of splitting will vary among different solute molecules, the hole observed on a different transition will be broader than the hole observed on the burning transition (Figure 1B). The transitions to the different excited states have transition dipoles oriented in different directions. Observation of the hole with the probe polarization parallel to the bleaching polarization favors probe absorption on the same transition; observation with the probe polarization perpendicular favors probe absorption on a different transition. Thus, the polarization dependence of the THB spectra can be used to determine the extent of additional broadening caused by solvent-induced splitting of the excited states and thereby the degree of anisotropy of the local solvent structure. This procedure is derived rigorously in section I1 and applied to experimental results in section V. Related ideas on correlations between nondegenerate states have recently been presented by Sevian and Skinner.25 0 1993 American Chemical Society
Transient Hole Burning of MnOo- in LiCl-6H20 A. Isotropic diagonal probe
off-diagonol probe
a b c ---
TTi
a b I
fast frequency perturbations is given by F(w), which is assumed to be the same for each of the three transitions. This distribution is taken to be a Gaussian with a standard deviation UF:
c
/
1 ' 1, B. Anisotropic diagonal probe
The Journal of Physical Chemistry, Vol. 97, No. 9, 1993 1759
off-diagonal probe
Figure 1. Transient hole burning on a solute with a degenerate excited state under isotropic (A) or anisotropic (B) solvent perturbations. The bleaching pulse (solid arrow) selects only molecules with one excited state (a) resonant with the pulse. Subsequent absorption measurements on the same transition (dashed arrows, diagonal probe) only detect bleaching at the frequency of the bleaching pulse. If the solvent perturbation are isotropic, the frequencies of the band c transitions will be perfectly correlated with the frequency of a. Bleaching measured on these transitions (dashed arrows, off-diagonal probe) will be confined to the frequency of the initial pulse (A). If anisotropy of the solvent interaction induces a randomsplitting of the excited states, bleaching on the b and c transitions will appear over a broader range of frequencies (B). The additional broadening caused by solvent dynamics is not illustrated.
In addition to the local anisotropy, these measurements also yield information equivalent to that fromTHB on a nondegenerate transition. The same decomposition into phonon and structural components found elsewhere is also found in this system. The phonon component is larger in magnitude than the structural component and must be included in realistic treatments of solvent effects on chemical processes. Considering the similar results found in studies of other systems,2.3 these features appear to be widespread.
II. Hole Burning with Degenerate States The isolated solute is taken to have a nondegenerate ground state Ig) and triply degenerate excited states la), Ib), and IC), as isappropriate for MnOa-. Thecaseofa doublydegenerateexcited state or of a degenerate ground state can be treated with minor pdification of the present derivation. The transition moments p to the three excited states are orthogonal in direction and equal in magnitude: As a result, the molecule is completely isotropic with respect to absorption of light with different polarizations relative to the molecular framework. In solution, the local solvent structure may not have the symmetry of the isolated solute and so can break the degeneracy of the excited states. The three transition frequencieswa, Ob, and wE will then differ, although the transition moments remain orthogonal. The states la), Jb),and IC) are constructed to be the eigenstates under this perturbation. The orientationof thesolvent anisotropy then defines theorientation of a local coordinateframe defined by $, 6, and i?. The orientation of this local frame relative to the laboratory frame is given by a set of rotation angles 0. Notice that the orientation of the local frame is determined entirely by the solvent structure, not by the molecular framework. The transition frequencies are assumed to be perturbed by solventdynamics both rapid and slow compared to the pulse widths in the transient hole burning experiment. The distribution of
Solvent dynamics slow compared to the time scale of the hole burning experiment also produce frequency shifts of the three transitions, which may be correlated to a greater or lesser degree depending on the anisotropy of the local structure. These correlationsare specified by the full joint probability distribution P(Oa,Ob,Wc), which will be taken to be a multivariable Gaussian distribution.26 Only the reduced forms are needed here:
2
2
(5) where n and m run over (a, b, c}. In these distributions and throughout the remainder of the paper, all transition frequencies are measured relative to the mean transition frequency in solution, so all the distributions are centered at zero. The widths of the distributions of single transition frequencies are given by the diagonalstandard deviations, u,,, Ubb, and a, and thecorrelations between pairsofdiffercnt transitionsaregiven by theoff-diagonal standard deviations, u,b u,, and uk. Since the axes have been labeled arbitrarily, they are assumed to have identical statistical properties: uaa= bbb = uccand Uab = uaC= uk. Thus, only uaa and y are needed to characterize the perturbations. The single-axis standard deviation u,, measuresthe total range of frequency perturbationsof a singleelectronic transition induced by slowly relaxing interactions. It is essentially identical to the width of the distribution of slow interactions measured in hole burning of nondegenerate transitions, denoted US in previous papers.'-3 The width results from both isotropic and anisotropic interactions. In contrast, y can only be measured in molecules with degeneratetransitions, since it is a measure of the correlation of the frequency perturbations of different transitions. Perfect correlation between the transition frequencies leads to y = 1, no correlation to y = 0, and perfect anticorrelation to y = -1. The degree of correlation is directly related to the degree of anisotropyof the slowly-relaxinginteractions. If the interactions are purely isotropic, the different transitions remain degenerate and therefore perfectly correlated. In this case, y = 1. On the other hand, if the interactions are anisotropic, splittings ofvarying size will occur between the different transitions, leading to lower values of y. A more specific interpretation of the value of y will be made at the end of this section. The absorption spectrum S as a function of frequency w and polarization direction 6 is given by unm
lunn
S(o.6) =
5
JdSJ do, do, doc I(nl&lg>I2F(o - 0,)p(oc,%oa)
n=a, .c
(6) where is the transition dipole direction and 0 represents the orientation of the molecule. The transition strength, as well as other constants unrelated to the shapeof the spectrum, have been left out for simplicity. As the average propertiesof each direction
1760 The Journal of Physical Chemistry, Vol. 97, No.9, 1993
Yu and Berg
are the same
s ( d ) = 3 ( (b*a)2)oRJdWa F("+Wa) The orientationally averaged term is equal to the absorption spectrum becomes
P('Qa)
(7)
so with eq 4
As expected, the absorptionspectrumis polarizationindependent.
It is sensitiveonly to the total frequency width of a singletransition caaand is broadened by both the isotropic and anisotropic components of the solvent perturbations. For hole burning, the situation is different. The burning and probing pulses are assumed not to overlap in time, so only processes where the burning pulse interacts before the probing pulse need to be considered. The fast interactions responsible for F(o)are assumed to be strong enough to cause rapid electronic dephasing, so excitation of coherent superpositions of different transitions does not need to be considered either. Consistent with the lack of fluorescence in Mn04-, stimulated emission from the excited state is also left out. If included, the behavior of stimulated emission t e m would be entirely analogous to the bleaching terms treated here. The hole burning spectrum H is defined as the change in absorbance at frequency o and polarization 6 after bleaching the system at frequency wo and polarization 4,. Under the current assumptions
The diagonal hole burning spectrum hd is essentially identical to the hole burning spectrum which would be measured if the excited state were nondegenerate.2 Theoff-diagonalhole burning spectrum ho is additionally broadened and shifted toward the absorption peak by any lack of correlation between the bleached and probed transitions, which is reflected in a value of y less than one. The experimentalspectra are characterized by Cab, bd, and UO, the widths of the absorption, diagonal hole burning and offdiagonal hole burning spectra, and by & and SLJ,the shifts of the diagonal and offdiagonal hole burning spectrafrom the absorption frequency. Equations 19 can be solved for the model parameters in terms of these experimental quantities: 2,
cab 2
ut
cab2[1 - (1
112
-%) Cab
]
(20b)
From the absorption spectrum and the diagonal hole burning spectrum, the broadening due to rapidly and slowly relaxing interactions can be separated, just as they could be with similar spectra on nondegenerate transitions. With the addition of the offdiagonal hole burning spectrum,the correlations between slow frequency perturbations in different directions can also be found. Thecorrelation coefficient y is more easily interpreted in terms of the average frequency perturbation, which is due to isotropic perturbations,
and the mean squared splitting away from this average caused by anisotropic perturbations bw2 =
y3
q
(wn-wo)2
n-a, ,c
The averages of these quantities are
The anisotropy parameter A gives directly the fraction of the
Transient Hole Burning of Mn04- in LiCIa6H20 slow broadening due to splitting of the excited state degeneracy. If A = 0, the slow broadening is only caused by isotropic interactions; if A = 1, the slow broadening results from only from splitting of the degeneracy.
III. Experimental Section Lithium chloride was dissolved in deionized water to form LiCI.6H20 and then KMn04-was added until the peakabsorption was 0.8at room temperature in a 1-mm samplecell. Thecell was sealed off and attached to the cold finger of a flowing cryostat cooled with either liquid nitrogen or liquid helium depending on the temperature range. The sample was surrounded by a heat shield except for a path for the laser beams. The heat shield reduced the thermal gradients in the sample caused by blackbody radiation from the surroundings. A silicon diode sensor on the cold finger was used to control the temperature; a second sensor mounted directly on the sample was used to measure the sample temperature and to check for thermal gradients within the system. The transient hole burning apparatus has been described in detail b e f ~ r e . ~Briefly, ,~ 0.4-ps pulses from a synchronously pumped dye laser were amplified in a chain of dye amplifiers at 10 Hz. A portion of this pulse was used to burn the hole in the Mn04- spectrum. The remainder of the pulse generated a white light pulse which interrogated the sample after a short delay. The change in the absorption spectrum induced by the burning pulse was measured with the continuum probe pulse. The polarization of the burning pulse was rotated by a half-wave plate to obtain spectra with the burning and probing polarizationseither parallel or perpendicular.
Iv. Data Analysis An a m r a t e model of the vibrationalstructure of the electronic absorptionband of the isolated Mn04- is needed to determine the solvent-induced effects on the spectra. The isolated-molecule spectrum is convolved with a Gaussian representing the solventinduced broadening and is shifted in frequency to match the experimental spectra. From this fitting, accurate values of the position of the 04 transition and the broadening of individual vibronic levels are obtained. The vibrational structure of Mn04- is particularly simple, consisting of a nondegenerate symmetric stretch V I , a doubly degenerate bend v2, a triply degenerate antisymmetric stretch v3 and a triply degenerate bend ~ 4 The . ~u2 and ~ u3 modes are not active in the absorptionspectrum. The main progression is in the uI mode with an additional weak progression in u4 built on each member of the v I progression. The frequency of V I in the excited state is UI' = 735 cm-I. From a model of harmonic modes which suffer a displacement in the excited state, the intensity Zua of the transition from the ground state level u" = a to the excited state level u' = is given by
where L is the modified Laguerre polynomial andS is the HuangRhys parameter describing the extent of di~placement.~~ The intensities of the vl(O+n) progression were fit to eq 26 with S = 2.1. Eight members of the progression were included in the model. The frequency of v4 in the excited state was taken as 3 15 ~ 1 1 1 - I . ~ ~ To each of the ul transitions, three members of this progression (0 0,1,2) were added with S = 0.1 and accounting for the degeneracy of higher members. This 0 K spectrum was optimized by fitting to low-temperature absorption spectra. At higher temperatures, hot bands and sequence bands also play a role. The intensities of these transitions were calculated from eq 26 multiplied by the appropriate Boltzman factor. Only
-
The Journal of Physical Chemistry, Vol. 97, No. 9, 1993 1761 the u2 and u4 vibrations are low enough in frequency to be significantly populated at room temperature. One additional hot progression in u4 was added (1 n). The ground-state frequency for u4 is 408 Three sequence bands in UP= 385 cm-I were also added.31 The positions of these transitions are dependent on the difference in the ground- and excited-state vibrational frequencies, which is not directly known. Since u2 and v4 are both primarily bending vibrations, the fractional change in the v2 frequency was assumed to be the same as the fractional change in the v4 transition. Thus, the v2 excited state frequency was taken as 297 cm-I. With this model, good fits to the absorption spectra and THB spectra could be found at all temperatures. The photophysics of MnOd- has several features relevant to the THB experiment. The transition of interest is the IAl IT2 transition with an origin near 17 700 cm-I. The lowest singlet state is the ITI transition whose origin is located near 14 OOO cm-1. There are also two low lying triplet states, the 'TI and 3T2.32 The permanganate ion is known to be nonfluorescent, and the excited state lifetime has been reported to be less than 30 ps.33 The unstructured high energy tail of the weak IA1 ITI absorption band overlaps the low energy side of the 'Al IT2 transition we wish to study. The 'TI contribution in this region was modeled as smoothly decaying toward shorter wavelengths. The decay was adjusted to give intensities of the IT2 transitions which match eq 26. This contributionto the absorptionspectrum wassubtractedoff before fitting with themodel forthe 'Tzvibronic structure. Our experiments show no evidence of stimulated emission in the region to the long wavelength side of the 0 4 absorption peak, even when the pump and probe pulses are overlapped in time. Thus, the lifetime of the IT2 state is much less than 1 ps. As a result, there is no stimulated emission component to the THB spectra. In contrasttoother THB e ~ p e r i m e n t s , l - f only ~ ~ - ground ~~ state bleaching effects are seen. On the other hand, the ground state recovery time at room temperature is measured by the transient absorption decay to be 18.8 ps. The recovery time lengthens at lower temperatures, but this phenomenon has not been characterized in detail. The IT2 state must decay rapidly to an intermediate state with a 18.8-ps decay time to the ground state. Presumably, this intermediate state is one of the low-lying electronic states mentioned above. Since the slowly decaying component of the broadening is expected to be highly temperature dependent and highly nonexponential, this short decay time does not offer a sufficient range for detailed studies of the structural decay in time. The measurements reported are mainly at a fixed decay time of 1.5 ps. The intermediate excited state does not have significant transition strength to the ground state, but absorption to a still higher electronic state is seen. The shape of this absorption was determined by assuming that solvent relaxation is complete in 1.5 ps at room temperature. The absorption spectrum was subtracted from the 298 K THB spectrum to find the smooth excited-state absorption spectrum. Slightly different excitedstate spectra were found for each polarization. To summarize, the raw THB spectra were first normalized to constant area and then the contributions from excited state absorption and bleaching of the IT1 transition were subtracted. The resulting ground-statebleaching spectra of the IT2 transition, Hll and HI were combined according to eqs 15 and 16 to find the diagonal and off-diagonal contributions, hd and ho. These were then fit with the temperature-dependent model of the vibronic structure of the IT2 band to determine the solvent-induced broadening.
-
-
--
V. Results and Discussion Transient hole burning spectra with a 1.5-ps delay and with probe polarizations both parallel and perpendicularto the burning
1762 The Journal of Physical Chemistry, Vol. 97, No. 9, 1993 1
Yu and Berg
I
I 6.0
io0 TQ 200 TEMPERATURE IK)
0
-. ..-* 460
500
540
Figure 4. (A) Slowly relaxing portion of the absorption width una. (B)
580
WAVELENGTH (NMI
Figure 2. Comparison of absorption spectra (solid) and diagonal THB spectra at 1.5 p (dashed) in the room-temperature liquid (297 K), the low-temperature liquid (145 K) and the low-temperature glass (38 K). Each spectrum has been normalized to constant area and displaced vertically. The differences between the spectra are due to slowly-relaxing structural interactions. The broadening of the absorption spectra at higher temperatures is largely due to hot and squencc transitions.
50
t 0
io0
Te 200 TEMPERATURE (Kl
300
300
Figure 3, Widths of absorption (u.k, W), diagonal THB (Ud, *) and off-diagonal THB (uo, 0 ) versus temperature. Lines to guide the eye have been added.
polarization were taken from 38 to 297 K. This range crosses the glass transition temperature T, = 139 K.34Combining the hole burning spectra gave the diagonal and off-diagonalspectra (cqs 15 and 16). Absorption spectra were also recorded over this temperature range. At room temperature, absorption and diagonal THB are identical (Figures 2and 3), indicatingthat all solvent interactions are subpicasecond. In both the low-temperatureliquid and glass, the diagonal THB spectrum is broader than the pump bandwidth, but narrower than the absorption spectrum. This result implies that some of the solvent interactions remain subpicosecond, but that others haveslowed down at lower temperatures. The diagonal THB and absorption spectra were analyzed quantitatively as described in the last section to yield the width induced by processes
Rapidly-relaxing portion of the absorption width U F (e). At higher temperatures, where the structural relaxation becomes rapid, the magnitude of the structural width is assumed to remain constant (A, dashed line). With thisaseumption, the phonon-modulatedwidth is found (B, 0 ) . The solid curve is a fit to cq 28.
relaxing in less than 1.5-psU F and the width induced by processes relaxing in longer than 1.5-ps una.These results are displayed in Figure 4. The most important result from these data is that the fast relaxation processes seen in the solid glass extends continuously across the glass transition into the liquid phase. Below the glass transition, the interactions are known to separate into subpicosecond phonon-modulated processes and static interactions with the frozen ~tructure.2~Since this division continues across the glass transition, a similar division of the liquid-phase dynamics into phonon-like motions around a temporary local structure at short times and slower rearrangement of the local structure at longer times is valid. At 200 K and above, the magnitude of the slow broadening is reduced, dropping to zero at room temperature. At the same temperatures, the amount of subpicasecond broadening is increasing rapidly. This effect is explained as the structural relaxation time decreasing with increasing temperature and crossing the 1.5-ps time scale of the experiment. As it d m so, more of the structural relaxation contributes to U F and less to a,. A reasonableand self-consistent determinationof the phononinduced and structural broadeninp can be made at these higher temperatures. At 175 K and below, the magnitude of the structural broadening is given directly by baaand is independent of temperature. The magnitude of the structural broadening is assumed to remain constant at higher temperatures (Figure 4A). Subtracting this width from the total absorption width gives the phonon-modulated width bph (Figure 4B): 2
(27) = 2 - baa 2 A simple model for the temperature dependence of phonon broadening in solids was derived by Lax3sand gives bph
up:
-% h mth( -)hu 2 ph 2kT
where x p h represents the phonon coupling strength. A fit of this model to our data is shown in Figure 4B. The fit gives Y = 145 cm-* for the phonon frequency and xph = 175 cm-1 for the phonon coupling strength. The phonon coupling strength found here is similar to the 123-cm-1coupling strength found for an organic solute, dimethyl-
Transient Hole Burning of Mn04- in LiCI.6H20
The Journal of Physical Chemistry, Vol. 97, No. 9, 1993 1763
300
0
200 TEMPERATURE (Kl
100 To
Figure 6. Anisotropy of the local structure determined from polarized THB spectra. Sincethe error range increases at the higher temperatures, the anisotropy should be regarded as constant to within experimental
460
'
500
'
540
WAVELENGTH (NH)
Figure 5. Comparison of diagonal (solid)andoff-diagonal (dashed) THB spectra at 1.5 ps in the room-temperature liquid (297 K), the lowtemperature liquid (145 K), and the low-temperatureglass (38 K). Each spectrum has been normalized to a constant area and displacedvertically. The differencesbetween the spectra aredue to slowly-relaxinganisotropy in the local solvent structure.
s-tetrazine, in a nonpolar solvent,n-b~tylbenzene.~ This similarity suggest that similar coupling mechanism are active in both systems; in particular, the large electricfieldspresent in LiCI-6H20 do not create a major, new interaction mechanism. The effective phonon frequency in LiC1-6H20is substantially higher than the phonon frequency in n-butylbenzene, which was 30cm-1or ltss.3 This result is not surprising in view of the stronger intermolecular forces and lighter molecules in the ionic solvent. The librational motion of H20 in particular is known to contribute a very high frequency component to the dynamics of aqueous systems.36 The rate of structural relaxation observed here is surprisingly high in comparison to other measures of structural relaxation. Halalay and Nelson have measured the frequency-dependent elastic modulus of a 13 mol 76 LiCl aqueous solution versus temperature and find a relaxation function which appears to be shared by other measures of structural relaxation, in particular frequency-dependent electric modulus.37 However, the average relaxation times found are too slow to account for the type of structural relaxation observed here. At room temperature, Halalay and Nelson's relaxation time is still 5.6 ps. If this were the relevant relaxation time in our experiments, narrowed hole burning spectra would be observed even at room temperature with our 1.5-ps time resolution. We observe the structural relaxation beginning to relax on the 1.5-ps time scale at temperatures as low as 200 K, where Halalay and Nelson's relaxation time is 6.4 ns. Despite the slight difference in concentration between the two experiments, it is clear that the THB experiments are measuring a different aspect of structural relaxation than macroscopic modulus relaxation experiments measure. The same conclusion was reached for THB measurements in glycerol.2 In addition to the diagonal spectra, which are similar to previously studied THB spectra for nondegenerate electronic transitions, the Mn04- system also yields off-diagonal spectra. These spectra are additionally broadened by any splitting of the degenerate transitions induced by slowly-relaxing anisotropy in the local structure. Figure 5 compares off-diagonal and diagonal
error. THB spectra at different temperatures (see also Figure 3). At room temperature, where there is no slowly-relaxing component to the solvent interaction, the two spectra are identical. In the low-temperature liquid and glass, where structural relaxation is slow, the off-diagonal spectra are broader than the diagonal spectra, indicating that the structural interactions are anisotropic. However, the off-diagonal spectra are not as broad as the full absorption spectra, so the structural broadening is not entirely due to anisotropic splitting of the excited state (Figure 3). These conclusions are quantified by using eqs 2Oc and 25 to extract the anisotropy parameter A. The results are shown in Figure 6. At the highest temperatures, the amount of slow broadening is too small compared to the error range to produce accurate values of A. The anisotropy of 0.27 is constant within the glassy range, as would be expected for an unchanging local structure. The anisotropy of the local structure remains constant in the liquid phase, until at higher temperatures the local structure relaxes within the timescale of the experiment. If there were a process which could average the anisotropy of the local structure without allowing the average perturbation of the structure to relax, the anisotropy would decrease before the magnitude of the slow broadening decreased. No such processes appears to be active. The closest available comparison to this result comes from the hydrated electron, which is believed to have a singly degenerate ground state and a triply degenerate excited state just as Mn04d0es.3893~ The transition between these states gives rise to an exceptionally broad visible absorption band. Computer simulations have attributed the width of this band to splitting of the excited state by theanisotropy of thesolvent envir~nment.~~ These simulations find that the distribution of transition frequencies averaged over all three excited states is only half of the total absorption width; the remainder of the width is due to splitting of the excited state degeneracy induced by anisotropy of the local solvent. In our notation, this result corresponds to A 0.25. The same qualitative conclusion is reached in both the simulations and in our experiment. The value of the anisotropy is neither close to one nor close to zero, showing that both isotropic and anisotropic solvent perturbations contribute substantially to the total solvent-solute interaction. Considering the large differences between the hydrated electron and a molecular solute like Mn04-, it seems likely that this conclusion will also apply to a wide variety of other systems. Symmetrical models of the solvent, for example most dielectric continuum models, may miss important aspects of solvation.
-
VI. Conclusions This paper shows that the solvation of a d - d electronic transition in an ionic solvent has many of the same qualitative
1764 The Journal of Physical Chemistry, Vol. 97, No. 9, 1993
features previously demonstrated for an n+r* transition in both polar and nonpolar organic solvent^.^,^ Most importantly, a division of the solvation into phonon and structural components is seen in all these cases. A number of computer simulations”l6 and recent experiments200nthe solvation of electronic transitions with large charge rearrangements have also distinguished a very rapid solvation process from a slower component. In both the THB studies of nonpolar solutes and in the studies of charge solvation, the rapid component of the solvation accounts for a substantial fraction of the total solvent interaction. Our interpretation of these motions in terms of a solid-state phonon model provides a useful semi-quantitative interpretation of the data. Despite the apparent ubiquity and large amplitude of these rapid solvation processes, they are only beginning to be included in analytical theories of s o l ~ a t i o n . ~ ~ ~ ~ This paper also demonstrates an experimental method for measuring the anisotropy of solvent interactions. The results constitute the first experimentaldemonstrationof the importance of including the anisotropy of the local environment in treating solute-solvent interactions. Solvation theories based on spherically symmetricmodels may leave out important features arising from the solvent anisotropy. Although the current experiments areconfined to measuring the anisotropy of structural interactions persistingfor more than a picosecond, themethodcan beextended to shorter times to measurethe anisotropy of structural or phononmodulated interactions at higher temperature.
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