J. Phys. Chem. 1995,99, 14561-14565
14561
Thermal Broadening of an Optical Transition in a Chromoprotein between 50 mK and 15 K J. Gafert, C. Ober, K. Orth, and J. Friedrich* Physikulisches Institut and Bayreuther Institut f i r Makromolekiiljorschung, Universitat Bayreuth, 95440 Bayreuth, Germany Received: May 24, 1995@
-
We measured the temperature dependence of the zero-fluence extrapolated hole width associated with the S So transition in protoporphyrin IX substituted myoglobin. The temperature was varied between 50 mK and 15 K. The experiments were done at two frequencies in the inhomogeneous band. We found that the hole width follows a single power law up to 10 K. Although the characteristic features of thermal line broadening are similar for the two frequencies, there are clearly discemible differences as well: The respective exponents are slightly different (1.38 vs 1.48 f 0.05), and the zero-temperature extrapolated hole widths differ drastically (12 vs 18 f 0.5 MHz). From the experiments we conclude that the broadening mechanism is most probably spectral diffusion and that the major contribution must stem from the protein itself.
Introduction Chromoproteins in glassy solutions represent highly interesting systems for optical line broadening studies. There are quite a few obvious reasons: First, protein solutions are spatially inhomogeneous systems. The nearby environment of the dye probe is different from the host glass. Interesting questions in this context concern the probe-lattice coupling, shielding effects, spectral diffusion behavior, etc. Second, a protein is a highly organized structure; hence, the nearby environment of the chromophore is highly organized. This raises the question as to the influence of the disorder modes on the line broadening mechanisms: Is it reduced, or does the protein itself provide a reservoir of disorder modes. From many experiments on proteins it is well-known that they show glasslike b e h a ~ i o r l - ~ despite the fact that their size is finite and the number of TLS is rather smal16v7 and, moreover, the TLS may be spatially correlated in the protein. The acronym TLS stands for “twolevel system”. They characterize structurally metastable regions in disordered solids and are modeled as double-well potentials. Apart from these questions of general interest which concern any chromoprotein system, myoglobin is especially attractive for an optical line width study. It is one of the best studied systems: There are accumulated photon echo experiments which cover a temperature range between 20 and 100 K. From these investigations the Debye-Waller factor is known, too.8 In addition to the photon echo studies, there is a hole-burning line width study on chlorophyllide substituted m y ~ g l o b i n . ~ In this paper we report on line width studies of protoporphyrin IX substituted myoglobin over a temperature range which covers more than 2 orders of magnitude, namely from 50 mK to 15 K. Together with the accumulated photon echo data, the temperature range investigated extends over 3.5 orders of magnitude. There is, however, one delicate point which concems all optical experiments on dye-protein systems: To what extent are the results characteristic for the protein? What is the influence of the host glass? We recently performed a series of spectral diffusion experiments in the millikelvin range on time scales of more than 200 h.Io The results from these experiments were quite surprising: The chromophore in the myoglobin apoprotein (protoporphyrin ‘Abstract published in Advance ACS Absrracrs, September 1, 1995.
0022-365419512099-14561$09.00/0
IX) seemed to be shielded from the host glass to a large degree. The important conclusion from these experiments then was that, at least for myoglobin, line width experiments essentially probe the protein. We performed our experiments at two frequencies in the inhomogeneous band. The reason for this was the following: For CO-myoglobin it was shown that frequency-structure correlations do o c ~ u r . I I - ~In~ addition to a continuous inhomogeneous distribution, there are discrete structural states, the so-called taxonomic states.I3 They correspond with quite distinct CO bond angles with respect to the heme plane. These angles, in tum, are thought to correspond with different substructures of the apoprotein. The kinetic behavior in the various taxonomic states is quite different. In our case the chromophore, namely protoporphyrin E, is different from the native one. The free base porphyrins can exist in a series of tautomeric states which differ by the inner-ring proton configurations. It has been known for some time that some of these states can be stabilized through the apoprotein.I4-l7 Hence, we have a situation similar to the taxonomic states: Different structural states of the chromophore correspond with different protein substructures. It was our goal to find out whether such a situation is reflected in the thermal line broadening behavior. Experimental Section Materials and Methods. Since narrow bandwidth hole burning is not possible with heme dyes due to their extremely fast intersystem crossing processes, the natural heme group was substituted by protoporphyrin IX (Figure 1). The porphyrins are among the most intensively studied hole-burning systems.18 The respective photoreaction is based on a phototautomerism of the inner-ring protons. Quite a series of tautomeric states is possible.I6 Horse myoglobin (Mb) from Sigma was deprived from the heme group by a butanon extraction at pH 2.3. The apoprotein was reconstituted with protoporphyrin IX dissolved in 0.1 M NaOH. In the iron-free Mb, the absorption ratio at 405 and 280 nm was 3.26. The final sample was obtained by mixing 2.4 mL of water-free glycerol with 1 mL of a Mb solution in water containing 290 mg of Mb. For comparative purposes (Figure 2, insert) protoporphyrin IX was also dissolved in a glass matrix. We chose a mixture of dimethylformamide and 0 1995 American Chemical Society
Gafert et al.
14562 J. Phys. Chem., Vol. 99, No. 39, 1995
Iq
CH CH ?- C -OH
HO-C-CH2CH2 II 0
= 16021
cm-'
'
0
hole area
I1
0
-200
Figure 1. Structure of protoporphyrin IX.
-100
100
0
frequency
/
I
200
MHz
Figure 3. Spectral hole at 57 mK for various laser fluences. The insert
shows the extrapolation procedure to zero fluence. Plotted is the hole width as a function of hole area. Sample: protoporphyrin IX substituted myoglobin.
23a 0
ITA,,y waiting time
/ hours
,
15400
15800
,
,
16200
V / em-' Figure 2. Inhomogeneous absorption spectrum of protoporphyrin IX substituted myoglobin (PP-Mb) at T = 1.5 K. The hole-burning wavenumbers (15 818 and 16021 cm-I) are indicated by mows.
Insert: a comparative temperature cycling hole-buming experiment for the chromoprotein and protoporphyrin IX directly dissolved in a host glass.1o"Slope": temperature cycle-induced hole broadening per degree of excursion temperature. "Waiting time": time, elapsed after having reached 100 mK by cooling from room temperature. glycerol in a volume ratio of 1:3 in order to ensure sufficient solubility of protoporphyrin IX. The sample was kept in sealed glass cuvettes with thicknesses of 0.4 and 1.2 mm for Mb and the glass sample, respectively. This yielded in both cases an optical density of 0.12 at the maximum of the long-wavelength band. Spectroscopic Measurements. The hole-buming experiments in the Mb sample were carried out at two different wavenumbers, namely, at Ybl = 16 021 cm-' and Vb2 = 15 818 cm-I (arrows in Figure 2). At each selected temperature a new hole was bumt in close vicinity of the selected wavenumber (&5 cm-I). Figure 3 shows a series of such holes as a function of irradiated energy. The temperature in this case was 57 mK. In the insert, the hole width is plotted as a function of the hole area which is, for sufficiently low fluences, proportional to the fluence. The width extrapolated to zero fluence is the quantity of interest. For the temperature variation and stabilization we used three different kinds of cryostats. Below 1.3 K we used a 3He-4He dilution refrigerator. The minimum temperature was about 50 mK. The cryostat is equipped with low-IR-transmittanceoptical windows to reduce heating of the sample by the 300 K blackbody radiation. The temperature was controlled with a Ge resistor and a carbon resistor and was accurate within 1-2 mK at the lowest temperatures and within about 10 mK in the 1 K range. Between 1.5 and 4.2 K we used a He-bath-type cryostat. Above 3.5 K we used a He-flow cryostat. In this temperature range the accuracy was better than 0.1 K. The hole-
burning laser system was a dye ring laser pumped by a 6 W Ar+ laser. It was operated with sulforhodamine B. Buming times were on the order of 1 min, and radiation power levels varied from 0.2 pWlcm2 in the dilution cryostat to 500 pWl cm2 in the He-flow cryostat. The bandwidth of the laser is specified to be in the range of 500 kHz. Although we could not check this value, we could safely assume that it was much narrower than the width of the 50 mK holes because there was no indication that the hole width approached a saturation (due to a finite laser bandwidth) as the temperature was lowered. Detection was made by reducing the laser power by 2-3 orders of magnitude, scanning the bumt part of the spectrum, and measuring the transmission. The radiation was coupled into the various cryostats with glass fiber cables followed by an appropriate optics.
Results Figure 2 shows the inhomogeneous broadened absorption spectrum of protoporphyrin IX substituted myoglobin. The arrows indicate the two wavenumbers where the hole-burning experiments were performed. The insert shows a temperature cycling hole-buming experiment as a function of waiting time.I0 The quantity plotted is the change of the hole width per degree of excursion temperature as a function of waiting time. The excursion temperature is the characteristic parameter of a temperature cycle. For the data series shown, it was varied between 100 mK and 1 K. As is evident, after waiting some 200 h at low temperature, a temperature cycle cannot induce significant broadening in myoglobin anymore. In the glass sample, on the other hand, temperature cycles performed after a waiting time of 250 h induce almost as much broadening as in the beginning of the experiment. Figure 3 shows a series of holes as a function of irradiation dose at a temperature of 57 mK. The zero-fluence extrapolated width of the holes, as shown in the insert, is 13.8 MHz. In the following we will call this extrapolated value the "quasihomogeneous" hole width. Figure 4 shows the thermal line broadening behavior below 1.2 K in a linear representation. The two data sets correspond with the two bum wavenumbers Vbl and Vb2, respectively. There are three noteworthy features: (i) The zero-temperature extrapolated hole widths yo differ significantly for the two wavenumbers: For Ybl we found a residual width of 12 f 0.5 MHz; for Yb2 the respective value is 18 f 0.5 MHz. (ii) The temperature dependence of the hole width follows a power law. (iii) As obvious from the data sets, holes bumt at Yb2 broaden
J. Phys. Chem., Vol. 99, No. 39, 1995 14563
Optical Transition in a Chromoprotein
.2
.O
.E
.6
.4 Tb
1.0
1.2
/K
Figure 4. Linear plots of the zero-fluence extrapolated hole widths as a function of temperature for the two bum wavenumbers (see Figure 2) in the low-temperature regime.
1 Vb,
0
= 16021 cm"
LX
15
PP-IX M b
, , , I . . . . , , , ,
20
25
I I I . . . l / I I I I . . . / I I 1 . I I .
30
3.5
4.0
45
50
log (Tb/mK) Figure 5. A log-log representation of the zero-fluence extrapolated hole width y as a function of temperature. yo is the respective value at zero temperature. The straight line has a slope of 1.38. Bum wavenumber: 16 021 cm-'. Sample: protoporphyrin IX substituted myoglobin. The accumulated echo data are taken from the literatureBand are indicated by open circles.
more strongly than holes b u n t at Ybl . The respective exponents are 1.48 and 1.38 (h0.05).Although these two numbers are rather close, the difference is significant. Figure 5 summarizes the temperature dependence of the quasihomogeneous hole width in a log-log representation. The data refer to Ybl, but a similar data set was obtained for Yb2 (except for the residual hole width and the respective exponent). Again we stress two features: (i) Over more than 2 orders of magnitude in temperature the quasihomogeneous hole width increases according to a single power law. There is no indication of a change in the line broadening mechanism between 50 mK and 10 K. (ii) Above 10 K, there is a clear turnover to a steeper temperature dependence. We stress that our data smoothly join the accumulated echo data obtained by Lin et aL8 with respect to the absolute magnitude as well as to the temperature dependence. Hence, for the first time, line width data of an organic material are known, which cover 3.5 orders of magnitude in temperature, Discussion
Local Character of the Dye Probe. We stressed in the Introduction the fundamental aspect of the question, what does the dye probe really probe? Is it mainly the host glass or mainly the protein? For an answer to this question, one has to know the interaction range of the relevant forces. From an experimental point of view, there are several possible approaches: One way is to perform comparative Stark effect experiments between a chromoprotein and the respective dye probe directly dissolved
in a host g l a s ~ . ~The ~ - *idea ~ is that the structural order in the protein may create a well-defined field at the chromophore which breaks a potential inversion symmetry of its n-electron system, thereby leading to a very characteristic pattern of the hole in an electric field. Experiments on free base, as well as metal protoporphyrins in myoglobin and cytochrome c, have shown that such a symmetry breaking does occur. The clear conclusion from these experiments was that the main contribution of the matrix fields at the chromophore site cannot stem from the random host material. In other words, despite their small size, proteins like myoglobin or even cytochrome c shield the chromophore quite well from the solvent. Another approach,I0 pertinent to spectral diffusion, is shown in the insert of Figure 2. Again, the chromophore in the glass is compared with the chromophore in the protein. This experiment demonstrates quite convincingly that the protein does shield the chromophore from the host material to a high degree: At the beginning of the experiment a temperature cycle from 100 mK to 1 K broadens the hole in the protein as well as in the glass. After 250 h, broadening in the glass is still large whereas in the protein it is significantly reduced. The conclusion is that the protein must have relaxed into a deep minimum state of its energy surface where it cannot be kicked out anymore. Moreover, the chromophore in the protein must be shielded to a high degree from the fluctuating fields of the solvent because temperature variation cannot induce much broadening anymore. Thermal Line Broadening Behavior in Myoglobin. Below 1 K the wavelength of thermal phonons is much too long to induce any significant strain which could lead to the observed line broadening. For instance, in many organic crystals the optical line width reaches its lifetime limited value already at temperatures as high as several kelvin, indicating that phonons have become ineffective in line broadening.2's22 Hence, it is obvious that the thermal line broadening below 1 K (Figure 4) must be due to spectral diffusion. Spectral diffusion is usually modeled within the TLS approach assuming thermal equil i b r i ~ m . * ~This - ~ ~model yields a linear temperature dependence provided the density of TLS states is constant in energy. As for proteins, the TLS model does not seem to be an adequate approach. First, spectral diffusion broadening decreases tremendously on typical time scales of 100 h. This is obvious from Figure 2 (insert) but was observed in timedependent line broadening experiments as well.'O This means that spectral diffusion in myoglobin is not an equilibrium phenomenon. We stress, however, that a "homogeneous line width experiment" of the type performed here does make sense, despite the nonequilibrium nature of the relaxation. The reason is that the time scale of this type of experiment (minutes) is short as compared to typical time scales on which the protein reaches equilibrium (-100 h). Second, although myoglobin was shown to have TLS-like excitations, there are only three of them.6 They are spatially confined to a narrow range determined by the dimension of the protein. Hence, homogeneity, an essential ingredient of the TLS model, is lost. However, spectral diffusion is confined neither to the presence of TLS nor to spatial homogeneity. It will occur in any kind of potential with a superimposed randomness where diffusivelike relaxation processes can take place. A possible way to model spectral diffusion in such a more general situation would be to start with a Langevin-type equation for the optical frequency and to calculate the conditional probability P(V,t/Vt,,O) for the selected frequency from a Fokker-Planck-type equat i ~ n .Such ~ ~ an approach would be more adequate for spectral diffusion processes in myoglobin, since it would automatically account for the nonequilibrium nature observed.
14564 J. Phys. Chem., Vol. 99, No. 39, 1995
In the simplest case, the system parameters which determine the characteristic features of the spectral diffusion broadening in such a description are the second moment of the frequency fluctuations (V2) and the respective correlation time ‘tp. The description of the respective temperature dependence, however, is only possible in a microscopic theory. There are a few specific features of such an approach which should be stressed: (i) The solutions of Fokker-Planck-type equations do not correspond with a Lorentzian distribution. (Note that the Fokker-Planck approach for a linear stochastic process is related to the so-called Gaussian approximation in inhomogeneous line shape theories.32) On the other hand, the holes in our experiments can be fitted quite well to Lorentzians. Here, we merely note that the tendency toward Lorentzian line shapes is pertinent to hole-burning experiments. It is due to the fact that burning in the wings of a hole is stronger (on a relative scale) as compared to the center as a consequence of saturation. (ii) Although we do not directly get the temperature dependence for the line width from a Fokker-Planck equation, one should keep in mind that a sufficiently complex potential gives rise to diffusive relaxation processes within a broad range of time scales. This is formally equivalent to averaging over a distribution of correlation times which flattens the temperature dependence. Hence, for a sufficiently complicated potential one does not expect a very different temperature dependence as compared to the TLS model. We measure power laws with exponents of 1.38 and 1.48 at the band maximum and in the red wing, respectively. Similar exponents have been measured in glasses. The most surprising result of our experiments is the fact that there is not the slightest indication that the line broadening mechanism changes between 50 mK and 10 K. This temperature range covers more than 2 orders of magnitude. If spectral diffusion prevails below 1 K, we leam from the data that it also prevails up to 10 K. Above 10 K the line broadening mechanism changes. The data indicate a crossover to a quadratic temperature dependence. This quadratic behavior prevails at least for another order of magnitude in temperature as is shown by the photon echo data of Lin et al.* We note that quadratic temperature dependences in optical line broadening have quite often been observed in glasses at higher temperature^.^^-^^ However, as to the mechanism responsible for the change in the thermal line broadening behavior, we can only speculate: One possibility could be a Raman-type phonon scattering process which enters a quadratic regime well below the Debye temperature. The implication would be quite a low Debye temperature of the protein solution of some 40 K. Frequency-Dependent Features. As to the observation (Figure 4) of different temperature dependences for the two burn frequencies (Ybl, VLQ) we feel that it is an interesting observation which fits into the scenario known from proteins. Again, we want to stress the significance of the data despite the similarity of the two exponents: it is obvious that thermal broadening in the red (Yb2) is steeper than in the band maximum (Ybl). Proteins are known for frequency-structure correlations.11-15J7 For instance, the ligand rebinding kinetics in CO-myoglobin depends significantly on absorption frequency. Consequently, the respective activation barriers must depend on frequency. The reason is that different structures are probed at different absorption frequencies. If frequency-structure correlations prevail, a frequency selective experiment becomes “site selective” in the sense that the ensemble average is no longer taken over all the structural variations. The different structures correspond with different
Gafert et al. potentials, and since spectral diffusion depends on the respective potential, we observe a frequency-dependent spectral diffusion behavior. There is an interesting implication: For a diffusive relaxation process in a sufficiently large system, one would expect self-averaging proper tie^:^^ The individual character of the systems should vanish on a sufficiently large time scale. For proteins, like myoglobin, this is obviously not the case, at least not on the time scale of our experiment. The proteins absorbing in the red wing retain their individual character as compared to the proteins absorbing in the maximum. The occurrence of frequency -structure correlation is supported by other observations as well: There are the different residual line widths for Ybl (12 MHz) and Vb2 (18 MHz). We relate this finding to different protein structures: Different substructures of the apomyoglobin can support different tautomers of the chromophore (or vice versa). Different tautomers have different lifetimes. This is what we observe. This interpretation is further corroborated by the fact that the thermal stability of the holes at the two frequencies is quite different.” We stress that similar observations have been made for mesoporphyrin IX substituted horseradish peroxidases5
Summary We investigated thermal broadening of spectral holes burnt into protoporphyrin IX substituted myoglobin at two different frequencies. The temperature range extended over more than 2 orders of magnitude, namely from 50 mK to 15 K. The line broadening mechanism is related to spectral diffusion. Up to 10 K the broadening is governed by a single power law with slightly different exponents for the two frequencies. This difference is related to frequency-structure correlations, which do not seem to have self-averaging properties. The spectral diffusion processes are protein-related. They are not interpreted within current theories of low-temperature glasses but are, in a qualitative way, associated with diffusion in a potential with superimposed randomness. As an appropriate approach to modeling a Fokker-Planck-type equation is suggested.
Acknowledgment. J.F. acknowledges many stimulating discussions with Helmut Brand and Fritz Parak. Financial support came from the DFG (Graduiertenkolleg “Nichtlineare Dynamik und Spektroskopie”) and the Fonds der Chemischen Industrie. References and Notes (1) Frauenfelder, H.; Parak, F.; Young, R. D. Annu. Rev. Biophys. Biophys. Chem. 1988, 17, 451. (2) Parak, F.; Knapp, E. W. Proc. Natl. Acad. Sci. U.S.A. 1984, 81, 7088. (3) Parak, F.; Hartmann, H.; Nienhaus, G. In Protein Structure: Molecular and Electronic Reactiviry; Springer-Verlag: New York, 1987; p 65. (4) Friedrich, J. Mol. Cryst. Liq. Cryst. 1990, 183, 91. ( 5 ) Zollfrank, J.; Friedrich, J.: Fidy, J.; Vanderkooi, J. M. Biophys. J . 1991, 59, 305. (6) Sing, G. P.; Schink, H. J.; von Uhneysen, H.; Parak, F.; Hunklinger, S. 2.Phys. B: Condens. Matter 1984, 55, 23. (71 Yam, I.-S.: Anderson. A. C. Phvs. Rev. B 1986. 34. 2942. (8) Lin,j. W.-I.; Tada, T.; Saikan, S.; Kushida, T.; Tani, T. Phys. Rev. B 1991, 44, 7356. (9) Boxer, S. G.; Gottfried, D. S.;Lockhart, D. J.; Middendorf, T. R. J . Chem. Phys. 1987, 86, 2439. (10) Gafert, J.; Pschierer, H.; Friedrich, J. Phys. Rev. Lett. 1995, 74, 3704. (1 1) Agmon, N. Biochemistry 1988, 27, 3507. (12) Campbell, B. F.; Chance, M. R.; Friedman, J. M. Science 1987, 238, 373. (13) Frauenfelder, H.; Sligar, S. G.; Wolynes, P. Science 1991, 254, 1598. (14) Friedrich, J.; Gafert, J.; Zollfrank, J.; Vanderkooi, J. M.; Fidy, J. Proc. Natl. Acad. Sci. USA. 1994, 91, 1029.
Optical Transition in a Chromoprotein (15) Gafert, J.; Friedrich, J.; Vanderkooi, J. M.; Fidy, J. J . Phys. Chem. 1994, 98, 2210.
(16) Fidy, J.; Vanderkooi, J. M.; Zollfrank, J.; Friedrich, J. Biophys. J . 1992, 61, 381.
(17) Gafert, J.; Friedrich, J.; Parak, F. J . Chem. Phys. 1993, 99, 2478. (18) Volker, S. Spectral Hole Buming in Crystalline and Amorphous Organic Solids. Optical Relaxation Processes at Low Temperature. In Relaxation Processes in Molecular Excited States; Fiinfschilling, J., Ed.; Kluwer Acad. Publ.: Dordrecht, The Netherlands, 1989; p 113. (19) Gafert, J.; Friedrich, J.; Parak, F. Proc. Natl. Acad. Sci. U.SA. 1995, 92, 2116. (20) Gafert, J.; Friedrich, J.; Vanderkooi, J. M.; Fidy, J. J . Phys. Chem. 1995, 99, 5223. (21) Volker, S.; Macfarlane, R. M.; Genack, A. Z.; Trommsdorff, H. P.; van der Waals, J. H. J . Chem. Phys. 1977, 67, 17. (22) Kikas, J.; Schellenberg, P.; Friedrich, J. Chem. Phys. Lett. 1993, 207, 143. (23) Selzer, P. M.; Huber, D. L.; Hamilton, D. S.; Yen, W. M.; Weber, M. J. Phys. Rev. Lett. 1976, 36, 813. (24) Hayes, J. M.; Jankowiak, R.; Small, G. J. In Persistent Spectral Hole Buming: Science and Application; Moemer, W. E., Ed.; SpringerVerlag: Berlin, 1988; p 153.
J. Phys. Chem., Vol. 99, No. 39, 1995 14565 (25) Breinl, W.; Friedrich, J.; Haarer, D. J . Chem. Phys. 1984,81,3915. (26) Friedrich, J.; Haarer, D. In Optical Spectroscopy of Glasses;
Zschokke-Granacher, I., Ed.; Reidel Publ.: Dordrecht, 1986; p 149. (27) Mijers, H. C.; Wiersma, D. A. Phys. Rev. Lett. 1992, 68, 381. (28) Jahn, S.; Muller, K. P.; Haarer, D. J . Opt. SOC. Am. B 1992, 9, 925. (29) Narasimhan, L. A.; Littau, K. A.; Pack, D. W.; Bai, Y. S.; Elschner, A.; Fayer, M. D. Chem. Rev. 1990, 90, 439. (30) Berg, M.; Walsh, C. A,; Narasimhan, L. R.; Littau, K. A.; Fayer, M. D. J . Chem. Phys. 1988, 88, 1564. (31) Zwanzig, R. Acc. Chem. Res. 1990, 23, 148. (32) Stoneham, A. M. Rev. Mod. Phys. 1969, 41, 82. (33) Hegarty, J.; Yen, W. Phys. Rev. Lett. 1976, 36, 813. (34) Brundage, R. T.; Yen, W. M. Phys. Rev. E 1986, 33, 4436. (35) Lee, H. W. J.; Huston, A. L.; Gehrtz, M.; Moemer, W. E. Chem. Phys. Lett. 1985, 114, 491. (36) Ambrose, W. P.; Moemer, W. E. Chem. Phys. 1990, 144, 71. (37) Frauenfelder, H.; Wolynes, P. Phys. Today 1994, Feb (Special Issue on “Physics and Biology”). JF’951455R
