J . Phys. Chem. 1991, 95, 10528-10531
10528
the latter case the injected space charge is always compensated by the sensitizer cations and the current is limited by trapping eventsg within the particles and at grain boundaries. interfacial Electron Transfer to Methylviologen in Solution. It has been possible to monitor spectroscopically in real time at 610 nm the conduction band electrons that reduce MVZ+. The real-time behavior of the conduction band electrons on stepping the applied potential between 0.00 and -1.00 V at -0,596 Hz can be seen in Figure 3a and is the same as that monitored at 900 nm under similar conditions; see Figure 2a. Upon addition of 1 X 10" M MV2+an increase in absorbance is observed, assigned to reduction of MV2+ to MV+; see Figure 3b. This reaction is possible at potentials more negative than -0.68 V.Io As expected upon stepping the applied potential to 0.00 V, MV+ is oxidized to MVZ+since the flatband potential is -0.52 V at pH 3.0. It is noted that formation and decay of the reduced form of methylviologen shows the same growth and decay behavior as the accumulation layer. The addition of 2 X M MV2+results in the transient shown in Figure 3c. It is noted that the MV+ yield remains constant and that the growth and decay behavior of the MV+ signal is, as before, the same as that observed for the accumulation layer. The fact that the growth and decay behavior of MV+ is the same as that observed for the accumulation layer indicates that filling of deep trap states is controlling the Faradaic processes of MVZ+. The fact that no increase in absorbance is ObSeNed upon increasing the concentration of MV2+by a factor of 2 suggests that only that MV2+present a t the surface of the TiOz particles in the membrane is reduced and that surface M concentration. saturation is reached at At pH 11.6 a significantly larger signal is observed following M MVZ+due to the fact that absorption of addition of 2 X MVZ+is enhanced." There is therefore an initial very fast component to the transient observed upon stepping the potential (9) Schwarzburg, K.; Willig, F. Appl. Phys. Lett. 1991, 58, 2520. (10) Grltzel, M. Heterogeneous Photochemical Electron Transfer, CRC Press: Boca Raton, FL, 1989; Chapter 2, Table I and references therein. (11) Furlong, N.; Wells, D.; Sasse, W. J . Phys. Chem. 1986, 90, 1107.
to -1.30 V corresponding to reduction of adsorbed MV2+. In this case no oxidation of MV+ is observed upon stepping the applied potential to 0.00 V at pH 11.6. This is as expected since the flatband potential (-1.03 V) is more negative than the redox potential of methylviologen. It also indicates that reaction with dissolved oxygen is not important, possibly because all the oxygen present at the membrane has been reduced. The fact that once the applied potential is biased to potentials more positive than +1.30 V oxidation of MV+ is observed is interesting. This may reflect enhanced electron tunnelling at these potentials or a band edge unpinning. Further detailed studies of this and other suitable Faradaic processes are currently being undertaken.
Conclusions The main conclusions to be drawn from the work presented here are the following: first, the growth and decay behavior of the accumulation layer, formed upon biasing a TiOz membrane electrode to potentials more negative than the flatband potential of the conduction band, is controlled by the compensation of space charge; second, the flatband potential of the conduction band moves to more negative potentials as H+ions present at the surface of the membrane are reduced. Third, redox processes of MVZ+ at the surface of a TiOl membrane, under acidic conditions, are controlled by deep trap filling. Finally, in general, a better understanding of the Faradaic processes at the surface of a metal oxide semiconductor membrane has been possible because the transient absorbance of both the charge carriers and the redox species could be monitored spectroscopically in real time.
Acknowledgment. D.F. acknowledges the cooperation of his colleagues at UCD and the support of Schering Plough Corp. and thanks Prof. M. Griitzel for his kind invitation to visit EPFL. We thank Prof. F. Willig for a preprint of his forthcoming letter. This work was supported by the Swiss Office FEd6rale d'Energie and the Swiss National Science Foundation. Registry No. TiOz, 13463-67-7; Ht,12408-02-5; H2, 1333-74-0; MV2+, 4685-14-7; LiC104, 7791-03-9; HC104, 7601-90-3; NaOH, 1310-73-2; M V , 78991-90-9.
Identification of Uncoordinated Cr(CO)5 Intermediate in Cyclohexane with Picosecond Time-Resolved I R Spectroscopy Julian R. Sprague, Steven M. Arrivo, and Kenneth G. Spears* Department of Chemistry, Northwestern University, Evanston, Illinois 60208-31 I3 (Received: June 14, 1991; In Final Form: September 30, 1991)
Photolysis of Cr(CO),.C6HI2 with 532-nm light was studied with picosecond transient IR spectroscopy. A subpopulation of transients corresponding to uncoordinated Cr(CO)5was observed at 1970 3 cm-'with a lifetime of 15 f 10 ps. A larger population of vibrationally excited Cr(CO)S rapidly formed C ~ ( C O ) ~ * Cwith ~ H excitation I~ in its C o stretching mode at 1945 cm-I. New experiments with UV photolysis of Cr(CO), at 300 nm identify vibrationally excited Cr(C0)6. These data are used to discuss the mechanism of photolysis and reaction.
*
Introduction Recently, we reported that the uncoordinated Cr(C0)5 species has a lifetime of =lo0 ps in cyclohexane.' This result was based on the interpretation of transients at a limited number of IR wavelengths acquired after photolysis of Cr(C0)6 with a short UV laser pulse at 266 nm. Since that time we have improved the apparatus to acquire data over the entire C O stretching region in 3-cm-I increments. In a prior report2 long-lived transients to
the high- and low-frequency side of the product band in perfluoroheptane were tentatively assigned to u = 0, 1, and 2 quanta population of a CO stretching mode of Cr(CO)S, largely based on the high-frequency feature a t the expected position of uncoordinated Cr(CO)5. Experiments described in this Letter were designed to determine if all of the long-lived transients were due to the same species. ~
(1) Wang,
L.:Zhu, X.;Spears, K. G. J. Am. Chem. SOC.1988,110,8695. 0022-3654/91/2095-10528$02.50/0
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(2) Spears, K. G.; Wang, L.; Zhu, X.;Arrivo, S . M. Proc. SPIE 1990, 1209, 32.
0 1991 American Chemical Society
The Journal of Physical Chemistry, Vol. 95, No. 26, 1991 10529
Letters 0.25
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0
100 200 300 400 TIME I N P I C O S E C O N D S (ARBITRARY ZERO)
500
Figure 1. Photodissociation of Cr(CO)&HI2 in cyclohexane by 532-nm excitation. Infrared probe pulse at 1958 cm-' with 2 ps per point for first 200 ps, 10 ps per point for the next 500 ps, and 64 laser shots/point. The solid curve is a convolution of the IRF with a bleach and two recovery rates of 20 and 100 ps.
0
100 200 300 400 500 600 TIME I N P I C O S E C O N D S (ARBITRARY ZERO)
Figure 2. Same as Figure 1, but with an infrared probe pulse at 1970 cm-I. The solid curve is a convolution of the IRF and a single exponential with a lifetime of 10 ps. The best fit lifetime is 15 i 10 ps. 0.15
I
Experimental Methods The new experiments take advantage of the fact that the product of this reaction, Cr(C0)5*C,&, has a 10 kcal/mol bond? is stable for many nanoseconds following the UV photolysis pulse, and has a broad visible absorption band centered at approximately 500 nma4 After a delay of 600 ps following the UV photolysis pulse, transients at all the observed wavelengths have relaxed. A second photolysis pulse at 532 nm selectively removes the cyclohexane ligand without additional loss of C O ligands or excitation of Cr(C0)6. The experimental apparatus has been described.'~~ Briefly, the concentration of Cr(C0)6 was 5 mM in cyclohexane. This solution was circulated through a sapphire jet which produced a sample thickness of -200 pm. In this work the time delay between the nominal 15-ps 300-nm UV pulse and the nominal 10-ps IR pulse was fixed at -600 ps. A point-by-point time scan of IR absorbance at a single wavelength is recorded by varying the time delay between a second photolysis pulse at 532 nm (-35 ps fwhm) and the IR pulse. Power densities of the 532- and 3 W n m pulses were 4.7 X 1O'O and 8 X 1O'O W/cm2, respectively. We will refer to these new experiments as UV/vis and prior experiments with UV photolysis of Cr(C0)6 as UV experiments. In the UV/vis experiments we scanned the region from 1986 to 1928 cm-' in 3-cm-I steps, and we report the major features below. All curves are fit with the measured IRF convoluted with exponential functions. An instrument response function (IRF) is directly measured for UV experiments. The direct IRF measurement for the UV experiments allows a rise time to be fit with an uncertainty of f 3 ps, where a rise time in the 0-3-ps range is unresolvable. The UV/vis experiment uses a response function indirectly from 532-nm autocorrelation measurements and IR durations. This indirect IRF introduces greater uncertainty for decay measurements in the time range 1 3 5 ps of the UV/vis experiments. An upper limit for a decay rate is obtainable from fits to the transient data. A lower limit can only be estimated by not allowing an unreasonably large amplitude factor, since very short decays would require a very large population to create an absorbance change similar to the data. In our case the amplitude factor for the bleach should approximately match the sum of transients. For the case of 1970 cm-' described in the text, we assign a best fit value of 15 ps with an error limit of f10 ps to account for both limits. The time equal to zero position in the ~~
(3) Yang, G. K.; Peters, K. S.; Vaida, V. Chem. Phys. Lett. 1986, 125 (5, 6), 566. (4) Simon, J. D.; Xie, X.J . Phys. Chem. 1986, 90, 6751. (5) Spears, K. G.; Zhu, X.; Yang, X.; Wang, L. Opt. Commun. 1988,66 (2,3), 167.
700
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200 300 400 500 600 TIME IN P I C O S E C O N D S (ARBITRARY ZERO) 100
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Figure 3. Same as Figure 1, but with an infrared probe pulse at 1943 cm-I. The solid curve is a convolution of the IRF with a single exponential having a lifetime of 117 ps and a slight baseline correction. The band center is estimated to be at 1945 f 3 cm-'.
figures is the beginning of the experimental scan, and the IRF defines the time position of pumpprobe pulse overlap. UV/Vis Experiments and Interpretation The E symmetry mode for co stretching of Cr(C0)5.C6H12 is centered near 1960 cm-1.'-6 Figure 1 is an IR transient of Cr(CO)5C6H12at 1958 cm-' following 532-nm photolysis of Cr(C0)5.C6H12in cyclohexane. This transient is similar from 1955 to 1961 cm-', and we estimate the band center as 1958 f 3 cm-'. The initial negative absorbance is due to dissociation of Cr(CO)5.C6H12,while the return to the baseline indicates reformation of starting material. Molecules that do not dissociate or that quickly recombine (110ps) into the u = 0 level will not contribute to a negative absorbance. The re-formation rate has only approximate exponential character, and we will discuss how this behavior is consistent with contributions from more than one reaction path. The recovery does not return completely to the original baseline, and we have shown that it is power dependent. This minor channel does not exhibit any new spectral features in the region of interest. Figure 2 is the IR transient at 1970 cm-' under the same experimental conditions as Figure 1. The lifetime of the transient is 15 f 10 ps. We note for later discussion that this short duration (6) Church, S. P.;Grevels, F.-W.; Hermann, H.; Schaffner, K. Inorg. Chem. 1985, 24,418.
10530 The Journal of Physical Chemistry, Vol. 95, No. 26, 1991
is in contrast to the >lOO-ps lifetime transient a t the same wavelength observed after photodissociation of Cr(C0)6 in the W experiment.] The transient band is spectrally broad from 1965 to 1975 cm-l and has a computer-deconvolved amplitude that is 20% of the bleach amplitude. Figure 3 is an IR transient at 1943 cm-I under the same experimental conditions as Figure 1. This transient exists between 1950 and 1940 cm-', and we assign a band center at 1945 f 3 cm-'. In Figure 3, the solid line is the convolution of the IRF and a single-exponential decay with a time constant of 117 ps. This transient may have a more complex decay, possibly including a component with a slower rise time. These data demonstrate that the 1970-cm-I feature on the high-frequency side of the product band is not derived from the same transient species absorbing at 1945 an-'on the low-frequency side of the product band. The product band at 1958 cm-' for Cr(C0)5C6H12is due to absorption from the v = 0 level of the E symmetry mode, and we expect absorption from the v = 1 level to be shifted to lower frequency according to anharmonicity. For gas-phase CO the anharmonic shift' is 27 cm-', and while the shift is unknown for Cr(C0)5-C6H12,it is reasonable that the 1945-cm-I transient band should be assigned to the v = 1 absorption with an anharmonicity of 14 f 3 cm-l. The decay of this transient is due to vibrational relaxation into the v = 0 state, which is nominally 145 ps for Cr(C0)6 in hexane,8 so the observed time scale for the decay is consistent with this relaxation process. The uncoordinated Cr(C0)5 molecule of C, symmetry is known from gas-phase work9~10 to be near 1986 cm-l. Because the solvent shift of the 2000-cm-l band of gas-phase Cr(C0)6 is 14 cm-', we would expect to observe uncoordinated Cr(CO)5 in cyclohexane near 1972 cm-'. This suggests that we should assign the 1970-cm-' feature to uncoordinated Cr(CO)5 in its v = 0 state, and with C4, symmetry. Prior estimates of expected frequency shifts from distortion of Cr(CO)5 into a D3* symmetry predict much lower frequencies6 than the observed band. The assignments require that the bleach recovery at 1958 cm-' be composed of at least two contributions, the vibrational relaxation from the rapidly formed product in its v = 1 state and the delayed reaction of Cr(CO)5 in its v = 0 state. These two contributions have amplitudes and decay constants given by the 1970and 1943-cm-l transients, and a sum of these two amplitudes gives a reasonable fit to the bleach recovery of the 1958-cm-' band, which is indicated by the solid line in Figure 1. The assignment of precise contributions of fast components for the bleach recovery is impossible without an experimental IRF; therefore, unlike the UV experiments, we cannot identify if a fast reacting subpopulation of Cr(CO)5 in its v = 0 state exists. The experimental transients directly demonstrate that at least two separate populations of Cr(CO)5 are created by the photolysis, with very different rates of product formation.
Letters 0.5
1
1 1987 cm-l
0.0
'
0
I
100
200
400 500 600 700 T I M E I N P I C O S E C O N D S (ARBITRARY ZERO) 300
Figure 4. Photodissociation of Cr(CO), in cyclohexane by 300 nm with an infrared probe pulse at 1987 at-'.The major contribution to the large negative absorbance (from the bleach of Cr(CO),) is a 140-ps exponentially rising absorbance.
about 16 f 3 cm-' suggests that we assign this absorption to Cr(C0)6 absorbing from u = 1 to u = 2. The vibrationally excited Cr(C0)6 results from a quantum yield for dissociation that is less than unity in liquids."J2 It is generally postulated that some recombination occurs with the CO fragment,I3 which would yield vibrationally excited Cr(CO)+ Another possible source of this signal is solvent-induced radiationless decay from the excited state of Cr(CO)6 to its ground state. These mechanisms require further study. This interpretation explains the dominant long-lived component of the 197O-cm-I band in the UV experiment. Because the lifetime of the uncoordinated Cr(CO)S species is short, the absorbance signal from the relatively long lifetime of vibrationally excited Cr(C0)6 masks small signals due to the uncoordinated species. However, in perfluoroheptane we see evidence for an uncoordinated species which is not completely masked by vibrationally excited Cr(CO)6.14
New UV Experiments Now that we have shown that the bands to the blue and to the red of the product band at 1958 cm-I are due to different species, we must discuss the origin of the long-lived transient band centered near 1970 cm-I in the UV experiment. The only IR-active C O stretching mode of Cr(C0)6 in the gas phase is a TI, mode at 2000 cm-l. As we mentioned above, in FTIR spectra the cyclohexane shifts this band 14 cm-I to 1986 cm-'. Figure 4 is an IR transient of Cr(C0)6 a t 1987 cm-] following UV photolysis at 300 nm. Clearly, the bleach of this band has a small =10-15% exponential recovery with a time constant of 140 f 10 ps. The amplitude coefficient and the rise time of this recovery match the amplitude and decay time of a transient band near 1970 cm-' in the UV experiment. Furthermore, the decay time is close to the vibrational relaxation time for Cr(C0)6 in hexane.s The anharmonicity of
Discussion The UV/vis experiment has identified at least two decay paths for high energy content Cr(CO)S. This is an important result that helps us understand the photolysis mechanism of Cr(C0)6 and the reasons for fast formation of some products. One path in the UV/vis experiment leads to Cr(CO)5 (E mode u = 0) having a lifetime of 15 f 10 ps and another path leads to Cr(CO)5 (E mode v = 1) that reacts quickly with solvent. A conceptual framework for the relaxation mechanism is that of radiationless decay from the initial excited-state Cr(CO)s to a ground-state Cr(CO)S surface. This radiationless decay populates different amounts of energy in the CO stretching modes and other, mostly low frequency, modes. Those Cr(CO)5 molecules with a large amount of energy (3-5 quanta) in CO stretching motions have very little energy in low-frequency modes. The long lifetime of energy in CO stretching effectively removes this energy from the RRKM energy pool that would have served to dissociate a weak bond, allowing fast reactions to occur. However, a molecule initially formed with most of the excess energy in lowfrequency modes and little in CO stretching modes will require energy to be removed by collisions before reaction with the solvent can occur. This collisional relaxation process takes time, which for our UV/vis experiments is observed to be about 15 ps for such a subpopulation. Fast reactions require CO stretching mode
(7) Herzberg, G.Molecular Spectra and Molecular Structure I . Spectra ojDiatomic Molecules, 2nd ed.; D. van Nostrand Co.: Princeton, NJ, 1950. (8) Heilweil, E. J.; Cavanagh, R. R.; Stephenson, J. C. Chem. Phys. Lerr. 1987,. 134, 18 1. (9) Wietz, E. J . Phys. Chem. 1987, 91, 3945. (10) Private communication with E. Weitz and R. Wells.
(11) Nasiclski, J.; Colas, A. J . Organomet. Chem. 1975, 101, 215. (12) Nasielski, J.; Colas, A. Inorg. Chem. 1978, 17, 237. (13) Burdett, J. K.; Grzybowski, J. M.; Perutz, R. N.; Poliakoff, M.; Turner, J. J.; Turner, R. F.Inorg. Chem. 1978, 17, 147. (14) Span, K. G.; Sprague, J. R.;Arrivo, S. M.; Zhu, X.;Wu, C.; Wang, L. To be published.
10531
J . Phys. Chem. 1991,95, 10531-10534 population, but not necessarily in the E mode since three other modes of different symmetry can also accept energy. The mechanistic information from these experiments is reasonably consistent with the available data from picosecond transient visible and resonance Raman experiments. The main observation of the early visible experiments was a fast rise time of 1-2 ps in c y ~ l o h e x a n edominated ~ ~ ~ ~ by Cr(CO)5.(solvent). We now can confirm that the fast reaction rate is possible because of efficient internal deposition of large amounts of energy in the CO stretching modes through a fast radiationless decay of the initially formed Cr(CO)5 excited state. Other visible absorption experiments at wavelengths to the red of the broad peak have measured a transient decay of about 20 ps in cyclohexane.I6 This transient could correspond to an absorbance of the naked Cr(CO)5 that we observe in the IR, since in our UV/vis experiments we found a 15 f 10 ps lifetime for this species. UV resonance Raman experiments detected the vibrationally excited symmetric stretching motion of CO with a lifetime similar to our value,I7 which is consistent with our observation of at least one quantum in the doubly degenerate E mode of the CO stretch. Also observed in the resonance Raman work was a similar long lifetime for M-CO stretching motions. That result suggests to us that the CO stretching modes at least partly decay internally into low-frequency modes. The long time for this process ensures that only rarely will sufficient excess energy be present to dissociate the weak metalsolvent bond once it is formed. Therefore, the large amounts of energy in the CO stretching modes can decay internally into (15) Joly, A. G.;Nelson, K. A. J . Phys. Chem. 1989, 93, 2876. (1 6) Lee, M.; Harris, C. B. J . Am. Chem. Soc. 1989, 11 I , 8963. (17) Yu,S.;Xu,X.;Lingle, R. Jr.; Hopkins, J. B. J. Am. Chem. Soc. 1990, 112, 3668.
M-CO motions without causing dissociation of the product, or externally by solvent collisions.
Summary By using a 532-nm photolysis laser pulse to remove the solvent ligand from Cr(C0)5-C6H12,we observed a 15 f 10 ps IR transient at 1970 cm-’ within the spectral region expected for uncoordinated Cr(CO)5. Multiple decay paths to product were observed. Cr(CO)5-C6HIZ is formed quickly with one quantum of vibrational excitation in the CO stretching mode of E symmetry, which has a nominal lifetime of 100 ps. An efficient nonradiative energy relaxation into isolated CO stretching modes can account for the fast reaction of the uncoordinated species with the solvent since this energy is quickly removed from the RRKM energy pool. Finally, the Cr(CO), lifetime indicates that in our UV photolysis of Cr(C0)6 the >lOo-ps transient at 1970 cm-l is dominated by vibrationally excited Cr(C0)6 rather than uncoordinated Cr(CO)+ These new results provide a mechanistic view of Cr(C0)6 and Cr(CO)5.C6H12 photolysis that is consistent with available transient visible and resonance Raman spectroscopic data. Additional descriptions of our data and its analysis, a more complete discussion of radiationless decay theory and RRKM theory, and comparisons with gas-phase and matrix data will be included in a full article.
Acknowledgment. We thank the Strategic Defense Initiative Organizations through the Medical Free Electron Laser Program for their financial support. We also thank Xinming Zhu and Changzheng Wu for assistance in data collection and Liang Wang for his computer programming. R@try No. Cr(CO)5, 26319-33-5; Cr(CO),, 13007-92-6; C6H12, 110-82-7.
Chemical Applications of Density Functional Theory: Comparison to Experiment, Hartree-Fock, and Perturbation Theory George Fitzgerald* and Jan Andzelm Cray Research, Inc., 655-E Lone Oak Dr., Eagan, Minnesota 55121-1560 (Received: July 22, 1991; In Final Form: October 21, 1991)
Density functional theory (DFT) offers an alternative method for the quantum mechanical computation of chemical properties. Although initial results have been very positive, the method still lacks the long history of calibration which exists for more conventional methods. This calibration is important for identifying particular strengths and weaknesses of each method. The present study attempts to establish such a calibration for DFT. Results are obtained for structures, vibrational frequencies, and heats of reaction. Results are generally comparable in accuracy to MP2 calculations. Certain properties are reproduced rather poorly by local density functional methods; the predicted values of some of these properties are improved by the use of nonlocal corrections, added perturbatively at the end of the local DFT calculation.
Introduction During the past decade, density functional theory (DFT)14 has become a standard approach in the investigation of structural, electronic, and magnetic properties of bulk solids, surfaces, and
interface^.^.^ (1) Hohenberg, P.; Kohn, W. Phys. Reo. 1964, 136, 864. ( 2 ) Kohn, W.; Sham, L. J. Phys. Rev. A 1965, 140, 1133. (3) Levy, M. Proc. Natl. Acad. Sci. U.S.A. 1979, 76,6062.
(4) Parr, R. G.; Yang, W. Density-Functional Theory of Atoms and
Molecules; Oxford University Press: New York, 1989. ( 5 ) Jones, R. 0.;Gunnarsson, 0. Reu. Mod. Phys. 1990, 61, 689. ( 6 ) Wimmer, E.; Krakauer, H.; Freeman, A. J. Adu. Electron. Electron Phys. 1985.65, 357.
0022-3654/91/2095-10531$02.50/0
The application of the method to chemistry was delayed due to the lack of ability to optimize molecular structures and calculate accurate heats of reactions. Only recently, the gradient geometry optimization technique was introduced to the DFT method and the nonlocal DFT potentials allowed for an accurate prediction of energetics of chemical reactions.’,* However, in contrast to Hartree-Fock and the many-body methods, such as MP2: the DFT method lacks the extensive and _____
(7) Density Functional Methods in Chemistry; Labanowski, J., Andzelm, J., Eds.; Springer: New York, 1991. (8) Ziegler, T. Chem. Rev., in press. (9) Hehre, W. J.; Radom, L.; Schleyer, P.; Pople, J. A. Ab Initio Molecular Orbital Theory; Wiley: New York, 1986.
0 1991 American Chemical Society
