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deuteron coupling constant to bond length and the discrepancy between the optimized and the experimental C-H bond length the difference between the calculated and experimental deuteron coupling constant for formyl fluoride is not unexpected. The 35Clquadrupole coupling constants for formyl chloride given in Table VI should be compared with the experimental values obtained by Takeo and Matsumura2 for HC035C1. The experimentally determined values for (-eqQ/h),,, (-eq&h)bb,and (-eqQ/h),, are, respectively,--50.9,30.07, and 20.83 MHz. The electric field gradient at the chlorine is dominated by the electronic contributions and particularly those of the highest occupied molecular orbitals which would be expected to contain the largest inaccuracies and as a result good agreement between theory and experiment for the 35Clquadrupole coupling constants in formyl chloride would not be expected. In contrast the field gradient at the hydrogen in formyl fluoride contains a large nuclear contribution and little contribution from the other occupied molecular orbitals and good agreement between theory and experiment is expected and obtained. In conclusion there is, in general, good agreement between theory and experiment for the equilibrium geometries and one-electron properties of formyl fluoride and formyl chloride. The one major disagreement, the length of the C-C1 bond in formyl chloride, may indicate a need for a chlorine basis set including d-type Gaussian type orbitals. References and Notes (1) I.C. Hisatsune and J. Heicklen, Can. J. Spectrosc., 18, 77 (1973). (2) H. Takeo and C. Matsumura, J. Chem. Phys., 04, 4536 (1976). (3) D. C. Frost, C. A. McDowell, and N. P. C. Westwood, Chem. Phys. Left., 51, 607 (1977). (4) E. Ferronato, L. Grifons, A. Guarniere, and G. Zuliani, Adv. Mol. Spectrosc., 3, 1153 (1962).
Hamnett et al. (5) R. F. Miller and R. F. Curl, J . Chem. Phys., 34, 1847 (1961). (6) 0. H. LeBlanc, V. W. Laurie, and W. D. Gwinn, J. Chem. Phys., 33, 598 (1960) (7) P. Favero, A. M. Mirri, and J. G. Baker, Nuovo Cimenfo, 17, 740 (1960). (8) P. Favero, A. M. Mirri, and J. G. Baker, J . Chem. Phys., 31, 586 (1956). (9) M. E. Jones, K. Hedberg, and V. Schomaker, J. Am. Chem. SOC., 77, 5278 (1955). (10) R. F. Stratton and A. H. Nielson, J. Mol. Spectrosc., 4, 373 (1960). (1 1) S.L. Rock, J. K. Hancock, and W. H. Flygare, J . Chem. Phys., 54, 3450 (1971). (12) S. G. Kukolich, J. Chem. Phys,, 55, 610 (1971). (13) D. E. Klimek, Ph.D. Dissertation, University of Wisconsin, Madison, Wisc., 1975. (14) I.G. Czismadia, M. C. Harrison, and B. T. Sutcliffe, Theor. Chim. Acta, 0, 217 (1966). (15) H. Basch, M.B. Robin, and N. A. Kuebler, J. Chem. Phys., 49, 5007 (1968). (16) L. C. Snyder and H. Basch, J. Am. Chem. Soc., 91, 2189 (1969). (17) L. C. Snyder and H. Basch, “Molecular Wave Functions and Properties”, Wley-Interscience, New York, 1972. (18) R. Ditchfield, J. Del Bene, and J. A. Pople, J. Am. Chem. Soc., 94, 703 (1972). (19) W. J. Hehre and J. A. Pople, J . Am. Chem. Soc., 92, 2191 (1970). (20) J. E. Bloor and 2. B. Maksic, J. Chem. Phys., 57, 3572 (1972). (21) S. Huzinaga and Y. Sakai, J . Chem. Phys., 50, 1371 (1969). (22) E. Clementi, J. Mehl, and H. Popkie, IBMOL5A User’s Guide, IBM Research Laboratory, San Jose, Calif. 95193. (23) D. B. Neumann, H. Basch, R. L. Kornegay, L. C. Snyder, J. W. Moskowitz, C. Hornback, and S. P. Liebmann, QCPE No. 199, The Polyatom (Version 2) Systems of Program for QuantitativeTheoretical Chemistry. (24) W. J. Hehre, W. A. Lathon, R. Ditchfield, M. D. Newton, and J. A. Pople, QAUSSIAN 70, QCPE No. 236, Quantum Chemistry Program Exchange, Indiana University, Bloomington, Ind. (25) W. H. Flygare, ”Magnetic Interactions and the Electronic Structure of Diamagnetic Molecules” in “Critical Evaluation of Chemical and Physical Sbuctural Information”, D. R. Lide and M. A. Paul, Ed., National Academy of Sciences, Washington, D.C., 1974. (26) C. W. Kern and M. Karplus, J. Chem. Phys., 40, 1374 (1964). (27) R. Ditchfield in “Critical Evaluation of Chemical and physical Structural Information”, D. R. Lide and M. A. Paul, Ed., National Academy of Sciences, Washington, D.C., 1974, p 578. (28) J. A. Pople and M. S. Gordon, J . Am. Chem. Soc.,89, 4253 (1967).
Photosensitization of Titanium(1V) Oxide with Tris(2,2’-bipyridine)ruthenium(II) Chloride. Surface States of Titanium( IV) Oxidet A. Hamnett, M. P. Dare-Edwards, R. D. Wrlght, K. R. Seddon, and J. B. Goodenough” Inorganic Chemistry Laboratory, Oxford OX1 30R, England (Received Aprll5, 1979)
Investigation of the photosensitization of single-crystalTiOz by [Ru(bpy),]Clz (where bpy = 2,2’-bipyridine) has revealed the existence of a slow-rise-timecathodic photocurrent in addition to the fast-rise-time anodic photocurrent reported by Clark and Sutin. Phenomenological analysis of the experiment provides a satisfactory quantitative explanation based on a modulation of an ongoing dark current by energy transfer from the dye to the solid. Two new experiments and an extensive literature implicate surface Of ions as the molecular species responsible for the slow kinetics. Some implications of these results for the photoelectrolysis of water by sunlight are also indicated. Introduction In 1972, Fujishima and Honda’ reported that a singlecrystal, n-type TiOz anode is “chemically stable” when activated by UV light to oxidize water to oxygen. The “energy crisis” and the high cost of single-crystalsolar cells had already awakened interest in the possibility of using semiconductor electrodes to photoelectrolyzewater directly with sunlight, and two relevant facts were quickly established? (1)a polycrystalline Ti02anode is as efficient and + A Contribution from the Oxford-Imperial Energy Group. 0022-3654/79/2083-3280$01 .OO/O
stable as a single-crystal TiOz anode for the oxidation of water to O2 and (2) at the optimum photon wavelength, Hz evolution at a platinum counterelectrode in an electrolyte purged of oxygen is 10 times more efficient if an n-type SrTi03anode is used. Since the electron affinity, x,of SrTi0, was also shown to be 0.2 eV smaller than that of TiOz, the energy-diagram model of Figure 1 for pH 0 was put f o r ~ a r dnot ~ , only ~ to account for these observations but also to provide a strategic map for the design of a better anode. In the cell modeled in Figure 1, the two electrodes are connected by a short circuit and the metallic 0 1979 American
Chemical Society
The Journal of Physical Chemistry, Vol. 83, No. 25, 1979 3281
Surface States of Titanium(1V) Oxide
ANODE
ELECTROLYTE
CATHODE
Figure 1. Energy level diagram for the photoelectrolysis process at an n-type semiconductor.
electrode is acting as a hydrogen electrode. Therefore, at equilibrium the Fermi energies, EF,of the semiconductor and metal are at the Ht/H2 level in the electrolyte. These energy levels alter very little during cell operation provided the photocurrent remains low enough for overvoltages to be neglected, a condition fulfilled in a cell driven by sunlight. For isolated, n-type Ti02,EF typically lies about 0.3-0.4 eV below the bottom of the conduction band energy E,; a similar relationship is assumed for the ideal oxide semiconductor shown in Figure 1,which has its isolated-crystal E, more than 0.4 eV above the H+/H2 level. The constraint of a common EF in the two connected electrodes is realized by electron transfer from the surface of the semiconductor to the bulk; emptying of the donor states near the surface places EFnearer the center of the energy gap E, at the surface, and the resulting internal electric field lowers E, in the bulk relative to its position for the free crystal. In the absence of a significant net charge density in either the Helmholtz layer in the liquid or on the surface of the semiconductor, E , at the surface is at the same level as in the free crystal. Therefore, the smaller the electron affinity, x,the larger the “band bending” at the surface and the greater the electric field in the “depletion region” (region of depleted donor electrons) at the surface. Equalization of the Fermi energy in the semiconductor with the Ht/H2 level in the electrolyte introduces an electric field that is primarily across the depletion region rather than across a Helmholtz layer in the liquid because of the much smaller density of donor states in the solid than mobile ions in the ele~trolyte.~ For a simple Schottky model, the width, w,of the depletion layer depends on the density of donor states, N D ,as well as on the mismatch, A E F , between the isolated and connected semiconductor5 W = ( ~ F ( E E o ) / ~ K ~ ~ N D ) ~ / ~ where eo is the magnitude of the electron charge and is the dielectric constant of the semiconductor. As one condition for chemical stability, the model of Figure 1 places the top of the valence band E, below the 0 2 / H 2 0level of the electrolyte. Photoelectrolysis of water is produced by absorption of a photon of energy hv > E, that creates an electron-hole pair in the depletion layer where it is separated by the internal electric field before it is able to recombine. The electron passes to the cathode; from there it is transferred to an H+ ion at the H+/H2level to produce dihydrogen gas. The hole moves to the surface of the semiconductor and, if adiabatic transfer occurs, must rise through surface states to the 02/H20level. (Electron transfer from the electrolyte to the surface hole is a complex reaction, and an overvoltage of unknown magnitude places the active charge-transfer level below the 0 2 / H 2 0 level.) There it receives an electron from 1/2H20to create H+ + 1/402. Thus the absorption of light in the anode to
0
1 2 band gap ( e V )
3
Figure 2. Theoretical energy conversion efficiency for sernlconductors operating as storage or photovoltaic devices as a function of bandgap (after Gerischere3).
create a separable electron-hole pair leads to the evolution of H2 and O2 at the cathode and anode, respectively. The model of Figure 1takes no account of surface states except for the recognition that electron transfer from H 2 0 to the anode to produce O2 must be to an empty surface state of comparable energy to the 0 2 / H 2 0level within the semiconductor energy gap Eg. The observation6 that the flat-band potential, Le., the bias field just needed to eliminate band bending, increases with increasing pH indicates that a more adequate treatment of the surface states is needed. Nevertheless, it follows from the simple model of Figure 1 and the solar spectrum, which has a maximum intensity at 500 nm or about 2.5 eV, that Hzcould be produced from sunlight with a theoretical efficiency of about 20% (see Figure 2 ) , if a stable anode material could be found having x 5 3.8 eV and E, = 2.1 eV. (We use the photovoltaic-device curve because the factor ( 1.23/Eg)is equivalent to the factor eAVo/E,,. where AVOis the opencircuit voltage of the photovoltaic device.) Several oxides other than TiOz and SrTiOBhave been reported stable and capable of oxidizing water when acting as an n-type anode activated by light;7-9however, none of them satisfy the criteria for efficient H2production at the counterelectrode on exposure to sunlight. Difficulties with identification of a suitable anode material have led to speculations about other cell configurations. Among these is the use of a photosensitized anode of large energy gap Egl0 The work reported in this paper provides a preliminary evaluation of such a strategy. Figure 3 provides a simplified model (in the spirit of Figure 1)for a photoelectrolysis cell utilizing a photosensitized anode. This cell configuration relaxes an important constraint of the semiconductor anode, viz. the need for an Eg < 2.4 eV to match the solar spectrum, see Figure 2. Absorption of the sunlight no longer occurs in the solid; that function is transferred to a sensitizer dye molecule in the electrolyte. If D is the ground-state dye molecule, the desired cell reactions become hu
-
D --+ D*’+ D* D*
-+
-
+ H+ 1/zH2 Ht + 1/402 +D e-
D+ + 1/zH20
D+ + e-
(electrolyte) (anode) (cathode) (electrolyte)
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The Journal of Physical Chemistry, Vol. 83, No. 25, 1979
*
t
ANODE
I
ELECTROLYTE
'
CATHODE
Figure 3. Energy level diagram for the photoelectrolysis process with a dye-sensitized n-type semiconductor.
The electron e- is donated to the anode conduction band where it is transported to the cathode for transfer to H+ ions in the electrolyte, as in the cell of Figure 1. In Figure 3, E D is the energy of the sensitizer ground state and ED* that of its excited state after molecular relaxation. Light of photon energy hv = (ED*, - ED)is absorbed, where ED,, is the excited-state energy before molecular relaxation. The lifetime of the excited state of the dye is 7,;the excited sensitizer must diffuse to the semiconductor surface and transfer the excited electron to the anode in a time Tt > kf, corresponding to concentrations of Y in excess of M, and k,y > kf, the only conceivable quenching agent is 0,; but even for this molecule a kgy = 0,2kf is estimated from the work of Gleria and Memming.36 Moreover, B would be primarily quenched to A by O2 (‘A)027138 with a lifetime of -1 ps in aqueous Reduction of (lA)O, at TiOz i s possible thermodynami-
ab’/at
-
cally,17but the rapid kinetics predicted for such a model is not compatible with the slow rise time of the cathodic current unless there is a rapid buildup of (lA)O2concentrations, which is not observed. If kgy > 1,the surface-state hole density reduces to p s = pS0
+ (P/eo)(u,ol/2 - u1/2)
(23)
Thus a change AQo in the surface charge modulates the band bending eOVIand hence any on-going dark current, which varies exponentially with V as expressed in eq 1. Moreover, an increase in p s produces a decrease in eoV and hence an increase in the cathodic dark current icd, which is why the photocurrent due to these processes is cathodic. The photoexcitations e,; ecb-create an excited electron distribution; thermally excited transfers ecb- e,; would return the system to the dark-state equilibrium. Following Lagowski et al.,42we assume that these thermal processes are initially slow compared to the photoexcitation rate. Creation of a dynamic equilibrium having (p, - p;) > 0 under steady-state illumination is established over a relatively long time; the rate of the thermal processes increases with ( p , - p,O) until it balances the rate of photoexcitation, which is proportional to the concentration of ([R~(bpy)~]~ at+the ) * surface, b(0,t). In the general reaction
-
A &B ki
diffusion
-
(electrode)
s
A
-
nbUthan(P, - p:) = krnb exp(-au)(ps - p:)
(26)
The rate of change of Qo is given by dp,/dt = k(N, - P , ) ~ o- k,nb exp(-au)(p, - p:)
(27)
the difference between the rates of excitation and recombination. From eq 23 dp,/dt = -(/3/2eou1/2) du/dt and eq 27 may be written
+ l)y] erfc (py)l/' dy = bo
-
+
where N,* = N , p:. To obtain an analytic solution for eq 28, it is necessary to recognize that the photocurrents are small compared to the dark currents. Moreover, to take advantage of this fact, it is convenient to note that u decreases under illumination until a steady-state value u, is reached such that duldt = 0, or (2eo//3)Kb~,* = 2 ( b 0 + k&, exp(-au,,))(u,01/2 (29)
Substitution of (29) into (28) gives -du/dt = 2k,nbd/2([ K
(u,:/~
exp(-cuv,,)]
X
- [K + e x p ( - a u ) ] ( ~ -, ~u~1 l~2 )~) (30)
-
with K kbO/krnb. Since the photocurrents are small compared to the dark currents, the changes 6 u,o - u 6,, u,o - us, (31) satisfy the condition 6 I6,,
