J. Phys. Chem. 1985,89, 3863-3869
TABLE II: Seven Highest Ionizations of Cyclobutrdiew" symmetry
VIP, eV Koopmans' theorem
1 B2g 3% 1B1" 4% 3B3u
7.50 12.34 12.88 14.59 15.03
3%
18.86
2BI,
18.97
3rd order
pole strength (intensity)
7.90 11.41 12.71 13.59 13.07 13.62 14.51 16.34 17.00 16.85 17.12 18.43
0.901 0.908 0.889 0.886 0.044 0.815 0.019 0.102 0.616 0.452 0.31 1 0.026
'Basis 2: q ( C ) = 0.3, aP(H) = 0.75; see text.
8.19 and 7.66 eV with a semiempirical configuration interaction method with two slightly different geometries. It is also dependent on the basis set, and in particular, Von Niessen et al.I9 have shown that for ionization from 7r orbitals, e.g. lBz, in ethylene, diffuse d functions are needed in the basis in order to account for correlation energy changes in the diffuse part of the charge cloud which are not spanned by the standard d-type functions. In view of this, we have repeated our calculations with the same standard Gaussian basis but with different (more diffuse) polarization (18) G.Lauer, K. W. Schulte, and A. Schweig, J . Am. Chem. SOC., 100, 4925 (1978). (19) W.Von Niessen, G.H. F. Diercksen, L. S. Cederbaum, and W. Domcke, Chem. Phys., 18,469 (1976).
3863
functions (ad(C) = 0.3, a,(H) = 0.75). Results for the first seven ionizations with this basis are given in Table 11. Comparison of the two tables shows that it is indeed the r-type ionizations (lBzgand lBl,) that have changed the most, increasing by 0.13 and 0.15 eV, respectively, while most of the remaining ionizations have changed by half this amount or less. The exception is the 4A, ionization which has increased by 0.2 eV, a relatively large and unexpected change, perhaps indicating that there are still deficiencies in the basis set. The qualitative picture remains the same though, and again the main lines for the 3Ag and 2BIgionizations show an orbital reordering compared to the Koopmans' theorem values. Recent work by Agren et al.,O involving partial geometry optimization within an MCSCF scheme using the same basis as for our first set of calculations has resulted in an alternative geometry for cyclobutadiene, with C-C bond lengths of 1S48 and 1.446 A (see structure 1 ) . However, an additional S C F calculation at this geometry gave a significantly higher energy (ESCF= -1 53.657 885 hartree) and, more importantly, worse values for the Koopmans' theorem IPS(e.g. 1BZs 7.21 eV) than with the geometry used here, indicating that, within the S C F scheme on which our approach is based, our geometry is more appropriate. The assignments proposed in ref 1 are essentially in agreement with the results reported here, although the energy gap between the two highest occupied r-type MOs we obtain here of 4.691431 eV for lBzg(r)-lBiu(7r) (or lb3&7r)-1b2,(r) in their labeling) is more in agreement with the one obtained by Schweig et a1.18 Registry No. Cyclobutadiene, 1120-53-2. (20) H. Agren, N. Correia, A. Flores-Riveros, and H. J. Aa. Jensen, submitted for publication in Int. J . Quantum Chem.
Kinetic Approach to the Photocurrent Transients in Water Photoelectrolysis at n-TiO, Electrodes. 1. Analysis of the Ratio of the Instantaneous to Steady-State Photocurrent P. Salvador Instituto de Catrilisis y Petroleoquimica (CSIC),Serrano, 1 1 9, 28006-Madrid, Spain (Received: October 16, 1984)
The transient photocurrent-time behavior observed during water photoelectrolysis with monochromatic band-gap light at n-Ti02 single crystals has been studied as a function of semiconductor band bending, & and photon flux, a,,. A kinetic model based on the photogeneration of surface species,intermediatesof the O2evolution reaction, allows a quantitative explanation of the main transient features. Two parallel mechanisms are involved in this model: (i) a time-dependent cathodic back reaction of photogenerated surface intermediates (mainly OH,. radicals and (H202)sspecies) with conduction band electrons, opposite to the anodic photocurrent; (ii) a band-bending modulation due to the accumulation of positive charge at the semiconductor surface produced by hole trapping at active OH- surface groups. Surface recombination via photogenerated OH,.radicals is the dominant reaction at small band bending. In the sequence of surface reactions leading to 0, evolution, hole flux toward the semiconductor-electrolyte interface is the limiting step at low 9,. At high enough light intensity the reaction is limited by the generation rate of Hz02species from photogenerated OH,. radicals. The rate constant of this reaction is estimated to be about 10-L'-10-12 cm2 s-'. At steady state the surface concentration of photogenerated species (OH,. and (HZO2),)depends on both @s and aWUnder monochromatic illumination (A = 380 nm, @, = 1015cm-2 s-l), and for negligible surface recombination (high &), the surface concentration of OH,. and (H202),reaches values of the order of 1013and 1014 cm-,, respectively. In the dark after illumination, and in the absence of oxidable electrolyte species other than H 2 0 molecules, the lifetime of OH,.radicals is very short (> klvo,both [OH,.],, and [(H202)s]st increase exponentially with 4,; moreover, [(H202),],,
