J. Phys. Chem. 1985,89, 3861-3863 of resolving spectra at a total rovibrational density of states S2500 per cm-I. The acetaldehyde system seems ideally suited for more detailed studies as it is a sufficiently small molecule that the combined use of vibrational spectroscopy and ab initio calculations has been used to provide a good vibrational force field.21 This can be further refined after completing a detailed spectroscopic analysis of the anharmonic coupling constants. A rich literature is already available on the internal rotor mode potential.22 These findings, when combined with high-resolution spectroscopic measurements of the positions of the perturbed rovibronic levels and the effects of isotopic substitution, will provide a sound basis for the development of the dynamical theory.
Acknowledgment. We thank Laser Analytics for sharing their time and their lasers acquiring the TDL spectra. V.A.W. also thanks the Hey1 Foundation for a Graduate Fellowship. This work was supported by the National Science Foundation Grant CHE-83- 18955. Appendix Simulated Band Contours. The calculated band contours for acetaldehyde were generated by using an asymmetric rotor program based on Birss’ XASYROT. Modifications of this program for use on a VAX/VMS operating system were made by R. C. Dempsey, and a listing can be found in his thesis?3 It is important to note that perturbations are not provided for in this program. The lower state rotational constants were taken from Bauder and Gunthard.22 The upper state rotational constants were varied to (21) K. B. Wiberg, V. A. Walters, and S.D. Colson, J . Phys. Chem., 88, 4723 (1984). (22) A. Bauder and Hs. H. Gunthard, J . Mol. Spectrosc., 60,290 (1976). (23) R. C. Dempsey, Ph.D. Thesis, Yale University, 1983. (24) H. D. Harmony, V. W. Laurie, R. L. Kuczkowski, R. H.
Schwendeman, D. A. Ramsey, F. J. Lovas, W. J. Lafferty, and A. G. Maki, J . Phys. Chem. ReJ Data, 8, 619 (1979).
3861
within *2% in attempts to find the best fit to the experimental spectrum. The best fit was found with A”-A’ = 0.01000, B”-B’ = 0.00344, C”-C’ = 0 and the band origin at 1748.7 cm-I. However, the lack of close agreement between the calculated and observed spectra indicates that these constants are only approximate. The relative proportion of B and A type bandshapes used to calculate this hybrid band was 0.42. This number was taken from the ratio of transition moments along Cartesian axes determined from a fitted force field and calculated dipole moment derivatives.21 The calculated energies were convoluted with a Lorentzian line shape. Density-ofstates Calculation. The potential function for the hindered rotation of the methyl group used in the density-of-states calculation was V = V3(1 - cos 37)/2. The Hamiltonian matrix elements are as described by Flygare.Is The potential barrier, V3,used for the acetaldehyde calculation was adjusted from the value of 400 cm-I (given by Bauder and GunthardU for a different Hamiltonian) to 440 cm-l in order to fit the lower torsional energy levels given in this same reference, when our approximate Hamiltonian was used. The lowest torsional energy levels (v = 0) have reported frequencies of 74.4 and 74.3 cm-l for the E and A components, respectively. We calculate both to be at 75.6 cm-I. Similarly, the second lowest levels (v = 1) are reported at 214.5 (E) and 216.3 (A) cm-I, whereas we calculate 218.1 and 218.7 cm-I, respectively. The same energy barrier was used for acetaldehyde-d,. The geometry used to calculate the moments of inertia was found in ref 22. The vibrational frequencies are found in ref 21. For the calculations on methyl formate, the vibrational frequencies were those of Susi and Zell,25and the potential barrier and geometry were taken from Registry No. Acetone, 67-64-1; methyl acetate, 79-20-9; acetaldehyde, 75-07-0; methyl formate, 107-31-3. (25) H. Susi and T. Zell, Spectrochim. Acta, 19, 1933 (1963). (26) R. F. Curl Jr., J . Chem. Phys., 30, 1529 (1959).
Predicted Valence Shell Ionization Spectrum of Cyclobutadiene N. Correia and J. Baker*+ Department of Quantum Chemistry, Uppsala University, 751 20 Uppsala, Sweden (Received: May 13, 1985)
The valence shell ionization spectrum of rectangular cyclobutadiene (1) is obtained via an EOM/propagator method within a full third-order treatment. The first ionization energy is found to be 7.90 eV which is in fair agreement with the experimentally inferred value of 8.0-8.5 eV.
Introduction The first ionization potential of cyclobutadiene is usually inferred from substituted compounds such as 2 and 3I because the high reactivity of the parent compound (1) makes it inaccessible Me Me
1
2
3
to a direct measurement. The inner valence part of the photoelectron spectrum is not even accessible by these means because this region is shadowed by the substituents. It is our aim here Present address: Research School of Chemistry, Australian National University, Canberra ACT 2601, Australia.
0022-3654/85/2089-3861$01.50/0
to present results obtained in an accurate calculation for the spectrum of 1. The method is briefly reviewed, and a short discussion of the results is given; a thorough review of the chemistry of 1 can be found in ref 2.
Method and Computational Procedure The scheme used in this paper to obtain the vertical ionization potentials (VIPs) of 1 is based on the equation of motion (EOM) method3 which is equivalent, as regarding the final working equations, to the Green’s function/propagator a p p r ~ a c h . It ~ has been presented by one of and applied to e.g. HF7 and C2H6, (1) E. Heilbroner, T. B. Jones, A. Krebs, G. Maier, K. D. Malsh, J. Pocklington, and A. Schmelzer, J . Am. Chem. Soc., 102, 564 (1980). (2) T. Bally and S. Massamune, Tetrahedron, 36, 343 (1980). (3) D. J. Rowe, Reu. Mod. Phys., 40, 153 (1968). (4) B. T. Pickup and R. McWeeny, Rep. Prog. Phys., 43, 1065 (1980).
0 1985 American Chemical Society
3862
The Journal of Physical Chemistry, Vol. 89, No. 18, 1985
Correia and Baker TABLE I: Predicted Valence Swctrum of Cvclobutadiene"
-~
3
2
5 >-
t
8
6
m w Z
7
I-
- 0.5-
symmetry
VIP, eV KooDmans' theorem
1Blg 3B2" 1BIU 4'48 3B3u
7.54 12.42 12.90 14.66 15.06
3 4
18.86
2B1,
19.01
2B2"
22.42
2B3"
24.85
1
9
7 10 10
IO
9
68 II
7
5
IONIZATION ENERGY (eV)
Figure 1. Predicted valence shell ionization 'spike spectrum" for cyclobutadiene (basis 1: q ( C ) = 0.75, ap(H) = 1.0; see text): 1, 1B2g;2, 3B2,; 3, lBlu;4, 4Ag; 5 , 3B3,; 6, 3Ag; 7, 2B1,; 8, 2BlU; 9, 2B3,; 10, 2Ag.
CzH4, and C2H2.* We present here a brief resume of the procedure used in the actual calculations, referring to those papers for details. The VIPs w are obtained from the equation
HC = wSC with the matrix elements of H and S given by
3 1.58
pole strength 3rd order 7.77 11.3s 12.56 13.39 13.09 13.58 16.28 17.00 19.03 22.90 16.92 17.14 18.67 20.03 22.33 21.34 21.63 22.34 23.33 24.64 25.13 25.56 26.06 26.15 27.76 28.38
(intensitvl ,I
0.905 0.910 0.895 0.895 0.053 0.816 0.073 0.689 0.033 0.025 0.512 0.274 0.044 0.692 0.01s 0.426 0.109 0.047 0.090 0.085 0.01 1 0.016 0.052 0.129 0.208 0.018
"Basis 1: q ( C ) = 0.75, ap(H) = 1.0; see text
h, represents the operator manifold which has been chosen to include operators of the type h l = (a 1 and h3 = (a,+aga,). q0is the reference state with respect to wkch the expectation values are calculated; in the present case it is the closed-shell R H F ground state corrected to second or third order in perturbation theory where appropriate. The procedure is then equivalent to a full third-order treatmentgJOand was termed "approximation scheme IV" in ref 5 . The geometrical parameters for our initial calculations were taken from ref 11, which have been essentially confirmed by another geometry optimization beyond H F by Hess et and are reproduced in Figure 1 together with the chosen coordinate system to avoid misunderstandings as regarding the symmetry labeling. The one- and two-electron integrals were calculated with the MOLECULE programL3using a (9s5pld + 4slp/3s2pld 2slp) Gaussian basis taken from Dunning and Hay14 with polarization functions cyd(C) = 0.75 and cyp(H) = 1.0. The S C F step was carried out by use of the EPSCF programI5 and gave an energy of EsCF= -153.663 593 hartree. The EOM calculations were performed using the 10 highest occupied and 30 lowest virtual orbitals; Le., we excluded the four lowest occupied orbitals (carbon 1s like) which have almost no effect on the predicted valence shell ionization spectrum.I6
+
(5) J. Baker, Chem. Phys., 79, 117 (1983). (6)J. Baker, Chem. Phys. Lett., 101, 136 (1983). (7) J. Baker, J . Chem. Phys., 80, 2693 (1984). (8) J. Baker, Int. J . Quantum Chem., 27, 145 (1985). (9) J. Jorgensen and J. Simons, J . Chem. Phys., 63, 5302 (1975). (10) M. F. Herman, D. L. Yeager, and K. F. Freed, Chem. Phys., 29,77 (1978). (1 1) H. Kollmar and V. Staemmler, J . Am. Chem. Soc., 100,4304 (1978). (12) B. A. Hess, P. Carsky, and L. J. Schaad, J . Am. Chem. SOC.,105, 695 (1983). (13) J. AlmlBf, Report 74-29, University of Stockholm, Institute of Physics. (14) T. H. Dunning and P. J. Hay, "Methods of Electronic Structure Theory", H. Schaeffer 111, Ed., Plenum Press, New York, 1977, p 1. (15) N. H. Beebe, G. D. Purvis, and H. A. Kurtz, "Quantum Theory Project", University of Florida, Gainesville, FL. (16) L.S.Cederbaum, W. Domcke, J. Schirmer, W. Von Niessen, G. H. F. Diercksen, and W. P. Kraemer, J. Chem. Phys., 69,1591 (1978).
Results and Discussion In Table I we present the ionizations obtained with the above procedure together with their respective pole strengths, which are approximated by the square of the relevant h , eigenvector component and give an estimate of the spectral intensity. The Koopmans' theorem values for the VIPs are also given. The predicted ionization spectrum follows the now familiar pattern of single peaks with high intensity in the outer valence region, with a gradual increase in the number of lines and a corresponding decrease in the pole strength as one approaches the inner valence region, where the simple one-particle picture of ionization breaks down," and the main line splits into several smaller lines which correspond to simultaneous ionization plus excitation. In particular, the 2BL,ionization splits into essentially two lines, the larger of which (at 16.92 eV) occurs before the main line for the 3A, ionization (at 17.00 eV), showing an orbital reordering with respect to the Koopmans' theorem values. The 3A, ionization itself has a significant satellite line (1 1 % of the main line) at 16.28 eV. The breakdown of the one-particle picture of ionization in the inner valence region is due to near degeneracies between the simple h , configuration a,llc/o) and excited h3 configurations u,+aiujl&,), where i and j represent occupied outer valence orbitals and u is a low-lying virtual; Le., the energy required to remove an electron from an inner valence orbital is similar to that for ionization plus simultaneous excitation from the outer valence region. Depending on their respective symmetries, such configurations can mix in the final state wave function. In the case of the 3A, and 2B1, ionizations the excited h3 configurations mainly responsible for the line splitting are (1BIu)-'(3BJ1( 1B3,*) and (3BzU)-*( lB2J1(1Au*) (for 3A,) and (4A,)-1(1Bz,)-1(1B3,*) (for 2B1,). The deeper one goes into the inner valence region, the more marked is the splitting, and for the 2B3, and 2A, ionizations there are a multitude of satellite lines. It should be noted that here vibronic coupling becomes much more important and the high resolution attained by our model should only be taken as a rough guide to average band positions, since there is no purely electronic process in this region of the photoelectron spectrum. The value of the first IP is very much dependent on the assumed geometry as shown by Schweig et a].,'* who obtained values of (17) J. Schirmer and L.S . Cederbaum, J . Phys. E , 11, 1889, 1901 (1978).
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 (
