3808
J. Phys. Chem.
1983,87,3806-3807
Quartet States of H, Karl Kaufmann, Martin Jungen, * Institute of Physical Chemistry, University of &sei, Basei, Switzerland
and Handoachlm Werner Institute of Physical and Theoretical Chemistry, University of Frankfurt, FRG (Received: July 15, 1983)
Energy leveb of linear quartet Rydberg states are predicted as well as dissociation limits and energies. Vertical emission frequencies for electronic transitions between excited states are estimated.
Introduction
Calculations and Results
The singlet ground state of H3+ has the shape of an equilateral triangle.’ H3 is not stable in its ground state but bound excited states can be formed from H3+by electron capture. These Rydberg states, first observed spectroscopically by H e r ~ b e r g , ~are - ~triangular, similar to the parent ion.6 According to calculations by Schaad7 and Ahlrichs8 the lowest triplet state of H3+ is stable in a linear symmetrical arrangement with a H-H distance of 2.457 ao. The dissociation energy to H + H2+ has been estimated to be 6.8 kcal/mol.8 One might expect a set of linear quartet Rydberg states of H, built on this triplet ion, but there is no experimental evidence for quartet ~ p e c t r a . ~ It is the aim of this letter to predict the energy levels of such linear quartets and to calculate the dissociation energies and
The calculations have been carried out in the frozen core (FRC) approximation.6J0 The basis consisted of a [6s,2p;3s,2p] Gaussian basis for the valence orbitals with exponents between 68 and 0.09 and a Rydberg basis constructed a t the center of the positive charge of the ionic core according to the prescriptions of ref 11. The Rydberg basis covers effective quantum numbers between 2.5 and 5.5, corresponding to seven Gaussian exponents between 0.03 and 0.0008. In order to account for reorganization and electron correlation effects refined calculations in the SCF’O and MC-SCF approximati~n’~J~ have been carried out for the lowest four quartet states with a reduced basis set. A subsequent CI with singly and doubly excited configurations yields total electronic energies including about 90 ?&
TABLE I: Quartet States of Linear H, state
Etotr‘ au
au
H,+ ,xu+ (Val)
4 ~ u +
zpnu 4r1g
3SOg 4 \ 3POu 4;u -g+ +
3 d n g 4rIu
3pnu
411g
3 d o g 45u+
3dhg 4 A u 4sog 4 ~ u 4pnu 4 2 ;
%ffd
- 1.11568/
+
4dng 4 n u
~ P T ,4n9, 4fn, 4 z g
4fn, 4r1g 4dog 4 ~ , + 4fh, 4 A g 4fPu 4 O g 4dhg 4 A u
5SOg 4 X U +
-0.24151 - 0.12406 -0.10611 -0.08258 -0.05853 -0.05510 -0.05563 -0.05312 -0.04760 -0.04058 - 0.03263 -0.03104 -0.03174 -0.03165 -0.03109 -0.03124 -0.03078 -0.03025 -0.02753
-0.25575g - 0.1 2 56 3 - 0.1064 2g - 0.08 27 6”.‘ - 0.0 5 93 3j - 0 .O577 7” - 0.0 56 76” - 0.0 534 7’ -0.04849” - 0.04 17 7j - 0.0 3 29 7j - 0 .O 3 214” -0.03190J -0.03165 -0.03156j -0.03124 -0.03078 -0.03039’ -0.02791’ ,8‘
1.398 1.995 2.168 2.458 2.903 2.942 2.968 3.058 3.211 3.460 3.894 3.944 3.959 3.975 3.980 4.001 4.030 4.056 4.232
Dee, au
dissoc lime
H + H,+ Xzxgi H + H + H H t H,* c3n, H H,* a3zg+ H + H,* e3xu+ H -c H,* d3n,
0.013
spont
0.011
spont
0.019 0.014
Orbital energy of the Rydberg electron in the FRC approximation.” Convert to total D _ , with R H H= 2.457 a,). energies by adding E,,,( H, +). Electron binding energy including the effects of reorganization and correlation between the Rydberg electron and the core. Effective principal quantum number. e See ref 15. f Total energy from ref 8. MC-SCF-SD-CI approximation. D,,, R H H 2.36 a,,, relaxation energy -0.000 72 au. D,,, R H H 2.41 a,, relaxation energy -0,0001 9 au.
’*
-
The correlation correction for the Rydberg electron has been estimated.
limits for the lowest few of them. In some cases also a geometry optimization was performed. (1)C.E.Dykstra, A. S. Gaylord, W. D. Gwinn, W. C. Swope, and H. F. Schaefer, J. Chem. Phys., 68,3951 (1978). (2)G. Herzberg, J. Chem. Phys., 70, 4806 (1979). (3) I. Dabrowski and G. Herzberg, Can. J. Phys., 58, 1238 (1980). (4)G. Herzberg and J. K. G. Watson, Can. J. Phys., 58,1250 (1980). (5)G.Herzberg, H. Lew, J. J. Sloan, and J. K. G. Watson, Can. J. Phys., 59,428 (1981). (6)Ch. Nager and M. Jungen, Chem. Phys., 70, 189 (1982). (7)L. J. Schaad and W. V. Hicks, J. Chem. Phys., 61,1934 (1974). (8)R.Ahlrichs, C.Votava, and C. Zirz, J.Chem. Phys., 66,2771(1977). (9)J. K. G.Watson, private communication.
-
of the electron correlation corrections. For higher states the electron correlation effects have been estimated by correcting the principal quantum number by a constant typical for the symmetry of the Rydberg orbital (see, e.g., ref 14). For the geometry variation only the FRC method was used but the equilibrium bond lengths were calculated (10)M. Jungen, Theor. Chim. Acta, 60,369 (1981). (11)M.Jungen, J. Chem. Phys., 74, 750 (1981). (12)H.-J. Werner and W. Meyer, J. Chem. Phys., 73, 2342 (1980). (13)H.-J. Werner and W. Meyer, J. Chem. Phys., 74, 5794 (1981). (14)K. Kaufmann, M. Jungen, and V. Staemmler, Chem. Phys., submitted.
0022-3654/83/2087-3806$01.50/00 1983 American Chemical Society
J. P h p . Chem. 1903, 8 7 , 3807-3808
TABLE 11: Vertical Emission Wavelengths ( A ) between Excited Quartet States of H,a 3pou4x;
uPPe; limit 3dn,
best estimate‘
lower limitd
4nu 6790 6165 6099 18805 16832 16349
3dog 4xu+ 3d6, 4 A u 4sag 4zu+ 4dng 4nu 4dog ‘xu+ 4d6, ‘Au 5sag 4zu+
-
best esti- lower uppe; mate‘ limitd limit
6509 6284 5839 4899 4819 4777 4645 3627
5958 5712 5376 4544 4481 4430 4326 3420
5871 5687 5320 4529 4460 4424 4310 3420
16794
15372
14808
12959 9089 8818
12019 8528 8308
11743 8474 8238
8250
7190
7140
(limit) 5505 5214 5274 a Geometry of H,+X 3 x U t :D,, with R H H = 2.457 a,. Neglecting electron correlation in both the upper and the lower states. ‘ See Table I. Neglecting electron correlation in the upper Rydberg state.
relative to the bond length of H3+as calculated with high precision.s The results are collected in Table I, where vertical electron binding energies for the Rydberg electron are given. In order to obtain total energies they have to be added to the total electronic energy of triplet H3+(-1.11568 a d ) . For the determination of the limits and energies of dissociation we have used the tables published by Huber
3007
and Herzberg.15 Note that the lowest and the third lowest quartet states (both 42,+)are dissociative. Relaxation of the second (411,) and fourth (42,+)states to their equilibrium geometry (see Table I) yields additional stabilization energies of 0.000 72 and 0.000 19 au, respectively. In Table I1 we give estimates for vertical emission wavelengths of electronic transitions to the two lowest bound quartet states. Since as a rule the contribution of electron correlation decreases with increasing excitation level,14upper and lower limits for the emission wavelengths can be estimated, neglecting the correlation energy either in both the upper and the lower states or only in the upper state. We observe that the strong transitions are situated in the infrared whereas higher members of the Rydberg series might be detected in the visible spectrum. Acknowledgment. This work is part of the project Nr. 2.420-0.82 of the Schweizerischer Nationalfonds. We thank the CIBA-Stiftung (Basel) for financial support. K. K. gratefully acknowledges a scholarship from the funds of the chemical industries. We thank Dr. J. K. G. Watson (Ottawa) for drawing our attention to this subject. Registry No. H,,12184-91-7. (15) K.P. Huber and G. Herzberg, “Molecular Spectra and Molecular Structure, IV. Constants of Diatomic Molecules”, Van Nostrand-Reinhold, Princeton, NJ, 1979.
Photocatalytic Hydrogen Production from Solutions of Sulfite Using Platinized Cadmium Sulfide Powder Mlchlo Matsumura, Yuklnarl Saho, and Hlroshl Tsubomura Department of Chemistry, Facub of Engineering Science, Osaka University, Toyonaka. Osaka 560, Japan (Received: July 14, 1983)
Platinized cadmium sulfide powder suspended in a solution of sodium sulfite produces hydrogen efficiently by visible light. Sulfite ions are oxidized to sulfate and dithionate ions.
Introduction Efficient production of hydrogen from water by use of solar energy is one of the most attractive targets for the research of photocatalytic reactions on semiconductors particles. Platinized titanium dioxide (TiOJ has been reported to produce hydrogen from aqueous solutions containing organic materials, such as methanol,’ solid carbon,2etc.,3 and even from water itself though with a low yield.4 Semiconductors having smaller band gaps are more important for solar energy utilization, since TiOp can absorb a very small part of the whole solar radiation. In a previous paper5 we found that methanol, formaldehyde, and formic acid were photocatalytically oxidized on platinized CdS. Hydrogen production was also reported to occur photocatalytically on platinized CdS with the sa(1) Kawai, T.; Sakata, T. J . Chem. Soc., Chem. Commun. 1980,694. ( 2 ) Kawai, T.; Sakata, T. J. Chem. SOC.,Chem. Commun. 1979,1047. (3) Kawai, T.; Sakata, T. Chem. Lett. 1981, 81. (4) Sato, S.;White, J. M. Chem. Phys. Lett. 1980, 72, 83. ( 5 ) Matsumura, M.; Hiramoto, M.; Iehara, T.; Tsubomura, H., submitted to J . Phys. Chem.
crificial oxidation of EDTA,6 cystein: ethan01,~etc. We report here photocatalytic hydrogen production from an aqueous solution of sulfite on platinized CdS. Recently Reber et a1.8 also worked independently on the reactions of sulfite on platinized CdS powder.
Experimental Section In our experiment, the photocatalyst was prepared by mixing and grinding 250 mg of CdS powder (99.999% pure, average size ca. 0.5 km) and 10 mg of platinum powder in an agate mortar. The photocatalyst was added to a 10-mL aqueous solution of sodium sulfite in a glass flask. Then, the solution was deaerated by repeated freeze-pump-thaw cycles. The solution was illuminated by a 500-W Hg lamp combined with a UV cutoff filter (Toshiba, L-39) whose transmittance at 390 nm is 50%. The amount of gas produced in the flask was measured by introducing it into ~
~~
~
(6) Darwent, J. R. J . Chem. Soc., Faraday Trans. 2 1981, 77,1703. (7) Sakata, T.; Kawai, T. J . Syn. Org. Chem. Jpn. 1981, 39, 589.
(8) Reber, J.-F.; Meier, K.; B a l e r , N. Int. Conf. Photochem. Conuers. Storage Sol. Energy, 4th, 1982.
0022-3654/83/2087-3807$01.50/00 1983 American Chemical Society
