J. Phys. Chem. 1987, 91, 3555-3559 Ti02, because of the >6 times greater amount of the weakly acidic surface hydroxyls.
Conclusion The significant p H dependence of the photocatalytic activity of T i 0 2 suspended in A g N 0 3 solution was correlated with the pH-dependent adsorption of Ag+ on the T i 0 2 surface. The adsorbed Ag+ seemed to exhibit the efficient ability to trapping photogenerated electrons, thereby enhancing the oxidation of water by the simultaneously generated positive holes. From the results of quantitative analysis of surface hydroxyls, the pH dependence of Ag+ adsorption was attributed to the positive surface charge on TiO,. Consequently, a TiO, powder having a large surface area with a high proportion of strongly acidic surface sites rather
3555
than readily protonated hydroxyls is favorable for the photocatalytic reaction.23 The rutile TiOz used in this study was disadvantageous due to the extensively higher surface density of the readily protonated hydroxyls, The effect of surface treatments on the improvement of photocatalytic activity is now under investigation. Registry No. TiOz, 13463-67-7; AgN03, 7761-88-8; H20, 7732-18-5; Ag, 7440-22-4;
02,
7782-44-7. ~
(23) A similar conclusion was derived by Oosawa and Gratzel. They reported that the photocatalytic activity of Ti02 suspended in an AgNO, solution was proportional to the reciprocal of the surface hydroxyl density: Oosawa, Y.; Gritzel, M. J . Chem. Soc., Chem. Commun. 1984, 1629.
Analysis of Paired Interacting Orbltals for Extended Systems. Application to the Protonation of Conjugated Carbon Chains and the Chemisorption of H, on Ni Surfaces Hiroshi Fujimoto* and Hiroshi Kawamura Division of Molecular Engineering, Kyoto University, Kyoto 606, Japan (Received: September 23, 1986)
The protonation of conjugated carbon chains and chemical interactions between H2 and nickel layers have been investigated theoretically. The analysis is based on the paired interacting orbitals which conveniently illustrate interactions between two systems. The interacting orbitals of clusters are compared with those of an extended sequenceof cells with respect to protonation of conjugated carbon chains. Then, the orbitals are shown to vary in chemisorption on metal surfaces, reflecting the mode of the interaction. It is shown that electron delocalization takes place on the face but that the overlap repulsion penetrates into the inner layers. The effects of cluster size on these bonding and antibonding interactions are discussed.
Introduction The concept of orbital interaction is a powerful strategy in chemistry.'*2 A number of experiments have been rationalized in terms of the frontier orbital interactions. On the other hand, we have shown in our previous papers that the local characteristics of chemical interactions can be displayed more properly by some sort of localized orbital^.^ They have been derived as the hybrids of usual molecular orbitals (MO's) by means of a pair of transformations of fragment orbitals for each given intera~tion.~ This theoretical treatment will be of great use when we discuss chemical interactions of large systems, e.g., reactivities and catalytic activities of organometallic system and solid surfaces. In this paper, we study adsorption of small chemical species to conjugated carbon chains and onto nickel films. We present the orbitals that participate actively in chemical interactions in these systems. Method Let us consider an interaction between two molecular systems A and B. In the following discussion, A is assumed to be a small species and B is either a cluster of atoms or a unit cell of a polymeric molecule. The electronic structure of the composite interacting system A-B can be determined by using the usual MO methods or the tight-binding calc~lations.~The interaction is represented in terms of various quantities associated with the first-order density matrix P,the (r, s) element of which is defined for the atomic orbital (AO) xr ( r = 1,2, ..., M) of A and the A 0 (1) Fukui, K. Theory of Orientation and Stereoselection;Springer-Verlag: West Berlin, 1974. (2) Hoffmann, R. Angew. Chem., Int. Ed. Engl. 1982, 21, 711. (3) Fujimoto, H.; Koga,N.; Fukui, K.J. Am. Chem. Soc. 1981,103,7452. (4) (a) Fujimoto, H.; Koga, N.; Hataue, I. J. Phys. Chem. 1984,88,3539. (b) Fujimoto, H.; Yamasaki, T.; Mizutani, H.; Koga, N. J . Am. Chem. Soc. 1985, 107, 6157. (c) Fujimoto, H.; Yamasaki, T. Ibid. 1986, 108, 578. (5) (a) Bloch, F. Z.Phys. 1928,52, 555. (b) Imamura, A. J . Chem. Phys. 1970.52, 3168. (c) Hoffmann, R. J. Chem. Phys. 1963.39, 1397. (d) IMS Computer Center Library Program No. 1103.
xs (s = M + 1, M + 2, ...,M + hJ)of B. The intermolecular part of this matrix is rectangular and in general of the order M X N . ( M is assumed to be smaller than N . ) By carrying out the coupled transformations of A O s or MO's within each of the two fragments simultaneously, one can reduce intermolecular part of this matrix to the form that has nonzero elements solely between several sets of paired interacting orbitals of the two fragment^.^ Now, the interaction is described simply by means of these orbital pairs (&, \Li) ( i = 1, 2, ..., M>.
(3* (3..., (;:)* paired interacting orbitals
h
l
r
..., $N
fragment A fragment B
unpaired inactive orbitals
The number of orbital pairs is determined by the smaller entity. For instance, H+ has a single orbital in minimal basis set caiculations and, accordingly, the intermolecular part of the bond order matrix will have a single nonzero element upon transformation, Le., M = 1 and, therefore, P'',, = 0 for i # 1. The interaction is represented simply by the 1s A 0 of the proton and one of the new rehybridized M O s of the larger fragment, irrespective of its size. As a consequence, a direct comparison of chemical interactions is attainable for systems analogous in character but different in molecular size.
Results and Discussion A Comparison of Crystal and Cluster Interacting Orbitals. Let us examine first of all the simplest system, an interaction between a proton and a conjugated carbon chain as sketched in Figure 1. A unit cell of the polymer chain was taken tentatively to be C2H2, C6H6,and CloHlo,and the electronic structures of the composite interacting system, e.g., (-CH==CH- 4- H+),, were determined by tight-binding calculations of the extended Hackel type.5 A proton was located tentatively at 1.5 A above the midpoint of the central C-C double bond in each case. Here the transformations of orbitals were carried out between a proton and the carbon chain.
0022-3654/87/2091-3555$01.50/0 0 1987 American Chemical Society
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Fujimoto and Kawamura
The Journal of Physical Chemistry, Vol. 91, No. 13, 1987 C2H4
H+
CsHa
H
/ /
H H H Figure 1. A schematic illustration of the model for protonation of conjugated carbon chains.
0.2204
0.2054
CioHiz
CpH2 0.2034 center 0.2429
adjacent
center 0.2048
adjacent
CioHio
center 0.2034
adjacent
Figure 2. Orbitals of polyacetylene cells taking part in the interaction with an attached proton on the center cell. T h e number below each orbital indicates the Mulliken overlap population between that orbital and the Is orbital of the proton sitting on the center cell. T h e proton Is orbital is not shown here.
In the latter, we considered not only the AO’s in the central cell that are relevant for interaction with the proton but also the AO’s in the neighboring two cell units on both sides of the central cell. The purpose of including the AO’s of neighboring cells is to see to what extent the interaction is localized in the central Figure 2 shows the dependence of the polymer orbital, that engages in the interaction with an attached proton, on the size of the unit cell. When the unit of the composite system is taken to be C2H2+ H’, the orbital of polyacetylene that donates electron density to the proton is seen to penetrate significantly into the adjacent cells. The extent of localization of this orbital in the central cell was estimated to be 91.4% by using the Mulliken population analysis.’ The structure unit (-CH=CH- + H’) is in excess of a proton when this unit is r e ~ e a t e d . ~On . ~ the other hand, the orbital is seen to be localized completely within each structural unit when the cell size is extended to (-CH=CH-),. The (-CH=CH-), unit also appears to be sufficiently large to adsorb a proton within a cell. The extent of localization has increased up to 96.8% for the C6H6 cell and 98.1% for the C l o H l o cell. Figure 3 illustrates the interacting orbitals that have been obtained for protonation of the corresponding monomeric molecules, C2H4 (ethylene), C6H8 (1,3,5-heptatriene), and CloH12 (1,3,5,7,9-decapentaene).They are localized beautifully around the double bond which is under attack by a proton. A comparison of the orbitals in Figures 2 and 3 leads to the conclusion that when ( 6 ) The bond orders between the AOs in different cells are defined in the tight-binding calculations. (7) Mulliken, R. S. J . Chem. Phys. 1955, 23, 1833. (8) A similar discussion holds for the case where a proton is located above one of the carbons. (9) The antibonding interactions between the proton in the center cell and those assumed to be located in the adjacent cells are another source of making the repetition of C,H,+ unit very unlikely.
Figure 3. Orbitals of ethylene, heptatriene, and decapentaene participating in the interaction with an attached proton. Numbers indicate the Mulliken overlap populations.
the unit cell is taken to be larger than a certain size, e.g., C6H.5 in this case, the interacting orbital of a polymeric chain can be practically replaced by the one that is obtained more easily for the monomeric molecule that has the same number of carbon atoms as the unit cell. The overlap population between a proton and the central cell of a polymer chain given in Figure 2 is slightly larger or smaller than that calculated for the corresponding monomeric system in Figure 3, depending upon whether the interaction penetrates into the adjacent cells in an out-of-phase manner or in an in-phase manner at the boundaries. However, the difference becomes less and less significant as the cell size increases. In the case of the CloHlounit, the overlap population calculated for the polymer chain, 0.2034,is the same as that obtained for CIOHI2+ H’. The results indicate that chemical interactions are local by nature, and therefore, characteristics of interactions in infinite crystal systems can be reproduced substantially in cluster calculations. Activation of the H-H Bond on the Nickel (IOO),(IIO),and ( I 1I ) Surfaces. The conventional description of chemical interactions between molecules by means of orbital interactions may not be applicable to large systems that possess band structures.” Hoffmann and his co-workers derived “crystal orbital overlap populations” for the cluster orbitals based on the density-of-state With a view to utilizing a simple concept of orbital interactions in surface chemistry more efficiently, it may be more preferable to rehybridize the MO’s so as to generate localized orbitals that participate virtually in chemical interactions with adsorbates. The local symmetry around the interaction sites is reflected explicitly in the shape of orbitals, and therefore, the results of the calculations will be grasped more easily in conjunction with our chemical intuition. Chemisorption of H2I39l4as well as other small species like C0,13h.15 N0,I6 and CH4,11on nickel surfaces has been investigated (10) Messmer, R. P. In The Nature of the Surface Chemical Bond Rhodin, T. N., Ertl, G., Eds.; North-Holland: Amsterdam, 1979; pp 51-1 11 and references cited therein. (11) Sailard, J.; Hoffmann, R. J . Am. Chem. SOC.1984, 106, 2006. (12) Sung, S.;Hoffmann, R. J . Am. Chem. SOC.1985, 107, 578. (13) As for theoretical calculations, see for example: (a) Blyholder, G. J . Chem. Phys. 1975.62, 3193. (b) Fassaert, D. J. M.; Avoid. A. M. Surf. Sci. 1976, 55, 291, 313. (c) Kobayashi, H.; Yoshida, S.; Fukui, K.; Tarama, K.; Kato, H. Chem. Phys. Lett. 1978, 53, 457. (d) Melius, C. F.; Moskowitz, J. W.; Mortola, A. P.; Ballie, M. B.; Rather, M. A. Surf. Sci. 1976, 59, 279. (e) Upton, T. H.; Goddard, W. A. Phys. Rev. Lett. 1979, 42, 4472. (f) Lundqvist, B. I.; Norskov, J. K.; Hjelmberg, H. Surf. Sci. 1979,80, 441. (g) Avdeev, V. I.; Upton, T. H.; Weinberg, W. H.; Goddard, W. A. Ibid. 1980, 95, 391. (h) Bohl, M.; Muller, H. Ibid. 1983, 128, 104. (i) Satoko, C.; Tsukada, M. Ibid. 1983, 134,1. 6 ) Ruette, F.; Hernandez, A,; Lundena, E. V. Ibid. 1985, 1.51, 103. (k) Umrigar, C.; Wilkins, J . W. Phys. Rev. Lett. 1985, 54, 1551. (I) Lee, C.; Depristo, A. E. J . Chem. Phys. 1986, 84, 485. (m) Piccito, G.; Siringo, F.; Baldo, M.; Pucci, R. Surf. Sci. 1986, 167, 437. (14) As for experimental studies, see for example: (a) Lapujoulade, J.; Neil, K. S. Surf. Sci. 1973, 35, 288. (b) Christmann, K.; Schober, 0.;Ertl, G.; Neumann, M. J . Chem. Phys. 1974, 60, 4528. (c) Winkler, A.; Rendulic, K. D. Surf. Sci. 1982, 118, 19. (d) Robota, H . J.; Vielhaber, W.; Lin, M. C.; Ertl, G. Ibid. 1985, 155, 101. (e) Hamaza, A . V.; Madix, R. J. J . Phys. G e m . 1985, 89, 5381.
Paired Interacting Orbitals for Extended Systems
short bridge stte
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The Journal of Physical Chemistry, Vol. 91, No. 13, 1987 3557 0
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