10450
J. Phys. Chem. 1992,96, 10450-10453
Second-Harmonic Generation Spectroscopy of Cinnamic Acid Adsorbed on Silica Surfaces W. M. K. P. Wijekoon,*it Z. Z. Ho,* M. W. Mull,$ C.C. Padrnabandu,l and W. M. Hetherington III*J Department of Chemistry, University of Arizona, Tucson, Arizona 85721 (Received: September 9, 1992)
Surface secondharmonic generation has been used to obtain the electronic spectrum of trans-cinnamic acid adsorbed on optically polished silica surfaces under high-vacuum conditions at 296 K. The pattern of the second-order susceptibility tensor for the first electronic transition is calculated from the results of PPP calculations with double CI. The spectra are consistent with the existence of one or more hydrogen bonds between the cinnamic acid and the surface. There is no evidence of the creation of photochemical products under the illumination conditions. The competitive process of twephoton absorption leads to the desorption of weakly bound surface species. At least two differnt desorption rates were observed, and the ratio is interpreted in terms of a difference of 0.85 kcal mol-' (0.03 eV) between two heats of adsorption.
Introduction Second-harmonic generation (SHG) has been established recently as an interfacially specific probe of interfacial species.l-* Although described thmreticallf and first observed' over 20 years ago, the technique has only recently been used in both reflection and trans"ion to study interfacial phenomena. Characterization of solid-liquid interfaces of electrochemical systems? investigation of adsorption4iesorption phenomena? determination of the orientation distributions of interfacial species,l*12 and observation of the electronic excited states of adsorbatesI3J4are some of the recent applications of SHG. SHG is a forbidden process in a medium with an inversion symmetry, in the electric dipole approximation. On a surface or at an interface, inversion symmetry is necessarily broken, and the second-order nonlinearity is nonvanishing in the electric dipole approximation. For this reason, SHG is an extraordinarily effective probe of an interface between two centrosymmetric media.1-5 Electronic spectra are very useful in studies the interaction of molecules with surfaces. Even though the absorption cross section of an adsorbate may be large, the absorption spectrum is often not detectable on a flat (nonpowder) surface because of either a low density or a dominating absorption in the substrate. Fluorescence emission/excitation spectra are generally not possible due to the existence of rapid radiationless decay channels on a surface or the presence of luminescnece from the substrate. Surface SHG has distinct advantages over other spectroscopic methods when these sorts of problems are present. The purpose of this work is to use the twephoton resonances in the second-order susceptibilityof cinnamic acid to obtain electronic spectra of the surface-bound species and, thus, learn about the nature of the molecule-surface bonds. Theory
The general expression for the SH intensity from an interface, for incident and radiated plane waves, is2J5
where x ( ~is) the macroscopic second-order electric dipole susceptibility tensor, c2 is the polarization of the surface field created at 2w, e, is the polarization of the applied surface field at w, Z, 'Present address: Photonics Research Laboratory, Department of Chemistr ,State University of New York at Buffalo, Buffalo, NY 14214. fYResent address: Optical Sciences Center, University of Arizona, Tuaon, 7 85721 .A_-- . - - .
'Preacnt address: Computer Centw, University of California at San Diego, La Jolla, CA 92023. Present address: Department of Physics, Texas A&M University, College Station, TX 77843. R a n t address: Department of Physics, Oregon State University, Corvallis, OR 97331-6507.
0022-3654/92/2096-10450$03.00/0
is the applied power, and il is the angle of incidence. Whether using the reflection or transmission geometries, the polarization vectors should be determined from the input and output polarizations, AI and X2, and the Fresnel transformations. In this study, the polarizations and the angle of incidence are fmcd, and the laser frequency is scanned. The Fresnel transformations will not be considered. For detailed calculations, the local field correction factors should also be considered.' For irregular or single-crystal surfaces with partially ordered adsorbed species, x ( ~is) the contraction of a sixth-rank orientation tensor with the third-rank microscopic tensor, where f is a distribution function and the brackets indicate that an orientation average is to be performed. The indices A, B, and C range over X,Y,or Z in the surface reference frame and a, b, and c range over x , y , or z in the microscopic reference frame. CA,is the direction cosine between axes A and a, and it can be expressed as a function of the Euler angles, 4, 8, and a, using the x convention, which describes the transformation between the two frames. #,e,and are assumed to be independent, although this need not be the case when restricted binding sites or restricted motions of molecules on a surface are considered. Translational distributions might need to be considered as well in particular situations. When performing SHG on any surface, it is important to consider all possible contributions to the effective susceptibility, x ( ~ ) The . bulk material itself may be noncentrosymmetric and capable of a substantial contribution, or it may contribute through the electric quadrupole and magnetic dipole interactions.* For a general case in which the bulk contributes xg), the bare surface contributes d2), and the adsorbate contributes xy), the expresion for the SHG signal becomes Z& =
le2*(xP'+ ,y,
+ xy):c~clJ2z,z
(3)
where the factors irrelevant to tbis discussion have been ignored. If the shapes of the three tensors are different, then it may be pcmible to choose a polarization condition which selects only the adsorbate term or an adwrbate-surface ~1088term.Furthermore, when either w or 2w lies close to an electronic resonance of the ) be greatly bulk, surfce or adsorbate, the corresponding x ( ~can enhanced. As observed in this work, ~ ( 2 and ) ~ for S O 2are small compared to the reasonably enhanced xy) for cinnamic acid. Usually, the adsorbate tensor arises from a distribution of microscopic tensors which is random in the angle 4 about the surface normal. In that case,1I x y ) has only four distinct com lex elements, aA = xyJx2,bB = x!2?,,, mA = xyJxx,and n A x ~ , ~ ~ ~ .
8)
O
O
U
0 0 0 a b 0
0
0 4 0 0 a - b a O
Q 1992 American Chemical Society
0"0 II,0
:] n
(4)
The Journal of Physical Chemistry, Vol. 96, No. 25, 1992 10451
Cinnamic Acid Adsorbed on Silica Surfaces TABLE I: States, I"q and Timition Moments for CinaOmic Acid used hl tbe CllCIddOIl O f B state calc, eV expt, eV r, eV 1 0 0 0 2 4.41 4.23 0.12 3 5.01 4.53 0.24 4 5.48 5.27 0.36 0.48 5 5.95 0.60 6 6.16
6nbC
=
~~
states
1-1 1+2 1-3 1-4 1-5 1-6 2-2 2-3 2-4 2-5 2-6
V
I states TTansition Moments
-
-0.0471 0.0444 0.4903 0.21 12 -0.1789 -0.5690 0.0642 0.0670 0.0593 0.0289 -0.3032
0.0493 0.0314 -1.2664 -0.2955 -0.0946 0.0461 -0.4742 0.0745 0.0304 0.0516 1.4012
-
3 3 3-4 3-5 3-6 4-4 4+5 4-6 5-5 5+6 6-6
Y
2
0.2366 -0.1044 0.1572 0.0165 -0,1957 0.1820 -0.0955 -0.2806 -0.1182 0.0206
-1.1091 0.8763 -0.5327 0.0682 0.3046 -0.4215 -0.0830 0.6254 0.0094 -0.6133
The 3 X 3 matrim are the X,U,and 2 matrices along the first rank (output photon). Since the input photons are degenerate, tensor elements differing only by the exchange of the last two indices are equal. This tensor does not exhibit the Kleinman ) symmetryI6 when there is some resonance enhancement. x ( ~can often have the same form by virtue of the native structure or the surface preparation procedure. A set of four experiments can be used to determine a, b, m, and n if x ( ~is) entirely real or imaginary. The simplest measurements to make are those involving s (xu),p (XZor YZ), and circular (positive helicity) polarizations. In the following expressions for five different experiments, we ignore the constants of eq 1 and relabel the harmonic intensity by the polarizations of the output and input fields. IPa= lm12 tan2 52
(5)
I , = 4\bl2sin2 Q
(6)
Zpp = tan2 Qln sin2 52 + (m
* 2a) cos2 QI2
(7)
Z, = tan2 Qlai - b cos Q12
(8)
tan2 Q ,z = I(m - n) sin2 Q & 2 cos Q(a cos Q + bi)12 (9) 4 where the upper sign is used for transmission and the lower for reflection. Z, is always zero for random Q distributions. The behavior of the SH signal as Q is varied can be different for reflation and t"w'sion measurements if b and a are sufficiently , additional three measurelarge. For a complex tensor, x ( ~ )an ments would be needed for complete specification. The simple ps and sp experiments immediately indicate whether or not b and m are significant. In the case of surface SHG considered in this work, 2w is coincident with or close enough to an electronic resonance of the surface species so that a few strong r r* or charge-transfer (CT) transitions dominate the contributions to 6." When this is true, then the pattern of 6 can be determined through the expression from third-order perturbation theory
-
where g) is the ground state and states i) and j ) are the r,r*and CT states. In practice, the states and eigenvalues appearing in this equation should be those of the interacting system. Phenomenologically useful tensors can be obtained with this expression by ignoring the vibrational structure of the electronic states and using somewhat arbitrary values for the damping terms, r,. In n-heptane solution, tram-cinnamic acid exhibits a strong electronic absorption band at 274 nm (36500 cm-I, 4.53 eV) accompanied with a very weak shoulder at 293 nm (34 100 cm', 4.23 eV)." The weak absorption at 293 nm is due to the r r* transition in the electrondonating styral group, and the strong band at 274 nm arises from the intramolecular charge transfer from the styral moiety to the electron-acceptingcarboxyl group.17 The r r*transition has been derived from the 'BZuexcited state of benzene. In the crystalline form, the charge-transfer band appears at 255 nm (39200 cm-', 4.86 eV), whereas in alkaline solutions it appears at 264 nm (37900 cm-',4.70 eV). As a result of this blue shift, the weak absorption band, which appears as a shoulder in the heptane solution spectra at 293 nm, becomes more distinct in the crystalline form.I7 For the calculation of the r,r*states and the transition moments among them, the Pariser-Parr-Pople (PPP) procedure'* was used with the inclusion of doubly excited configurations. The core integrals (W, in eV), the onscenter integrals ( Y in ~ eV), and the nuclear charges (2)used in the calculations were the following: carbon = 11.42, 10.84, and 1.00; oxygen (OH) = 34.43, 19.46, and 2.0; oxygen (H =) 17.28,14.58,and 1.00. The two-center electron-repulsion integrals, y, were calculated using the method of Nishimoto and Metaga.I9 The resonance integrals were calculated from the formula 6, = 6, U ( R , - k), where R, is the bond length between the neighboring atoms r and s, & = 1.397 eV, Bo = 2.43 eV, and A@ = 3.45 eV. The inclusion of double CI resulted in better transition energies and transition moments for cinnamic acid. The transition energies are in good agreement with the previous calculations of Hofmann et a1.,2O and they are in reasonable agreement with the experimental values. Table I displays the transition energies as well as the transition moments and arbitrary line widths used in the calculation of the second-order susceptibility tensor, 6. 0 has been calculated for cinnamic acid for the purpose of determining the pattern of the tensor under the condition of a two-photon resonance with the first excited state. Equation 10, summed over only the singlet *-electron states, is a reasonable approximation to 6 because the case considered exhibits a resonant condition (2hv M). The inclusion of the u electrons would add another contribuion to 6, but in the preresonance and resonance regions, its relatively small magnitude would not affect the analysis to be made below. Any calculation of the harmonic intensity using eq 10 depends upon the transition moments taken to the sixth power. Since the accuracy of the transition moments presented is not known, each tensor element has a significant uncertainty.
-
-
+
TABLE Il ~
w, eV
dYYY
2.05 2.10 2.15 2.20 2.25 2.30
3 4 7 -3 + 31i 0 3
&Y
-1 5 -19 -27 - 2i 5 - 10% -7 - 2i -18 - i
8,
411
27 31 35
48- 141 58+i 73 + 21
-a -8 -8 -17 + 22i -18 -20
B?Y?
26 28 28 59-7i 63 73 + 2i
A?? -97 - i -110-2i -126-3i -145- 141 -177 -Si -225 - 81
a
14 16 19+ 1 16 + 16i 22+ i 29 + i
b 0 0 0 0 0 0
~
m
n
12 13 14 22- 16i 25 30
2 33 + i 40 + i 37 27i 48 25 63 + 2i
+ +
Wijekoon et al.
10452 The Journal of Physical Chemistry, Vol. 96, No. 25, 1992
Table I1 displays the complex 8 and x ( ~tensors ) for cinnamic acid calculated from eq 10 at several different laser frequencies. In both cases, the tensor elements are useful for only relative comparisons. The six lowest states were used in the calculation of 8. The I”s used are arbitrary, and the qualitative analysis of the effect of on the SHG proms is valid regardless of the exact values. For a detailed comparison of calculation to experiment, a more explicit evaluation of eq 10, involving the complete vibrational manifold of each state and exact I”s, will be required. Due to the lack of symmetry, 8 has six n o m tensor elements. With a weak transition at 4.41 eV and a very strong one at 5.01 eV, the real parts of the elements are significant even when 20 is coincident with the first transition. The real parts arise from ) calcontributions from the higher states. In Table 11, x ( ~was culated, following the procedure of ref 8, assuming that the molecules are adsorbed on a surface that is so rough that the orientation distribution is uniform over the following angular ranges: 0 < $C < 2 ~0;< 8 < ~ / 20; < @ < 2%. This calculation contribution to the signal leads to the conclusion that the will be about the same as the nonresonant contribution.
Experimeacrl Aspects A detailed description of the spectrometer used in these studies has been reported previously.14 The dye laser was synchronously pumped by the frequencydoubled output of a cw Nd3+:YAGlaser which was modelocked and Q-switched at 500 Hz. The average dye laser pulse energy was 1.5 pJ. The individual pulses were 70 ps in duration and had a spectral line width of less than 1.6 cm-’. A computer controls the intracavity prism and the etalon tuning elements and also monitors the wavelength continually with a 1-m monochromator to which the laser was fiber-opticallycoupled. Noise and artifacts arising from fluctuations of the dye laser pulse energy, pulse duration, and transverse mode quality were removed by a normalizBtion scheme. About 0.4% of the laser beam was focused onto a KDP crystal, and the frequencydoubled output was detected using a photomultiplier tube. During the spectral scan, the KDP was continuously phasematched by the computer. When it was necessary, the laser beam was attenuated by computer-controlled, calibrated neutral density filters which were inserted in front of the KDP crystal. This frequencydoubled output was used directly to normalize the surface SHG signal. The laser beam was focused onto the surface with a 1 5 0 ” focal length lens and the angle of incident was 45O. The maximum power density encounter on the surface was 100 MW The incident polarization was parallel to the plane of incidence, and both SH polarizations were collected. The generated SH beam was directed through filters and apertures to remove the colinear fundamental, scattered laser light, and any fluorescence and then dircckd onto a photomultiplier tube. Between 1 and lo00 photons were generated per pulse train, and as many as 1500 pulse trains were accumulated for each data point. The surface employed for this investigation was an optically polished Si02 flat (0.25-in. thickness and 1.0-in. diameter). It was mounted inside a vacuum chamber which was capable of maintaining a base pressure of 2 X lod Torr. An aluminum structure was used to hold the silica flat inside the vacuum chamber. Prior to placement within the chamber, the surface was cleaned and etched with an rf plasma in an argon atmosphere for a period of 45 s. rrans-Cinnamic acid (vapor pressure 10-L10-3 Torr at room temperature) was purified by vacuum sublimation before using. The SHG spectrum of adsorbed cinnamic acid was Torr. The typical taken at a pressure of less than 1 X scanning time was about 30 min. In desorption studies, the laser was tuned to an appropriate frequency and the second harmonic signal was rccotdedas a function of time. To lean about the effect of prcasure on the photo-induced desorption rate, the experiment Torr. All the desorption was done at pressures of lo4 and studies were carried out under active pumping conditions. Obaewations and Discussion The energy of adsorption of HO-and HN-bearing aromatic molecules on the surfaces of silica powders has been observed to
570
575
580
585
590
595
2 w (nm) Figure 1. (A) SHG spectrum of the plasma-etched silica surface prior to e x p u r e to cinnamic acid; (B)SHG spectrum of the tram-cinnamic acid adsorbed on an optically polished silica surface at a pressure of 2 X lo-’ Torr.
depend not only on the presence of surface hydroxyl groups but also on the specific types of hydroxyls. Free hydroxyl groups provide larger blue shifts in the first T,T* transition (e.g., phenol and aniline).21*zzWhen the hydroxyl density is high, hydrogenbonded hydroxyls are presents on the surface, and the observed spectral shifts are smaller. If n,r* transitions are involved (e.g., nitrobenzene), the large excited-state dipole moment leads to spectral red shifts regardless of the density of the hydroxyl groups.21*22 Adsorption of unsaturated aliphatic carboxylic acids on silica powders has been observed to be based upon three adsorbatesurface interactions. At low surface coverages, adsorption is governed by hydrogen bonds between surface hydroxyl groups and the carboxyl group. At the higher coverages, dimerization of the acid on the surface is the predominant process. Also, the interaction of the unsaturated hydrocarbon chain with the surface hydroxyl groups O C C U ~ S . ~ ~ , * ~ In the solid state, trans-cinnamic acid exists in two crystalline forms with different unit cell dimensions. By sublimation, both a and 8 forms are obtainable. The a form develops a (010) face, Upon and the 8 form develops a (001) plane under ~ublimation.’~ irradiation with ultraviolet light, a-trum-Cinnamic acid dimerizes to yield a-truxyllic acid, whereas 8-trans-cinnamic acid dimerizes into 8-truxinic a ~ i d . * ~ * ~ ~ Figure 1B shows the SHG spectrum of Cinnamic acid adsorbed on an optically polished silica surface at 296 K. The SH peak at 578 nm (17 300 cm-l) is due to the first r,r* electronic transition of cinnamic acid at 289 nm. This strongly suggests that the chargetransfer band has been shifted to a higher energy value as in the case crystalline material.17The feature at 578 nm (17 300 cm-’) is the first feature to appear upon exposure of the surface to cinnamic acid and is associated with the T r* transition of the isolated spades. As the expure increases,broad bands appear in the 645-588-nm (1 5 500-17 OOO-cm-’) region, and these arise from the growth of aggregates. The SHG process has the character of both o n e and two-photon transitions, and thus, the shape of an SH spectrum is Micult to interpret at this time. In order to resolve the origin of the different types of cinnamic acid present on the surface, SHG investigations were made at 4 K. However, the low-temperature (4 K)spectrum was too congested, and a meaningful analysis could not be made. Figure 2 displays the laser-induced desorption data of adsorbed cinnamic acid. When the laser is tuned to a two-photon resonance (578 nm; 17 300 cm-I), the SH signal decays rapidly during the first 3 min and then decays more slowly. When w = 601 nm (16 650 cm-l), in this case there is only a very small desorption compared to the on-resonance desorption. This weak desorption is a result of the fact that a small amount of cinnamic acid in the form of aggregates exhibits a resonance at twice that frequency. When the laser field is blocked after desorption has occurred, the signal recovers even at lW5Torr. Introduction of a new dose of cinnamic acid always leads to the reappearance of the SH signal. The decay curve of Figure 2 can be decomposed into two contributions. One decay is approximately 4 times larger than
-
Cinnamic Acid Adsorbed on Silica Surfaces
The Journal of Physical Chemistry, Vol. 96, No. 25, 1992 10453 interpretation of the susceptibility tensor can be based upon the few electronic states very close to the two-photon resonance conditions. With improvements such as single-crystal surfaces, ultrahigh vacuum, and complete polarization studies, the spectrum for a limited number of adsorption sites can be interpreted in terms of the molecular structure and orientation in each site.
Acknowledgment. This research was supported by the USAF Rome Air Development Center and the National Science Foundation. TIME (seconds)
Figure 2. log-scale desorption curve of tram-cinnamic acid adsorbed on a fused silica surface at a pressure of 2 X 1W5Torr. The laser frequencis were w = 578 nm (17 300 cm-I) in the case of on-resonance excitation and o = 601 nm (16 650 cm-I) in the case of off-resonance excitation.
that of the other. This indicates there are at least two types of surfambound cinnamic acid species present on the surface. The more strongly bound surface species is probably bound to the surface through hydrogen bonds to two silanol groups, as in the casc of adsorption of unsaturated aliphaticcarboxylic acids in silica The more weakly bound surface species is probably bound by a single hydrogen bond. It is known that aliphatic carboxylic acids adsorb on oxide surfaces in such a manner that their alkene group and carboxylic acid group interact with the oxide surface ~imultaneously.~~+~~ The same argument may be made for the adsorption of cinnamic acid on silica. The observed small blue shift in the r,# transition may be indicative that the styral moiety is perturbed upon adsorption. Since the silica surface used in this work is mountainous on the molecular scale, it is quite likely that a cinnamic acid molecule, bound through the carboxylic acid groups, can experience an interaction between the styral portion and the polar surface. In order to calculate the difference in the binding energies of the two dominant surface species, the following simple kinetic scheme was considered:
- kr
kd
A, A,* A Here A, is the surface density of the adsorbed species, k, is the rate constant for relaxation without desorption (both radiative and nonradiative), and kd is the desorption rate constant. By assuming a larger rate for simple relaxation than for desorption and identical Arrhenius preexponential factors, one can obtain In
(2) h~ RT
where A(AdE) is the difference in binding energies of the two surface species and kldand k2d are the rates of desorption of the two surface species. The experimentally obtained kld/k2d ratio is 4.0 f 0.4. Hence, A(AE) = 0.85 kcal mol-l (0.03 eV). This difference is much smaller than that expected between two species whose interactions differ by one hydrogen bond. Thus, the situation is more subtle than the simple picture of one or two hydrogen bonds; other aspects of the adsorption sites must be important.
conclusions Surface SHG spectroscopy can be performed to observe the electronic states of adsorbed molecules, with great sensitivity. The
References and Notes (1) Shen, Y. R. Principles of Nonlinear Optics; John Wiley & Sons: New York, 1984. (2) (a) Shen, Y. R. J . Vac. Sci. Technol. 1985,83, 1464. (b) Shen, Y . R. In Chemistry Structure of Interfaces; Hall, Richard B., Elliot, Arthur B., Eds.; VCH Publishers: Deerfield Beach, FL, 1986. (c) Shen, Y. R. In Spectroscopic and Diffraction Techniques in Interfacial Electro Chemistry; Gutierrez, C., Melendres, C., Eds.;Kluwer Academic Publishers: Amsterdam, 1990. (d) Shen, Y. R. Nature 1990,337, 519. (e) Chen, C. K.; de Castro, A. B.; Shen, Y. R. Phys. Rev. Lett. 1981, 46, 145. (f) Heinz, T. F.; Chen, C. K.; Ricard, D.; Shen, Y. R. Phys. Rev. Lett. 1982, 48, 478. (3) Richmond, G. L.; Robinson, J. M.; Shannon, V. L. Prog. Surf. Sci. 1988, 28, 1. (4) (a) Bhattacharyya, K.; Castro, A,; Sitzmann, E. V.; Eisenthal, K. B. J . Phys. Chem. 1988,89, 3376. (b) Zhao, X.; Subrahmanyan, S.;Eisenthal, K. B. Chem. Phys. Lett 1990, 171, 558. (c) Castro, A.; Ong, S.;Eisenthal, K. B. Chem. Phys. Lett. 1989,163,412. (d) Castro, A.; Sitzmann, E.; Zhang, D.; Eisenthal, K. B. J. Phys. Chem. 1991, 95, 6752. (5) (a) Lupke, G.; Marowaky, G.; Sieverdes, F. In Organic Molecules for Nonlinear Optics and Photonics; Messier, J., et al., Eds.; Kluwer Academic Publishers: Amsterdam, 1991. (b) Marowsky, G.; Lupke, G.; Stienhoff, R.; Chi, L. F.; Mobius, D. Phys. Rev. B 1990, 41, 4480. (6) Blffimbergen, N.; Pershan, P. S . Phys. Rev. 1962, 128, 606. (7) Brown, F.; Parks, R. E.; Sleeper, A. M. Phys. Rev. Lett. 1965,14,1029. ( 8 ) (a) Richmond, G. L. Lungmuir 1986, 2, 132. (b) Corn, R. M.; Romagloni, M.; Levenson, M. D.; Philpott, M. R. Chem. Phys. Lett. 1984,106, 30. (9) Zhu, X. D.; Daum, W.; Xiao, Xu-Dong; Chin, R.; Shen, Y . R. Phys. Rev. E 1991, 43, 11571. (10) Rasing, Th.; Shen, Y. R.; Mahn Won Kim; Valint, P.; Bock, J. Phys. Rev. 1985, 31A, 537. (11) Mazely, T. L.; Hetherington, W. M. J . Chem. Phys. 1987,86,3640. (12) Hicks, J. M.; Kemnitz, K.; Eisenthal, K. B.; Heinz, T. F. J . Phys. Chem. 1986, 90, 560. (13) Heinz, T. F.; Tom, H. W. K.; Shen, Y. R. Phys. Rev. A 1983, 28, 1883. (14) Van Wyck, N. E.; Kcenig, E. W.; Bayer, J. D.; Hetherington, W. M. Chem. Phys. Lett. 1985, 122, 153. (1 5) Mizrahi, V.; Sipe, J. E. J . Opt. Soc. Am. B 1988, 5, 660. (16) Kleinman, D. A.; Ashkin, A.; Boyd, G. D. Phys. Rev. 1966,145,338. (17) Janaka, J. Bull. Chem. SOC.1963,36, 838. (18) Pariser, R.; Parr, R. G. J. Chem. Phys. 1953, 21, 466, 767. Pople. J. A. Trans. Faraday. Soc. 1953, 49, 1375. (19) Nishimoto, K.; Metaga, N. 2.Phys. Chem. 1957, 12, 335. (20) Hofmann, H. J.; Vetter, R.; Epperlein, J. J. Signul AM1 1973.3, 211. (21) Anderson. J. H.; Lombardi, J.; Hair, M. L. J. ColloidInter/acialSci. 1955, 50, 519. (22) (a) Hair, M. L. Infrared Spectroscopy in Surface Chemistry;Dekker: New York. 1967. (b) Leermaker. P. A.: Thomas. H.T.:, Weis.. L. D.: James. F. C. J. Am. Chem.'Soc. 1966, 88, 5075. (23) Marshal, K.; Rochester, C. H. J. Chem. Soc., Faraday Trans. I 1975, 71, 1754. (24) Hasagawa, M.; Low, M. J. D. J. Colloid Interfacial Sci. 1969, 30, 378. (25) Nakamura, K.; Kikuchi, S.Bull. Chem. Soc. 1967, 40, 1027. (26) (a) Bernstein, G. I.; Quimby, W. C. J . Am. Chem. SOC.1943, 65, 1845. (b) Nakanishi, F.; Nakanishi, H.; Tsuchiya, M.; Hasegawa, M. Bull. Chem. SOC.1976, 49, 3096.
