J. Phys. Chem. 1983, 87,1697-1701
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Optical Frequency Doubling and the Internal Structure of Quasi-Crystals G. R. Meredlth," D. J. Williams, Webster Research Center, Xerox Corporation, Webster, New York 14580
S. N. Flshman, E. S. Goldburt, and V. A. Krongauz Department of Structural Chemistry, The Weizmann Insttute of Science, Rehovot, Israel (Received: October 18, 1982)
The effects of applied static electric fields on the optical frequency doubling in predominantly first-generation quasi-crystals produced by irradiation of aliphatic solution of a spiropyran compound is reported. These measurements allow refinement of our conception of the internal structure of quasi-crystal globules. A model for the globule cores consisting of weakly interacting molecular stacks is investigated and shown to be consistent with the field dependence of frequency doubling if the physically reasonable restrictions that (1)the unit dipole moment is 2-10 D and (2) the difference in nearest neighbor interaction energies between parallel and antiparallel orientations of dipolar species in the stacks is less than -0.1 eV are fulfilled.
Introduction Some interesting spontaneous ordering processes, which are driven by sudden change of solute character, occur on irradiation of solutions of spiropyran compounds dissolved in aliphatic The solute changes, evidenced by dramatic photochromic effects, are associated with conversion of spiropyrans to merocyanine forms. Various photochemical and aggregation result in the formation of submicron-size globules constituted of crystallike cores covered with an amorphous material. Many experimental techniques have been used to characterize and probe the nature of these globules. In this paper the structure of these quasi-crystalline globules is further considered in connection with new data on their nonlinear optical properties. In an earlier report second harmonic generation (SHG) was used to characterize the globule structures6 The important feature of SHG for these studies is that it is an optical method sensitive to the noncentrosymmetric ordering which has been associated with the crystallike cores. This noncentrosymmetric nature, as discussed below, has previously been inferred from the gross behavior of these globules in electric fields. To summarize our earlier SHG results, we found that, indeed, quasicrystals (threads of aligned connected globules formed in an electric field) exhibited SHG. Further, the SHG and the optical polarization of the harmonic were sensitive to application of electric fields both parallel and perpendicular to the threads. A comparison of the magnitude of the SHG signals to that from electric field induced second harmonic generation in nitrobenzene convinced us that the effect was a true second-order phenomenon and not simply a thirdorder response involving the static electric fields used for perturbation. In addition, no SHG was observed from globules formed in the absence of an aligning field, but SHG could be induced in them by subsequent electric field application. Besides these characteristics, memory and restoring tendencies associated with the field dependence of the induced SHG were generally seen.
The observation of SHG we took as verification of the crystallike and noncentrosymmetric nature of the cores. Optical and electron microscopic examination of the quasi-crystals subjected to the perturbing fields showed no morphology changes compared to original unperturbed threads. Since the samples that we studied consisted largely of second-generation and higher generation globules (globules hypothesized to contain six, for second-generation, or significantly more, for higher generation, crystallite basic core forming particles), we mentioned that the above observations might be attributed to changes in the mutual orientations and arrangements of crystallites within globules and that, due to this, no further conclusions about the internal structure were then possible. We also found that the SHG compliance (that is, the tendency for SHG to follow changes in the zero-frequency electric field magnitude and direction, to relax quickly, and to lose the asymmetry associated with the structure created during quasi-crystal formation in the presence of an aligning field) increased with time. This increase was also dependent on the extent of reverse polarity and nonparallel field perturbation to which the threads were subjected. The increased compliance, it was suggested, may have been an inherent globule characteristic, may have been due to internal "damage" caused by this treatment, or may have been a particular effect due to softening of the amorphous material and disturbance of the core structure by solvent action of the dodecane or Vaseline which were used to reduce the optical roughness of the samples. The strong effects of the relatively weak electrostatic field on the SHG in quasi-crystals was the most puzzling problem which did not find a clear explanation in the previous publication.6 In an attempt to provide such an explanation we will consider below a model for the internal globule core structure consisting of an assembly of molecular stacks with relatively weak interstack interaction. An additional SHG experiment, conducted on largely first-generation quasi-crystals and consistent with the model, will be presented.
(1) V. A. Krongauz and A. A. Parshutkin, Photochem. Photobiol., 15, 503 (1972). (2) V. A. Krongauz, S. N. Fishman, and E. S. Goldburt, J. Phys. Chem., 82, 2469 (1978). (3) V. A. Krongauz, Isr. J. Chem., 18, 304 (1979). (4) V. Krongauz, J. Kiwi, and M. Gratzel, J.Photochem., 13,89 (1980). (5) Y. Kalisky and D. J. Williams, Chem. Phys. Lett., 86, 100 (1982), and data to be submitted for publication. (6)G. R. Meredith, V. Krongauz, and D. J. Williams, Chem. Phys. Lett., 87, 289 (1982).
Experimental Section The experimental procedures have been described in previous publications.2,6 In this work quasi-crystals were prepared from solutions of 1-[P-(methacryloy1oxy)ethyl]-3,3-dimethyl-6'-nitrospiro[indoline-2,2[2H-1]benzopyran]. Concentrations were kept low and irradiation flux was adjusted to allow the production of predominantly first-generation quasi-crystals. The quasi-crystal
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0
I
1
30
35
LOG (Applied Voltage)
- 2000
1
-1000 0 IO00 APPLIED VOLTAGE (VOLTS)
2000
Figure 1. Second harmonic intensity detected from a sample of threads as a function of applied voltage. The history of the treatment is depicted with arrows showing the progression of time. Discrete observation data points not explicitly shown fall within the smooth curves drawn here. The point marked START is the initial signal observed before application of any perturbation fields to the sample.
threads produced from solution were allowed to deposit on glass slides as solvent evaporated, as described previously.6 The distance between electrodes, corresponding to the total parallel extent of the threads, was 0.10 cm. Electron microscopy studies on the final samples showed them to be composed of 90% first-generation material. Due to the conditions required to accomplish this the threads deposited on the slide were less numerous and less densely packed than in our earlier SHG studyU6 For SHG studies the samples were ”index matched” with a small quantity of Vaseline petroleum jelly which was applied to the threads and then compressed with a thin cover slip. Strips of aluminum foil had been placed across the slide prior to this step in approximately the same location as the electrodes used during quasi-crystal formation. These strips were later connected to a high-voltage power supply for application of fields to the threads. This was done to prevent a completely blocked electrode configuration which was observed earlier to give spurious effects. This sandwiching procedure was performed immediately prior to SHG study to minimize the contact time with the very slowly acting petroleum solvent. The characteristics of the SHG apparatus have been described earlier.6s7 We repeat only that the laser employed was a Q-switched Nd3+:YAG laser operating a t a wavelength of 1.064 pm and the harmonic was detected after spectral filtering at 532 nm.
Results The purpose of these experiments was to investigage the electric field dependence of SHG in first-generation quasi-crystals. Prior to electric field application SHG from unperturbed threads was observed, thus confirming the permanent nature of the noncentrosymmetric property. Voltage was applied to the samples with polarity variously the same or opposite to that used in the thread-formation process. The SHG was observed to be significantly affected by the voltage application. In Figure 1 the history of treatment of one sample is illustrated. There are a number of features which we would like to emphasize. The SHG intensity from the (7) G. R. Meredith, Reu. Sci. Instrum., 53, 48 (1982).
Figure 2. log-log plot of apparent equilibrium second harmonic intensity from a sample of threads vs. voltage. A line with slope of 2 has been drawn as a reference to emphasize the nearly quadratic relationship.
sample was observed to change rapidly on adjusting the applied voltage, followed by a period of further slower change in the same direction. Therefore, several minutes were spent after each voltage adjustment to allow the SHG to reach its steady-state value. In the figure one can follow the history by tracing the curve which begins at the “start” point, the previously unperturbed sample SHG response, in the direction of the arrows. An example of the dual fast-slow response occurs on the positive-going branch where, at 2000 V, the voltage was suddenly returned to zero. The signal fell quickly, as indicated by the dashed line which connects to a relatively high SHG intensity at 0 V, and continued to decrease over 5 min to a value consistent with earlier ones. The 2O00-V voltage was then reapplied. The signal rose quickly, as indicated again by the dashed line, to a level somewhat below the earlier 2000-V SHG intensity. After a wait of several minutes a steady-state signal, essentially the same as observed earlier, was obtained. Similar behavior was subsequently observed on suddenly decreasing the voltage from 2500 V. During the original low-voltage portion of the experiment an asymmetry in response to negative and positive polarities was observed, although an attempt to actually locate a voltage corresponding to the minimum SHG intensity would have been difficult due to relaxation behavior and the apparent evolution of the sample. However, if one looks at the accumulation of data including higher voltage portions as a smoothed curve, the asymmetry is obvious. The appearance is that of a parabola with minimum occurring in the vicinity of -450 V. Figure 2 is a plot of the logarithm of the steady-state SHG intensity vs. applied voltage determined at a later time with the same sample. We show this to emphasize the nearly quadratic behavior of the response.
Discussion These measurements of SHG and its electric field dependence allow us to extend our conception of the crystalline globule cores. The original conclusion that the globule cores are crystalline was based on the X-ray diffraction pattern of globules, on the discrete electron diffraction of exposed microcrystals in incompletely formed globules, and on the optical anisotropy of quasi-crystals in the spectral range of the core absorption band. A strong red shift in the optical absorption spectrum of cores together with textures observed in electron microscopy permitted us to assume that the crystals include, somehow, structures similar to the Scheibe stacks which are known for many cyanine molecules. Presumably the large permanent dipole moment of the cores is determined by this
Internal Structure of Quasi-Crystals
molecular packing. It was shown earlier that for stacks of molecular dipoles a parallel configuration of dipoles with a tilt relative to the stack axis less than 54” is energetically more favorable than the antiparallel configuration.* The former configuration obviously results in a nonzero net dipole moment of the stack, and the results show that the dipole moments of different stacks do not cancel one another. Earlier we assumed that cores having permanent dipole moments are formed spontaneously even in the absence of an electric field? The electric field dependence of SHG described above makes this assumption less unambiguous. Before we proceed with discussion of the nature of the cores, it is appropriate to describe a few properties of SHGe9 SHG is a coherent phenomenon. For this reason the phase relationships among the oscillating polarization densities in all volume elements of a sample are important, as are all phase perturbations which occur in the propagation of the harmonic field from these elements to the observation point. On a microscopic level the relationship of phases of polarization oscillation can be used to understand why centrosymmetric media composed of noncentrosymmetric units do not cause frequency doubling. Inversion of a unit causes a 7~ phase shift in the component of the dipole moment oscillating a t frequency 2w which is due and proportional to the square of the electric field oscillating a t frequency w , since the microscopic secondorder polarizability is a polar third-rank tensor. Therefore, a pair of these units related by inversion would broadcast effectively no harmonic dipole field if they are separated by a distance small compared to the wavelength of light. Since a t the extremely small molecular scale the packing density of such nonlinearly polarizable units is very high, the cancellation is complete and one says without reservation that the macroscopic second-order susceptibility, x ( ~ )is, identically zero. When one deals with noncentrosymmetric units which are not on the molecular scale, but approach the wavelength of light, the question of mutual orientation and spacing becomes crucial. Consider, for instance, two identical nonlinearly polarizable particles of size approximately 1/10 the wavelength of 2 0 frequency light. If they are an inversion pair, they will broadcast the harmonic in a quadrupole pattern. In the nodal regions little harmonic is detected, and in the lobes the magnitude of the harmonic depends as much on the phase retardation difference for propagation from the particles to the observation point as it does on the actual magnitude of the nonlinear response of each particle. In our experimental geometry we monitor only the portion of radiation pattern in an f/16 cone normal to the plane containing the threads. That plane is also normal to the propagation axis of the laser, assuring, to the extent that the laser wave front is planar and the sample optically thin, that globules experience nearly equally phase-retarded fundamental electric fields. In the two-particle example we would observe little harmonic even though the individual particles might show an extremely high nonlinear response. Clearly, then, although in the Introduction it was claimed that SHG is a sensitive probe of the noncentrosymmetric ordering associated with the globule cores, the coherent optical nature makes its observation also dependent on details of the orientations and placement of other globules. One of the possible explanations of the significant electric field dependence of SHG is that the microcrystals (8)V. A. Krongauz and E. S. Goldburt, Chem. Phys. Lett., 60, 251 (1979). (9) N. Bloembergen, “Nonlinear Optics”, W. A. Benjamin, Reading, MA, 1965.
The Journal of Physical Chemistry, Vol. 87, No. 10, 1983
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can be rotated inside the amorphous envelopes by the field, thusly improving the alignment in the field direction both within and among globules. The latter must be considered in light of the preceding comments. Internal motion could be particularly, important in the quasi-crystals of the second and higher generations for which rotational freedom of the crystallites within a core might favor less dipolar total globule configuration in zero field. However, the SHG signal from the samples composed predominantly of first-generation globules, which would be expected to retain alignment due to the same dipolar interaction between globules within a thread which is considered to be responsible for the unique one-dimensional thread formation, is equally affected by the field. Moreover, it is very difficult to conceive how the microcrystals embedded in the rather rigid amorphous material can be rotated there without destroying the globules. Another explanation of the behavior is that the external electrostatic field brings about reorientation of molecular dipoles within stacks resulting in an increase of the stack alignment and dipole moment. We will pursue the implications of such a model. Consider a stack of n dipoles ( n >> 1) in which the dipoles occur arbitrarily parallel or antiparallel to each other, all at an angle CY relative to the stack axis. The number of parallel and antiparallel neighboring pairs in a nonhindered system can be determined by thermodynamic equilibrium conditions. If this king type model is restricted to a Hubbard type (nearest neighbor) interaction, analytical expressions for the net alignment and electric field behavior can be obtained. Taking the interaction energy of neighboring dipolar species to be u(t7) = ~ ( 1 1 and ) u ( f i ) = u(1t) and considering the energies of the dipolar species in the stack, independent of the neighboring orientations, to be u(t) and u ( l ) ,define the following thermodynamic quantities: s = exp(-u(tt)/kTl
(1)
E. = exp(-u(t)/kTl = t exp(pt.E/kTl
(2)
Here 5 is a factor taking into account internal energy and -pt-E is the energy of the molecular dipole in an applied electric field, E = E6, when local field phenomena are discounted. One can choose a reference potential energy such that
(3) Obviously, also since p~ = -pt exp(-u(i)/kT) = la-’
(4)
Using the matrix method of calculationlo (see also ref ll),one can show that the classical partition function of
the system is 2 = T r (G”)
where G is the 2
X 2
(5)
matrix
The probability distribution functions of pairs and singletons were calculated from 2 according to theoretical expressions and taking into account eq 5 and 6:
(10) H, Kramers and G. Wannier, Phys. Rev., 60, 252 (1941). (11) T. M. Birstein and D. B. Ptitzin, ‘Konformatsii Makromolekul”, Nauka, Moscow, 1964.
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+ q)/2r(l + r - q ) (8) wJi = d [ a In z/a In (u-ls)] = (r - q)/2r(l + r - q ) (9) W f = W l t + W t J = (1+ (a - a-I)[(. - cr-1)2 + 4s-4]-'/2}/2 wtt = n-'[d In Z/d In
(US)]
= (r
(10) w, = W J J + W f : = (1- (a - a-l)[(a - d
) 2
+ 4s-4]-'/2)/2 (11)
where q = (a - a-l)/2cT
r = [q2 +
0-2~-4]1/2
(12)
(13)
In the absence of a static electric field (i.e., u = 1, q = 0, and r = s - ~ )s alone determines the correlations among neighboring dipoles.
+ s2) UJtt = W J i = 1 / 2 ( 1 + s-2)
(14)
W b t / w t j = s2
(16)
ZJtJ
=
WJf
= 1/2(1
(15)
For s much smaller than unity the unfavorable energetics of parallel neighbors leads to predominantly antiparallel ordering. Conversely, large s favors parallel alignment with antiparallel pairs appearing as imperfections establishing domain boundaries between ordered regions. As mentioned above, according to spectral data ow system should be treated as one with large s for which antiparallel pairings are relatively rare. The net alignment, Q, is easily determined in the above model. Q = Wt - W , = sinh (pt.E/kT}/[sinh2 ( p y E / k q + s-4]1/2 (17) We are interested in the effect of the field E on the total alignment, which can be characterized by the behavior of Q or wt, since W J = 1 - wt. It can be shown that awt/dE has only one sign over the entire range of E implying that wt is a monotonically increasing function of E. Also it can be shown that wt exhibits one or three inflections as a function of E. One inflection always occurs a t E = 0 and the other two occur when, and if, E satisfies cosh (2p+. E / k q = s - ~- 2. For s4 L 'I3 these last two inflections do not appear. Further, it can be seen that the effect of the neighbor interaction alters the degree of alignment induced by the field. For instance, near E = 0 the net alignment is approximately ( Q ) I + ~N s2(pt.E/kr)
(18)
This indicates that larger s improves the electric field alignment susceptibility over the noninteracting dipole case (s = 1) provided certain limits are not exceeded. These limits are associated with saturation of the alignment and are determined from the derivative d 2 w t / ( d s dE). for E satisfying cosh (2pt.ElkT) < (1+ s - ~ )increased neighbor interactions would increase the electric field alignment susceptibility, but at larger fields the opposite holds due to saturation of the alignment. For comparison of the model with the experiments let us complete the expansion of Q in the parameter s and variable x = pt-E/kT.
Q= S'X
- (6)-'(3s6 - s2)x3
+ (120)"(45~'~- 30s6 + s2)x5 + ...
(19) Since s is greater than unity for our situation, this expansion converges quickly only for small x. Since our
Meredith et al.
experiments showed the SHG intensity, which is proportional to Q2, to be quadratic in x (disregarding the asymmetry effect), the ratio of the two leading terms can place limits on s. Adopting a 20% limit for detection of deviations from quadratic SHG response (the size of which is shown in Figure 2), one finds Smax
= 1[1+ O . ~ / ( X ~ J ~ I / ~ ) ' ~ ~
(20)
We do not know the magnitude of pf,but certain bounds can be established. The deduction of a lower limit of the globule and hence the core dipole moment (lo4D)puts a lower limit of 1 D on the dipolar species of the stacks.2 Next an estimate of the dipole moment based on the idealized zwitterion picture of the photolyzed spiropyran is lptl 1 40 D. This is unrealistic since for comparison we note that some stilbene-related and merocyanine type species have normal or "extreme" charge-separated states exhibiting dipoles in the ranges 8-17 or 22-32 D, respectively.12J3 This undoubtedly establishes the upper limit for the dipole moment of our dipolar species. Limits of the interaction energies then are
-
u(t1) - u(tt) 5 L = (k7"/2) In ([I + 0*6(kT/~+.Emax)~]/3) (21) where L is determined from eq 20, 3, and 1. Some values, taking pt+ = 0.8 as a noncrucial estimate of the cosine of the angle of the molecular dipole axes with the field direction, are L = 0.13,0.11,0.09,0.07, and 0.06 eV for Ipf( = 2, 5 , 10, 20, and 30 D, respectively. These limits are comparable in magnitude to heats of fusion of molecular crystals. An estimate of the electrostatic interactions must also be made. While it is perhaps overly simplistic for these extended polarizable charge distributions,14 one can idealize the interaction between two dipoles in a coplanar configuration by
[u(tl) - u(St)Id-d = - ~ ( I P ~ I ~ /-I3~cos2 ~ ~a)) ( I (22) where r connects the dipoles and CY is an angle between r and pt. Maximum values at fixed spacing occur when CY = 0. If the dipoles are separated by 7.4 A, one of the interplanar spacings corresponding to the observed X-ray diffraction pattern,I5 the cy = 0 values would be 0.025,0.15, 0.6, 2.5, or 5.6 eV for the cases lpfl = 2,5, 10, 20, or 30 D, respectively. Since most of these are larger than the limits established on s, the model must require that 54O 44' > N > amin with aminN Oo, 25O, 49O, 53O37', or 54'18' for the same cases, if the dipole interaction makes a major contribution to u(t i)- u(? ?). Considering the enormity of the dipolar interaction for dipoles of 20 D or larger at these spacings, it would be very unlikely that the restriction to the angular region in which this interaction is minimized would occur. Such large dipoles could occur only in the event that other intermolecular interactions (as discussed, for instance, in ref 14) could compensate the dipoledipole energy by (1)stabilzing the cy = 54O configuration relative to the dipole energy favored smaller CY configurations or (2) substantially reducing u ( t 1) - u ( t t) from the dipoledipole levels. Both of these require pairwise interactions of 1 eV or greater, extremely large values. Even though deduced from the simplified dipole picture, the restriction (12) A. L. McClellan, "Table of Experimental Dipole Moments", Vol. 2, Rahara Enterprises, El Cerrito, 1974, p 633. (13) B. F. Levine, C. G.Bethea, E. Wasserman, and L. Leenders, J . Chem. Phys., 68,5042 (1978). (14) K. Norland, A. Ames, and T. Taylor, Photogr. Sci. Eng., 14, 295 (1970). (15) V. A. Krongauz and E. S. Goldburt, Nature (London),271, 43 (1978).
J. Phys. Chem. 1883, 87, 1701-1707
of lptl I10 D, required for internal consistency of the model, is a realistic expectation for the dipole moment.12J3 We conclude that the suggested model is consistent with the experiments if, reasonably, lptl is in the range of approximately 2-10 D and u ( t l )- u ( t t ) is less than -0.10 eV. Obviously this model is very crude and does not take into consideration that in a real stack dipolar molecules are not geometrically symmetrical (i.e., a molecule may not fit into the same space on rotating 180° about an axis perpendicular to the dipole), are not necessarily situated exclusively within one plane, and might adopt other than strictly parallel and antiparallel orientations, and that CY may be a function of E. The model gives, therefore, only a qualitative idea of the effects of the electric field. It requires that the interaction between dipoles of different stacks be small compared to the interactions within stacks. In the case of strong three-dimensional molecular interaction a potential barrier for the field-induced reorientation of molecular dipoles must be so high that it is inconceivable that fields of 10-20 kV/cm would produce any significant effect. Estimates of the field-induced reorientation against a force constant typical of molecular crystal librational motions show a shift of equilibrium orientation by less than degree. Presumably, then, the cores must be composed of a more or less ordered assembly of stacks with a structure reminiscent of smectic liquid crystals. Probably this is the cause of the poor X-ray diffraction pattern of the quasi-crystals. Two important aspech of the SHG experiments are not described by this model: observation of a residual SHG
1701
signal prior to field perturbation and the asymmetric SHG response to fields of different polarity. These effects may be due to the fact that dipoles within the stacks are subjected not only to the applied field but also to the fields arising from surrounding molecules, stacks, and globules. While the globules were formed in the presence of an aligning field, removal of that field would leave correlated nonzero interstack field and interglobule fields, preserving the inequality W T> WJ.The asymmetry must be associated with a higher ordering or arrangement of stacks which somehow does not allow for a hysteresis symmetric about zero voltage. The latter point touches on the possibility of a distribution of nonidentical stacks, another factor not treated by our simple model. One final suggestion to explain the electric field dependence of the SHG is presented. It is possible that the stacks themselves are pushed by the electric field against the surrounding stacks and amorphous material. Since the dipole moment of stacks must be relatively large, the torque which they exert against their surroundings may be enough to allow slight twists or perhaps alteration of the strains developed in the material upon removal of the aligning field used in the thread-forming process. Details of why or how an alignment substantially larger than the zero-field residual is created later in comparable fields are unclear, which reduces, in our eyes, the probability that this explanation is appropriate. Registry No. 1-[@-(Methacryloyloxy)ethyl]-3,3-dimethyl-6'nitrospiro[indoline-2,2'- [2H-11benzopyran] , 25952-50-5.
Comparison of Multiphoton Ionization-Fragmentation Behavior of Benzene, Fluorobenzene, and Toluene David W. Squlre, Michael P. Barbalas,+ and Richard B. Bernsteln" Department of Chemistry, Coiumbie University, New Yo& New York 10027 (Received: November 2, 1982)
The relative intensities and fragmentation pathways of benzene and fluoro- and methyl-substituted benzene under multiphoton ionization have been compared as a function of both excitation wavelength and laser pulse power. A two-photon excitation resonant with the I L b band was utilized. The results of Goodman and Rava (1981) for the relative total ion intensities are confiied. The fragmentation is found to be laser power dependent but essentially wavelength independent over the range 500-534 nm. The energetics and the fragmentation results imply a standard resonance enhanced multiphoton ionization 2 + 2 process to form the molecular ion, followed by a one-photon absorption and photodissociation of the excited molecular ion to yield the observed fragments.
Introduction The coupling of multiphoton ionization with mass spectrometric detection has been used to elucidate the multiphoton spectroscopy of a variety of molecular systems.1*2 The systematics of the various processes which occur during the production of ionic fragments during multiphoton ionization have been recently reviewed.'b+ The multiphoton spectroscopy of a variety of substituted aromatic compounds has been ~ t u d i e d . ~ ~ *Goodman *~-~~ and Rava (GR) have explored the two-photon behavior of a series of monosubstituted benzenes and developed a 'Current address: Hoffman-La Roche, Inc., Nutley, NJ 07110. *Current address: Occidental Research Corp., Imine, CA 92713.
perturbation theory to explain their They treat the shifts in frequency and intensity of the so-called (1)R. B. Bernstein, J. Phys. Chem., 86,1178 (1982). (2)U.Boesl, H.J. Neusser, and E. W. Schlag, J. Chem. Phys., 72,4327 (1980). (3)P.M.Johnson and C. E. Otis, Annu. Reu. Phys. Chem., 32, 139 (1981). (4)M.A.Duncan, T. G. Dietz, and R. E. Smalley, J.Chem. Phys., 75, 2118 (1981). (5) D. A.Lichtin, R. B. Bernstein, and K. R. Newton, J. Chem. Phys., 75,5728 (1981). (6) W. Dietz, H. J. Neusser, U. Boesl, E. W. Schlag, a n i S.H. Lin, Chem. Phys., 66,105 (1982). (7)B. A. Heath, M. B. Robin, N. A. Keubler, G. J. Fisanick, and T. S.Eichelberger, IV,J. Chem. Phys., 72, 5565 (1980). (8)A. Sur, J. Knee, and P. Johnson, J. C h e n . Phys., 77, 654 (1982).
0 1983 American Chemical Society
