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Rotational coherence spectroscopy and structure of the perylene-benzene van der Waals complex
Volume 182, number 5
CHEMlC4L PHYSICS LETTERS
9 August 1991
Rotational coherence spectroscopy and structure of the perylene-benzene van der Waals complex Paul W. Joireman. Leslie L. Connell, Shane M. Ohline and Peter M. Felker ’ Department
ojChemistry
andBiochemistry,
Vniversl/y
oJCal[forma,
LosAngeles, Ct.4 90024-1569,
USA
Received 17 May 199 I
Rotational coherence spectroscopy has been used to measure rotational constants for four isotopomers of the aromatlc-aromatic dimer petylene-benzene. Possibilities for the vibrationally averaged dimer geometry have been deduced from the measured values. In the geometries the benzene moiety is close to centrally bound to the perylene and such that its ring plane is parallel or nearly parallel to the plane of the perylene. The geometries are discussed in terms of both the intermolecular forces between the spccics and the structural results for other aromatic dimcrs.
1. Introduction Recent advances in rotational coherence spectroscopy (RCS ) [ l-81 have rendered the high-resolution rotational spectroscopy of large isolated species much more feasible than in the past. As a result, RCSbased structural studies of a number of large molecules [ l-91, molecule-rare gas van der Waals complexes [ 2,5], and hydrogen-bonded complexes [ 71 and clusters [lo] have been reported. Such results point to the capabilities of RCS schemes and encourage one to apply them in the structural characterization of other types of species for which such information is needed. One important class of species for which information on geometries is quite sparse is that comprised of aromatic-aromatic dimers. Simply by virtue of the size of aromatic rings and the length of intermolecular bonds, these dimers are necessarily “large” species in the context of rotational spectroscopy. Due to this, there have been just three aromatic dimers whose geometries have been obtained by rotationally resolved frequency-domain spectroscopy- (s-tetrazine) z [ 111, s-tetrazine-benzene [ 121, and ( dimethyl-s-tetrazine)z [ 13 1. Geometrical features of two other species - fluorene-benzene [ 141 and fluorene-toluene [ 151 - have been obtained ’ NSF Presidential Young Investigator 1987-92. 0009-2614/91/$
from RCS experiments. Clearly, there is a need for more such results if one is to characterize the detailed nature and variety of interaromatic interactions Perylene-benzene is an aromatic-aromatic dimer that has been the subject of both experimental [ 161 and theoretical [ 16,171 study. The vibronic spectroscopy of Doxtader et al. [ 161 has revealed that the species exhibits a large (385 cm-’ ) shift in its S, w So O”,band relative to that of bare perylene. It has been argued that such a shift indicates a substantial overlap of the n-electron clouds of the two monomers in the complex. This conclusion is reinforced by a calculation [ 161 of the dimer geometry based on an atom-atom point charge plus “6-12” model of the intermolecular potential. The calculation predicts an equilibrium geometry in which the benzene moiety is centrally bound to the perylene, with the rings parallel and 3.3 A apart. In contrast, Price and Stone [ I7 ] have performed a distributed multipole analysis of the electrostatic contribution to the interaction energy between perylene and benzene that suggests such a “parallel-stacked” geometry is energetically unfavorable. This discrepancy renders the perylene-benzene system one for which geometrical information might be expected to be particularly valuable. In this Letter we report measurements of the rotational constants of four isotopomers of the pery-
03.50 0 1991 - Elsevier Science Publishers B.V. (North-Holland)
385
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CHEMICAL PHYSICS LETTERS
dimcr by RCS. The results of these measurements have been used to characterize the geometry of the species. It is found that those geometries consistent with the measured constants are reasonably close to the central binding one put forth by Doxtader et al. [ 161. The results are discussed in the light of both the previous work on the dimer and the work on the structures of other aromatic-aromatic species. lene-benzene
2. Experimental the apparatus used in obtaining RCS traces by the method of time-resolved fluorescence depletion (TRFD) [ 6 ] has been described previously [ i,9, IO]. Briefly, the picosecond laser system consists of a home-made cavity-dumped dye laser pumped by the frequency-doubled output of a Q-switched modelocked Nd:YAG laser (Spectron). A portion of the unconverted fundamental of the Nd:YAG and the fundamental of the dye (LDS 698) were mixed in a P-barium borate (BBO) crystal to obtain excitation pulses in the spectral region of interest by sum-frequency generation. The mixed output from the BBO crystal was then directed into a Michelson interferometer in which the variably delayed arm consisted of a retroreflector mounted on a stepper motor-ddven translation stage. The output of the interferometer, consisting of pump and probe pulse trains with parallel polarizations, was then crossed perpendicular to the axis of a continuous free jet expansion, consisting of perylene and benzene. a few millimeters downstream of the nozzle (approximately50 pm in diameter). The mixing of benzene with perylene was accomplished in the following way. helium, at approximately 150 psig, aas passed over benzene (at room temperature) and directed through a small needle valve. The output from the needle valve was combined with He at approximately 80 psig and passed over a heated sample F’ of perylene. Total fluorescence was collected with an elliptical mirror, de-
tected with a photomultiplier tube and averaged by a boxcar integrator. The output of the integrator as If’The tip of the nozzle was maintained at =230-250°C.
The temperature of the bulk perylene sample was significantly
lower.probablyless than 200°C.
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a function of interferometer delay was sent to a computer for storage and processing. Two isotopomers of perylene (A,?from Sigma and d,* from Cambridge Isotope Labs) and benzene ( hb from Aldrich and db from Cambridge Isotope Labs) were used to create four isotopically distinct species for study. In the experiment the data were obtained by exciting the 0: transition of the S, ++S, electronic transition of each complex. Each transition is localized in the perylene moiety and polarized parallel to the long axis of perylene [IS]. The excitation frequency of the h,,-h, dimer is 23680 cm-‘, which constitutes a shift of -385 cm-’ from the perylene electronic origion [ I6 1.The resonance frequency for
the A,+& dimer was found to be essentially identical. The transition frequencies of the d,, dimers were found in the following way. First, the perylened,,S, ++S, band was located at z 24 111cm- ‘. Then, the region 385 cm-’ to the red of this resonance was searched for benzene-dependent resonances. Benzene-dependent bands found in this region were attributed to the 0: bands of the d,&, and d,,-d, complexes. The fluorescence versus delay traces obtained from a TRFD experiment generally slope upward as the delay increases, This increase, which results from finite excited-state lifetimes [ 61, slight delay-line misalignments, and laser beam divergence, has been removed numerically from the data reported here. After obtaining an RCS trace the transients observed were assigned, and preliminary values for the rotational
constantsof the dimer were calculatedfrom their positions. Relevant portions of the RCS trace were then
fit to theory [ 31 using a nonlinear least-squares procedure. In the fits, rotational constants were used as
while the temperature (5 K) and the transition moment direction were fixed to assumed values. The best-fit values of the rotational constants obtained in this way arc the ones reported. fitting parameters,
3. Results The top of fig. I shows an RCS-TRFD trace for the h,2-d, perylene-benzene dimer. Traces for the h,&,, d,,-h, and d,,-d, isotopomers exhibit analogous features. The experimental trace shown in fig. 1 clearly exhibits two prominent transients. aside
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CHEMICAL PHYSICS LETTERS
1
L I
0
I
I
I
I
500
1003
1500
2000
Delay
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(4 h2-d6
I 2500
(psec)
1 (b)“““+
26 MHz
Fig. I. Experimental (top) and calculated (bottom) TRFD trace for the perylene-benzene h,,-d, isotopomer. The calculated trace was obtained by using the Bt C and B-Cconstants listed in the secondcolumnof table 1 and by takingU-B-C to equal 228 MHz. A temperature of 5 K and a Gaussian temporal response of 32 ps fwhm were assumed.
from the T=O feature. There is a positive-going transient at 1228 ps and a negative-going one at 2464 ps. Given the equal spacings of the features, it is clear that they are of the same type. Now, two types of RCS transients having alternating polarities have been identified: “hybrid” and “J-type” transients. Hybrid transients [ 71, which arise when the vibronic transition moment is hybrid-type [ 19 1, have essentially equal magnitudes regardless of polarity. However, the positive-going J-type transients (in TRFD traces) tend to be measurably smaller than the negative-going ones [ 3,4]. Based on this consideration, it is apparent from the data that the observed transients are Jtype. Thus, the transient positions are given by 5% n/2(B+ C) if the species is near-prolate or zz n/2(A+B) if the species is near-oblate (A, B, and C being the principal rotational constants of the species). As we shall explain in section 4, a near-oblate geometry for the dimer is not at all reasonable given the experimental results. Thus, we proceed here under the assumption of near-prolate geometry. In addition to information on B+ C, information about the magnitude of B-C is also available from the RCS traces of the perylene-benzene isotopomers. In particular, simulations of RCS traces show that there are features in the region of the first J-type transient at l/2 (B-t C) whose characteristics depend markedly on B-C. The origin of these features
1100
1200
1300
Delay (psec)
1400
1500
TRFD traces in the region of 1/2(B+C) for perylenebenzene isotopmers. (a) ExperImental (#) and calculated (numbered traces) for the h,,-d, species. (b) Experimental (??) and calculated (numbered traces) for the &-h6 species. The number next to each calculated trace corresponds to the value of B - C used to calculate that trace. The trace just below the experimental trace corresponds to the best-fit trace. The values of Bt C used are gwen in the second column of table 1, and 2‘4-B-C was taken as 228 MHz for h,,-d, and 225 MHz fordIz-h6.
(“asymmetry transients”) will be dealt with elsewhere [20]. Here, we need only recognize that fitting observed RCS traces in the region of 7% 1/2(Bt C) will yield values for both BSC and B-C. Fig. 2 shows experimental and calculated traces in this region for the (a) h,&, and (b) d,,h6 perylene-benzene isotopomers. The sensitivity of the smaller features in the calculated traces to BC values is apparent. From such comparisons of observed and calculated traces we obtain the B+ C and B-C constants listed in table 1 for the four isotopomers. The estimated uncertainties in the measured values are &0.75% and &20%, respectively. Unfortunately, no information of any precision can be extracted from our data in regard to the A rota387
Table 1 Measured and calculated rotational constants (in MHz) forperylene-benzene isotopomers lsotopomer
Rotational conslant meas. aJ
talc. b,
talc. ‘)
413 ?I
413
413
22
22
404
404
404
20
20
20
d,>-h,: BSC
385
384
384
B-C
22
24
24
d,,-d,: B+C B-C
316 24
376 22
376 22
h,z-h,: BtC B-C h,l-de: BtC B-C
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4. Structure determination Assuming that monomer geometries remain unchanged upon complexation six parameters are necessary to describe the structure of perylene-benzene. Three of these we choose to be the polar coordinates (R, 0, @) which fix the benzene center-of-mass with respect to the perylene-fixed axis system (see fig. 3) #2.The other three we choose to be the Euler angles (q3,0, u/) describing the orientation of the benzene-fixed axis system with respect to the perylene axes. (We use the convention of ref. [ 221 in defining the Euler angles.) The value of the angle v/, correFor footnote see next page.
a) Estimated uncertainties in BtC and B-C are 20.75% and + 20%, respectively. b1Constants corresponding to the best-fit geometry, see text and fig. 3. c, Constants corresponding to the best-tit parallel-displacedgeometry, see text and fig. 4.
tional constants
of the isotopomers
since there are
no transients in the traces whose positions
are sen-
sitive to the value of A. This situation arises because the vibronic transition moment direction in the complexes is either parallel-type or very nearly so. While such a transition moment direction precludes measurement of A [ I-41, we can, nevertheless, use the fact that the data imply a axis polarization to provide a check on the validity of the geometries that we derive from the measured rotational constants. If we assume that the vibronic transition moment in perylene-benzene is along the perylene long axis, as it is in bare perylene. then any dimer geometries we derive must have u principal axes that coincide, or nearly coincide, with the perylene long axis. Finally, we note that the experimental values quoted in table I represent averages of the So and S, rotational constants of a given species since both ground- and excited-state rotational coherences enter into TRFD traces [S]. To derive structural information from these values we make the reasonable assumption that the differences between the S, and S, constants are less than the experimental uncertainties.
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Y
Y
E&3 & X
X
FIN.3. Two views of the perylene-benzene geometrythat tits the measured rotational constants best. The pertment structural parameters for the geometry are gwen in the text. The rotational constants associated with the geometry are given In table I. At the bottom ofthe figure theaxis conventlons that were employed are shown.
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sponding to a final rotation about the benzene sixfold axis, has no effect on the principal rotational constants. Thus, we henceforth fix this angle to 0”. Below, we present the results of nonlinear leastsquares fits to the observed rotational constants in which the above-mentioned structural parameters were used as fitting parameters. Before we present these results, however, it is useful to consider some “high-symmetry” limiting cases for the dimer geometry. These cases allow one to determine structural parameters analytically from the measured values for the B and C constants. In so doing, one gains an appreciation of the kinds of geometries that are likely to be consistent with the observed rotational constants and a feel for the uniqueness of those geometries. We consider seven geometry cases: (1) parallel-stacked (8 and 19=0” ), (2) parallel-displaced along the perylene x axis (@ and (LO’), (3) and (4) the two types of “T-shaped” geometries in which a dimer symmetry plane is coincident with the perylene xz plane (@=O”, 0=90”, and @=90’ (case 3 ) or 0” (case 4) ), (5 ) parallel-displaced along the perylene y axis (@=90”, Q=O’), and (6) and (7) the two types of T-shaped geometries in which a dimer symmetry plane is coincident with the perylene J,Z plane (@=90”, 0=90”, and $=O’ (case 6) or 90” (case 7) ). For each of these cases one can determine both R and 8 for all isotopomers from the measured values of B and C. The situation for case 1 is even simpler, however. In particular, it is straightforward to show that for a parallel-stacked geometry (assuming a near-prolate species) II”) = Z(P’tZ(B’, where Ii”‘, I:‘), and Z:B’ are the moments of inertia about the c principal axes of perylene-benzene, bare perylene, and bare benzene, respectively. (In general, when we write ZjD) we mean
‘? The peryleneright-handedCartesian axis system we have used has its origin at the perylene center-of-mass. The x axis is oriented along the long axis of petylene and the z axis is perpendicular to the petylene plane. Note that this is not in accordance with the standard convention for axis labeling of Dzs molecules (see ref. [ 2 1] ). However, our axis system is much more convenient in regard to specifying the dimer geometry. The benzene axis system (using to define the Euler angles) has its origin at the benzene center-of-mass, itsy axis in-plane and bisecting two C-C bonds, and its z axis perpendicular to the benzene plane.
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CHEMICAL PHYSICS LETTERS
the moment of inertia of the dimer about its jth principal axis. Analogous meanings apply to I:‘) and I,(“’ for the perylene and benzene monomers.) This relation is far from being obeyed by any of the dimer isotopomers. Thus, the data rule out a parallelstacked vibrationally averaged structure. For cases 2 to 4, values of R can be obtained directly from the measured values of B for the dimers. The following expression is readily derived [ 231:
where Z=Zi’) tZbB) for cases 2 and 3, I= ZAP)t Z>B)for case 4, and p is the reduced mass K3of the dimer. Values of 8 for these cases can be obtained directly from the measured values of C for the dimers. One has cos2@=
I~D’(Z~D’-I-I’-pR2)tI(I’+,uR2) pR’(Z-Z’)
where Z=Z(p)+Z(B) and Z’=Z~P)+ZJB) for case 2, Z=Z~p’+Z~” andaZ’=ZjP’+Z~B’ for case 3, and I= Zip’ t IL”) and I’ =Zl” t IL”) for case 4. For cases 5 to 7 values of R can be obtained from the measured values of B and C as follows [ 23 ] :
where Z=Z~~p)+Z~p)tZ,~cB)tZJB) for cases 5 and 6 and Z=Zb’) +I:” t 216” for case 7. Values of 8 for these cases can be determined from cos2~= (Z:D’-IJD’)2-(I-Z’t~R2)2 4,uR2(I’ -I)
’
where Z=Zi’) tZiB) and Z’=ZbP) +I/,‘) for case 5, Z=ZJ’) tZhB) and I’ =Zhp) tZ!B) for case 6, and Z=Z!‘) tZAB) and Z’=ZbP) tZbB) for case 7. Values of R and 8 extracted from the experimental results for cases 2 to 7 are given in table 2 for the /r&r6 isotopomer. (For each case similar values obtain for the other isotopomers. ) One notes several implications of these values. First, only a fairly narrow range of R values (3.33 to 4.0 A) characterizes all of the cases. Second, all of the values of 8 are such that near-central binding of the benzene to the pers3 The reduced mass of the dimer is defined as follows: y=M(P)M(B)/(M(P’tM(B)), where IW(‘~ is the total mass of the perylene monomer and IV(‘) is the total mass of the benzene monomer.
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Table 2 Valuesof R and B for the h,,-h, perylene-benzene
for geometry
cases 2 to 7 Geometry case
R (A)
@ (deg)
11 displaced case 3: x axis 1 displaced I case 4: x axis I displaced 2 case 5: y axis 11 displaced case 6: y axis 1 displaced 1 case 7: y axis 1 displaced 2
3.56 3.56 3.34 3.81 3.81 4.00
17.3 23.6 27.0 8.1 7.3 6.5
case 2: x axis
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evident. Moreover, the best-fit geometry is consistent with the qualitative conclusions presented in the preceding paragraph. To address the uniqueness of the geometry of fig. 3 two principal questions are relevant. First, how unique is the position of the benzene center-of-mass with respect to perylene’s? Second, how unique is the deviation from parallel ring planes? In regard to the first issue we have found the following: as @ is varied from 0” to 90”, geometries consistent with the observations
(to within our experimental
uncertainty)
are found for R increasing steadily from 3.55 to 3.8
ylene applies. Third, all of the T-shaped cases that are consistent with the measured rotational constants are readily seen to be unreasonable dimer geometries: nonbonded carbon-carbon and carbonhydrogen distances are considerably too short. For example, the R and 0 values for case 3 imply that one benzene carbon is only about 2 A from the perylene plane and one benzene hydrogen is only about 0.9 A away. In contrast, the parallel-displaced cases have entirely reasonable nonbonded atom-atom distances In short, then, the qualitative picture of the dimer’s vibrationally averaged geometry that emerges from the preceding analysis is one that involves nearcentral binding, approximately parallel ring planes, and a distance of 3.55 to 3.88 A separating the mon-
omer centers-of-mass. A more general and quantitative
search for possible dimer geometries was performed by fitting the measured dimer rotational constants while varying geometrical parameters in a weighted, nonlinear leastsquares fitting procedure. In order to assess the uniqueness of the geometries obtained by this procedure two things were done. First, fits were performed in which one parameter was fixed to a certain value and the others allowed to vary. Then, the value of the fixed parameter was changed and the same procedure repeated, etc. In this way the uniqueness of any given parameter was assessed. Second, a wide range of initial parameters was used in the fits. Fig. 3 shows two perspectives of the structure that gives the best fit to the measured rotational constants. It is defined by the values (R, 0, @)=(3.62 A, 15”, 19’) and (4, 8, u/)=(135”, - 3 lo, 0’ ). The values of the rotational constants corresponding to this structure are compared with the measured values in table 1. Close agreement is 390
A and 0 decreasing steadily from about 17” to 9”. Those geometries corresponding to @near 0” tit the data marginally better than those corresponding to @ near 90”. Thus, the conclusion obtained by a consideration of cases 2 through 7 above is borne out the dimer is characterized by near-central binding and a narrow range of acceptable R and 0 values. In regard to the tilt of the benzene plane with respect to that of perylene, we find that dimer geometries
having widely different /3and $ angles ae consistent with the data. Nevertheless, two conclusions can be made. First, given the range of possible R and 0 values, the only energetically reasonable values for 101 are small ones; for 0 too large some atoms on the perylene and benzene moieties become closer than the sum of their van der Waals radii. For example, even in the best-fit geometry of fig. 3, there are carboncarbon distances of about 2.9 A between the two moieties, a value that would probably give rise to significant exchange repulsion. Second, the assumption of parallel ring planes leads to only slightly worse fits than if the 4 and 8 angles were allowed to float in the fitting procedure. For example, the parallel-displaced structure shown in fig. 4 (R=3.67 A, 0= 14”, @=32”! $=O’, /LO”) yields the rotational constants given in the last column of table 1. The conclusion is that only parallel-plate, or near parallelplate, geometries are consistent with the experimental results. A last point to be addressed in regard to the dimer structure is the assumption that the species is nearprolate. We have performed geometry fits such as those described above under the assumption that the measured RCS traces correspond to a near-oblate species (i.e. instead of B+ C and B-C being measured, ASB and A-B were). The results of the fits
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Fig. 4. best-fit dimer geometry obtained by constraining the benzene to be parallel to theperylene plane (r$=O” and 0=0”). The pertinent structural parameters for the geometry are given in the text. The distance between the benzene and perylene planes is 3.57 A.
strongly indicate that the near-oblate assumption is wrong. First, the geometries have R values that are very large (5 A). Second, and more important, the geometries are such that the vibronic transition moment is perpendicular-type (i.e. the perylene long axis is perpendicular to the c axis of the dimer). Simulations clearly show that such a transition moment cannot reproduce the observed RCS traces. In comparison, the geometries of figs. 3 and 4 are such that the perylene-localized transition is almost purely parallel-type (i.e. a axis polarized in a near-prolate top). RCS simulations based on these geometries do reproduce the observed traces. One such simulation is compared with the experimental trace in fig. 1.
5. Conclusion A mentioned in section 1, Doxtader et al. [ 161 and Price and Stone [ 171 have both performed calculations pertaining to the geometry of perylene-benzene and have come to contradictory conclusions. There are several possible reasons for this discrepancy. First, while Doxtader et al. [ 161 account for both dispersion-repulsion and electrostatic interactions in their calculation, they treat the electrostatics in a somewhat rudimentary way - that is, by way of distributed point charges. Price and Stone [ 17 1, on the other hand, have employed a more sophisticated treatment of the electrostatics. However, they have
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not included the effects of dispersion quantitatively in their calculations. Finally, both groups have neglected the effects of polarization interactions. The results presented in this paper are most consistent with the parallel-stacked geometry predicted by Doxtader et al. [ 161. To be sure, there are differences between our results and those of ref. [ 161. Our results clearly indicate a significant, albeit small, deviation from strictly central binding. And, the experimentally derived ring plane-to-ring plane distance (ranging from 3.37 to 3.78 A, depending on the value of @) is larger than that predicted by the calculation (i.e. 3.3 A). Nevertheless, the gross features of the experimental geometry match those of ref. [ 161. This agreement is somewhat surprising given the level of approximation at which the electrostatic interaction energy was calculated therein. Given this, it is pertinent to try to rationalize the success of the atom-atom, point charge plus “6- 12” model used by doxtader et al. [ 16 1. One obvious rationalization is that dispersion-repulsion terms dominate in the intermolecular forces binding the dimer. Such dominance is predicted by the calculation of ref. [ 161 and would be expected given the number of atoms associated with the two monomers. The real issue, however, is not that the dispersion-repulsion contributions are larger than others, but that they are so favorable for near central binding that they overcome the apparently unfavorable electrostatic interactions [ 171 for such geometries. In this regard it is instructive to bring up a consideration of polarization interactions. Castella et al. [ 241 have performed semi-empirical calculations of the geometries of van der Waals dimers between perylene and substituted benzenes. In the calculations electrostatic, dispersion-repulsion and polarization interactions were all included. (Unfortunately, the group did not report calculations on perylene-benzene. ) One finding of their study is that attractive polarization contributions to the dimer binding energies, although relatively small, are nevertheless similar in magnitude to electrostatic contributions. Thus, in perylene-benzene it may be that polarization serves to cancel the effects of electrostatic repulsion for near central binding, thereby allowing dispersion-repulsion terms to dominate. This possibility can account for the conclusion of Price and Stone [ 171, who did not consider the effects of polarization. And, the success of Doxtader et 391
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al. [ 161 might then be attributed, in part, to a fortuitous underestimation of electrostatic repulsion by the point charge model. Notably, the geometries predicted by Castella et al. [ 241 for perylene-phenol and perylene-aniline have very similar features to our case 2 perylene-benzene geometries [see table 2). Clearly, the application of the method of ref. [ 241 to a calculation of the perylene-benzene geometry could be very instructive. In relation to other aromatic-aromatic dimers whose geometries have been determined by experiment perylene-benzene has several common features. One feature is parallel, or near-parallel, ring stacked on one another. This attribute also obtains in (dimethyl-s-tetrazine)2 [ 111. tetrazine-benzene [ 12 1, fluorene-benzene [ 141, and fluorene-toluene [ 151. A second feature is the distance between ring planes. For the dimers just mentioned, ring plane separations range from 3.6 to 3.8 A, values similar to those reported here for perylene-benzene, Third, the near-central binding in perylene-benzene also occurs in the only other two aromatic-aromatic dimers that involve a multiring aromatic and have been studied by rotational spectroscopy (i.e. fluorenebenzene and fluorene-toluene). These common features are important in two respects. First, they imply that the kinds of interactions which dominate in determining aromatic-aromatic dimer structures may be rather invariant to the specifics of the monomers involved. This is good news in regard to the development of semi-empirical, quantitative descriptions of interaromatic interactions. Second, they can serve as qualitative guides in predicting the gross features of unknown aromatic dimer structures. RCS experiments aimed toward providing a larger aromaticaromatic structural data base are currently in progress in this laboratory and will be reported on in future publications.
Acknowledgement
This work was supported by National Science Foundation grant CHE 88-l 3470 and by grant 22728AC6-C from the donors of the Petroleum Research Fund administered by the American Chemical Society.
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References
[ 11 P.M. Felker, J.S. Baskin and A.H. Zewail,J. Phys. Chem. 90 (1986) 724. [2] J.S. Baskin, P.M. Felker and A.H. Zewail, J. Chem. Phys. 84 ( 1986) 4708. [3] P.M. Felker, J.S. Baskin and A.H. Zewail, J. Chem. Phys. 86 (1987) 2460. [4] J.S. Baskin. P.M. Felker and A.H. Zewail, J. Chem. Phys. 86 (1987) 2483. [ 51 J.S. BaskinandA.H.Z.ewail, J. Phys.Chem. 93 (1989) 5701; N.F. Scherer, L. Khundkar, T. Rose and A.H. Zewail, J. Phys. Chem. 9 I (987) 6478. [6] M.J. Cdte, I.F. Kauffman, P.G. Smith and J.D. McDonald, J. Chem. Phys. 90 (1989) 2864; J.F. Kauffman, M.J. Catt. P.G. Smith and J.D. McDonald, J. Chem. Phys. 90 (1989) 2874. [7]L.L. Connell, T.C. Corcoran, P.W. Joireman and P.M. Felker, J. Phys. Chem. 90 (1990) 1229. [ 81T.C. Corcoran, L.L. Connell, G.V. Hartland, P.W. Joireman, R.A. Hertz and P.M. Felker, Chem. Phys. Letters 170 (1990) 139; G.V. Hartland, L.L. Connell and P.M. Felker, J. Chem. Phys., m press. [9] L.L. Connell, T.C. Corcoran, P.W. Joireman and P.M. Felker, Chem. Phys. Letters 166 ( 1990) 5 10. [IO] L.L. Connell, S.M. Ohline, P.W. Jolreman and P.M. Felker, J. Chem. Phys. 94 (199 I ) 4668. [ 111 CA. Haynam, D.V. Brumbaugh and D.H. Levy, J. Chem. Phys. 79(1983) 1581. [ 121 D.H. Levy, C.A. Haynam and D.V. Brumbaugh, Faraday Discussions Chem. Sot. 73 (1982) 137; [ I3 ] CA. Haynam, D.V. Brumbaugh and D.H. Lcw, J. Chem. Phys. 8 1 ( 1984) 2282. [ 14) P.W. Joireman,L.L. Connell, S.M.0hlineandP.M. Felker, J. Phys. Chem., in press. [ 15 ] P.W. Joireman, L.L. Connell, S.M. Ohline and P.M. Felker, to be submitted for publication. [ 16lM.M. Doxtader, E.A. Mangle, A.K. Bhattacharya, SM. Cohen and M.R. Topp, Chem. Phys. 101 (1986) 413. [ 171 S.L. Price and A.J. Stone, 3. Chem. Phys. 86 (1987) 2859. [IS] S.4. Schwartz and M.R. Topp, J. Phys. Chem. 88 (1984) 5673. [ 191 G. Herzberg, Molecular spectra and molecular structure, Vols. 2 and 3 (Van Nostrand, Princeton, 1945 ) [201 P.W. Joireman, L.L. Connell, S.M. Ohline and P.M. Felker, to be sumitted for publication. [21] R.S. Mulliken, J. Chem. Phys. 23 ( 1955) 1997. [22] J.D. Graybeal, Molecular spectroscopy (McGraw-Hill, New York, 1988) pp. 58, 59. [23] P.M. Joireman, L.L. Cannel]. S.M. Ohlineand P.M. Felker, to be submitted. [24] M. Castella, P. Mill%, F. Piuzzi, J. Caillet, J. Langlet, P. Claverie and A. Tramer, J. Phys. Chem. 93 (1989) 394 I.
CHEMlC4L PHYSICS LETTERS
9 August 1991
Rotational coherence spectroscopy and structure of the perylene-benzene van der Waals complex Paul W. Joireman. Leslie L. Connell, Shane M. Ohline and Peter M. Felker ’ Department
ojChemistry
andBiochemistry,
Vniversl/y
oJCal[forma,
LosAngeles, Ct.4 90024-1569,
USA
Received 17 May 199 I
Rotational coherence spectroscopy has been used to measure rotational constants for four isotopomers of the aromatlc-aromatic dimer petylene-benzene. Possibilities for the vibrationally averaged dimer geometry have been deduced from the measured values. In the geometries the benzene moiety is close to centrally bound to the perylene and such that its ring plane is parallel or nearly parallel to the plane of the perylene. The geometries are discussed in terms of both the intermolecular forces between the spccics and the structural results for other aromatic dimcrs.
1. Introduction Recent advances in rotational coherence spectroscopy (RCS ) [ l-81 have rendered the high-resolution rotational spectroscopy of large isolated species much more feasible than in the past. As a result, RCSbased structural studies of a number of large molecules [ l-91, molecule-rare gas van der Waals complexes [ 2,5], and hydrogen-bonded complexes [ 71 and clusters [lo] have been reported. Such results point to the capabilities of RCS schemes and encourage one to apply them in the structural characterization of other types of species for which such information is needed. One important class of species for which information on geometries is quite sparse is that comprised of aromatic-aromatic dimers. Simply by virtue of the size of aromatic rings and the length of intermolecular bonds, these dimers are necessarily “large” species in the context of rotational spectroscopy. Due to this, there have been just three aromatic dimers whose geometries have been obtained by rotationally resolved frequency-domain spectroscopy- (s-tetrazine) z [ 111, s-tetrazine-benzene [ 121, and ( dimethyl-s-tetrazine)z [ 13 1. Geometrical features of two other species - fluorene-benzene [ 141 and fluorene-toluene [ 151 - have been obtained ’ NSF Presidential Young Investigator 1987-92. 0009-2614/91/$
from RCS experiments. Clearly, there is a need for more such results if one is to characterize the detailed nature and variety of interaromatic interactions Perylene-benzene is an aromatic-aromatic dimer that has been the subject of both experimental [ 161 and theoretical [ 16,171 study. The vibronic spectroscopy of Doxtader et al. [ 161 has revealed that the species exhibits a large (385 cm-’ ) shift in its S, w So O”,band relative to that of bare perylene. It has been argued that such a shift indicates a substantial overlap of the n-electron clouds of the two monomers in the complex. This conclusion is reinforced by a calculation [ 161 of the dimer geometry based on an atom-atom point charge plus “6-12” model of the intermolecular potential. The calculation predicts an equilibrium geometry in which the benzene moiety is centrally bound to the perylene, with the rings parallel and 3.3 A apart. In contrast, Price and Stone [ I7 ] have performed a distributed multipole analysis of the electrostatic contribution to the interaction energy between perylene and benzene that suggests such a “parallel-stacked” geometry is energetically unfavorable. This discrepancy renders the perylene-benzene system one for which geometrical information might be expected to be particularly valuable. In this Letter we report measurements of the rotational constants of four isotopomers of the pery-
03.50 0 1991 - Elsevier Science Publishers B.V. (North-Holland)
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dimcr by RCS. The results of these measurements have been used to characterize the geometry of the species. It is found that those geometries consistent with the measured constants are reasonably close to the central binding one put forth by Doxtader et al. [ 161. The results are discussed in the light of both the previous work on the dimer and the work on the structures of other aromatic-aromatic species. lene-benzene
2. Experimental the apparatus used in obtaining RCS traces by the method of time-resolved fluorescence depletion (TRFD) [ 6 ] has been described previously [ i,9, IO]. Briefly, the picosecond laser system consists of a home-made cavity-dumped dye laser pumped by the frequency-doubled output of a Q-switched modelocked Nd:YAG laser (Spectron). A portion of the unconverted fundamental of the Nd:YAG and the fundamental of the dye (LDS 698) were mixed in a P-barium borate (BBO) crystal to obtain excitation pulses in the spectral region of interest by sum-frequency generation. The mixed output from the BBO crystal was then directed into a Michelson interferometer in which the variably delayed arm consisted of a retroreflector mounted on a stepper motor-ddven translation stage. The output of the interferometer, consisting of pump and probe pulse trains with parallel polarizations, was then crossed perpendicular to the axis of a continuous free jet expansion, consisting of perylene and benzene. a few millimeters downstream of the nozzle (approximately50 pm in diameter). The mixing of benzene with perylene was accomplished in the following way. helium, at approximately 150 psig, aas passed over benzene (at room temperature) and directed through a small needle valve. The output from the needle valve was combined with He at approximately 80 psig and passed over a heated sample F’ of perylene. Total fluorescence was collected with an elliptical mirror, de-
tected with a photomultiplier tube and averaged by a boxcar integrator. The output of the integrator as If’The tip of the nozzle was maintained at =230-250°C.
The temperature of the bulk perylene sample was significantly
lower.probablyless than 200°C.
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a function of interferometer delay was sent to a computer for storage and processing. Two isotopomers of perylene (A,?from Sigma and d,* from Cambridge Isotope Labs) and benzene ( hb from Aldrich and db from Cambridge Isotope Labs) were used to create four isotopically distinct species for study. In the experiment the data were obtained by exciting the 0: transition of the S, ++S, electronic transition of each complex. Each transition is localized in the perylene moiety and polarized parallel to the long axis of perylene [IS]. The excitation frequency of the h,,-h, dimer is 23680 cm-‘, which constitutes a shift of -385 cm-’ from the perylene electronic origion [ I6 1.The resonance frequency for
the A,+& dimer was found to be essentially identical. The transition frequencies of the d,, dimers were found in the following way. First, the perylened,,S, ++S, band was located at z 24 111cm- ‘. Then, the region 385 cm-’ to the red of this resonance was searched for benzene-dependent resonances. Benzene-dependent bands found in this region were attributed to the 0: bands of the d,&, and d,,-d, complexes. The fluorescence versus delay traces obtained from a TRFD experiment generally slope upward as the delay increases, This increase, which results from finite excited-state lifetimes [ 61, slight delay-line misalignments, and laser beam divergence, has been removed numerically from the data reported here. After obtaining an RCS trace the transients observed were assigned, and preliminary values for the rotational
constantsof the dimer were calculatedfrom their positions. Relevant portions of the RCS trace were then
fit to theory [ 31 using a nonlinear least-squares procedure. In the fits, rotational constants were used as
while the temperature (5 K) and the transition moment direction were fixed to assumed values. The best-fit values of the rotational constants obtained in this way arc the ones reported. fitting parameters,
3. Results The top of fig. I shows an RCS-TRFD trace for the h,2-d, perylene-benzene dimer. Traces for the h,&,, d,,-h, and d,,-d, isotopomers exhibit analogous features. The experimental trace shown in fig. 1 clearly exhibits two prominent transients. aside
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1
L I
0
I
I
I
I
500
1003
1500
2000
Delay
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(4 h2-d6
I 2500
(psec)
1 (b)“““+
26 MHz
Fig. I. Experimental (top) and calculated (bottom) TRFD trace for the perylene-benzene h,,-d, isotopomer. The calculated trace was obtained by using the Bt C and B-Cconstants listed in the secondcolumnof table 1 and by takingU-B-C to equal 228 MHz. A temperature of 5 K and a Gaussian temporal response of 32 ps fwhm were assumed.
from the T=O feature. There is a positive-going transient at 1228 ps and a negative-going one at 2464 ps. Given the equal spacings of the features, it is clear that they are of the same type. Now, two types of RCS transients having alternating polarities have been identified: “hybrid” and “J-type” transients. Hybrid transients [ 71, which arise when the vibronic transition moment is hybrid-type [ 19 1, have essentially equal magnitudes regardless of polarity. However, the positive-going J-type transients (in TRFD traces) tend to be measurably smaller than the negative-going ones [ 3,4]. Based on this consideration, it is apparent from the data that the observed transients are Jtype. Thus, the transient positions are given by 5% n/2(B+ C) if the species is near-prolate or zz n/2(A+B) if the species is near-oblate (A, B, and C being the principal rotational constants of the species). As we shall explain in section 4, a near-oblate geometry for the dimer is not at all reasonable given the experimental results. Thus, we proceed here under the assumption of near-prolate geometry. In addition to information on B+ C, information about the magnitude of B-C is also available from the RCS traces of the perylene-benzene isotopomers. In particular, simulations of RCS traces show that there are features in the region of the first J-type transient at l/2 (B-t C) whose characteristics depend markedly on B-C. The origin of these features
1100
1200
1300
Delay (psec)
1400
1500
TRFD traces in the region of 1/2(B+C) for perylenebenzene isotopmers. (a) ExperImental (#) and calculated (numbered traces) for the h,,-d, species. (b) Experimental (??) and calculated (numbered traces) for the &-h6 species. The number next to each calculated trace corresponds to the value of B - C used to calculate that trace. The trace just below the experimental trace corresponds to the best-fit trace. The values of Bt C used are gwen in the second column of table 1, and 2‘4-B-C was taken as 228 MHz for h,,-d, and 225 MHz fordIz-h6.
(“asymmetry transients”) will be dealt with elsewhere [20]. Here, we need only recognize that fitting observed RCS traces in the region of 7% 1/2(Bt C) will yield values for both BSC and B-C. Fig. 2 shows experimental and calculated traces in this region for the (a) h,&, and (b) d,,h6 perylene-benzene isotopomers. The sensitivity of the smaller features in the calculated traces to BC values is apparent. From such comparisons of observed and calculated traces we obtain the B+ C and B-C constants listed in table 1 for the four isotopomers. The estimated uncertainties in the measured values are &0.75% and &20%, respectively. Unfortunately, no information of any precision can be extracted from our data in regard to the A rota387
Table 1 Measured and calculated rotational constants (in MHz) forperylene-benzene isotopomers lsotopomer
Rotational conslant meas. aJ
talc. b,
talc. ‘)
413 ?I
413
413
22
22
404
404
404
20
20
20
d,>-h,: BSC
385
384
384
B-C
22
24
24
d,,-d,: B+C B-C
316 24
376 22
376 22
h,z-h,: BtC B-C h,l-de: BtC B-C
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4. Structure determination Assuming that monomer geometries remain unchanged upon complexation six parameters are necessary to describe the structure of perylene-benzene. Three of these we choose to be the polar coordinates (R, 0, @) which fix the benzene center-of-mass with respect to the perylene-fixed axis system (see fig. 3) #2.The other three we choose to be the Euler angles (q3,0, u/) describing the orientation of the benzene-fixed axis system with respect to the perylene axes. (We use the convention of ref. [ 221 in defining the Euler angles.) The value of the angle v/, correFor footnote see next page.
a) Estimated uncertainties in BtC and B-C are 20.75% and + 20%, respectively. b1Constants corresponding to the best-fit geometry, see text and fig. 3. c, Constants corresponding to the best-tit parallel-displacedgeometry, see text and fig. 4.
tional constants
of the isotopomers
since there are
no transients in the traces whose positions
are sen-
sitive to the value of A. This situation arises because the vibronic transition moment direction in the complexes is either parallel-type or very nearly so. While such a transition moment direction precludes measurement of A [ I-41, we can, nevertheless, use the fact that the data imply a axis polarization to provide a check on the validity of the geometries that we derive from the measured rotational constants. If we assume that the vibronic transition moment in perylene-benzene is along the perylene long axis, as it is in bare perylene. then any dimer geometries we derive must have u principal axes that coincide, or nearly coincide, with the perylene long axis. Finally, we note that the experimental values quoted in table I represent averages of the So and S, rotational constants of a given species since both ground- and excited-state rotational coherences enter into TRFD traces [S]. To derive structural information from these values we make the reasonable assumption that the differences between the S, and S, constants are less than the experimental uncertainties.
388
Y
Y
E&3 & X
X
FIN.3. Two views of the perylene-benzene geometrythat tits the measured rotational constants best. The pertment structural parameters for the geometry are gwen in the text. The rotational constants associated with the geometry are given In table I. At the bottom ofthe figure theaxis conventlons that were employed are shown.
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sponding to a final rotation about the benzene sixfold axis, has no effect on the principal rotational constants. Thus, we henceforth fix this angle to 0”. Below, we present the results of nonlinear leastsquares fits to the observed rotational constants in which the above-mentioned structural parameters were used as fitting parameters. Before we present these results, however, it is useful to consider some “high-symmetry” limiting cases for the dimer geometry. These cases allow one to determine structural parameters analytically from the measured values for the B and C constants. In so doing, one gains an appreciation of the kinds of geometries that are likely to be consistent with the observed rotational constants and a feel for the uniqueness of those geometries. We consider seven geometry cases: (1) parallel-stacked (8 and 19=0” ), (2) parallel-displaced along the perylene x axis (@ and (LO’), (3) and (4) the two types of “T-shaped” geometries in which a dimer symmetry plane is coincident with the perylene xz plane (@=O”, 0=90”, and @=90’ (case 3 ) or 0” (case 4) ), (5 ) parallel-displaced along the perylene y axis (@=90”, Q=O’), and (6) and (7) the two types of T-shaped geometries in which a dimer symmetry plane is coincident with the perylene J,Z plane (@=90”, 0=90”, and $=O’ (case 6) or 90” (case 7) ). For each of these cases one can determine both R and 8 for all isotopomers from the measured values of B and C. The situation for case 1 is even simpler, however. In particular, it is straightforward to show that for a parallel-stacked geometry (assuming a near-prolate species) II”) = Z(P’tZ(B’, where Ii”‘, I:‘), and Z:B’ are the moments of inertia about the c principal axes of perylene-benzene, bare perylene, and bare benzene, respectively. (In general, when we write ZjD) we mean
‘? The peryleneright-handedCartesian axis system we have used has its origin at the perylene center-of-mass. The x axis is oriented along the long axis of petylene and the z axis is perpendicular to the petylene plane. Note that this is not in accordance with the standard convention for axis labeling of Dzs molecules (see ref. [ 2 1] ). However, our axis system is much more convenient in regard to specifying the dimer geometry. The benzene axis system (using to define the Euler angles) has its origin at the benzene center-of-mass, itsy axis in-plane and bisecting two C-C bonds, and its z axis perpendicular to the benzene plane.
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the moment of inertia of the dimer about its jth principal axis. Analogous meanings apply to I:‘) and I,(“’ for the perylene and benzene monomers.) This relation is far from being obeyed by any of the dimer isotopomers. Thus, the data rule out a parallelstacked vibrationally averaged structure. For cases 2 to 4, values of R can be obtained directly from the measured values of B for the dimers. The following expression is readily derived [ 231:
where Z=Zi’) tZbB) for cases 2 and 3, I= ZAP)t Z>B)for case 4, and p is the reduced mass K3of the dimer. Values of 8 for these cases can be obtained directly from the measured values of C for the dimers. One has cos2@=
I~D’(Z~D’-I-I’-pR2)tI(I’+,uR2) pR’(Z-Z’)
where Z=Z(p)+Z(B) and Z’=Z~P)+ZJB) for case 2, Z=Z~p’+Z~” andaZ’=ZjP’+Z~B’ for case 3, and I= Zip’ t IL”) and I’ =Zl” t IL”) for case 4. For cases 5 to 7 values of R can be obtained from the measured values of B and C as follows [ 23 ] :
where Z=Z~~p)+Z~p)tZ,~cB)tZJB) for cases 5 and 6 and Z=Zb’) +I:” t 216” for case 7. Values of 8 for these cases can be determined from cos2~= (Z:D’-IJD’)2-(I-Z’t~R2)2 4,uR2(I’ -I)
’
where Z=Zi’) tZiB) and Z’=ZbP) +I/,‘) for case 5, Z=ZJ’) tZhB) and I’ =Zhp) tZ!B) for case 6, and Z=Z!‘) tZAB) and Z’=ZbP) tZbB) for case 7. Values of R and 8 extracted from the experimental results for cases 2 to 7 are given in table 2 for the /r&r6 isotopomer. (For each case similar values obtain for the other isotopomers. ) One notes several implications of these values. First, only a fairly narrow range of R values (3.33 to 4.0 A) characterizes all of the cases. Second, all of the values of 8 are such that near-central binding of the benzene to the pers3 The reduced mass of the dimer is defined as follows: y=M(P)M(B)/(M(P’tM(B)), where IW(‘~ is the total mass of the perylene monomer and IV(‘) is the total mass of the benzene monomer.
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Table 2 Valuesof R and B for the h,,-h, perylene-benzene
for geometry
cases 2 to 7 Geometry case
R (A)
@ (deg)
11 displaced case 3: x axis 1 displaced I case 4: x axis I displaced 2 case 5: y axis 11 displaced case 6: y axis 1 displaced 1 case 7: y axis 1 displaced 2
3.56 3.56 3.34 3.81 3.81 4.00
17.3 23.6 27.0 8.1 7.3 6.5
case 2: x axis
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evident. Moreover, the best-fit geometry is consistent with the qualitative conclusions presented in the preceding paragraph. To address the uniqueness of the geometry of fig. 3 two principal questions are relevant. First, how unique is the position of the benzene center-of-mass with respect to perylene’s? Second, how unique is the deviation from parallel ring planes? In regard to the first issue we have found the following: as @ is varied from 0” to 90”, geometries consistent with the observations
(to within our experimental
uncertainty)
are found for R increasing steadily from 3.55 to 3.8
ylene applies. Third, all of the T-shaped cases that are consistent with the measured rotational constants are readily seen to be unreasonable dimer geometries: nonbonded carbon-carbon and carbonhydrogen distances are considerably too short. For example, the R and 0 values for case 3 imply that one benzene carbon is only about 2 A from the perylene plane and one benzene hydrogen is only about 0.9 A away. In contrast, the parallel-displaced cases have entirely reasonable nonbonded atom-atom distances In short, then, the qualitative picture of the dimer’s vibrationally averaged geometry that emerges from the preceding analysis is one that involves nearcentral binding, approximately parallel ring planes, and a distance of 3.55 to 3.88 A separating the mon-
omer centers-of-mass. A more general and quantitative
search for possible dimer geometries was performed by fitting the measured dimer rotational constants while varying geometrical parameters in a weighted, nonlinear leastsquares fitting procedure. In order to assess the uniqueness of the geometries obtained by this procedure two things were done. First, fits were performed in which one parameter was fixed to a certain value and the others allowed to vary. Then, the value of the fixed parameter was changed and the same procedure repeated, etc. In this way the uniqueness of any given parameter was assessed. Second, a wide range of initial parameters was used in the fits. Fig. 3 shows two perspectives of the structure that gives the best fit to the measured rotational constants. It is defined by the values (R, 0, @)=(3.62 A, 15”, 19’) and (4, 8, u/)=(135”, - 3 lo, 0’ ). The values of the rotational constants corresponding to this structure are compared with the measured values in table 1. Close agreement is 390
A and 0 decreasing steadily from about 17” to 9”. Those geometries corresponding to @near 0” tit the data marginally better than those corresponding to @ near 90”. Thus, the conclusion obtained by a consideration of cases 2 through 7 above is borne out the dimer is characterized by near-central binding and a narrow range of acceptable R and 0 values. In regard to the tilt of the benzene plane with respect to that of perylene, we find that dimer geometries
having widely different /3and $ angles ae consistent with the data. Nevertheless, two conclusions can be made. First, given the range of possible R and 0 values, the only energetically reasonable values for 101 are small ones; for 0 too large some atoms on the perylene and benzene moieties become closer than the sum of their van der Waals radii. For example, even in the best-fit geometry of fig. 3, there are carboncarbon distances of about 2.9 A between the two moieties, a value that would probably give rise to significant exchange repulsion. Second, the assumption of parallel ring planes leads to only slightly worse fits than if the 4 and 8 angles were allowed to float in the fitting procedure. For example, the parallel-displaced structure shown in fig. 4 (R=3.67 A, 0= 14”, @=32”! $=O’, /LO”) yields the rotational constants given in the last column of table 1. The conclusion is that only parallel-plate, or near parallelplate, geometries are consistent with the experimental results. A last point to be addressed in regard to the dimer structure is the assumption that the species is nearprolate. We have performed geometry fits such as those described above under the assumption that the measured RCS traces correspond to a near-oblate species (i.e. instead of B+ C and B-C being measured, ASB and A-B were). The results of the fits
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Fig. 4. best-fit dimer geometry obtained by constraining the benzene to be parallel to theperylene plane (r$=O” and 0=0”). The pertinent structural parameters for the geometry are given in the text. The distance between the benzene and perylene planes is 3.57 A.
strongly indicate that the near-oblate assumption is wrong. First, the geometries have R values that are very large (5 A). Second, and more important, the geometries are such that the vibronic transition moment is perpendicular-type (i.e. the perylene long axis is perpendicular to the c axis of the dimer). Simulations clearly show that such a transition moment cannot reproduce the observed RCS traces. In comparison, the geometries of figs. 3 and 4 are such that the perylene-localized transition is almost purely parallel-type (i.e. a axis polarized in a near-prolate top). RCS simulations based on these geometries do reproduce the observed traces. One such simulation is compared with the experimental trace in fig. 1.
5. Conclusion A mentioned in section 1, Doxtader et al. [ 161 and Price and Stone [ 171 have both performed calculations pertaining to the geometry of perylene-benzene and have come to contradictory conclusions. There are several possible reasons for this discrepancy. First, while Doxtader et al. [ 161 account for both dispersion-repulsion and electrostatic interactions in their calculation, they treat the electrostatics in a somewhat rudimentary way - that is, by way of distributed point charges. Price and Stone [ 17 1, on the other hand, have employed a more sophisticated treatment of the electrostatics. However, they have
9 August I99 I
not included the effects of dispersion quantitatively in their calculations. Finally, both groups have neglected the effects of polarization interactions. The results presented in this paper are most consistent with the parallel-stacked geometry predicted by Doxtader et al. [ 161. To be sure, there are differences between our results and those of ref. [ 161. Our results clearly indicate a significant, albeit small, deviation from strictly central binding. And, the experimentally derived ring plane-to-ring plane distance (ranging from 3.37 to 3.78 A, depending on the value of @) is larger than that predicted by the calculation (i.e. 3.3 A). Nevertheless, the gross features of the experimental geometry match those of ref. [ 161. This agreement is somewhat surprising given the level of approximation at which the electrostatic interaction energy was calculated therein. Given this, it is pertinent to try to rationalize the success of the atom-atom, point charge plus “6- 12” model used by doxtader et al. [ 16 1. One obvious rationalization is that dispersion-repulsion terms dominate in the intermolecular forces binding the dimer. Such dominance is predicted by the calculation of ref. [ 161 and would be expected given the number of atoms associated with the two monomers. The real issue, however, is not that the dispersion-repulsion contributions are larger than others, but that they are so favorable for near central binding that they overcome the apparently unfavorable electrostatic interactions [ 171 for such geometries. In this regard it is instructive to bring up a consideration of polarization interactions. Castella et al. [ 241 have performed semi-empirical calculations of the geometries of van der Waals dimers between perylene and substituted benzenes. In the calculations electrostatic, dispersion-repulsion and polarization interactions were all included. (Unfortunately, the group did not report calculations on perylene-benzene. ) One finding of their study is that attractive polarization contributions to the dimer binding energies, although relatively small, are nevertheless similar in magnitude to electrostatic contributions. Thus, in perylene-benzene it may be that polarization serves to cancel the effects of electrostatic repulsion for near central binding, thereby allowing dispersion-repulsion terms to dominate. This possibility can account for the conclusion of Price and Stone [ 171, who did not consider the effects of polarization. And, the success of Doxtader et 391
Volume182,number5
CHEMICAL PHYSICSLETTERS
al. [ 161 might then be attributed, in part, to a fortuitous underestimation of electrostatic repulsion by the point charge model. Notably, the geometries predicted by Castella et al. [ 241 for perylene-phenol and perylene-aniline have very similar features to our case 2 perylene-benzene geometries [see table 2). Clearly, the application of the method of ref. [ 241 to a calculation of the perylene-benzene geometry could be very instructive. In relation to other aromatic-aromatic dimers whose geometries have been determined by experiment perylene-benzene has several common features. One feature is parallel, or near-parallel, ring stacked on one another. This attribute also obtains in (dimethyl-s-tetrazine)2 [ 111. tetrazine-benzene [ 12 1, fluorene-benzene [ 141, and fluorene-toluene [ 151. A second feature is the distance between ring planes. For the dimers just mentioned, ring plane separations range from 3.6 to 3.8 A, values similar to those reported here for perylene-benzene, Third, the near-central binding in perylene-benzene also occurs in the only other two aromatic-aromatic dimers that involve a multiring aromatic and have been studied by rotational spectroscopy (i.e. fluorenebenzene and fluorene-toluene). These common features are important in two respects. First, they imply that the kinds of interactions which dominate in determining aromatic-aromatic dimer structures may be rather invariant to the specifics of the monomers involved. This is good news in regard to the development of semi-empirical, quantitative descriptions of interaromatic interactions. Second, they can serve as qualitative guides in predicting the gross features of unknown aromatic dimer structures. RCS experiments aimed toward providing a larger aromaticaromatic structural data base are currently in progress in this laboratory and will be reported on in future publications.
Acknowledgement
This work was supported by National Science Foundation grant CHE 88-l 3470 and by grant 22728AC6-C from the donors of the Petroleum Research Fund administered by the American Chemical Society.
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9 August 1991
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