J . Phys. Chem. 1989, 93, 6601-6610 complexes studied previously has a covalent double M-C bond by spin pairing of the electrons in the M do-orbital with the CH2 a-orbital, and the M d,-orbital with the CH2 *-orbital, relative to metal M+ and the ground state (3Bl) of CH2. However, in the case of (RuCH2)+three degenerate excited states (4A2,4BI,and 4B2), 12.9 kcal mol-' above the ground state, show a completely different bonding character: u-donor/*-acceptor M-C bonds. At the highest level of correlation employed by Carter and Goddard,12 the bond energy for (RuCH2)+ (4A2)dissociating to d7 Ru+ and CHI (IAl) was found to be 65.8 kcal mol-' (nearly as strong as = 68.0 kcal mol-'), the covalent ground state D,[(RUCH~)+(~A,)] and it can be compared with our best estimated value for the (CuCH2)+ 'Al ground state of 57 kcal mol-'. In fact, the optimal Ru-C bond length, 1.93 A (3.65 ao) for the 4Az (RuCH2)+state is very similar to the one obtained for the 'Al (CuCH2)+, 3.63 a. (see Table I), and in both cases the optimal HCH angle in the complex resembles more free ('Al) C H 2 than (3BI) CH2 value. Considerably more u charge transfer than *-donation was also found for the 4A2 (RuCH2)+carbene-like state. For (CrCH2)+, at a same level of theory," the carbene state 6Al lies 18.8 kcal mol-' above the methylene 4Bl ground state. At the highest level of correlation consistent energy calculation" the (CrCH2)+ 6A, binding energy was found 38.7 kcal mol-' with the Cr+-C bond length longer, 2.32 A (4.38 ao), than the Cu+-C bond distance. In fact, when a point charge is placed at 4.38 a. from the CH, 'A, unit, the calculated binding energy is about 44 kcal mol-'. The reason why Cu+ can get closer to the carbon atom than the Cr+ atom can be related with the smaller size of the d orbitals
6601
of copper monoion than Cr+ atom. The more diffuse half-filled d-orbitals of Cr+ prevent the metal from moving nearer toward the CH2 unit due to the increasing repulsion of the C-H bonds, making negligible the *-donation. In contrast, the r-backbonding is more effective in the carbene (RuCHZ)' due to a larger overlap of the orbitals inducing to a stronger bond. Thus, bond strengths in charged-metal-carbene complexes can be viewed as mainly determined by electrostatic effects between the charged metal and the CH2 'Al unit. The M-C distance will depend on the intrinsic nature of the metal (electronic configuration, size of the orbitals, electronegativity, and so on). It is that different nature of the metal which finally determine the effectiveness of the u-donor/*-acceptor extent. The CuCH, species has been recently studied by using the same techniques as reported in the present paper138 and at the CASSCFIMRSDCI level,'3b finding a binding energy for the ,BI ground state of the same order of magnitude as for the (CuCH2)+ ground state. However, the type of bonding is quite different in the two cases,ionic with covalent character for the neutral complex and "electrostatic" (point-charge-bulk-charge interactions) for the monoion. Thus, we are facing two different types of bonding with similar strengths. The versatile type of the M-CH2 interaction is once more evidenced. Acknowledgment. The present work was supported by the CICYT project No. 714184. Registry No. Cu+, 17493-86-6; CH2, 2465-56-7; (CuCH2)+, 117130-08-2.
Vibrational Shlfts In p-Dlchlorobenrene-Rare Gas van der Waals Complexes W. D. Sands,+L. F. Jones, and R. Moore**$ Department of Chemistry, VCU Box 2006, Virginia Commonwealth University, Richmond, Virginia 23284-2006 (Received: October 3, 1988; In Final Form: April 26, 1989)
Fluorescence excitation spectra have been obtained for jet-cooled p-C6H4C12and p-C6D4C12and their van der Waals complexes with Ar and Kr. The van der Waals shifts for the origins of the Ar and Kr complexes are the same for both p-C6H4CI, and p-C6D,C12; however, the van der Waals shifts for vibronic transitions in the complexes are isotopically dependent. The vibrationally dependent van der Waals shifts are largest for this appears to be a general property of complexes of rare gases with aromatic systems. The effect of vibrational excitation of q 6 a of p-dichlorobenzene on the van der Waals potential is modeled by using the results of ab initio normal-mode calculations and atom-atom pair potentials. The model calculations the vibrationally dependent shift are not in quantitative agreement with experiment, but they correctly predict that for is larger for Kr complexes than for Ar complexes, and, for a given rare gas atom, the vibrationally dependent shift is larger for complexes than for p-C6D4C12complexes. Additionally, the model calculations lend support to our tentative identification of in p-C6D4C12-He.
m,
a
a
I. Introduction In recent years, rare gas van der Waals complexes of aromatic six-member ring systems have been used as model systems for the study of intramolecular vibrational redistribution and vibrational predissociation dynamics. The spectroscopy of these model systems is sufficiently well characterized that one is able to investigate the details of energy migration from the high-frequency ring vibrations of the polyatomic into the low-frequency vibrations associated with the motion of the rare gas atom against the ring. The energy migration is observed in fluorescence spectra of the complexes as vibrational predissociation and/or intramolecular vibrational redistribution, depending on whether or not sufficient 'Permanent address: Department of Chemistry, University of Pittsburgh, Pittsburnh. PA 15260. *Pres% address: Department of Chemistry, University of Pennsylvania, Philadelphia, PA 19104.
energy has been transferred to the low-frequency motions to break the van der Waals bond. One of the characteristics of rare gas van der Waals complexes that makes them amenable to the aforementioned studies is that the properties of the molecular portion of the complex tend to be little affected by complexation. For example, in the excitation spectrum of an expansion containing complexed and uncomplexed molecules, the spectrum of the van der Waals complex appears as a "shadow spectrum" of the bare molecule spectrum. The vibronic bands of the van der Waals molecule are only slightly shifted from the corresponding vibronic bands of the bare molecule, and the shift is very nearly the same for every band. Thus, complexation has little effect on the electronic and vibrational structure of the molecule.' (1) Levy, D. H. Adu. Chem. Phys. 1981, 47(1), 323.
0022-365418912093-6601$01.5010 0 1989 American Chemical Society
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The Journal of Physical Chemistry, Vol. 93, No. 18, 1989
Some exceptions to this general observation have been noted in cases where the normal mode excited in the vibronic transition has a component of the atomic displacements along the direction of the van der Waals bond. Examples include excitation of ovs-tetra~ine-Kr,~ p-difluoroertones of vlba in s-tetra~ine-Ar,~,~ ben~ene-Ar?,~ and pyrimidine-(Ar, N2),6V16b in s-tetrazine-Ar? V I 6 in b e n ~ e n e - H e , ~ and * ~ v7 in glyoxal-(Ar, Kr).9 Of these complexes, s-tetrazine-Ar is most well characterized. Rotational contour analysis indicates that the Ar is situated on the out-of-plane C2 axis at a distance from the plane of the aromatic ring of 3.43 A in So and 3.40 A in S1.Io The electronic origin of the complex is red-shifted 22.4 cm-I from the bare molecule rigi in,^.^ and the van der Waals stretching mode has The dissociation energy a frequency of 43 cm-l in both Soand of the complex has been bracketed between 280 and 380 cm-1.2J' In the excitation spectrum of the complex, vibronic bands that exhibit much smaller red shifts contain overtones of v16a or than do other vibronic bands. V16a also plays an important role in the SIvibrational predissociation dynamics and intramolecular vibrational energy redi~tribution.~*"-~~ In vibrational predissociation, if sufficient energy is available to break the van der Waals bond and to liberate a vibrationally excited s-tetrazine fragment, dissociation channels that result in excitation of vIba are favored. However, direct excitation of q 6 a does not enhance dissociation.2 In intramolecular vibrational redistribution, levels that contain quanta of v16a are preferentially populated in the energy redistribution process.z11'*13 The rates of both vibrational predissociation and intramolecular vibrational redistribution are level dependent Weber and Rice have but are on the order of 5 X lo8 presented a qualitative explanation of the SI dynamics in which the modulation of the van der Waals bond by vibrational excitation of v16a, the available density of states, and the energy gap law all govern the distribution of intermediate and final states in vibrational predissociation and intramolecular vibrational redistribution.I5 Curiously, the spectroscopic and dynamical behavior of s-tetrazine-Ar is profoundly different in In the fluorescence spectrum of the complex, vibronic bands that contain overtones of v16a are red-shifted slightly more than are the other vibronic bands. Additionally, the rates of intramolecular vibrational redistribution and vibrational predissociation are at least an order of magnitude slower than in The strong coupling between the van der Waals modes and the ring modes that is evident in SI apparently is absent in So. In the fluorescence excitation spectrum of p-difluorobenzeneare Ar, the electronic origin and all other transitions except red-shifted 30 f 2 cm-I from the corresponding bare molecule feature^.^ The red shift of is only 16 cm-'.' However, v16a (labeled v8 in ref 4 and 5) does not appear to play the same role s-1.2311913914
m
m
~~
~~~~
~~
~~
~~
(2) Brumbaugh, D. V.; Kenney, J. E.; Levy, D. H. J . Chem. Phys. 1983, 78, 3415. ( 3 ) Weber, P. M.; Rice, S. A. J . Chem. Phys. 1988, 88, 6120. (4) Butz, K. W.; Catlett, D. L.; Ewing, G. E.; Krajnovich, D.; Parmenter, C. S. J . Phys. Chem. 1986, 90, 3533. (5) Jacobson, B. A.; Humphrey, S.; Rice, S. A. J . Chem. Phys. 1988,89, 5624. (6) Abe, H.; Ohyanagi, Y . ;Ichijo, M.; Mikami, N.; Ito, M. J. Phys. Chem. 1985, 89, 3512. (7) Stephenson, T. A.; Rice, S . A. J . Chem. Phys. 1984, 81, 1083. (8) Rosman, R. L.; Rice, S. A. J . Chem. Phys. 1987, 86, 3292. (9) Halberstadt, N.; Soep, B. J . Chem. Phys. 1984, 80, 2340. (10) Haynam, C. A.; Brumbaugh, D. V.; Levy, D. H. J. Chem. Phys. 1984, 80, 2256. (1 1) Ramaekers, J. J. F.; van Dijk, J. K.; Langelaar, J.; Rettschnick, R. P. H. Faraday Discuss. Chem. SOC.1983, 75, 183. (12) Ramaekers, J. J . F.; Langelaar, J.; Rettschnick, R. P. H. In Picosecond Phenomena III; Eisenthal, K. B., Hochstrasser, R. M., Kaiser, W., Laubereau, A., Eds.; Springer-Verlag: Berlin, 1982; p 264. (13) Heppener, M.; Kunst, A. G. M.; Bebelaar, D.; Rettschnick, R. P. H. J . Chem. Phys. 1985,83, 5341. ( 1 4 ) Heppener, M.; Rettschnick, R. P. H. Structure and Dynamics of Weakly Bound Molecular Complexes; Weber, A,, Ed.; D. Reidel: Dordrecht, 1987; p 553. ( 1 5 ) Weber, P. M.; Rice, S. A. J . Phys. Chem. 1988, 92, 5470.
Sands et al. in the predissociation dynamics as in s-tetrazine, since no emission is observed from levels containing quanta of v16a in the p-difluorobenzene fragment following vibrational predissociation. Excitation spectra of complexes of pyrimidine with Ar and N, were obtained by Abe et aL6 In these spectra, also displays a smaller red shift than the other vibronic features. Spectra of perdeuteriopyrimidine-Ar were also obtained, but the van der was not reported. The structure of the Waals shift for complex is similar to s-tetrazine-Ar with the Ar atom located almost directly above the center of the ring at a distance from the plane of the ring of 3.45 f 0.05 A in So and 3.43 f 0.05 A in Abe et al. claim that v16a does not play a special role in the predissociation dynamics, although predissociation of 6bZ and 6a' in pyrimidine-Ar results in 99% and 92% of the pyrimidine photofragment formed in the level 16a1, respectively. Evidence in favor of their assertion is obtained from excitation of 5, which relaxes by resonance fluorescence and predissociation to 6a'. N o emission is observed from levels containing quanta in q 6 a although several are energetically accessible. Stephenson and Rice have investigated the relaxation dynamics of complexes of benzene with He, Ne, and Ar.' In benzene and v1tb are degenerate. The transition 6h16: appears as a doublet, reflecting the two components of vibrational angular momentum. In the excitation spectrum of benzene-He, the transitions are observed 6.5 cm-I to the blue of 6;16$, whereas the van der Waals transitions to the vibronic origin $ and other vibronic bands are blue-shifted 2.5 f 0.5 cm-' from the bare molecule bands. Stephenson and Rice make no mention of v16-dependentshifts in the spectra of Ar or Ne complexes. Rosman and Rice have studied the relaxation dynamics of complexes of He with a number of partially deuterated benzenes.8 The vibrational levels populated after relaxation vary widely among the isotopic species. Differen= between branching ratios observed for relaxation in C6H6-He and C6D6-He are especially difficult to interpret. It is interesting to note that although complexation of rare gas atoms to the aromatic ring always has a large effect on the frequency of levels that contain quanta of v16a do not always appear to play an important role in intramolecular vibrational redistribution or vibrational predissociation of the complexes (viz., pyrimidine6 and p-diflu~robenzene~*~ and sometimes CsH,+,,D,8). However, in theoretical treatments that address the specific case of vibrationally dependent van der Waals shifts and vibrational predissociation in rare gas complexes of six-member aromatic rings, the same term in the perturbation expansion that gives rise to the vibrational shift is also important in the predissociation dynamic~.~J~ In this paper we report the results of our experiments on complexes of Ar and Kr with p-C6H4C12and p-C6D4C12. (Hereafter, when we wish to refer to a specific isotopic species of p-dichlorobenzene, we will use its chemical formula; when we wish to refer to p-dichlorobenzene in a generic sense, we will use the word "p-dichlorobenzene".) Herein we use the Wilson notation for benzene for the labeling of the normal modes.I8 Of course, substitution (or deuteration) produces qualitative changes in the normal modes, so that the normal modes of p-dichlorobenzene are labeled by the Wilson number that corresponds most closely to the benzene vibration of the same number. Also, for a given normal mode, substituted benzenes that contain heavy atom substituents (mass >25 amu) often have very different vibrational frequencies from those that have the same substitution pattern but that have light substituents.19 For example, the frequency of vTa, the C-X symmetric stretch, is 328 cm-I for p-dichlorobenzene20 and 1255 cm-' for p-difluorobenzene.21 Thus, the
m
(16) Sugahara, Y.; Mikami, N.; Ito, M. J . Phys. Chem. 1986, 90, 5619. (17) Ewing, G. E. J . Phys. Chem. 1986. 90, 1790. (18) Wilson, E. B. Phys. Rev. 1934, 45, 706. (1 9) Varsanyi, G. Vibrational Spectra of Benzene Derivatives; Academic Press: New York, 1969. (20) Scherer, J. R.; Evans, J. C. Specrrochim. Acra 1963, 19, 1739. (21) Green, J. H. S. Specrrochim. Acta, Parr A 1970, 26, 1503.
p-Dichlorobenzene-Rare Gas van der Waals Complexes low-frequency modes of p-dichlorobenzene will, in general, correspond to a different set of normal modes than for benzene, the azabenzenes, and p-difluorobenzene. The dichlorinated benzenes thus represent a different class of aromatic systems in which to study intramolecular vibrational redistribution and vibrational predissociation dynamics. Yl6a is one of the normal modes that is little affected by para substitution of the benzene ring by heavy atoms. Excitation spectra of complexes of rare gas atoms bound to p-dichlorobenzene in a supersonic jet expansion reveal the same vibrationally dependent van der Waals shifts for as are observed in the aforementioned complexes. We observe vibrationally dependent shifts that are different for the two isotopic species of p-dichlorobenzene. We have also obtained computational data on the normal modes of p-C6H4C12and p-C6D4C12. From the atomic displacements obtained from the normal-mode calculations, we are able to explain qualitatively the isotopic dependence of the vibrational shifts in the context of the modulation of the van der Waals potential by excitation of VI68 in SI. 11. Methods A . Experiments. The details of the experimental apparatus are given elsewhere.22 Briefly, fluorescence excitation spectra are obtained with a pulsed supersonic jet apparatus and a frequency-doubled Nd:YAG-pumped dye laser. He, or a mixture of Ar or Kr in an excess of He, is passed over a room-temperature sample of pulverized p-C6H4C12(Aldrich, 99+%) or p-C6D4C12 (ICN Biomedicals, 98% D / H ) crystals. The backing pressure for all spectra shown in this paper is 1 atm; the vapor pressure of p-dichlorobenzene is ca. 0.5 Torr. The gas mixture enters the vacuum chamber through a pulsed valve with a nozzle diameter of 0.76 mm. The axes of the supersonic expansion, the excitation laser, and the fluorescence collection optics are mutually perpendicular. The laser beam has a bandwidth of ca. 0.15 cm-' and intersects the supersonic expansion 16 nozzle diameters from the orifice. Wavelengths were measured with an arc lamp calibrated 0.85-m monochromator and are estimated to be accurate to within f l cm-I. The Ar van der Waals complexes were formed in a 3% Ar/He expansion. As will be discussed below, van der Waals complexes of p-dichlorobenzene with one and two Ar atoms are readily observed. Attempts were also made to form p-dichlorobenzene-Ar by using pure Ar as the carrier gas. Backing pressures were varied between 0.1 and 2 atm, but no features that could be attributed to van der Waals molecules were observed. Instead, as the backing pressure was increased, the intensities of the bare molecule features decreased, and the intensity of a continuous background increased. This continuous background is also apparent in expansions where the 3% Ar/He mixture is used as the carrier gas, but not in pure He expansions. We attribute the continuous background to the presence of a distribution of pdichlorobenzene-Arn clusters, where n > 2. The Kr van der Waals complexes were formed in a 3% Kr/He expansion. A 5% Kr/He mixture was also used, but the intensities of the van der Waals features were reduced relative to bare molecule features when compared to the 3% Kr/He mixture. Additionally, the intensities of the bare molecule features decreased and a continuous absorption background was observed to increase in intensity as the fraction of Kr in the gas mixture was increased. Again, we attribute the background to the formation of clusters containing more than two Kr atoms. B. Computations. The details of the computational method will be published elsewhere.23 Molecular geometries, force constants, normal coordinates, and vibrational frequencies for So p-C6H&12 and p-C6D4C12were calculated by using the HONDOS program by King, Dupuis, and RysZ4on an IBM 3081D mainframe computer. Because of the large size of p-dichlorobenzene (22) Sands, W. D.; Moore, R. J . Phys. Chem. 1989, 93, 101. (23) Moore, R.; Jones, L. F.; Sands, W. D.; Shillady, D. D. Manuscript in preparation. (24) HONDOS: Dupuis, M.; Rys, J.; King, H. F. QCPE No. 403.
The Journal of Physical Chemistry, VOL 93, No. 18, 1989 6603
HC-CH HC-CCI mean C-C C-H c-CI
HONDOS"
GAUSSIAN 86'
STO-3/2G
6-31G*
experimental'
1.403 1.405 1.405 1.087 1.798
1.383 1.073 1.738
1.395 1.085 1.74
"References 23 and 24. bReference25. CMonocliniccrystal, ref 27.
(74 electrons and 12 atoms) and run-time limitations, we were forced to use a minimal basis set for these calculations. This basis, which we designate STO-3/2G, consists of an STO-3G basis for inner shell electrons (1s for C and H; Is, 2s, and 2p for C1) and an STO-2G basis for valence electrons (2s and 2p for C; 3s and 3p for CI). The molecular geometries are optimized at the S C F level to a gradient of lo-' hartree/bohr (-40 cm-'/A). The force constants are obtained by finite difference of analytical first derivatives of the potential by using a step size of 0.001 bohr. The normal modes are obtained without transforming to internal COordinates, and the six zero-frequency modes that correspond to molecular translation and rotation are used as a criterion for the quality of the calculation. In all cases the calculated frequencies of the zero-frequency modes are less than 10 cm-' and they typically are less than 1 cm-I. In order to ascertain the reliability of the results of the calculations by use of the minimal basis, a comparison was made of molecular geometries and normalized Cartesian eigenvectors for selected normal modes of benzene and benzene-d6 obtained by using the STO-3/2G basis and the split-valence 6-31G basis. The C-C and C-H bond lengths were found to be only ca. 0.01 8, longer when calculated in the 6-3 1G basis. Also, no significant differences were found in the relative amplitudes of the atoms as given by the normalized Cartesian eigenvectors of the normal modes. Rohlfing and Rohlfing have calculated the vibrational frequencies for p-C6H4C1225and p-C6D4C1226by using the GAUSSIAN 86 system of codes, a polarized 6-31G* basis, and analytical second derivatives in the determination of the force constants. A comparison of the optimized bond lengths for the two basis sets is given in Table I. Although their calculated frequencies are closer to the experimental values than are ours, we find that deuterium and chlorine isotope shifts and the normalized Cartesian eigenvectors for the normal modes are very similar for both calculations. We conclude that the calculations performed with minimal basis STO-3/2G yield reasonably accurate molecular geometries and a good representation of the atomic displacements of the vibrating molecule. 111. Results A . Experiments. The results of our spectroscopic experiments
on the rare gas complexes of p-dichlorobenzene parallel those of Weber and Rice on the rare gas complexes of s-tetra~ine.~ In order to facilitate a comparison of our work to theirs, we use, as much as possible, the same notations and conventions. Consequently, in the following discussion and in the tables, red shifts are given a positive sign. Fluorescence excitation spectra of the origin region Of pC&C12 and p-C6D4C12in a 3% Ar/He expansion are shown in Figure 1. Pressure-dependent features are observed to the red of the bare molecule origin and are attributed to the formation of van der Waals clusters. The red shift in the positions of the @ bands of the van der Waals molecules indicates that the complexes are more tightly bound in S1 than in So; this shift is termed the electronic shift. For both the protonated and deuterated molecules the electronic shift is 33 cm-' for the mono-Ar complex and 66 cm-I for the di-Ar complex. The van der Waals stretch for the (25) Rohlfing, E. A.; Rohlfing, C . M. J . Phys. Chem. 1989, 93, 94. (26) Rohlfing, C. M. Personal communication. (27) Tables of Interatomic Distances and Configurationsin Molecules and Zons;Special Publication No. 18; Sutton, L. E., Ed.; The Chemical Society: London, 1965.
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The Journal of Physical Chemistry, Vol, 93, No. 18, 1989
Sands et al.
b lko"
I 1
U I
i I
I
300
320
8
340
Frequency (cm-l)
Figure 3. Fluorescence excitation spectrum of p-C6H4CI2in a pure He Frequency (cm-l)
Figure 1. (a) Fluorescence excitation spectrum of the origin region of p-C,H4CI2 in a 3% Ar/He expansion. (b) Fluorescence excitation spectrum of the origin region of p-C6D4C12under the same conditions. I n both spectra features ascribed to the mono-Ar complex are marked with a single bar, and features due to the di-Ar complex are marked with a double bar. The feature marked with an asterisk in (b) is the origin of impurity C6HD3C12(see ref 22).
expansion in the neighborhood of 300 cm-I above the origin. Only transitions that can be ascribed to the bare molecule are observed. These are 7a&the C-CI symmetric stretch, at 302 cm-l, 16ai, an overtone of a C-C-C out-of-plane bend at 335 cm-l, and 9bA, a vibronically induced C-CI in-plane bind at 341 cm-I (see :f 19, 22, and 25).
0,"
1 I
i 0," 260
260
300
320
Frequency (cm-')
i -60 -40 -20
0
Frequency (cm-')
Figure 2. (a) Fluorescence excitation spectrum of the origin region of
p-C6H4C12in a 3% Kr/He expansion. (b) Fluorescence excitation spectrum of the origin region of p-C6D4CI2under the same conditions. The feature marked with an asterisk in (b) is the origin of impurity C6HD3C12(see ref 22). -
mono-Ar complexes, v d , is also observed with a frequency of 43 cm-I. No features were observed that could be attributed to overtones of van der Waals bending motions. These are typical values for Ar complexed to a six-member aromatic ring.24 The fluorescence excitation spectra of the origin region of p-C6H4C12and p-C6D4C12in a 3% Kr/He expansion are shown in Figure 2. As is the case with the Ar complexes, both the protonated and deuterated molecules exhibit the same electronic shift of 52 cm-I and have the same van der Waals stretching frequency of 37 cm-'. We did not observe any features in the spectra that would indicate the presence of di-Kr complexes or that could be attributed to overtones of bending motions. In Figures 3-8 are shown spectra of p-C6H4CI2and p-C6D4C12 in the vicinity of 300 cm-I above the electronic origins. In Figures
Figure 4. Fluorescence excitation spectrum of p-C6D4C12in a pure He expansion in the vicinity of 300 cm-' above the origin. The same bare
molecule features that are seen in Figure 3 are shown here. 7aA is observed at 301 cm-', 16ai at 284 cm-', and 9bi at 316 cm-I. The feature marked with an asterisk is 16ai for C6HD3CI2,which is present as an impurity (see ref 22). The weak feature that is observed with a 7-cm-I blue shift from 16ai tentatively has been assigned to The corresponding feature in the spectrum ofpC6H4C12(Figure 3) is not observed, most likely because if it is there it is buried under 9b&which is only 6 cm-' above 16ai.
m.
TABLE 11: Vibrational Frequencies
(a") in SIp-C&,CI2
and
p -CGD&I2' V,*b
VOh
302 34 1 P-C6H4C12 P-C6D4C12 301 316 a Reference 22. C6H43SC12 or C6D435C12.
VI.%
161.5 142
3 and 4, the backing gas was pure He; in Figures 5 and 6, 3% Ar/He; and in Figures 7 and 8, 3% Kr/He. The vibronic bands in this spectral region have been assigned to 7ab 9bh, and 16a$2us vTa is the C-Cl symmetric stretch, ugb is the in-plane C-Cl bend, and q 6 a is an out-of-plane C-C-C bend.I9 The frequencies of these vibrations in SI of the uncomplexed molecules are given in Table 11. (SeeFigure 9 for a representation of some of the normal
p-Dichlorobenzene-Rare Gas van der Waals Complexes
The Journal of Physical Chemistry, Vol. 93, No. 18, 1989 6605
.-x Y
16a
B
Y
E
3
al
8 m
t
s E
260
320
300
280
Frequency (cm-')
*x .m
i
16ag
Figure 8. Fluorescence excitation spectrum of p-C6D4CIzin a 3% Kr/He expansion in the vicinity of 300 cm-' above the origin. The total shifts for and are 48 and 30.5 cm-I, respectively.
m
TABLE III: van der Waals Shifts
"I I
ll
320
300
Frequency (cm-')
Figure 5. Fluorescence excitation spectrum Of pC6H4C12 in a 3% Ar/He expansion in the vicinity of 300 cm-' above the origin. The total shifts for @ and are 30 and 13 cm-I, respectively.
I
280
260
340
9b;
il
cl
E
3
v
B
p-C6H4C12-Ar p-C6D4C12-Ar p-C6H4Cl2-Ar2 p-C6D4C12-Ar2 p-C6H4Ci2-Kr p-C6D4Clz-Kr p-C6D4CI2-He (?)
( c d "
@
9 3
33 33 66 66 52 52
30
b
51 48
8
Red shifts carry a positive sign.
a
TABLE I V Vibrational Shifts (an-')'
E
m
63 33 30
@ 32 b 64
13 16
49 47
48 45
29 30.5 -7
Obscured.
m6xa169a 260
280
Freauencv
300
3iO
Icm-')
Figure 6. Fluorescence excitation spectrum Of p-CsD4C12 in a 3% Ar/He expansion in the vicinity of 300 cm-' above the origin. The total shift for 16aois 16 cm-l. Apparently, @ is buried under 16a& which is separated from 9bb by 32 cm-I.
Ill1
260
260
300
320
340
Frequency (cm-') Figure 7. Fluorescence excitation spectrum of p-C6H4C12 in a 3% Kr/He expansion in the vicinity of 300 cm-l above the origin. The total shifts are 50 and 29 cm-I, respectively. for o$ and
p-C6H4Cl2-Ar p-C6D4Cl2-Ar p-C6H&-Kr p-C6D4CI2-Kr p-C6D4C12-He (?)
-3 -1 -4
0 -3 -3 -5
-1 -4
-1
-20 -17 -23 -21.5 -76
"Red shifts carry a positive sign. bAssuming that the electronic shift is zero.
modes Of p-CsH&.) In the spectra shown in Figures 5-8 we observe pressure-dependent spectral features that we assign to the transitions 9b:,and in the van der Waals molecules. We also observe, but do not show the spectra, van der Waals features that we assign to @ and We see hints of the transitions in the spectra shown in Figures 5 and 7, but the bands are so weak that a definitive assignment cannot be made. We searched for van der Waals features associated with excitation of the first but also lacked overtone of the out-of-plane bends v l l and sufficient signal to background to detect them. For the most part, the red shifts of the vibronic bands differ only slightly from the electronic shifts observed for the origins. A notable exception is seen in the case of excitation of the overtone of the out-of-plane bending mode V16a in the van der Waals molecules. For each of the complexes that we have studied, the magnitude of the red shift for 16ag is significantly smaller than the electronic shift. The shift attributable to vibrational excitation is the vibrational shift and is defined as the total shift of the vibronic band less the electronic shift. The van der Waals shifts are summarized in Table 111, and the vibrational shifts are given in Table IV. In the spectrum of p-C6D4C12shown in Figure 4, we tentatively assign a weak band that is 7 cm-I blue-shifted from 16aa to in p-C6D,C12-He. We were able to observe this feature only when we probed the expansion shortly after the pulsed valve was opened.
a.
$,
6606 The Journal of Physical Chemistry, Vol. 93, No. 18, 1989 c1
I
I
Sands et al. TABLE V: Force Constants and Reduced Masses for vlk k16e9
N/m
!J~a(P-C6H4C12)r !46a@-C6D4C12)3 amu
SO
SI
31.85 2.510 3.199
3.915 2.405 3.346
B. Computations. The purpose of the ab initio HONDOS computations is to provide information on atomic displacements of V16a so that the modulation of the van der Waals potential can be calculated. The HONDOS output includes a triangular Cartesian force constant matrix and frequencies, force constants, and normalized Cartesian eigenvectors for each normal mode. In the program, the Born-Oppenheimer approximation is used in the computation of the potential surface, and so the force constants and elements of the Cartesian force constant matrix are isotopically independent. Ab initio computations of vibrational frequencies typically yield frequencies that are larger than the experimental frequencies.28 Our calculations are no exception; for vIk we obtain a value of 464 cm-I in p-C6H4C12and 41 1 cm-I in p-C6D4C12,as compared to the experimental values of 405 and 367 cm-I, respectively.2' In the harmonic approximation, a normal coordinate, Ql, is related to the individual atomic displacements by 1
I
Figure 9. Normal modes of p-C6H4CI2.The normal-mode displacements
given for the in-plane modes are proportional to the components of the normalized Cartesian eigenvectors from the HONDOS calculation and thus are not related to any measure of the actual atomic displacements when any of the normal modes are excited. The lone out-of-plane vibration, &+,a. is represented only by indications (+ and -) of which atoms move out of the plane. These symbols are not meant to be representative of the relative magnitudes of the displacements. If the expansion is probed at successively later times, the feature gradually disappears. Evidently, the expansion has different properties when the valve first opens than it does at later times, after a steady flow is established, which favors the formation of He complexes. Also, this feature is absent in the spectra shown in Figures 6 and 8, which were obtained with Ar and Kr mixed in with the He. We believe that if He complexes are formed during the expansions with the mixed gases, they are consumed by a displacement reaction with Ar or Kr, which are more strongly bound than He. Unfortunately, we cannot confirm the assignment by examination of the spectrum of the He expansion of pC6H4C12, since the transition 9bh is only 6 cm-I above 16ai and would totally obscure the van der Waals feature. We observe no other bands in the spectra of He expansions of p-C6H4C12 or pC6D4C12 (maximum backing pressure of 11 atm) that could be ascribed to He complexes, which indicates that the electronic shift is small compared to the bandwidth of the bare molecule transitions. Examination of the vibrational shifts listed in Table IV reveals the following trends: (1) With one exception (9b:,in pC6H4C12), the vibrational shifts for the Kr complexes are larger than for the Ar complexes. (2) The vibrational shifts for i$ are much larger than those for any other vibronic transition. (3) For a given rare gas atom and in-plane normal mode, the vibrational shifts are larger for p-C6D (21, than for p-C6H4C12. (4) For a given rare gas atom and 16a0, 4 the vibrational shifts are smaller for p-C6D4C12 than for P-C&C12. The magnitude of the vibrational shift is indicative of the extent of coupling between van der Waals motions and ring 16af exhibits the largest vibrational shift in pdichlorobenzene and in rare gas complexes of other six-member aromatic ring systems.2d The coupling between the vibrating ring and the van der Waals stretching motion will form the focus of this report. In particular, we have, for the first time, experimental and computational data on an isotopically substituted system. In this system the van der Waals potential is identical for both isotopic species, and so changes in vibrational shifts as a result of deuteration are dependent only on differences in the atomic displacements when V16a is excited.
where F is the Cartesian force constant matrix and kl and PI are the force constant and normalized Cartesian eigenvector for mode I , respectively. The frequencies of V16a in SI p-C6H4C12and p-C6D4C12are known (Table 11), and so the SI value of k I h can be obtained from the computed So value of k16a by scaling the So force constant:
This averaging is necessary since the calculated So deuterium shift is not exactly equal to the experimental SI shift. The So and SI force constants and reduced masses for V16a for p-C6H&12 and p-C6D4C12are given in Table v. The results of the ab initio computations indicate that in p C6D4C12the displacements of the C atoms from the plane of the ring are decreased relative to p-C6H4C12,whereas the displacements of the deuterons are increased slightly relative to the protons. The out-of-plane displacements of the atoms in p-C6H4C12and p-C6D4C12for vIh at the classical turning point for u = 0 are given in Table VI. In this table the atoms are numbered by standard nomenclature; Le., chlorinated C atoms are labeled C I and C4, etc. IV. Discussion A . Geometry of the Complexes. The geometry of the p-dichlorobenzene complexes is crucial to the interpretation of the spectroscopic data and any model that might be used to rationalize the experimental observations. Ideally, a rotational band contour analysis would be used to identify a geometry that is consistent with experimental band contours. Unfortunately, under our experimental conditions, we observe no rotational substructure for any of the vibronic bands in p-dichlorobenzene or any of its van der Waals complexes. We therefore infer a geometry for the rare gas van der Waals complexes of p-dichlorobenzene by analogy with s-tetrazine-Ar. In s-tetrazine-Ar the equilibrium position of the Ar atom is directly above the center of the aromatic ring at a distance above the plane of 3.40 A.1o We assume that the similarity between the spectroscopy of the rare gas van der Waals complexes of p-dichlorobenzene and s-tetrazine is indicative of similar complex geometries. In particular, the frequency of the van der Waals stretching fundamental in SIis 43 cm-I in both p-dichlorobenzene-Ar and s-tetrazine-Ar; in both systems large
The Journal of Physical Chemistry, Vol. 93, No. 18, 1989 6607
p-Dichlorobenzene-Rare Gas van der Waals Complexes .t
TABLE VI: Atomic Displacements (A) for vI6
CI P - C ~ H ~ C I ~0 P - C ~ D ~ C I ~0
c2
c3
c 4
c 5
c 6
CII
-0.0268 -0.0229
0.0268 0.0229
0 0
-0.0268 -0.0229
0.0268 0.0229
0 0
m;
vibrational shifts are associated with the transition finally, both systems obey the "additivity rule" when a second Ar is complexed to the ring, which indicates that the second Ar occupies a site equivalent to the first, namely, on the C2axis on the other side of the ring. All the available evidence thus points to a C2u geometry for p-dichlorobenzene-Ar, with the Ar directly above the center of the aromatic ring. Benzene-ArZ9 and pyrimidineArI6 also have similar structures. The similarity between the spectra of the Ar and Kr complexes (see Tables 111and IV) leads us to conclude that the Kr complexes have the same geometry as the Ar complexes. B. Vibrational Shift Model. We choose the model of Weber and Rice3 in an attempt to calculate the vibrational shifts observed in our spectra. The vibrational shift, AEln, is defined as the difference in vibrational energy for the excitation of n quanta of mode 1 in the bare molecule and the van der Waals molecule:
AElnis calculated to first order, where the perturbing potential V represents the coupling between the van der Waals modes and the ring mode I , and is given as a Taylor series expansion of the van der Waals potential U along the relevant normal coordinate
Q/
CI4 0 0
H2
H3
HS
H6
-0.0525 -0.0528
0.0525 0.0528
-0.0525 -0.0528
0.0525 0.0528
TABLE VII: Atom-Atom 6-12 Parameters
C-He C-Ar
C-Kr H-He H-Ar
A ~ . ,cm-I
r X 2 ,A
23.3 80.8 93.8 26.9 90.0
3.35 3.84 3.92 3.08 3.60
H-Kr CI-He C1-Ar
CI-Kr
Ax., cm-I
rx2, A
103 83.6 288 343
3.68 3.75 4.22 4.33
model potentials to the calculation of van der Waals energy levels for complexes of rare gas atoms and aromatic molecules.35 In their treatment of these systems the van der Waals complex is considered to be constituted of two particles, the aromatic molecule and rare gas atom. The van der Waals modes arise from relative translation of the two particles along the Cartesian axes. The van der Waals modes are assumed to be uncoupled anharmonic oscillators, so that motion in the z direction (stretching) is independent of that in the x or y directions (bending). The potential surface can thus be modeled as a product of three separate one-dimensional potential functions. The vibrational frequencies and anharmonicities for the three van der Waals modes are obtained by fitting a Taylor series expansion or a Morse potential to the 6-12 form of eq 6. Again, to conform to the model of Weber and Rice,3 we choose to represent the van der Waals potential in the z direction by a Morse potential
U = e[exp(-2P(z - zo)) - 2 exp(-p(z - zo))]
U(0) is not included in the expansion since it is subtracted out in the second term of eq 3. In this treatment, the harmonic approximation is used for the ring modes of the polyatomic molecule, and the zero-order wave function is written as the product Il,,)lijk),where i represents the quantum number for the van der Waals stretching mode and j and k are the quantum numbers for the bending modes. Since the van der Waals bond is cold, i , j , and k are all zero. Integrating over QI yields where Q/,02is the square of the amplitude of the zero-point motion , kl being the force in mode 1 and is equal to h / ( k l p l ) 1 / 2with constant and p~ being the reduced mass for mode 1. The value of Ql,2is calculated by using values of k, and p/ that are obtained from a b initio computations of the normal coordinates of p C6H4C12 and p-C&4C12. In order to evaluate (OOO~(~zU/~Q~)o~OOO), a van der Waals potential must be assumed in which one can calculate U(QI) explicitly. For this purpose we choose a 6-12 atom-atom pair potential, where the van der Waals potential is assumed to be the sum of the pair potentials between the rare gas atom and the individual atoms in the p-C6H4CI2moiety
In this model rXa represents the distance from the rare gas atom X to the a t h atom in the aromatic molecule. The principal value of the 6-12 form is that a potential can be calculated easily for any desired configuration of the atoms in the complex. The 6-12 potential has been used extensively for the calculation of model potentials of rare gas atoms bound to aromatic syst e m ~ Menapace . ~ ~ ~ and Bernstein have successfully applied 6-12 (29) Fung, K.H.; Selzle, H. L.; Schlag, E. W. 2.Naturforsch., A 1981,
36, 1338.
(30) Ondrechen, M. J.; Berkovitch-Yellin, Z.; Jortner, J. J . A m . Chem.
SOC.1981, 103, 6586.
(7)
Here E is the dissociation energy from the bottom of the potential well, p is the range parameter, a measure of the curvature of the potential near the minimum, and zo is the equilibrium van der Waals bond length. We obtain E, 0, and zo as adjustable parameters by fitting eq 7 to the results of calculations of U(QJ made by using eq 6.36 The final result obtained by Weber and Rice for the vibrational shift for excitation of non-totally-symmetric (in the point group of the van der Waals molecule) ring modes is
where p = ue/ode,with we the frequency of the Morse oscillator and usethe anharmonicity. We obtain (#t/aQ?)o by fitting ~ ( Q I ) to a Taylor series expansion in Q t 6 E(QJ = t(0)
+ L( 2 *)f2 aQ?
+
&(
$)f4
+ ...
(9)
The coefficients of odd powers of Q, are all zero by symmetry when Ql is non-totally-symmetric. C. Calculation of the van der Waals Potentials. To reiterate, the van der Waals potential is taken to be the sum over pairwise interactions of the rare gas atom, X, with each atom, a,in the p-dichlorobenzene molecule (eq 6). For the C-X and H-X interactions, the parameters Axa and r x 2 in eq 6 are the same as those used by Ondrechen et al. in their calculations of the van der Waals potentials of rare gas atoms bound to t e t r a ~ e n e .The ~~ (31) Even, U.; Amirav, A.; Leutwyler, S.;Ondrechen, M. J.; BerkovitchYellin, 2.;Jortner, J. Faraday Discuss. Chem. SOC.1981, 73, 153. (32) Babbitt, R. J.; Ho, C.-J.; Topp, M. R. J . Phys. Chem. 1988, 92, 2422. (33) Leutwyler, S.;Boesiger, J. Z . Phys. Chem. 1987, 154, 31. (34) Leutwyler, S.; Jortner, J . J . Phys. Chem. 1987, 91, 5558, and references contained therein. (35) Menapace, J. A,; Bernstein, E. R. J . Phys. Chem. 1987, 91, 2533. (36) Bevington, P.R. Data Reduction and Error Analysis for the Physical Sciences; McGraw-Hill: New York, 1969.
6608
The Journal of Physical Chemistry, Vol. 93, No. 18, 1989
Sands et al.
TABLE VIII: 6-12 and Morse Potential Parameters for p -Dichlorobenzene-X
Dissociation Energies and van der Waals Bond Lengths from EQ 6 p-C6H4CI2-Ar p-C6H&12-Kr p-C&C12-He De,cm-’ 565 677 148
A
zo,
3.42
3.50
2.92
Morse Parameters from Eq 7 p-C6HaC1,-Ar p-CnHdC1,-Kr p-CnHdCI,-He t,
cm-’
Lf
A-l
20,
A
we, cm-l w,xe, cm-l
-
v,A(calcd), cm-I z(exptl), cm-l
565 1.34 3.43 46.67 0.96 44.75 43
677 1.31 3.51 38.34 0.54 31.25 31
148 1.41 2.94 14.52 9.40 55.72
C-X interaction parameters were taken by Ondrechen et al. from the data of Crowell and Steele” on the heats of adsorption of rare gases on graphite. The H-X parameters used by Ondrechen et al. were obtained by using the combination rules
and H2-H2 data given in ref 38. The parameters for the Cl-X interactions were evaluated by using the combination rules as shown in eq 10 and CI2-CI2data given in ref 38. These parameters are listed in Table VII. In order to generate a potential for p-C6D4Cl2-He, He-C, He-H, and He-C1 parameters were needed. The He-H and He-CI parameters were obtained from eq 10 as described above. The parameters for He-C were obtained by first generating an estimate for Acc and rcco by use of the graphite adsorption data of Crowell and Steele3’ and the gas-phase data for Ar and Kr as given in ref 38 and the combination rules given in eq 10. A H ~ C and rHeCowere then calculated from eq 10 by use of the estimated values of Acc and rCCoand gas-phase data for He.38 The He parameters are also given in Table VII. The geometry of p-dichlorobenzene was taken as the optimimum geometry obtained from the HONDOS calculation (Table I). The sum in eq 6 is evaluated as a function of the distance of the rare gas atom X from the center of mass of thep-dichlorobenzene molecule along the C2axis perpendicular to the plane of the ring. The dissociation energies, De, and equilibrium van der Waals bond lengths, zo, so obtained are listed in Table VIII. The van der Waals bond length calculated for p-dichlorobenzene-Ar, 3.42 A, is within a few hundredths of an angstrom of those calculated for Ar complexes of benzene, s - t e t r a ~ i n e , ) ~ and tetracene30and is also similar to the experimentally determined bond lengths of Ar complexes of benzene,29 s-tetrazine,1° and pyrimidine.16 The bond dissociation energy, De = 565 cm-I, is much larger than the calculated De for benzene-Ar (393 or that measured for s-tetrazine-Ar.2v1i The difference between benzene and p-dichlorobenzene is, obviously, the substitution of two chlorine atoms for two protons. It is easy to imagine how the presence of CI atoms can increase the calculated binding energy without changing the van der Waals bond length; the substitution for the large value of A,
