5506
J. Phys. Chem. 1993,97, 5506-5518
Vibrations of SI(‘Bzu) pDifluorobenzene-d4. Sl-So Fluorescence Spectroscopy and ab Initio Calculations Harry J. Elston,+Emest R. Davidson, and Fred G. Todd Department of Chemistry, Indiana University, Bloomington, Indiana 47405
Charles S. Parmenter’ Joint Institute for Laboratory Astrophysics, University of Colorado, Boulder, Colorado 80309 Received: January 4, 1993; I n Final Form: March 10, 1993
The SI(1B2,)So(1A,) spectroscopy of p-difluorobenzene-d4 (CaD4F2, pDFB-d4) cooled in a supersonic free jet expansion has been characterized by fluorescence excitation (FE) and dispersed fluorescence. The 0; band lies at 36 987 f 1.0 cm-1 (vacuum). The FE band assignments have provided the values of 11 S1 fundamentals. The pattern of Franck-Condon allowed vibrational activity and of vibronically induced transitions is similar to that of pDFB-hd. An exception concerns the a8 mode v4 that is a prominent source of progressions in d4 on account of harmonic mode scrambling but inactive in h4. Bands involving an out-of-phase mode (US) that undergoes large frequency change in many aromatics upon formation of rare gas van der Waals complexes have anomalously large intensity when S1 overtones are excited but normal Franck-Condon intensity for SOovertones. This singular behavior occurs in both h4 and d4. Four Fermi resonances have been detected. A compilation of SIand SOfundamentals for both molecules identifies those cases where correlation between SIand SOmodes is provided by the Franck-Condon mapping of dispersed fluorescence. The vjllvjl’ ratios for such modes match closely in h4 and d4. This empirical correlation is also observed to hold in the frequencies calculated with ab initio theory. The correlation may be used to estimate (f5%) the values of all but six SId4 fundamentals that remain unobserved in the spectroscopy. Ab initio as well as semiempirical MOPAC calculations have predicted the structure, the vibrational frequencies, and the normal-mode coordinates in both states of both molecules. All predict pDFB to be planar with DZh symmetry in both states. The usual a b inifio scaling to replicate SO frequencies holds well (f5%)also for the S1frequencies. Several cases of mode mixing appear in comparisons of SIwith SOmotions and of h4 with d4 motions. Other modes are predicted to interchange identities upon electronic excitation. The discovery of this mode switching also reveals that one in-plane C-C stretching mode undergoes a 50% increase in frequency with electronic excitation.
Introduction As we recount below, the IAg-IB2,, (SI-&) spectroscopy of p-difluorobenzene@DFB) has been well explored in both mom temperatureand cold jet experiments. In addition to the intrinsic interest in the spectroscopy itself, the work has been motivated by the unusual accessibility of pDFB for study of collisional vibrational energy transfer,I4 of nonradiative transitions,5*6of intramolecularvibrational redistrib~tion,~-~l and of van der Waals complexes.12J3 These results have generated interest in the corresponding dynamics of perdeuterio-p-difluorobenzene(c6D4Fz), an isotopomer that we call pDFB-d4 or d4as opposed to h4. In support of these efforts, we present here a study of the SI& spectroscopy of pDFB-d4 vapor aided by computational explorationsof both h4 and d4. Our emphasis is directed toward understanding the dominant vibrational activity in the S I S o spectrum and in characterizing the SI level structure with particular interest in the relative vibrational characteristics of the isotopomers. We have used SI SOfluorescence excitation (FE) spectra of d4 in a cold jet to obtain SIvibrational level positions. Analysis of thedispersedsinglevibronic level (SVL) fluorescence produced by pumping FE bands secures the FE band assignments. Those assignments have led to the evaluation of 11 SIvibrational fundamentals. We show how SOand SIfundamentalsof h4 derived earlier can provide fairly reliable (f5%) estimates for many of
-
* To whom correspondence should be addressed. Permanent address: Department of Chemistry, Indiana University, Bloomington, IN 47405. Present address: Illinois Department of Nuclear Safety, 1301 Knotts St., Springfield, IL 62703. +
0022-3654/93/2091-5506$04.00/0
those d4 SI fundamentals not seen in our spectroscopy. The computationalexplorations reveal the correlations between modes in the two isotopomers as well as between the SI and SOstates. The calculationsalso uncover a surprisinglylarge (50%)increase in the frequency of an in-plane C-C stretching vibration that would have otherwise escaped detection even though the mode is seen in the h4 spectroscopy. The ~ B Z ~ - I(SI-S0) A ~ pDFB transition occurs by the allowed in-plane py transition moment (z axis coincident with the F-F axis, x axis out of plane14). Almost all of the spectroscopy involves pDFB-h4. Some of the early probes15J6 of the electronic spectroscopy provided SIrotational constants from 300 K 0; rotational band contour analyses that were consistent with retention of D2h symmetry in the SI state and with the IBZII-IAg electronic assignment. Three studies of the SI-& vibrational structure have been reported following Cooper’s17 first explorations. Coveleskie and Parmenterlsused 300 K SVL fluorescence spectroscopy to secure the general pattern of vibrational activity and to confirm and extend the assignments of SI fundamentals. Robey and Schlagl9 added considerably to the identification of SI fundamentals with their study of the two-photon transition. Most recently, Knight and Kable (KK)20have reported an SVL fluorescence study of the cold jet spectroscopy notable for its comprehensive coverage and careful analysis. We rely heavily on their work for our d4analysis. All of these studies are dependent on ground-state IR and Raman determination of So fundamentals. The most recent is the comprehensivevapor (and liquid) explorations of Zimmerman and Dunn21(ZD), who have provided a considered evaluation of all the SOfundamentals in both h4 and d4. 0 1993 American Chemical Society
Vibrations of SI(IB2") p-Difluorobenzene-d4
The Journal of Physical Chemistry, Vol. 97, No. 21, 1993 5507
ThepDFB-d4 electronic spectroscopy is by comparison sparse, there being a only a report by Childs, Dunn, and Francis of the low-temperature (4.2 K) fluorescence spectra of solid solutions of h4 and d4, a study that also includes the h4 phosphorescence spectrum.22 Unremarked by the authors, but unmistakable in their vibrational assignmentsof the S1 So fluorescence, is the prominent activity of a symmetric mode v4 in d4 that is totally inactive in the h4spectrum. As a preliminaryeffort to our present study, Davidson, Elston, and Parmenter23have confirmed this activity by observations of FE and of SVL fluorescence from d4 in a cold jet expansion. Their computational explorations of the pDFB vibrational characteristics suggest that the activity is a consequence of harmonic mode scrambling.
I
149 cm-l'
-
Experimental Detaib pDFB-d4 was obtained from Aldrich Chemical Co. (stated purity 98 atom % d4) and was used without further purification in a supersonic free jet expansion with argon as a carrier gas. The sample and argon were premixed by bubbling approximately 40 psi of argon through apDFB-d4 reservoir held at 0 OC, achieving a seed ratio of less than 0.1%. This samplegas mixture was then admittedto avacuumchamber via a commerciallyavailable pulsed nozzle of diameter D = 0.8 mm operating at a repetition rate of 10 Hz. The expansion chamber pressure was maintained at less than 5 X 10-4 Torr (nozzle operating) by a 6-in. diffusion pump. pDFB-d4 was excited in the collision-free region of the expansion, some 25-30 nozzle diameters downstream from the exit of the nozzle, by a Lambda Physik EMG2OlE excimer laser pumping a Lambda Physik FL2001 dye laser at 10 Hz. For output in the region 36 900-38 100 cm-I, Coumarin 540A dye was used in conjunction with a KDP doubling crystal (Lambda Physik Model FL30). For frequenciesgreater than 38 lOOcm-I, Coumarin 503 dye was used in conjunction with a KDP doubling crystal (Lambda Physik Model FL3 1). The excitation spectrum is not corrected for variations in laser power that occur over these frequency ranges. Total fluorescence was imaged withf/2 optics at right angles from the intersection of the laser and the molecular beam onto a 9813QA EM1 photomultiplier tube (PMT). A spatial filter was used to reduce scattered light. Single vibronic level fluorescence spectra were collected by dispersing fluorescence with a 1.7-m Czerny-Turner monochromator operated in the fourth order. SVL fluorescence spectra were normalized for pulse-to-pulse fluctuations in laser power by ratioing the signal collected from the monochromator to the signal obtained from the PMT used to collect total fluorescence. A R2079 Hamamatsu PMT operated at a gain of 1 X lo7was used to collect fluorescence from the monochromator. The photomultiplier was coupled to a home-built gated detection system that also controlled the timing. The data acquired by the gated detection system was then processed by an IBM PC for storage, manipulation, and display. With one exception, the spectral resolution for all dispersed fluorescence spectra is 10 cm-I. Dispersed fluorescence from the SIzero-point level was obtained with 3-cm-1 resolution. Wavenumber calibration for the monochromator was achieved with lines from a low-pressure mercury arc lamp and a He-Ne laser. The accuracy is f l cm-1 for the spectral range of interest. Results The 0; Band Position. The pDFB-d4 0; band maximum occurs at 36 987 f 1.O cm-I in a 5-10 K spectrum. We derive this value from a measurement of the d4 0; band position relative to that of h4. The data are shown in Figure 1 which contains a segment of the fluorescenceexcitation spectrum that encompasses the 0; bands of d4and of h4. The band maxima are separated by 149 f 1.0 cm-I, with the uncertainty generated principally by the combined effects of the dye laser scanning accuracy and the laser bandwidth. The h4 0; rotational origin is known from analysis of the 300 K band contourI5to occur at 36 837.9 f 0.2
36800
36900
37000
Excitation Frequency (cm-')
Figure 1. A segment of the fluorescenceexcitation spectrum showing the 0; bands of a pDFB-hd and pDFB-dd mixture. The relative intensity of the bands is not significant.
-
TABLE I: Assignments of SI So pDFB-4 Fluorescence Excitation Bands That H8ve Been Confirmed by Analysis of Dispersed Fluorescence Generated by -ping the Band obsd displacement' 0 238 307 377 406 542 62 1 714 753 778
assignt
obsd displacement
assignt
0; 30;
884 920
16: 26;27;
80' 27; 6: 26; 7:8b 6A8: 27;
95 1 1017 1087 1101 1187 1244 1550 1595
5;
814 6: 1639 823 4: & l cm-l from the 0; band at 36 987 cm-I.
7:
5;30: $8: 28: $6; 3: 5: 4:s; 4:
cm-l. Our d4 0;value cited above is obtained from the separation of the h4 and d4 band maxima relative to this h4 origin. Corrections from the separation of band maxima from the rotational origins at the low jet temperature probaly do not exceed the 1.0-cm-1 uncertainty of the band separation measurement. The rotational temperature of the jet spectrum was determined by modeling of the h4 0; band contour with the known rotational constants.lsJ6 The Fluorescence Excitation Spectrum. The fluorescence excitation spectrum is displayed in Figure 2 with displacements from the 0; band marked for many bands. The diaplacements are i 1 .Ocm-I. A small number of bands are from thepDFB-Ar van der Waals complex. Those with displacements277,793, and 1214 cm-I are the most visible examples. Such van der Waals bands almost invariably occur 30 cm-I to the red of the corresponding monomer band with about 5% of the monomer intensity.I2 On thescaleofthe presentationin Figure2,detectable van der Waals bands accompany only the most intense monomer bands. Fluorescence excitation assignments are listed in Table I. It includes only those assignments and observed band displacements that have been confirmed by analysis of dispersed fluoresence obtained by pumping the band in question. These bands involve 11 SImodes, and it is from these assignments that the SI fundamentals are obtained. Assignments of other bands in the fluorescence excitation spectrum can be inferred from these fundamentals. Fluorescence after Exciting the 0; Band. Figure 3 shows the dispersed fluorescence acquired by pumping the electronicorigin. Only the most intense bands appear at the displayed scale. The relative intensities are approximately correct. The 3-cm-I bandwidths are established by the spectrometer resolution.
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Elston et al.
The Journal of Physical Chemistry, Vol. 97, No. 21, 1993
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Excitation Frequency (cm-‘)
!Ag)fluorescence excitation spectrum of jet-cooledpDFB-d4. Displacements (in cm-I) from the 0; band are given above the spectrum. Band assignments confirmed by analysis of dispersed fluorescence generated by pumping the band are given in Table I. The relative band intensities are deceptive because the laser power rises continually during the scan to higher energy. It has increased from the 0; power by about 5 times near 0; + 1100 cm-I and 20 times near 0; + 1700 cm-I. In addition, the display of fluorescence intensity in the upper and lower segment has each been normalized to the largest band in the segment.
Figure 2. A segment of the SI -SO (]Bzu
+
Table I1 lists band displacements(f3 cm-I) from the 0; band with assignmentsand relative intensities. The displacementsare effectively SOvibrational level energies, and the assignments are based on ZD’s fundamentals or overtones. All displacements except five are within 4 cm-I of the values predicted with Z D s fundamentals with the harmonic assumption. The pattern of vibrational activity that emerges from the assignmentsis consistent with that seen in the SI-& fluorescenceexcitationspectrum and, with the exception of v4 activity, generally in accord with that of h4.2“
Our observation of 8: at 741 cm-1 differs from ZD’s harmonic prediction of 734 cm-1. The ZD prediction is derived from their observation of 82 = 734.1 cm-1 in electronic spectroscopyz4from which they use the harmonic assumption to derive V8” = 367 cm-I . Our observed value is close to ZD’s observation of a Raman vapor band at 738 cm-1 attributed to 82. The 29: band occurs with an 840-cm-I displacement whereas Z D s fundamental would predict 848 cm-1 in the harmonic approximation. The choice of alternative assignmentsis sparse, and noneis even marginally acceptable. Theassignmentis secured by ZD’s Raman observation of the vapor overtone 2~29”= 839 cm-I. The 7: band at 1526 cm-l has the largest deviation from ZD’s harmonic prediction. A much closer match would be obtained by the alternative assignment 24:, a vibronically-induced transition for which the calculated displacement is 1523 cm-I. The reasons for our seemingly unlikely assignment are set forth below in our presentation of assignments from SI levels involving Y,’. The two other bands with displacements differing substantially from ZD’s predictedvalues occur at 1713 and 1738 cm-1. With ZD’s harmonic frequencies, they would be assigned without problems as 13: and 4;, respectively. As described later, however, the terminating levels 1 3 2 and 42 appear stronglymixed, and more proper zero-order assignments interchange the order. Fluorescence after Exciting agModes. Of the six a, modes in pDFB-d4, only four have sufficient vibrational activity to allow explorationby SVL pumping, namely, v3, v4,v5, and V6. The most favorable Franck-Condon factors for reaching SIlevels contain-
ing these totally symmetric modes occur in the absorption bands
XA. The assignment of the SVLF spectra from levels XI are, with some exceptions, straightforward. They are based on the criteria used earlier for the h4 assignments.18,20For example, the strong bands in fluorescence from a symmetric level XI will contain activity only in a, modes. The progression XL is usually prominent and occurs with relative Franck-Condon intensities qualitatively consistent with those predicted from the analogous progression in the 0; spectrum. SVL fluorescence spectra after pumping the bands 3A, 5;. and 6; are shown in Figure 4. For comparison, they are aligned by their pump positions and are displayed with the 00 fluorescence spectrum. Assignments of progression members in the pumped mode are marked. Other assignments may be inferred by comparison with the 00 fluorescence spectrum. Two anomalies from the expected pattern of band intensities are apparent in the spectra of Figure 4. One occurs in the 31 spectrum where the 3;6: band (-446 cm-I) is almost missing. By comparison with the 0“ spectrum, we would expect its intensity to be about half that of the 3;5: (-794 cm-I) intensity. The second concerns the 5;8: band (-742 cm-I) occurring in 51 emission. Its relative intensity is anomalously large. The 4l dispersed fluorescence spectrum is displayed in Figure 5. As we have discussed elsewhere,23v4 is special in that it is active in the d4 molecule but not in h4. It is also special in that it is involved with Fermi resonances strong enough to generate extra bands visible even in survey fluorescence spectra. One occurs in the SI state as the Fermi resonance 41...162.Another occurs in the SOstate as 42...132. For these reasons, we display the 4l fluorescence spectrum separatelyfrom that of the other XI spectra. For later discussion of the Fermi resonances, it is displayed in comparison with spectra from 00 and 4151. Consistentwith expectationsof small Franck-Condon factors, activity involving v 1 and v2 has not been observed. Since the C-D stretch VI’’ = 2309 cm-I, the SIfrequency should be in the region 2100-2300 cm-I. Similarly, v i should be in the region 14001500 cm-I. SVL pumping of bands in these regions of the
Vibrations of
SI(~ B z Jp-Difluorobenzene-d4
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The Journal of Physical Chemistry, Vol. 97,No. 21, 1993 5509
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4:
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-2000
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43 6:
I
- 1600
- 1800
Displacement ( c m
4y5:
-1
I
I
I
I
- 1400
I
I
I
,
- 1200
)
Figure 3. A segment of the 00 pDFB-d4 fluorescence spectrum excited by pumping the 0; band at 36 987 cm-I marked with an asterisk. The scale shows displacement from the 0; position. With the exception of 0; band that contains scattered exciting light, intensities are approximately correct.
TABLE II: Band Positions, Assignments, and Relative Intensities in 00 Fluorescence from SIPDFB-d4 disdacement"
0 310 (+1) 406 (0) 445 (+1.3) 615 (-1) 741 (-7) 793 (0) 828 840 (+8) 865 (+2) 891 (+1.6) 1102 (+2) 1198 (+2) 1237 (+2)
assiint
0: 30: 27: 6: 267 8: 57 29: 4: 6: 5y30: 16: 5y67
intb
5.9 3.3 46 5.9 9.2 72 13 34 100 10 8.6 8.3 57
displacementa
1248 (+1.7) 1281 1313 (-0.2) 1526(+34) 1582 (+0.9) 1589 (-3) 1597 1657 (+2.9) 1692(+4) 1713 (+21) 1738 (-22) 2035 (-2.7) 2040 (+2.7)
assignt
37 476: 7; 477; 5: 4y5y 3:6y 4; 13:
intb 88 9.1 25 12 13 21 7.8 41 26 15 15 18 25
q A3 cm-' to lower energy from the pumped 0; band at 36 987 cm-I. Parenthetical numbers give the difference A = ZD - obs between values predicted from ZD's fundamentals (harmonic assumption) and observed. b Relative to that of 47 band.
fluorescence excitation spectrum has yielded no evidence for U I or u2 activity. Neither mode is active in h4. Fluorescence after Exciting a, Modes. Bands involving U S appear predominantly. The transitions 8; (in fluorescence excitation) and 8: (in 00 fluorescence) are examples. The fluorescence excitation assignment is secured by analysis of fluorescence obtained by pumping the 8; band at 0; + 307 cm-I. The assignment gives usr = 153cm-1 assuming harmonicbehavior. This mode has an unusually large-frequencyshift between the SI and SOstates (vgrr = 367 cm-I). A similar change occurs in h4. Fluorescence spectra from levels Xn where u, is an asymmetric mode have a distinct signature relative to spectra from levels involving symmetric modes. (i) The most intense band is always X:. (ii) This transition is always the first band of appreciable intensity to the red of the pump position. (iii) The vibrational structure to the red of the Xi band always replicates that of the 00 fluorescence spectrum. These characteristics hold for fluo-
rescence generated by pumping either Franck-Condon allowed bands such as Xi or vibronically induced bands such as %. A segment of the 82 fluorescence spectrum is shown in Figure 6. It is displayed with spectra from other Xnlevels to demonstrate these characteristics. All spectra have been aligned by their first intense band X,"to the red of the pump band. In turn, the set is aligned by this band with the 0; band of 00 fluorescence. The replicationofvibrationalstructureintheentireensembleofspectra is clearly seen. Such correspondence is sure evidence that the emission spectra are each from a level containingonly asymmetric modes. For each spectrum, the displacement of the X,"band from the pump band X: is nu,". Thus, reference to ZD's SO fundamentals usually secures the identity of uX. For 8* emission, the observed 8; fluorescence band displacement from the 8; pump is 744 cm-' compared with ZD's value 2vSfr= 2 X 376 = 734 cm-1 assuming harmonic behavior. In this case the correspondencecan be improved since ZDobservedirectly 2uS" = 738 cm-l in both the IR and the Raman vapor spectrum. Table I11 gives a listing of the observed vs calculated displacements of X,"bands from the X: pump band for all the spectra in Figure 6. The correspondence is generally good. Activity in the other a, mode, u7, occurs as the 7h8; fluorescence excitation band at 0; 621 cm-I. The dispersed fluorescence spectrum after pumping this band is shown in Figure 7. Since the assignment requires some discussion, we display the entirefirst 2800cm-1 of thespectrum. Thespectrumfitscriterion (iii) presented above for emission from a level containing only asymmetric vibrations. Thus, the dominant fluorescence band at 1134 cm-I from the pump position is presumably an X: transition from the pumped level Xn.Franck-Condon factors require that the pump transition occurs with Au = even, giving a transition Xi or, less likely, Xi. On this basis, then, the 1134-cm-I dispersed fluorescence interval corresponds to 2u/ or 4u," generated by the fluorescence transitions Xi or X :. None of the Sod4fundamentals matches, however, such an expectation. Consider next that the 0; 621 cm-l pump transition is of the type XA or q Y h , Both are Franck-Condon forbidden for asymmetric vibrations. They would necessarily derive intensity as vibronically induced transitions. For our purposes, they are conveniently described in terms of Condon deviation~25.~~ that are expressed as an expansion of the electronic transition moment
+
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Elston et al.
5510 The Journal of Physical Chemistry, Vol. 97, No. 21, 1993
2800
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2400
2200
2000
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1400
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Displacement f r o m Pump (cm
800
-1
600
400
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0
)
Figure 4. Segments of pDFB-dd dispersed fluorescence from the symmetric levels 6l, SI, and 3l excited by pumping the indicated XA transitions at the indicated displacements (cm-I) from the 0; band. The Oo fluorescence spectrum is included for comparison. The spectra are aligned by their pump bands. Except for the pump band (asterisk), the relative intensities within each spectrum are approximately correct. The intensities of the spectra are normalized to each other by their most intense band. The progression members XL have been assigned in each spectrum.
2000
1800
1600
1400
1200
1000
800
Displacement from Pump ( c m
600 -1
400
200
0
)
Figure 5. Segments of the SVL fluorescence spectra from the levels 00,41, and 4IS1.They are aligned by their pump positions marked with an asterisk. The displacement (cm-I) of the pump position from the 0; band is noted.
Me about the vibrational coordinate origins (QJO Me = Me(Q0)
E)
+ C(
0Qi
+
TT(s ) F Q j +
(1)
Symmetry restrictions associated with the totally symmetric partial derivatives constrain the vibrational activity. For the forbiddencomponents of the electronic transition moment based
on the fix or pz electric dipole operators, Qi or the product QiQj must be of symmetry b,, (for ccx) or bs, (for ccz) to match the symmetry of the respective Me components. These are the requirementsof ordinaryfirst- and second-order Herzberg-Teller transitions. For the allowed component of Me, based in pDFB on p,,, Qi or the product QiQ, must be totally symmetric. An absorption transition producing a strong Xi fluorescence band obtains intensity from the first-order term in eq 1. Thus,we search for a bl, or a b3, SOfundamental to match the 1 134-cm-' fluorescence interval. None occurs.
Vibrations of SI(IBzu)p-Difluorobenzene-d4
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The Journal of Physical Chemistry, Vol. 97, No. 21, 1993 5511
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P
2800 2600 2400 2200 2000 1800 1600 1400 1200 1000 800
600
400
200
0
Displacement from pump (cm-’)
Figure 7. Dispersed fluorescence after pumping the 7A8A fluorescence excitation band at 0; 621 cm-I. The displacement of the most intense Franck-Condon fluorescence band 718 from the pump position is 1134 cm-I. That band serves as the origin for progressions in v3, v4, v5, and V6. The displacements of those progression members from the 7181 origin are given in square brackets.
+
-744
cm-I, and 281291= 1155 cm-1. We list their harmonic values in order of increasing distance from the observed vi’ v/ = 1 134 cm-I. Any of these levels could be sufficiently perturbed from their harmonic energy positions to be viable possibilities. A clear choice emerges when we impose the additional requirement that v; + v ’ = 621 cm-I, the displacement of the XAYA pump band from 0,.8 When compared to v,” v,,” = 1 134 cm-I ,we see that the combined fundamentals must decrease about 55% upon electronic excitation. Such a large decrease is distinctive, and it would certainly occur also in the analogous vibrations of h4. Since the SIand SOfundamentals are known20 in h4, we can turn to the h4 (vi vy’)/(vi’ + v,,”) ratios for guidance. In the order of mode pairs used above, the observed ratios are 73, 101, 56, and 79%. By this view, only the pair v7 + V 8 is acceptable. Thus, the 0; + 621 cm-I transition in fluorescence excitation seems securely assigned as 7A8A. The assignment is supported by the observation that the 7A8: transition also occurs in h4 fluorescence excitation. In fact, the transition also serves as the origin for progressions in several nontotally symmetric modes in the light molecule. The 7i8: assignment allows determination of v7’. If we adopt the harmonic value vg’ = 153 cm-l as described above, we obtain v7‘ = 468 cm-I. Activity in v7 occurs also as the Franck-Condon allowed transition 7; in fluorescence excitation at 0; 951. The SVL fluorescencefrom pumping this band is shown in Figure 6 where the distinctive signature of emission from an asymmetric mode (or modes) is displayed. That mode, however, necessarily has an unusually large frequency shift in the SIstate. The observed X:or Xi fluorescence displacement of 1525 cm-l combines with the XA or Xi displacement of 951 cm-I in fluorescenceexcitation to give the ratio v,’/vX,, = 0.62. This value is close to the ratio v7‘/v7“ = 0.60 obtained from the 7h8A and 7:8: bands discussed above. The match of ratios suggests strongly that we are dealing with v7, particularly since the h4 experience20 shows that possibilities for such large frequency changes are limited to au modes. We see further that the calculated (harmonic) band positions are feasible. The FE band 7; is predicted to occur at 0; + 936 cm-1 (observed at 951 cm-I), and 7; fluorescence should lie at 7; - 1560 cm-1 (observed at 1525 cm-I). Admittedly, the comparisons require that the v7 overtones in both states have rather large and positive anharmonicities, but ironically this is further evidence for the v7 assignment. Both of these unusual vibrational characteristics are observed for v7 in h4 where several Av7 = 2 transitions also occur. In fact, KK have evaluated the large positive v7 h4 anharmonicity explicitly. By their method, we obtain an approximate v7’ anharmonic correction term 2-77 = +7.5 cm-l (d4) that is similar to their h4 value +9.5 cm-I.
+ +
2200 2000 1800 1600 1400 1200 1000 800
Displacement f r o m X:
600
400
200
0
(cm-’)
Figure 6. Segments of fluorescence spectra from levels XI or X2of asymmetric modes. The spectra are aligned by their X: fluorescence transitions. Those labeled XI occur from pumping the analogous Xh transition, and those labeled Xi are after pumping the Xi band. The displacement (cm-I) of the pump band from 0; is given to the right as a positive number. The observed displacement (cm-I) of the Xl or X: fluorescence band from the pump transition is given to the right as anegativenumber. At thebottom,theOOfluorescencespectnunisincluded with some assignments for comparison. Its 0; band is aligned with the X: transitions of the other spectra. Vertical lines at constant displacements illustrate the coincidence of bands in the spectra. The intensities of spectra are normalized by their X: bands. The relative band intensities within a spectrum are approximately correct. The 0; band is obscured by scattered light.
TABLE Ilk Observed Displacements in cm-l of Fluorescence Bands X: in the Fluorescence from Levels XmReached by Pum~ineX2 for Asymmetric Vibrations X: band displacements“ Pump transition obsd calcd 30;
310
8:
744
311 734
27;
412
406
26;
616
614
16;
1198
1200
7:
1525
1560
28;
1464
1462
“ Displacement from the pump transition. Calculated displacements use ZDs fundamentals with the harmonic assumption. The second-order term of eq 1 corresponds to pump transitions of the type XAYA that would produce a strong XtY f fluorescence band with the 1 1 34-cm-1 displacement from the pump. No possibilities for vi’ v,,” = 1 134 cm-1 occur within the symmetry constraints for either Herzberg-Teller component. On the other hand, four near matches occur for transitions using the allowed Me component where Qr and Qj must be of the same symmetry species. In terms of the SOenergy levels of XtY: fluorescence, they are 151171= 1138 cm-l, 211221= 1146 cm-I, 7181= 1147
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Elston et al.
5512 The Journal of Physical Chemistry, Vol. 97, No. 21, 19‘93
+
The alternative assignment 24; for the FE band 0; 951 cm-l is suggested by the close match of the calculated fluorescence displacement 241 = pump - 1523 cm-l with the 1525-cm-I observed value. While this b38 mode could be active in a vibronically induced transition, several points discourage the assignment despite the numerology. First, there is no V24 activity in the one-photon h4 spectroscopy. Second, as we shall show later, there is no indication in the various sets of calculatedpDFB2 4 a large frequency d4 frequencies (see below) that ~ ~ undergoes change in the excited state. Most compelling, however, is the observed20 ratio v2.,‘/v24’’ = 0.94 in h4. We will show later that the h4 and d4 u:/uX,, ratios match closely for every case where experimentalvalues are available. Adoption of the V24 assignment giving v24’/u2.,‘’ = 0.60 in d4 would be an unexplained exception to the pattern. FluorescenceInvolvingthe bl, Made us. No evidence for activity of this sole bl, mode has yet been found in the d4 electronic spectroscopy. The search for u9 bands in d4 is complicated by the near degeneracy of Z J ~ ” and v26” at 614 cm-I. The appearance of the diagnostic fluorescence bands with displacements from excitation of 614 cm-I (Xi transitions) or 2 X 614 cm-l (X: transitions) always involves the problem of disentangling the two possibilities. Pumping the fluorescence excitation band at 0; + 542 cm-I yields the fluorescence spectrum displayed in Figure 6. By the criteria above, the fluorescence is from a level involving only asymmetric modes. The first prominent fluorescence band X: has the 614-cm-I displacement of vgJJ or Y26”. Thus, the pump band is either 9; or 26;. The arguments below suggest that the band is solely the 26; transition, and we have so assigned it. Only the unlikely coincidence of a near degeneracy of u9 and v26 in borh the S I state and the So state would allow both to contribute to the intensity of the 0; 542 cm-I fluorescence excitation pump transition. The proposed fluorescence excitation transitions 9; and 26; would each be vibronically induced. 26; would occur with the in-plane transition moment (through the F atoms, via pz)or, in alternativelanguage, borrow its intensity by vibronic mixing of the SIstate with the B1, S2 state. Such transitions induced by AZJ= f l activity in b3gmodes (including 26; itself) are known in h4 and in other para-dihalogensubstituted benzenesa20 On the other hand, the 9; transition would occur necessarily with the out-of-plane transition moment px involving vibronic mixing with some unidentified B3,,electronic state. The strong mr* transitions of the aromatics occur with in-plane transition moments so that an induced out-of-plane transition strong enough to detect in our spectroscopy is unlikely. On this basis, we rule out u9 participation in the fluorescence excitation band. The transition 9; is unknown in the h4molecule. KK have given an extensive discussjon of vibronically induced transitions in pDFB-h4. Activity in u9 would occur more probably as the transitions 9; and 9;. Each has been identified in h418v20where the near degeneracy between u9“ and V26” does not occur. No transition with a secure 9; assignment has been found in the d4fluorescence excitation spectrum. The assignments 9; and 26; are indistinguishable in the d4 Oo SVL fluorescence spectrum. Activity in blu Modes. Of the five bl, modes, only ~ ~ appears 1 3 in the d4 electronic spectroscopy. A band with the nominal assignment 13; occurs in Oo fluorescence (Figure 3), and bands containing a 13; component appear in fluorescence from 4l and 4IS1(Figure 5). Wediscusslater theevidence for a strong 132...42 Fermi resonance that provides intensity to ~ ~transitions 1 3 that are intrinsically weak on account of a small 13; Franck-Condon factor. We have not found a band involving ~ ~ 1 in 3 ’ the fluorescence excitation spectrum. Activity in bza and bzu Modes. Although all three b2 modes should be of sufficiently low frequency to appear as X,B transitions in the first 1500cm-1of the fluorescenceexcitation spectrum,
+
only V I 6 activity has been identified. It occurs as the transition 16; at 0; 884 cm-1. The 162 fluorescencespectrum is displayed in Figure 6, where its structure and the X: displacement secures the fluorescence excitation assignment. None of the five b2, vibrations has been observed, either as Av = 2 transitions or in combination with other vibrations. Activity in ba Modes. Two of the five b3,vibrations are observed in fluorescence excitation as one-quantum vibronically induced transitions. As with the case of v26 discussed previously in connection with vg, these first-order Herzberg-Teller transitions state with the obtain intensity by vibronic mixing of the lB2, (SI) lBl, (S2) state. While induced transitions are needed to reach the levels XI, the subsequent fluorescence will be dominated by allowed transitions. Franck-Condon factors usually require that all fluorescence transitions of appreciable intensity contain the component Xi,just as the Xi transition component occurs in emission from X2 levels. Thus, XI emission from levels reached by forbidden transitions have the same emission signatures as that for X*emission discussed above. Figure 6 contains emission spectra from the two vibronically active b3gmodes, produced by exciting the 26; and 27; fluorescence bands. As discussed above, attribution of the 26; assignment involved some argument. The other assignment, however, is straightforward. Note that 27; at 0; 377 cm-’ in fluorescence excitation is just 31 cm-*to the red of 6; at 0; 406 cm-1. The displacement is close to that expected for the 6; band of thepDFB-d4-Ar van der Waals complex.I2 The +277-cm-I band is, however, too intense for a van der Waals attribution. More specifically, the appearance of the fluorescence spectrum shows with certainty that the band is 27; of the free aromatic. Allowed Franck-Condon activity has been confirmed for V27 appearing as 27; in the fluorescence excitation spectrum. The 27; band intensity is anomalously large, suggesting a 272...51 Fermi resonance. The 26; transition would occur at the same displacement of the $8; band in fluorescence excitation, but no evidence for 26; absorption appears in the SVL fluorescence. The 24; band would occur near 0; 1902 cm-l in fluorescence excitation, nearly coincident with an observed band, but the assignment has not been checked by SVL fluorescence. Activity in bL Modes. Bands involving even quantum changes occur for all three b3,, modes. The band 29; is prominent in Oo fluorescence and is a component of bands in the fluorescence from many levels. Its intensity in these fluorescence transitions is anomalously large. We propose in a later section that agroundstate Fermi resonance is responsible. The analogous 29; band, expected to be weak in fluorescenceexcitation,has not been found. In contrast, both v2Bl and ~3o’occurin the fluorescenceexcitation spectrum as the transitions 28; and 30;. The fluorescence spectra from pumping these bands are included in Figure 6 where the signatures are unmistakable. The transition 30; is extremely weak in 00 fluorescence, and 28: is undetectable. Progressions in Totally Symmetric Modes. The ag modes u3, v4, u5, and V6 each appear in fluorescence progressions of the type Yx or Y:. The progressions occur from origins Y: or YA or are built on other origins that give the progressions X,” Yx where vx is a nontotally symmetric mode. The relative intensities of progression members can be obtained reliably from the SVL fluorescence spectra. Some intensities of Y, O type progressions are shown in Figures 8-1 1. Figure 8 displays the 3: intensities. Those of the 3; and 3: members can be measured directly from the Oo fluorescence spectrum. The 3: member is, however, actually the 0 : band and is obscured by scattered exciting light. We have obtained the relative intensity of that member by measurement of 5; and $3: band intensities that should be in the same ratio as 3; and
+
+
+
+
Vibrations of SI (lBzu)p-Difluorobenzene-d4
The Journal of Physical Chemistry, Vol. 97,No. 21, I993 5513
1 .o
0.8
.-+-
I
I
Progressions in 6:
I
Progressions in 3:
26,
(0
c a
&
c
-
0 7 T
0.6
0 C
.o +
dlI
I 1
0.4
0 0
0.50
i
G
0.2
i
.
V 27:
30
1 I
0.0 0
2
1
Figure 11. Observed and calculated relative intensities for the 6; progression members. The layout is as in Figure 9.
n Figure 8. Observed and calculated (bars) relative intensities for 3; progression members observed in the Oo fluorescence spectrum. The sum of intensities, observed or calculated, is normalized to unity. Calculated intensities were made with 6 = 1.00 and D = 0.85. Progressions in 4:
0 0; 26:
V 27,
+l
30:
0Colt 6 = 1 03 0=1 0
0
1
2
Figure 9. Observed and calculated relative intensities for the 4; progression members. Those marked 30; or 8:, etc., are X:4; band intensities taken from the Xnfluorescence spectrum. 6 and D give the Parameters used for the calculated intensities. The layout is as in Figure 8. 100
Progressions in 5 :
0 75
0 50
0 25
6 = 1 01 D=O 8
0 00
r $ 7 2
Figure 10. Observed and calculated relative intensities for the 5; progression members. The layout is as in Figure 9.
3:. The measured 5'30 intensity is normalized to the 3; intensity, and the resulting 54 ktensity is reported as 3:. The Y: progression intensities for u4, us, and vg are obtained similarly except that the X:Yy band is not entangled with others. In fact, the opposite problem occurs for the 4: and the X:4: bands. The terminating level 42 or Xn42 is in strong Fermi resonance with a Franck-Condon dark state so that the intrinsic X:4: band intensity is spread over two neighboring and separately resolved bands. They are the bands with nominal assignments 4: and 13: in the Oo fluorescence spectrum. These intensities have been summed for the measurements reported in
Figure 9. For common reporting of all measurements, the sum of observed intensities in each progression has been normalized to unity.
Discussion The Vibrational Fundamentalsof pDFB. Our SI-& spectroscopy has led to the determination of 11 SIfundamentals in d4. They are listed in Table IV together with a tabulation from the best values of fundamentals for the SOstate of both molecules and the SI state of h4. None is corrected for anharmonicities. All 30 SOfundamentals are known for both molecules, and 24 SIfundamentals have been reported for h4. We propose below a method to obtain estimates of d4 SIfundamentals for which a corresponding h4 value is known. If the reliability of the estimates is accepted, the determination of pDFB fundamentals is almost complete in both states of both molecules. Only six SIfundamentals of each molecule remain to be obtained. The SO values of both molecules are, with the few noted exceptions, taken directly from ZD's considered determinations using their IR and Raman vapor spectra. Their mode labeling for each molecule is in order of decreasing frequency within a symmetry ~ 1 a s s . lAs ~ ZD advise, this labeling alone must not be used to infer correlation between the hq and d4 nuclear motions. The SI h4 values in Table IV are taken without change from KKs listing. Correlation between SIand So modes is often difficult to achieve for reasons quite apart from changes in the nuclear motions upon electronic excitation. With dispersed SVL fluorescence, however, the Franck-Condon mapping of the SI potential energy surface upon that of the SOstate often provides secure connections. As noted by our footnotes to Table IV, the labeling of 15 SIfundamentals has been established by this technique. The remaining nine values are obtained from onephoton20or t w o - p h ~ t o nS~I~S Ospectroscopy without benefit of the SVL fluorescence mapping. We have presented these values in square brackets not to impugn the assignment but to signal that consideredjudgement about a labeling correlationis required if it becomes an issue of importance. The SI d4 values are all from this work, and all are correlated with the SOd4 labeling by SVL fluorescence. We have taken care tonote whichvaluescomefromobservationof theSI fundamental as opposed to those derived with the harmonic assumption from overtone or combination levels. An experimental correlation between h4 and d4 modes is provided by the ratio u,'/uP in the two molecules. One expects matching ratios in h4 and d4 if the vibrational motions are similar, provided that a perturbation peculiar to one isotopomer is not present. The u[/u," ratios for those modes whose SIvs SOcorrelations are establishedby dispersed SVL fluorescence are listed in Table IV. The ratios in d4 faithfully track the h4 ratios even though the values among different modes span a large range, 0.42-1 .O.
Elston et al.
5514 The Journal of Physical Chemistry, Vol. 97, No. 21, 1993
TABLE I V ExDerimentallv Determined Vibrational Fundamentals (cm-l) in the SOand SIStates of pDFB-h and DDFB-L
1(2)
3088
2309
1615 1595 1257.3 1249.7 1251l.S 3(74 866.9 [ 11161' 4 ( 9 4 1140 858.6 793.0 81@ 5 (1) 449.8 446.3 41wg 6 (6a) 780 583f 7 (17a) 945 8 (16a) 421.5' 367 1759 614 [588]' 9 (loa) 800 2276 10 (20a) 3073 1440 [1335]' 11 (19a) 1514 12 (13) 1228 1129 [1015]' 937g 13 (18a) 1014 858 14 (12) 740 685 [666]' 928 780 67W 15 (5) 692 600 5288 16 (4) 2748 17 (lob) 374 358 2307 18 (2Ob) 3073 2(84
19 (19b) 20 (14) 21 (15) 22 (18b)
23 (7b) 24 (8b) 25 (9b) 26 (6b)
27 (3) 28 (11) 29 (16b) 30 (17b)
1633 1306 1085
348 3085 1617 1285 635 446' 838
1244h 0.99 1.00 823h 0.98 0.95
778h 0.95 0.98
406h 0.91 0.91
468i 0.62 0.60 153k 0.42 0.42
442k 0.76 0.74
1328 1286 802
[1591]' [ 1 1001' 343.5 352g
2304 1523
[1516]'
1008
[933?]'
614
5588
(4061 73 1
403g 6198 43w 12W
542h 0.88 0.88 377h 0.90 0.93 549k 0.74 0.72
505 424 157.5 155.5 1 19k 0.76 0.77 a Mulliken axis convention (ref 14) with x axis out-of-planeand z axis coincident with the F-F axis. The Mulliken convention(ref 14) is used for SOmode labeling. The labeling in parentheses is by analogy with benzene using Wilson's benzene labeling (Wilson, E. B., Jr. Phys. Rev. 1934,45,706). The SI labeling is correlated with the SOlabeling for the respective isotopomer where possible. See text. All except three are as listed by Zimmerman and Dunn (ZD, ref 21) from their vapor-phase IR and Raman observations. The Vz7 (d4) value is derived by ZD from their unpublished electronic spectra. The YE (h4) and Y27 (h4) values differ from those listed by ZD. Values as listed by Knight and Kable (ref 20). Our brackets indicate modes for which correlation with the SOmode by SVLF spectroscopyhas not been made. e This work. All are correlated with the SOmode by SVLF spectroscopy./Correlated with the SOmode by SVLFspectroscopy. Coveleskieand Parameter (ref 18). 9 Correlated with the SOmode by SVLF spectroscopy. Knight and Kable (ref 20). This work, &1 cm-I, from direct observation of the SIfundamental. From SlSo spectroscopy,Knight and Kable (ref 20). J This work, from observation of an SI combination level. This work, from observation of the SIovertone, f l cm-l, with the harmonic assumption. From twophoton S l S o spectroscopy, Robey and Schlag (ref 19). The correspondence of v,'/v/' ratios suggests a method to estimate missing SI fundamentals in d4. One simply scales the d4 So fundamental by the v,'/v/' ratio observed in h4. By this method, 13 additional SId4 fundamentals can be obtained. The estimates should be within 5% of the actual values, judging from the agreement between known h4 and d4 ratios. Of course, misassignment of an SIh4 mode or a substantial change in nuclear motion in the isotopomer may introduce a larger error. Computational Explorationof pDFB Vibrations. Theoretical calculations of the equilibrium structure and frequencies of SO and SI of both molecules were done using MOPAC 6.OZ7 and GAUSSIAN9228for SI;the MOPAC parameters EXCITE, NOANCI, FORCE, GRADIENT, and PRECISE were used to obtain the optimized structure and frequencies for a wave€unction with one electron excited from b2, to a, to give a restricted open shell Hartree-Fock approximation to the first IB2, state. (The r MOs of D2h pDFB are b3u,bl,, bz,, a,, b3,, and b3, in order of increasing energy with the first three fully occupied in SO.)In the GAUSSIAN calculation, the 6-31G* basis was used, and the optimized structure and frequencies were determined for the
SoSCF
1.378 1.385 1.073 1.331 122 119 120
SOME2
1.390 1.396 1.085 1.357 122 119 120
SoMOPAC
1.422 1.402 1.097 1.296 120 120 120
s, SCI
1.410 1.410 1.071 1.315 125 118 120
SlMOPAC
1.449 1.382 1.089 1.319 123 119 120
Figure 12. Optimized structuresof and SIpDFB at various levels of theory. Bond lengths are in angstroms and bond angles in degrees.
HartreeFock (SCF) and second-order Moller-Plesset perturbation theory (MP2) energies of SO.The structure and frequencies for SIwere found from a calculation using all singly excited configurations (SCI). This gave a wave function containing large components of both b2, to a, and bl, to b3,. Since the possibility of a non-Dzh structure for SIpDFB has been a recurring t o p i ~ , ~ J the ~ - results ~ ~ , ~of~our - ~calculations ~ on the& structureareofparticular interest. They aresummarized in Figure 12. There is no hint in these calculations of lowered symmetry or nonplanarity in either SOor SIpDFB. All structures were optimized with planar D2h symmetry imposed. The resulting frequencies were all real, indicating that the resulting structures were true minima. The large decrease in V8 between SOand SIindicates a substantial decrease in the S1 force constant for out-of-plane ring distortion. The bond lengths for SIin the MOPAC calculation changed, compared with those for SO,in the direction predicted for removing an electron from an orbital that was CI-C2bonding and C& antibonding. The C-C bond lengths for SIin the SCI calculation remained nearly equal in accord with the two-configuration nature of the wave function. For benzene these two configurations enter with equal weight in the SI state (IB2" in &A), and this benzene state is generally believed to retain D6h symmetry. The calculated vibrational frequencies are given in Table V where they are in every case listed in order of decreasing value within each symmetry. The entries are actually we values for vibrational energies expressed as wo = we(u + I/*) - wdx,(U + l/2) z.... The observed fundamentals in Table IV are v = w1 - wo
-
we.
Geometric mean scaling factors based on the ratio of observed v to SCF SOand SCI SIcalculated we frequencies were separately determined. Both were 0.90. All SCF and SCI values in Table V have been scaled by this factor. A scaling factor of this magnitude is well-established for SCF frequencies and is known to give good agreement with experiment in many molecules. This scaling procedure has not been documentedfor SCI but is expected to apply since SCI produces a similar uncorrected quality wave function. The MP2 frequenciesdo not follow such a simple scaling relation. The lower MP2 frequencies we are generally already in good agreement with experimental v values, but the higher ones are about 5% too high. Part of this difference is certainly due to anharmonicity rather than an error in we. The error in MOPAC frequencies is not systematic. The larger frequencies are too large, indicating that MOPAC overestimates the energy required to stretch a C-H bond. Some of the lower frequencies, on the other hand, are too low so the semiempirical MOPAC frequencies cannot be systematically improved by scaling.
Vibrations of SI (IBz,,)p-Difluorobenzene-d4
The Journal of Physical Chemistry, Vol. 97, No. 21, 1993 5515
TABLE V Cltlcuhted Vibrational Frequencies for So, h4 mode a.
1 2 3 4
5 a, bl, bl,
bZg b2”
b3*
b3”
6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
and SIpDFB-4 md pDFB-4 So, d4 SI,h4
2533 1820 1664 965 894 430 842 315 645 2512 1718 1229 856 748 880 548 218 2528 1659 1462 885 404 2502 1048 689 504 439 738 396 42
d4 0.97 1.00 0.97 0.98 0.93 0.63 0.28 0.59 1.01 0.96 1.00 0.99 0.97 0.76 0.76 0.70 1.01 1.26 1.13 0.98 1.02 1.00 0.81 0.98 0.87 0.92 0.83 0.88 0.76
+ 50% other excitations, single excitation CI, scaled by 0.9.
MOP
expt
SCF“
MP2b
MOP
expt
SCIc
MOP
3070 1646 1264 1134 842 440 975 428 828 3056 1530 1229 1000 725 950 691 378 3070 1416 1148 1054 338 3058 1630 1281 629 436 857 517 162
3270 1692 1314 1189 878 455 881 417 796 3257 1577 1262 1042 754 848 507 363 3270 1483 1449 1130 347 3259 1685 1319 648 442 810 501 160
3417 1824 1644 1271 1013 462 1035 370 910 3406 1791 1424 1100 817 1039 680 352 3414 1528 1159 1138 398 3406 1671 1358 654 514 925 563 140
3088 1615 1257 1140 859 450 945 422 800 3073 1514 1228 1014 740 928 692 374 3073 1633 1306 1085 348 3085 1617 1285 635 446 838 505 158
2276 1617 1252 850 786 437 787 376 644 2258 1456 1134 844 674 803 605 365 2277 1337 1127 790 334 2263 1601 1004 609 406 743 435 160
2424 1667 1301 888 819 452 696 373 619 2405 1501 1163 88 1 701 620 507 354 2424 1467 1390 827 343 2409 1659 1032 628 412 695 425 158
2525 1820 1633 990 899 460 868 313 709 2507 1783 1302 883 778 913 600 326 2519 1475 1175 885 394 2505 1661 1053 632 486 803 479 137
2309 1595 1250 867 793 446 780 367 614 2276 1440 1129 858 685 780 600 358 2307 1328 1286 802 343 2304 1523 1008 614 406 731 424 155
3096 1594 1265 1112 821 407 583 128 483 3083 1463 1235 962 711 707 526 270 3092 1679 1360 1041 347 3071 1364 1209 552 397 689 473 123
3426 1824 1678 1260 989 433 1011 369 832 3415 1722 1398 1021 789 1022 613 235 3424 1663 1515 1215 407 3411 1354 707 535 442 883 440 43
MOPAC frequenciesare not in sufficiently good agreement with experiment to serve as a reliable guide to spectral assignments. The scaled SCF SO frequencies for h4 are within 3% of experimentalvalues except for modes 19 and 20, which are 20% less than the observed fundamentals. Using exactly the same force field with masses appropriate for d4 gave similar accuracy except for mode 20, which is low by about 10%. The scaled SCI SIfrequencies are of similar accuracy. The worst case seems to be mode 8, which is computed to be 50 cm-I (30%) lower than the observed frequency. This mode has been reported to have a negative force constant at a lower level of theory.29 All levels of ab initio theory tend to underestimate this force constant. The general agreement between our scaled ab initio results and the experimentalfrequencies indicates that this level of theory should be a reliable aid to further spectral assignments. The correspondence of normal modes from state-testate and between isotopomers is a persistent question addressed perhaps most satisfactorily by computation. Do the normal modes, listed in Table V by decreasing frequency within each symmetry, correspond across the table? We explored this question by computing the overlap of the normal-mode vectors. The details of the procedure are set forth elsewhere.23 The comparisons are made with the SCF calculations for SO and theSCIcalculationsfor SI. Examinationofthevector overlap shows that the correspondence among modes across the table is generally good, with some notable exceptions involving in-plane modes. The mixing of aBmodes 4 and 5 has been discussed bef0re.~3 We find the b2,, modes 19, 20, and 21 involved with mixing and also the b3g modes 24 and 25. The display in Figure 13 summarizesthe mixings. The correlations between SOand SI modes of a given isotopomer are analogous to the spectroscopic problem known as Duschinsky mixing.23 The correlation between h4 and d4 in the SOstate and in the SIstate are examples of harmonic mode scrambling.23 We finally turn to the d / d ’ ratios in Table V. The empirical correlation of hq and d4 ratios seen with the experimental
2295 1562 1254 826 773 404 496 106 378 2276 1391 1125 832 655 607 459 257 2289 1679 1270 777 342 2267 1296 982 531 374 617 383 122
d/J’ ?.
1.01
MOP
SCF scaled by 0.9. MP2 not scaled. SCI = 0.62 (bZg-, au) + 0.33(blg+ b3,)
SI,d4 MOP
1.01 0.97 1.00 0.98 0.98 0.93 0.60 0.30 0.58 1.01 0.96 1.00 0.96 0.98 0.74 0.76 0.71 1.01 1.19 1.18 0.99 1.03 1.00 0.84 0.94 0.88 0.91 0.80 0.91 0.76
MP26
= MOPAC EXCITED for SI.e v’ of SCI for SI,v” of SCF for SO.
SCIc
h4
SCF“
expt
1251 11161 818 410 583 175 [588] 13351 10151 937 [666] 670 528 274 15911 11001 35215161 [933] 558 403 619 438 120
zz: 21
21
expt
1244 823 778 406 468 153
442
542 377 549 119
:‘a
....'...
1713
0.66142>+0.7511 32> 1737
1726.5
-
1723.5
14~>
CALCULATED
1132> ,,'
Acknowledgment. The JILA Visiting Fellowship (C.S.P.) that has been so helpful with this work is deeply appreciated, as is financial support from the National Science Foundation and the NATO Collaborative Research Grants Program, Grant SA.52-05 (RG.0215/89). We thank Mr. Brian D. Gilbert and Dr. Christopher J. Purse11 for helpful interactions.
References and Notes
I.,
1713 0 75142>-0 66)132>
Figure 14. Schematic illustrations of the 42...132 Fermi resonance in pDFB-d.+ The Fermi resonance is revealed by a pair of bands at
-
displacements 1713 and 1737 cm-I in fluorescence from each of three levels Oo, 4I,and 4 ' 5 ' . The top schematic labeled "harmonic" shows the observed level energies in cm-I (right) relative to the zero-order 42 and 132 energies (left) calculated from ZDs fundamentals using the harmonic approximation. The schematic labeled 'calculated" shows the level energies and level descriptions obtained by using the twdevel perturbation theory treatment of the Fermi resonance.
4I and in 4I5l emission. In both cases, the band at smaller displacementarising presumably from transitionsto the perturbed level 132 has the larger intensity. This situation is impossible if thedark Franckxondon level 132acquiresintensity from mixing with 42. A perturbed dark state (1 32) band intensity could never ex& the intensity of a band terminating in a perturbed light state (42). Thus, we are forced to adopt one of two possibilities. (i) The order of the zero-order positions in SId4 are interchanged from the harmonic predictions so that 42 lies below 1 32. (ii) The dark level interacting with 42 is misassigned. The second alternativeseems improbable. A search using ZD's fundamentals reveals no overtones other than 132close enough to the nominal 42 position for strong interaction. Interaction with a combination level XIYis subject to symmetry constraints that require v, and v, to occur within the same symmetry species. With this limitation, theclosest possibility is 191221at 1671 cm-I, some 63 cm-' below the nominal q2 position. In addition to its remote location, recall that we seek a level above 42. A massive perturbation from interactions other than with 42would be required to make this level a plausible contender. By default, we conclude that the 132...42 level interaction has been correctly assigned and therefore that the zero-order positions must be inverted from the harmonic values to place 42below 132. On this basis, a standard two-level Fermi resonance treatment can be used to describe the interaction. For the calculation, we haveused the band intensity ratioZ(1713 cm-I)/1(1738 cm-1) = 1.3 (an average of the observed ratios listed in Table VII), and we have acknowledged that the 13: Franck-Condon factor is effectively zero so that we are dealing with interaction between a "dark" and a "light" state. The resulting description of the 42...132 Fermi resonance is given in Figure 14. It is a strong interaction between close-lying zero-order levels. The calculated interaction matrix element W 12 cm-I. The zero-order level separation is only 3 cm-l as opposed to the 18 cm-I harmonic separation calculated from the fundamentals. The level mixing coefficients correspondto almost equal mixing, 44% of one level and 56% of the other. Two additional ground-state Fermi resonances are suggested by the anomalously large intensities of bands in Oo fluorescence.
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Elston et al.
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