8302
J . Phys. Chem. 1994,98, 8302-8309
The 198-225-nm Transition of Norbornadiene Xing Xing, Aharon Gedanken,? Abdol-Hakim Sheybani,* and Ruth McDiarmid’ Laboratory of Chemical Physics, National Institute of Diabetes and Digestive and Kidney Diseases, National Institutes of Health, Bethesda, Maryland 20892-0510 Received: March 1, 1994; In Final Form: June 6,1994’
An optical and two-photon resonant multiphoton ionization and photoacoustic spectroscopic investigation of the second transition region of norbornadiene was conducted on static and jet-cooled samples. Transitions to both the 3s Rydberg and the NV2 valence states were observed. The substructure of the 3s Rydberg % transition was deduced to arise from fundamentals, overtones, and combinations of ai, u4, Vg, v10, and v12 and overtones and combinations of a2, V I S ,and v20 vibrational modes. Displacements from the ground-state equilibrium geometry were determined for the a1 modes. The 3s Rydberg state was shown to decay rapidly to the higher energy NV2 valence state via the u20 vibrational mode when energetically possible. The diffuse substructure of the NV2 transition was deduced to arise from v7, a n ethylenic CH bending mode. Comparisons were made between results obtained here and those observed for similar molecules, observed for other states of this molecule, and calculated for these states of norbornadiene.
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I. Introduction Norbornadiene (NB), bicyclo[2.2.1] hepta-2,5-diene, is a strained, nonplanar, formally unconjugated molecule. It is the prototype for through-space A interaction.’ The lowest excited state of the molecule is Az; hence, an optical transition to this state is symmetry-forbidden, When excited to this state, norbornadiene undergoes rapid cycloaddition to quadricyclene.* Because of the simplicity and efficiency of this reaction, norbornadiene has been proposed as a potential energy storage system.’ The low-resolution electron energy loss spectrum of this transition shows no substructure: in accord with the above description of the photophysics of the lowest excited state of norbornadiene. The second “transition” of norbornadiene is composed of many narrow bands superimposed on a broadly structured backgro~nd.~ This spectral region has been shown, by variable parameter electron energy loss spectroscopy4 and by environment-perturbation optical absorption spectroscopy,s to be composed of two different transitions: the narrow bands constitute a Rydberg transition, and the broadly structured background constitute a valence transition. The excited Rydberg state is the B, 3s Rydberg state. The excited valence state is presumably one of the B2 A A* states of the molecule. (The electronic-state manifold of norbornadiene is fully discussed in ref 6. In brief, the formally unconjugated A orbitals of the molecule combine to give four valence A molecular orbitals. The lowest two valence orbitals are populated in the ground electronic state. Transitions from populated to vacant valence orbitals are designated NV1, NV2, etc., in order of increasing energy. In addition, there are transitions from the occupied molecular orbitals to large radius, atomlike orbitals called Rydberg orbitals.) This interpretation of the experimental spectrum is supported by a high-level ab initio calculation6 although, because of results obtained in a limited calculation, the two-transition interpretation of this spectral region has been q~estioned.~ The main vibrational progression of the structured component of the second “transition” of norbornadiene has been suggested to be a progression in the lowest frequency a1 “wing-flapping” mode of norbornadiene.5 (This is u12, a skeletal deformation in which the two ethylenic halves of the molecule move apart.) The
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t On leave from Department of Chemistry, Bar-Ilan University, RamatGan, Israel. f On leave from Department of Chemistry, Shiraz University, Shiraz, Iran. Abstract published in Aduance ACS Absrracts, August 1, 1994.
origin of the progression is unknown. The upper-state frequencies and displacements of the ”wing-flapping” and other FranckCondon-active modes of norbornadiene have been calculated for transitions from the ground to the lowest energy A2 and BI states in a limited (CIS/6-31+G) ab initiocal~ulation.~ Thecalculated frequency of the “wing-flapping” mode in the lowest B1 state of norbornadiene is in reasonable agreement with the observed, but as the origin of the experimental system is uncertain, the displacement prediction has not been confirmed. No other upperstate vibrational frequencies have been reported or assigned. This investigation was conducted to determine the frequencies, displacements, and photodynamics of the two states excited in the region of the second Utransition“of norbornadiene. Optical absorption, resonant multiphoton ionization (REMPI), and photoacoustic (PA) spectroscopic measurements were made on static and jet-cooled samples. The existence of two independent states in this region of the spectrum of norbornadiene was, of course, confirmed. The transition origin and the frequencies and displacements of four a l vibrational modes and the frequencies of two a2 modes in the 3s Rydberg state and the transition origin and frequency and displacement of one a l mode in the second valence-excited state of norbornadiene were identified. The excess energy-dependent lifetime of the 3s Rydberg state and of the second valence-excited states of norbornadiene were estimated, and the opening of a second decay channel for the 3s Rydberg state and the coupling mechanism to this channel were observed and analyzed. These results will be discussed in conjugation with an assessment of the theoretical predictions for these states and for the first valence-excited state of norbornadiene. 11. Experimental Part
The experimental methods have been described previously in detail.* Briefly, the optical spectrum of room temperature, gasphase samples of norbornadiene were measured with a Cary 15 spectrophotometer with a resolution of approximately 10 cm-1. This is smaller than the observed bandwidths. The sample pressures in the 10-cm cell were between 0.1 Torr and full vapor pressure, 22 Torr. One set of REMPI measurements was made on a conventional supersonic molecular beam coupled with a time-of-flight (TOF) mass spectrometer. The molecular beam was obtained by expanding 3 atm of Ar seeded with 10-20 Torr of norbornadiene through a pulsed 500-gm nozzle (Newport BV-100) into a chamber pumped by two turbomolecular pumps (Alcatel 5150
This article not subject to U S . Copyright. Published 1994 by the American Chemical Society
The 198-225-nm Transition of Norbornadiene
Ill ' I ' '
The Journal of Physical Chemistry, Vol. 98, No. 34, 1994 8303 '
'
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'
I
L
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49060
47520 45180 44740 FREQUENCY (cm-1)
43300
Figure 1. Optical absorption spectrum of 0.2-Torr room temperature norbornadiene vapor in a IO-cm cell.
1
I 47080 46560 46040 45520 45000 RESONANT ENERGY (cm-1) Figure 2. The (2 + 1) REMPI spectrum of jet-coolednorbornadiene (20 Torr of norbornadiene seeded into 3 atm of Ar). L
47600
structured, near continuum. Additional sharp bands superimposed on another continuum lie to the blue of the spectral region presented here.6-9 At our experimental resolution the structured bands are seen to form at least two overlapping progressions of regularly spaced subbands. The lower energy members of the progressions have double-peaked or even triple-peaked structures, in contrast to the single peaks characteristic of the latter members of the progression. The position of each subband that appears in Figure 1 and the apparent intensities of the first 9 or 10 subbands of the system were measured.I0 The first question to be resolved concerned the origin of the sharp system. Because of the great increase of intensity in each of the main progressions with vibrational quantum number, the small frequency interval between the members of the main progression-approximately 365 cm-'-and the magnitude of the lowest frequency ground-state a1 fundamental of the molecule-41 7 cm-l "-the irregular appearance of the origin region of the spectrum was tentatively assigned as arising from interleaved "cold" and "hot" vibrational progressions in this low-frequency a l mode. The frequencies of the origin region of the transition are presented in the first column of Table 1. It is, however, advantageous to first consider the better resolved, cold REMPI results before further analyzing these bands. The Resonant Multiphoton Ionization Spectrum. The (2 1) resonant multiphoton ionization (REMPI) spectrum ofjet-cooled norbornadiene between experimental wavelengths of 414 and 445 nm is presented in Figure 2. The spectrum is seen to resemble the optical spectrum in consisting of a large number of closely spaced bands with an irregular-appearing origin region but differ from it in being better resolved and in lacking thequasi-continuous underlying component of the optical absorption spectrum. The greater resolution of the REMPI spectrum is due to the much colder temperature of the jet-cooled sample, estimated, from the expansion conditions, to be around 10 K. The presence of the vibrational structure suggested above to arise from "hot" vibrational bands in the ground electronic state is due to the essential failure of Ar to cool very low-frequency vibrational fundamentals.12 The latter is confirmed in Figure 3, by comparing the lower energy region of this spectrum with that obtained by coexpanding norbornadiene with Ar butane, an effective vibrational quencher . I 2 The resonant wavelengths of the well-resolved vibrational 111. Results and Analysis subbands of the REMPI spectra were measured. They are presented in the second column of Table 1. Transition frequencies The results obtained here and the analyses of these results are corresponding to these and to the optical bands are presented in logically divisible into several sections: observations, vibrational the third column of this table. Based on the REMPI bands that analyses, lifetime analyses, etc. These subjects will be treated persist in the presence of butane, the ground-state ~ 1 frequency 2 individually. of 417 cm-I,l1 and the vibrational analysis of the prominent hot The Optical Absorption Spectrum. The optical spectrum of and cold bands observed in the red region of the transition, the gaseous, room temperature norbornadiene from 198 to 225 nm (50 500 to 44 500 cm-I) is presented in Figure 1. As b e f ~ r e , ~ . ~ origin of the structured transition was assigned at 45 260 cm-1 and the main vibrational progression to zqz, the wing-flapping this spectrum shows narrow bands superimposed on a slightly
and 5101). The residual pressure in the chamber was about 5 X 10" mbar when the valve was operating at 10 Hz. On some occasions 450 Torr of butane was added to 2.5 atm of argon for the expansion gas. The ions of different mass were separated in a 70-cm-long flight tube and detected by a two-stagemicrochannel plate detector (Hamamatsu MCP). Although the ions of different masses were separated and individually detected, the spectrum obtained was mass-independent. Other REMPI measurements were made simultaneously with photoacoustic (PA) measurements on static samples of norbornadiene. In this case, a biased electrode was placed inside the PA cell for ion collection. PA signals were detected by a condenser microphone (Knowles Model BT-1759). Both REMPI and PA signals were amplified and sent to the data acquisition system for further processing. Spectra were measured on samples consisting of approximately 10 Torr of norbornadiene mixed in approximately a 1:4 ratio with Ar for better detection of the acoustic signals. In some cases only REMPI measurements were made. In these cases the Ar was omitted. The laser system consisted of a dye laser (Quanta-Ray PDL2) pumped by a seeded Nd:YAG laser (Quanta-Ray DCR-3). The typical laser intensity was of the order of lo9W/cm2. When desired, the light intensity was attenuated with cross polarizers. The wavelength was calibrated with a pulsed wavemeter (Burleigh) with an accuracy of l .Ocm-'. Circular or linear polarization of the laser light was produced by a double- and single-Fresnel rhomb arrangement, the former generating a wavelengthindependent method of rotating the plane of polarization of the laser light incident on the latter, the latter generating circularly or linearly polarized light. Since the main results desired from this experiment were the positions of the bands, the light intensity dependence of the signal, and the relative intensities of closely spaced transitions, the spectra were not normalized for the wavelength dependence of the light intensity. Norbornadiene was purchased from Wiley Organics and vacuum-distilled when used. Argon (99.995%, chromatographic grade) was used as supplied. Butane (99.9%, research grade) was purchased from Matheson and used as supplied. Calculations associated with the Franck-Condon factors and the spectral fits were carried out with Mathcad 4.0. Spectral manipulations were conducted with Grams/386.
+
+
8304
The Journal of Physical Chemistry, Vol. 98, No. 34, 1994
TABLE 1: Spectrum and Assignments of the 3s Rydberg optical absorption (nm) 228.38 227.44 227.14 226.85 225.30 pa 225.07 p 224.09 223.80 223.60 223.40 223.20 p 222.97 p 222.02 221.82 221.59 221.38 221.15 p (shoulder) 220.20 220.00 219.56 219.35 p 219.13 p 218.18 217.98 217.78 217.35 p 2 16.49 215.58 p 214.80
REMPI signal (nm)
442.75 442.30 p, h 441.87 p
438.67 ph 438.25 p
435.17 p, h 434.72 p 431.60 sh 432.95 435.17 ph 43 1.25 p 43 1.05 sh 430.61 429.35 428.07 427.82 p 427.58 427.25 p 426.07 425.60 lp 425.25 425.02 424.64 sh 424.50 p 424.27 lp 424.16 sh 423.92 lp 423.7 1? 422.62 422.40 422.07 421.67 Ip 421.20 p 420.92 lp 420.72 lp 420.40 419.12 418.90 418.40 Ip 418.00 417.67 p 417.42 417.17 416.80 416.44 416.20 415.86 415.16 414.81 p 414.52 p 414.22
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Xing et al.
2 Transition of Norbornadiene
transition energy (cm-I)
displacement (cm-1)
43 787 43 968 44 026 44 082 44 385 44 431 44 625 44 683 44 723 44 763 44 803 44 849 45 041 45 082 45 128 45 172 45 218 45 262 45 413 45 455 45 546 45 592 45 636 45 834 45 876 45 918 45 959 46 007 46 019 46 195 46 328 46 377 46 398 46 446 46 582 46 727 46 749 46 775 46811 46 941 46 992 47 031 47 057 47 099 47 114 47 140 47 152 47 179 47 202 47 324 47 348 47 386 47 430 47 483 47 515 47 538 47 574 47 719 47 744 47 801 47 847 47 885 47 913 47 942 47 985 48 026 48 054 48 093 48 174 48 215 48 249 48 284
-1475 -1294 -1236 -1 180 -877 -83 1 -637 -579 -539 -499 -459 -413 -22 1 -1 80 -134 -90 -44 0 151 193 284 330 374 572 614 656 697 745 757 933 1066 1115 1136 1184 1320 1465 1487 1513 1549 1679 1730 1769 1795 1837 1852 1878 1890 1917 1940 2062 2086 2124 2168 222 1 2253 2276 2312 2457 2482 2539 2585 2623 265 1 2680 2723 2764 2792 2831 2912 2953 2987 3022
calc displacement (cm-1) obs obs 1165 -862 (-878) obs -638 -580 -553 -49 1 457 -417 -206 -175 -121 -86 4 3
assignmentb
165 199 284 328 obs 570 613 obs 698 obs obs obs 1070 obs 1131 obs 1307 obs obs 1502 1559 1677 1726 1771 obs 1839 obs 1872
12'4 1203 19°1200112Oo 12!3 or 20021200 1202 (656)10 1214 (656)10 1203 1234 1223 12'2 120' (656)10 1213 (656)'o 1202 12'3 1222 12'1 orig (656)10 12z3 (656)'o 12'2 1232 1221 12'0 (656)'o 1222 (656)'o 12'1 (656)'o 12O0 1231 1220 (757)'o lZo0 (933)'o lZo0 124' 1230 (757)'o 12'0 (1184)'o 12'0 (933)'o 12'0 (1465)'o 1240 (757)'o 1220 (1184)'o 12'0 (656)'o P 2 (656)'o U41 (656)Io n 3 0 (1795)'o (1465)'o 12'0 1250 (757)10 1230
1929
(1184)'o 1220
2046 209 1 2143 2169 obs 2244 2299
(656)'o 1262 (656)'o 125' (656)'o n 4 0 (1795)'o 12'0 1260 (757)10 12d0 (1 184)Io 1230
2460 2508 2540 obs 2609 267 1
(656)'o 1261 (656)'o 1250 (1795)'o 12*0 12T0 (757)10 12S0 (1184)I0 1240
obs 2978 3036
1280 (757)'o 12'0 (1184)10 1 2 5 ~
p = local peak, sh = shoulder, lp = little local peak, h = hot. 12 = ~ 1 2 . Other numbers identify upper state frequency of vibrational mode. Superscripts (subscripts) are upper (lower) state vibrational quantum numbers.
The 198-225-nm Transition of Norbornadiene
The Journal of Physical Chemistry, Vol. 98, No. 34, 1994 8305
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TABLE 2 _Analysis of the Vibrational Subbands of the 3s Rydberg X Transition of Norbornadiene
t
Upper-State Vibrational Frequencies from from intensity analysis frequency analysis frequency displacement 374 656 757 933 1184 1465 1795 46850
46480 46110 45740 45370 45000 RESONANT ENERGY (cm-1) Figure 3. The (2 1) REMPI spectrum of jet-cooled norbornadiene: upper spectrum, 20 Torr of norbornadieneseeded into 3 atm of Ar; lower spectrum, 20 Torr of norbornadiene seeded into 450 Torr of butane + 2.5 atm of Ar.
3.0
780
0.9
1174 1465
0.8 0.9
Assignment groundstate calc 3s Rydb fundamentala freq displacec
+
skeletal deformation vibrational mode. Displacements of the observed bands from this origin were then calculated and are presented in column 4 of Table 1. The next step in the spectral analysis is to organize the remaining experimental bands into progressions of overtones and combinations. This process was handicapped by several factors. (1) Because the intensities of the members of the progression in v12 increase so greatly with increasing vibrational quantum number, it is difficult to find subsidiary upper-state vibrational origins. If, on the other hand, we attempt to identify the maxima of the subsidiary v12 progressions and extrapolate backward to their origins, it is necessary to assume that the frequencies of the v12 overtones are equal to the vi + v12 combination bands. This assumption is not necessarily valid. (2) In the ground state the frequency differences between several of the a l fundamentals are around 360 cm-l. A difference of 360 cm-1 approximates the frequency interval between successive members of the v12 progression in the 3s Rydberg state. Since upper-state fundamental frequencies of polyatomic molecules are generally similar to those of the ground state, it is difficult to differentiate between different v12 overtones originating on different upper-state fundamentals. With these caveats in mind, the best set of upperstate vibrational frequency identifications is presented in column 6 of Table 2,and the corresponding calculated displacements are given in column 5. The apparent fundamental frequencies have been collected in the first column of the upper half of Table 2. We will discuss their assignments below. Two further features of the REMPI spectrum should be noted. (1) The experimental bandwidths obtained for the first few members of the ~ 1 progression 2 depend on the intensity of the laser light. The bandwidths observed a t the lowest usable light intensity, around 1.5 GW/cm2 = 1028 photons/(cm2-s), are presented in Table 3. These widths appear to be constant for the first few members of the progression(s), around 16 cm-1, and then rapidly increase with vibrational quantum number (or excess energy). The increasing bandwidths observed for u > 5 correctly indicate that the bandwidths above u = 5 increase with excess energy. However, since bandwidths independent of laser power were never attained for the lower members of the vibrational progression, it cannot be determined whether the observed 16cm-1 bandwidth of the lower vibrational quanta is due to rotationally unresolved substructure or an experimental artifact. In the latter case, the widths of subbands of u < 5 are probably smaller that those observed here. This uncertainty not withstanding, the observation that the vibrational bandwidths increase greatly above0 = 5 remains valid. (2)Both the increase in REMPI intensity with u and the absolute REMPI intensity reach maximum values at a lower v l 2 quantum number than do those in the optical spectrum. (Compare Figures 1 and 2.) We will return to these topics below.
375
observed 3s Ryd frw displacec
species vib modes a1 C=Cstr 1579 1518 1.18 1465 0.9 CH2scis 1455 1465 0.22 CH def 1232 1261 0.07 CH def 1109 1108 0.59 C-C str 938 958 0.52 933 (small) C-C str 877 867 0.00 skelet def 777 782 0.50 780 0.9 CH def 729 807 0.48 'wing-flap" 417 383 2.92 375 3.0 a2 CHdef+ 885 863 (856)d C-C str ring def 726 694 ring def 440 363 (328)c a Reference 1 1. b Reference 7. In mass-reduced normal-coordinate units. l/2(656). e (1 174-328).
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TABLE 3 Bandwidths of the v12 Progression in the 3s Rydberg X Transition of Norbomadiene vib bandwidth vib bandwidth quantum no. (fwhm), cm-l quantum no. (fwhm), cm-' 0 1
2 3
15 16 15 16"
4 5 6
16 24 32-43b
At the lowest usable power this band had a bandwith of 13 cm-1. Estimated. Band overlapped.
Analysis of the Optical Spectrum: Simulationof the 3s Rydberg Spectrum and Determination of the Valence Spectrum. Since the origin, the upper-state vibrational frequencies of the FranckCondon-active modes in the 3s Rydberg X transition and their experimental intensities are now known, we next simulated the experimental spectrum of norbornadiene and determined the displacements of the 3s Rydberg state from the ground state along the Franck-Condon-active coordinates. In addition, the absorption spectrum of the underlying NV2 X transition can be obtained by subtracting the simulated spectrum from the optical absorption spectrum. The spectral synthesis of the 3s Rydberg X transition was carried out in stages. First, the intensity progression of vl2, the dominant Franck-Condon-active vibration, of the optical spectrum was simulated using the observed frequencies, an assumed harmonic potential, and an assumed constant bandwidth as parameters. An initially assumed displacement (in mass-reduced normal coordinate units) along the v12 coordinate was varied until the relative calculated Franck-Condon factors for the v12 overtones reproduced the relative observed band intensities. Next, eq 1, the vibrational part of the transition moment integral, was solved using the experimental transition frequencies, calculated Boltzmann factors, observed bandwidth, and converged Franck-Condon factors calculated above for v12 as parameters and Franck-Condon factors calculated for the second, third, and fourth most prominent excited-state vibrations (760, 1170, and
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8306 The Journal of Physical Chemistry, Vol. 98, No. 34, 19'94 I " " "
50500
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~
,
"
"
'
"
'
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43100 46900 45700 FREQUENCY (cm-1) Figure4. Synthesized optical spectrumof the 3s Rydberg
of norbornadiene. See text for details.
'
-2
~
44500
transition
50500
48100 46900 45700 44500 FREQUENCY (cm-1) Figure 5. Difference speztrum,Figure 1- Figure 4. This is the adsorption spectrum of the NV2 X transition of room temperaturenorbornadiene
calculation employed ground" and excited-state experimental vibrational frequencies and variable coordinate displacements. v are the experimental frequencies, and y is the bandwidth. The summations runs over all necessary quanta, k and I , in the four active modes, i, in the ground (9) and excited (e) states. Although our goal is to synthesize the optical spectrum, we first synthesized the better resolved REMPI spectrum (y = 15 cm-I fwhm) so not to delude ourselves that possibly incorrectly determined substructure hidden under the broader (40 cm-1 fwhm) optical spectra was well fitted by the calculation. Displacements along the three free vibrational modes were varied in the Franck-Condon factor calculations until a solution of eq 1 reasonably reproduced the REMPI spectrum. The attempt to fit the spectrum was handicapped by the assignment problems discussed above plus an additional difficulty arising from the unknown, but observable, increase in bandwidth with increasing excess energy. For the latter we simply assumed that the error introduced by setting the bandwidth to that observed at low vibrational quantum number is small. A satisfactory fit to the REMPI spectrum was obtained. Finally, the desired objective, the 3s Rydberg X optical spectrum, was simulated by solving eq 1 again using as parameters the observed optical bandwidth, the REMPI frequencies, and the converged displacements obtained in the REMPI simulation. The transition frequencies and displacements were then slightly adjusted to better reproduce the structured part of the optical spectrum. The final calculated spectrum is presented in Figure 4, and the final frequencies and displacements are given in columns 2 and 3 of the upper half of Table 2. We will discuss these below. To demonstrate the goodness of fit, the synthesized optical spectrum (Figure 4) was subtracted from the experimental optical spectrum (Figure 1). The difference spectrum is presented in Figure 5. In this figure, the residual narrow structure arises predominantly from a mismatch of the observed and assumed bandwidths. The great decrease in the intensity of the narrow structure relative to the intensity of the broad underlying absorption as compared with the optical spectrum (Figure 1) demonstrates that the synthesized spectrum, which extends over 5000 cm-1 and encompasses overtones and combinations in all four of the treated modes, well reproduces the majority of the sharp features of the experimental spectrum. The broad, quasi-structureless underlying absorption of the optical spectrum, which has become the dominant absorption feature in Figure 5 , is the optical-absorption spectrum of the second valence transition (NV2 X) of gaseous norbornadiene. It strongly resembles the spectra of norbornadiene + 136 atm of
-
49300
-
vapor.
1460 cm-l) as variables. As before, the Franck-Condon factor
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Xing et al.
N25a and of a low-temperature norbornadiene film.5b Both latter techniques are believed to suppress Rydberg transitions.13 If necessary, a comparison of Figure 5 and those of ref 5 again confirms the usefulness of these techniques. An attempt was made to deconvolute the diffuse structure of Figure 5 to determine the frequency of the visible vibration and the displacement of the molecule along this mode. Because of the sparsity of substructure in this transition and the background arising from the strong transition to the blue? a unique solution could not be obtained. However, it is unquestionable that the NV2 % transition of norbornadiene contains three bands separated by 1000-1050 cm-1, that the intensity of the second band is stronger than the first, and that the bandwidth (fwhm) of the first band is around 300 cm-I. Since the intensity of the second band is stronger than the first, but the third probably not much stronger than the second, the displacement of the molecule along this coordinate is probably near 2 in mass-reduced normalcoordinate units. In summary, we were able tojatisfactorily simulate the optical spectrum of the 3s R y d b e r g t X transition of norbornadiene and thereby determine the displacements of the excited state from theground along the four most prominent vibraticnal progressions and isolate the spectrum of the NV2 t X transition of norbornadiene from the observed optical spectrum. These subjects will be discussed below. The Two-Photon Resonant Photoacoustic Spectrum of Norbornadiene. The experimental results presented in Figures 1-5 show that in this spectral region two transitions, one valence and one Rydberg, are detected by optical spectroscopy, and only the Rydberg transition is detected by two-photon REMPI spectroscopy. Both transitions are both one- and two-photon-allowed. Analogous observations have been made on other polyenes, for which it has been argued that the lifetimes of the valence-excited states are too short to permit the absorption of the third photon needed for ionization.14 If true, an efficient nonradiative decay mechanism must exist for excited valence states which should generate a strong photoacoustic signal.15J6 The two-photon resonant photoacoustic spectrum of norbornadiene was, therefore, studied to determine whether the valence transition could be observed by this technique. The two-photon resonant photoacoustic (PA) spectrum of room temperature norbornadiene is presented in Figure 6. Also presented in Figure 6 is the simultaneously obtained (2 + 1 ) REMPI spectrum of norbornadiene, whose assignment is known. The details of the spectra are power-dependent; thus, although difficult to obtain because of the much greater sensitivity of the REMPI than the PA technique, it is important to compare PA and REMPI spectra measured with the same laser power. This was done in the experiment presented in Figure 6 . A comparison of the REMPI and PA spectra presented in Figure 6 suggests that a competition exists between the physical +
The Journal of Physical Chemistry, Vol. 98, No. 34, 1994 8307
The 198-225-nm Transition of Norbornadiene I " " "
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1
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"
' " " " 1
.70
RESONANT ENERGY (cm-1)
Figure 6. Simultaneouslymeasured two-photon resonant spectra of 10 Torr of norbornadiene+ 40 Torr of Ar at room temperature: upper, ( 2
+ 1) REMPI signal; lower, photoacoustic signal.
processes giving rise to the two signals: the PA spectrum has negligible intensity at low "wing-flapping" quantum number and rapidly increases in intensity with increasing quantum number whereas the REMPI spectrum increases in intensity only slightly with increasing v12 quantum number a t low quantum number, and then decreases in intensity where the PA spectrum becomes strong. Although the P-A and REMPI spectra differ in the details of the 3s Rydberg X transition, they resemble each other in shoFing only continuous background underlying the 3s Rydberg X peaks: they both lack the broadly structured underlying absorption observed in the optical absorption spectrum (Figure 1). The continuous background observed in the REMPI and PA spectra most likely arises from nonresonant absorption a t the high laser powers necessary for the PAmeasurement. The absence of a valence signal from both the two-photon resonant REMPI and PA measurements suggests that a t least in norbornadiene the inability to observe the NV2 transition by a two-photon resonant technique is due not only to the probably short lifetime of the excited valence state but also to its exceedingly low twophoton cross section. The different details of the 3s R y d b e r g c transition detected by REMPI and PA spectroscopies suggest that the decay rate of the 3s Rydberg state of norbornadiene increases with increasing excess energy. This phenomenon had already been suggested by the increase in bandwidth with increasing vibrational quantum number in the jet-cooled REMPI spectrum. The next section addresses the subject of the the upper-state lifetime, Lifetimes of the 3s Rydberg and NV2-Valence States of Norbornadiene. The results presented in Figure 6 indicate that a competition exists between the ionization and decay rates of the 3s Rydberg state of norbornadiene that determines the lifetime of the 3s Rydberg state and that the resultant lifetime depends either on the vibrational quantum number of the excited state or on its vibrational energy. Such competition has been described by a set of kinetic eq~ations.~7-19In these the (wavelengthdependent) ion current, i ( v ) , is expressed as a function of the (wavelength-dependent) one- and two-photon cross sections, u(1) and &), the number of molecules, N, the (wavelength-dependent) photon flux, Z,and the (wavelength-dependent) nonradiativedecay rate of the resonant excited state, y(v). If the excited-state population can be assumed to be approximately constant during the laser pulse, the ion current is described by eq 2.1'
-
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w
According to eq 2, the frequency dependence of y, the decay rate, can be determined from the power dependence of the signal at different frequencies. An experiment was conducted to determine the frequency (or vibrational quantum number) dependence of the decay rate. The results of this experiment, the REMPI signal of room temperature norbornadiene at four different light intensities, are
48340
47746 47152 46558 45964 45370 RESONANT ENERGY (cm-1) Figure 7. The (2 + 1) REMPI spectra of 5-Torr room temperature
norbornadieneat different light intensities, The strongest intensity, the upper curve, is approximately 1.5 GW/cm2. Intensities decrease downward.
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presented in Figure 7. In agreepent with eq 2, the REMPI intensity of the 3s Rydberg X transition depends on laser power. In addition, the relative power dependence of an individual vibrational subband depends on its vibrational quantum number (or frequency). These results confirm our hypothesis that the lifetimes of the different vibrational levels of the 3s Rydberg state depend on vibrational quantum number (or excess energy). (Although we know that each "band" displayed in Figure 7 contains several different vibrational subbands, since they are not resolved each "band" will be treated as an entity.) The intensity of each band was measured at each of the laser powers. The light intensities were insufficiently well determined to permit the absolute values of y ( v ) for the 3s Rydberg state of norbornadiene to be deduced. However, according to eq 2, for those frequencies where y is small compared to a(l)Zthe relative light intensities can be deduced from the experimental data; under this condition i is proportional to I ] / * . The ratios of the peak heights, the i, for any pair of laser intensities were found to be constant for u = 1, 2, and 3. From these, the relative laser intensities were deduced. Therelativedecayratesofu(vl2) = 1-7ofthe3s+Wtransition of norbornadiene were obtained from graphic solutions of eq 2. The latter are presented in Figure 8. In Figure 8 the slopes of the curves equal 1/Nu(2) and the intercepts equal y/Nu(l)a(2) in units of (GW/cm)3/intensity. For clarity, the figure has been divided into two parts; the lower contains data for u = 1, 2, 3, and 4 and the upper for u = 5 , 6 , and 7. (In reality, the two sets of curves overlap.) The graphic solutions of eq 2 for u = 1-4 are linear and extrapolate to approximately the same, very small value of P / i , hence y. The relative two-photon cross sections deduced from the slopes of the curves for ~ ( ~ 1 2=) 1-4 have the same relative magnitudes as do those measured directly, as desired. The graphic solutions of eq 2 are not linear above u = 4. The extrapolated linear portions of the curves converge to intercepts much larger than those of v = 1, 2, 3. The relative two-photon cross sections deduced from the slopes of linear extrapolations of the curves agree closely with their measured values, except for u = 5 . This agreement gives support to the extrapolation procedure. The relative decay rates deduced from the slopes and intercepts of Figure 8 are presented in Figure 9. The invariance of the relative decay rates for u ( u I 2 )< 4 indicates that for these values of u, or vibrational energies, y is appreciably less than Zu(1). For typical values of d l ) , 10-18 cm2,I7 and the experimental laser intensity of approximately 1028 photons/(cm2 s), y(u(v12)
