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Vibronic Structure of the 3s and 3p Rydberg States of the Allyl Radical† Michael Gasser, Jann A. Frey, Jonas M. Hostettler, Andreas Bach,* and Peter Chen Laboratorium fu¨r Organische Chemie, ETH Zu¨rich, CH-8093 Zu¨rich, Switzerland ReceiVed: August 5, 2009; ReVised Manuscript ReceiVed: October 11, 2009
Resonance-enhanced multiphoton ionization combined with electronic ground state depletion spectroscopy of jet-cooled allyl radicals (C3H5) provides vibronic spectra of the 3s and 3p Rydberg states. Analysis of the vibronic structure following two-photon excitation of rovibrationally cold allyl radicals reveals transitions to the 3pz (2A1) Rydberg state with an electronic origin at 42230 cm-1. More than 40 transitions to vibrational levels in the partially overlapping spectra of the 3py (2B2) Rydberg state and the 3s (2A1) Rydberg state are identified and reassigned on the basis of predictions from ab initio calculations and results and simulations of pulsed-field-ionization zero-kinetic-energy photoelectron spectra obtained recently using resonant multiphoton excitation via selected vibrational levels of these two Rydberg states (J. Chem. Phys. 2009, 131, 014304). Depletion spectroscopy reveals that the transition to the short-lived 3px (2B1) Rydberg state in vicinity of three-state same symmetry conical intersections predicted theoretically carries most of the oscillator strength of these coupled 3s and 3p Rydberg states. The results allow for the first time to experimentally derive the energetic ordering of the 3p Rydberg states of the allyl radical. 1. Introduction The allyl radical, C3H5, is probably the best-understood polyatomic radical, and its electronic spectrum and dissociation dynamics have been studied extensively using a range of methods.1-22 The allyl radical is stable in the electronic ground state but becomes reactive following electronic excitation and subsequent nonradiative decay to dissociate predominantly to allene and a hydrogen atom.11,12 Accordingly, there are many spectroscopic studies of the allyl radical in the visible and ultraviolet region of the spectrum. Callear and Lee first found an intense band system in the ultraviolet (UV) with sharp bands and an underlying continuous absorption after flash photolysis of allylic compounds in the gas phase.2,3 More recently, several groups studied the vibronic structure of the allyl radical in the same spectral range using resonance-enhanced multiphoton ionization (REMPI).4-8 Hudgens and Dulcey first observed a prominent band centered at 40080 cm-1 in two-photon excitation, which they assigned to the origin band of the B˜ (2A1) 3s Rydberg state,4 an assignment that was later confirmed.5,8 Blush and Minsek et al.6,7 later observed a rich vibronic structure in one-photon excitation in the same spectral range and based on an analysis of the partially resolved rotational structure attributed vibronic bands to a 2B2 r 2A2 and a 2B1 r 2A2 electronic transition, which both carry oscillator strength. They interpreted the surprising appearance of numerous nominally forbidden bands as a signature of strong vibronic coupling between the B˜ (2A1) 3s Rydberg state and an excited state of 2B1 symmetry induced by an out-of-plane distortion that led to a proposed doublewell potential in the B˜ (2A1) 3s Rydberg state. ˜ (2B1) is According to recent ab initio calculations,23-25 the A a valence excited state, while the four next higher lying excited states have predominant 3s and 3p Rydberg character with a planar (C2V) geometry,25 similar to that of the allyl cation. The energetic ordering of the close lying 3s (2A1), 3px (2B1), 3py (2B2), and 3pz (2A1) states, however, could not be established †
Part of the special section “30th Free Radical Symposium”.
unambiguously from these calculations and does not agree with the experimentally derived ordering of the excited states.6,7 Moreover, the 3pz Rydberg state has not yet been experimentally observed, in contrast to transitions to the B˜ (2A1) 3s Rydberg state that also do not carry any oscillator strength in one-photon excitation.4,5,8 The study described here revisits the electronic spectrum of the allyl radical in the spectral region of the 3s and 3p Rydberg states in the light of our recent pulsed-field ionization zero kinetic energy (PFI-ZEKE) studies for which these states were the resonant intermediate states.22 We probe the vibronic structure of jet-cooled allyl radicals using REMPI and UV depletion spectroscopy26 combined with REMPI detection; see Figure 1. Analyzing the vibronic structure of the REMPI spectra of rovibrationally cold allyl allows for the first time observation of transitions to the 3pz Rydberg state. A partially rotational state-selected UV depletion spectrum permits identification of the transition to the short-lived 3px Rydberg state in a molecular beam that carries most of the oscillator strength of these coupled electronically excited states. This allows for the first time to experimentally derive the energetic ordering of the 3p Rydberg states of the allyl radical. 2. Experimental Section The experimental apparatus is a modified version of one described previously,21,27 and we give only a brief description here. We generated a clean pulse of allyl radicals either by supersonic jet flash pyrolysis28 of 1,5-hexadiene using pyrolysis conditions optimized for highest conversion efficiency or by photolysis of allyl iodide (Aldrich Fine Chemicals, 98%). For photolytic generation of allyl radicals, we expanded allyl iodide seeded in 3 bar of helium into a quartz capillary tube (0.9 mm i.d., 22 mm in length) attached to the 0.8 mm orifice of a 20 Hz pulsed valve (General Valve Series 9).29 The fourth harmonic output (266 nm) of a Nd:YAG laser (Spectra Physics, GCR series) provided UV light for photolysis of allyl iodide in the quartz capillary tube approximatively 2 mm from its exit. The output of a Nd:YAG-pumped dye laser (Radiant Dyes Nar-
10.1021/jp907524s 2010 American Chemical Society Published on Web 10/30/2009
Rydberg States of the Allyl Radical
J. Phys. Chem. A, Vol. 114, No. 14, 2010 4705 3. Computational Methods We calculated the excitation energies of the five lowest doublet excited states of the allyl radical at the multireference configuration interaction singles and doubles (MR-CISD) level of theory using the Molpro program package.30 We used the DZP basis set of Dunning31 and we augmented the carbon atom basis with two diffuse s and p functions using the exponents from the diffuse part of the Dunning-Hay DZ++ basis set.32 The state averaged multiconfiguration self-consistent field (SAMCSCF) orbitals with a CAS(3,7) active space containing the three π orbitals and the 3s and 3p Rydberg orbitals provided the reference wave function for the MR-CISD calculations. We calculated the harmonic vibrational frequencies of the excited states at the MR-CISD level of theory using numerical force constants and scaled them by a factor of 0.94 that we determined by minimizing the root-mean-square deviation to the experimental fundamental wavenumbers. 4. Experimental Results and Analysis
Figure 1. Schematic energy level diagram for multiphoton ionization of the allyl radical, C3H5. (a) 2 + 2 resonance-enhanced multiphoton ionization; (b) 1 + 1 resonance-enhanced multiphoton ionization; (c) the depletion method where the absorption of the short-lived 3px Rydberg state is measured by depletion of the ground state population probed by a delayed second laser pulse which monitors the ion signal intensity using 1 + 1 REMPI via the B˜ 121 state. A schematic representation of allyl and the definition of the principal and inertial axis systems are also shown.
rowscan) provided UV or visible light needed for recording the 1 + 1 and 2 + 2 REMPI spectra of the allyl radical. We used a collimated laser beam with a pulse energy of 1-2 mJ/pulse for recording the 1 + 1 REMPI spectra and used a 300 mm focal length lens to focus the fundamental dye laser output (4.5 mJ/pulse) into the skimmed radical beam in the source of a linear time-of-flight mass spectrometer to obtain the 2 + 2 REMPI spectra. The ions were detected using double microchannel plates. The high intensity needed for two-photon electronic excitation led to an ac Stark shift of 9.9 cm-1 that we determined by extrapolation of the band positions measured at pulse energies of 4.5, 2.5, 1.5, and 0.75 mJ and corrected for. We used the output of a second dye laser (Radiant Dyes Narrowscan) pumped by another Nd:YAG laser (Spectra Physics, GCR series), which was aligned anticollinearly with the REMPI detection laser beam to record UV/UV depletion spectra. We tuned the REMPI detection laser to the intense transition at 40300 cm-1 while scanning the depletion laser from 41500 to 45000 cm-1 to obtain the UV/UV depletion spectra as shown schematically in Figure 1. The pulse energy of the depletion laser dropped from 2 mJ/pulse in the wavenumber range from 41500 to 43800 cm-1 down to 1 mJ/pulse at higher wavenumbers because of the reflecting characteristics of the folding mirrors. We measured overlapping spectra with matched depletion laser pulse energies and adjusted the recorded signal intensities accordingly in the UV/UV depletion spectra. In these experiments, both the REMPI laser and the photolysis laser operated at 20 Hz while the depletion laser ran at 10 Hz repetition rate. A laser shot-by-shot subtraction scheme of the ion signal intensity yielded the depletion spectrum. We routinely observed a REMPI signal intensity depletion of ∼30-40%. We used neon optogalvanic hollow cathode lamps for wavelength calibration of the two dye lasers.
Figure 2 shows the 2 + 2 and 1 + 1 REMPI overview spectra as well as the UV/UV-depletion spectrum of the allyl radical in the 39300-45000 cm-1 region. As in our previous work, the analysis of the vibronic structure is based on symmetry assignments obtained from simulating the rovibronic band envelopes and isotopic band shifts.6,8 For the present work, we used additional predictions from high-level ab initio calculations and results from our recent study of resonance-enhanced multiphoton threshold ionization of allyl via the 3s and 3p Rydberg states.22 4.1. The B˜ (2A1) 3s Rydberg State. 4.1.1. The 2 + 2 REMPI Spectrum. The intense band at 40046 cm-1 in the 2 + 2 REMPI spectrum corresponds to the origin of the B˜ (2A1) state, the 3s Rydberg state forbidden in one-photon excitation;4-6 see Figure 2. Only totally symmetric vibrational levels are expected to contribute to the 2 + 2 REMPI spectrum. In addition to the prominent band arising from the fundamental of the bending mode (ν7),8 we also observe its first overtone 785 cm-1 above the origin from which we determine the anharmonic constant χ7, 7 ) +1.5 cm-1. To higher wavenumber, we also assign bands to the B˜ 61 and B˜ 41 states with fundamental wavenumbers of ν˜ 6 ) 1011 cm-1 and ν˜ 4 ) 1436 cm-1, respectively. Several combination bands involving the bending mode also appear in the 2 + 2 REMPI spectrum, and the ˜ (2A1) 3s positions of all observed vibrational levels of the B Rydberg state with their assignments are listed in Table 1 (in the notation iν′′ν′, where i designates the vibrational mode with ν′′ (ν′) quanta of excitation in the ground (excited) electronic state). The band intensities in the 2 + 2 REMPI spectrum are similar to those predicted by the Franck-Condon factors for excitation to an “ionlike” Rydberg state.16 A single intense ∆ν ) 0 transition dominates the PFI-ZEKE photoelectron spectra obtained by resonant multiphoton excitation via vibrational levels of the B˜ (2A1) state,22 which is consistent with a planar geometry for the allyl radical in that state also predicted by ab initio calculations.25 4.1.2. The 1 + 1 REMPI Spectrum. We first focus on the 39000-41000 cm-1 wavenumber region of the 1 + 1 REMPI spectrum of the allyl radical recorded using the pyrolysis and photolysis radical sources. Comparing the two REMPI spectra displayed in Figure 3 reveals that many bands are absent in the spectrum obtained with help of the photolysis nozzle and that the rovibronic band envelopes are much less pronounced. This observation indicates that the pyrolytically generated allyl radicals are cooled less efficiently in the jet resulting in
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Figure 2. The 1 + 1 REMPI (a) and the 2 + 2 REMPI (b) overview spectra of the allyl radical. The depletion spectrum (c) of the allyl radical obtained by monitoring the UV-laser depletion of the ion signal intensity produced with 1 + 1 REMPI via the B˜ 121 state. The vertical scale has been chosen so that the maxima of the spectra have similar amplitudes and do not reflect the relative photoionization signals.
transitions from vibrationally excited ground state radicals, as discussed below. The original interpretation6,7 of the 1 + 1 REMPI spectrum of the allyl radical obtained by supersonic jet flash pyrolysis, however, has been done assuming that hot bands are unimportant. A thorough analysis of the vibronic structure appearing in the 1 + 1 REMPI spectrum of the allyl radical is mandatory, because several bands previously assigned6,7 to vibrational levels of two different electronically excited states including a band assigned to the fundamental of the conrotatory twisting mode of the terminal methylene groups (ν12) in the B˜ state are missing in the 1 + 1 REMPI spectrum of rovibrationally cold allyl radicals. The first prominent band to lower wavenumber in both the 1 + 1 REMPI spectra shown in Figure 3 appears near 40300 cm-1 and was first assigned by Minsek et al.7 to the electronic origin of a 2B1 r 2A2 electronic transition. We recently measured the PFI-ZEKE photoelectron spectrum via this transition, and the results led us to consider alternative assignments for that band.22 The rotational contour of that vibronic band is displayed in Figure 4. We calculated the vibronic band origin by simulating33 the rotational contour of the type A band7 of this near prolate asymmetric top using the rotational constants for the vibrationless electronic ground state reported by DeSain et al.34 As in our previous work, the extended sub-band head rotational structure at higher rotational temperatures proved to be highly sensitive to the excited state rotational constants. Excited-state rigid-rotor rotational constants of A′ ) 1.6265 cm-1, B′ ) 0.368 cm-1, and C′ ) 0.301 cm-1 and a rotational temperature of 264 K yielded the best agreement between experiment and simulation for the pyrolytically generated allyl radicals. We found that Trot ) 5.5 K and the same excited-state rigid-rotor rotational constants gave the best match for the spectrum obtained from photolytically generated allyl radicals; see Figure 4b. At this low rotational temperature, the band contours are rather insensitive to changes in the excited state rotational constants and we therefore used these rotational constants also for simulating all other rovibronic bands, which leads to an estimated uncertainty for the band origins of (2 cm-1. For hot and sequence bands
we also used these rotational constants, because often the corresponding ground-state rotational constants are unknown resulting in an estimated uncertainty of (4 cm-1 for these band origins. The band origin of this transition lies at 40300 cm-1 or +254 cm-1 relative to the 000 transition of the B˜ state. Ab initio calculations predict that the lowest frequency vibrational mode in the 3s and 3p Rydberg states as well as in the cationic ground state is the conrotatory twist of the terminal methylene groups (ν12) of b1 symmetry with vibrational frequencies ranging from 265 to 317 cm-1; see Table 2. Given what we observe in the UV/UV depletion experiment (see below) and considering also our recent observation that in the PFI-ZEKE photoelectron spectrum measured via this transition a single intense band corresponding to the cationic 121 state appears and that a single ∆ν ) 0 transition also dominates the PFI-ZEKE photoelectron ˜ spectra obtained through all other vibrational levels of the B state,22 we here reassign the band at +254 cm-1 to the B˜ 121 state. This assignment is consistent with the observed band type in the 1 + 1 REMPI spectrum, since a transition from the vibrationless electronic ground state with Γve′′ ) A2 symmetry to the B˜ 121 state with Γve′ ) B1 symmetry is vibronically allowed in one-photon excitation and with the transition moment oriented along the long axis of allyl (y(a) in Figure 1) gives rise to a type A band profile. Further evidence supporting our new assignment comes from the band that appears at +522 cm-1 in the 2 + 2 REMPI spectrum (Figure 2) of rovibrationally cold allyl radicals. This band cannot correspond to any other low˜ state because their fundamental frequency fundamentals in the B wavenumbers are ν˜ 7 ) 391 cm-1 and ν˜ 9 ) 594 cm-1, respectively, and therefore must be assigned to an overtone or combination band. The only candidate is the first overtone of ν12 allowed only in two-photon excitation. From the fundamental as well as the first overtone of ν12, we determine the anharmonic constant χ12,12(B˜) ) +7.0 cm-1, which is very similar to that ˜ +) ) +8.5 determined for the cationic ground state (χ12,12(X -1 22 cm ).
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TABLE 1: Transition Wavenumber in cm-1 and Assignments of the Bands Observed in the 1 + 1 and 2 + 2 REMPI Spectra of the Allyl Radicala electronic state B˜ (2A1) B˜ (2A1) B˜ (2A1) B˜ (2A1) B˜ (2A1) B˜ (2A1) B˜ (2A1) B˜ (2A1) B˜ (2A1) B˜ (2A1) B˜ (2A1) B˜ (2A1) B˜ (2A1) B˜ (2A1) B˜ (2A1) B˜ (2A1) B˜ (2A1) B˜ (2A1) B˜ (2A1) B˜ (2A1) B˜ (2A1) B˜ (2A1) B˜ (2A1) B˜ (2A1) B˜ (2A1) B˜ (2A1) B˜ (2A1) B˜ (2A1) B˜ (2A1) B˜ (2A1) B˜ (2A1) B˜ (2A1) B˜ (2A1) B˜ (2A1) B˜ (2A1) B˜ (2A1) B˜ (2A1) C˜ (2B2) C˜ (2B2) C˜ (2B2) C˜ (2B2) ˜ ( 2 A1 ) D ˜ ( 2 A1 ) D ˜ ( 2 A1 ) D ˜ ( 2 A1 ) D
experiment
assignment
1+1 1+1 1+1 1+1 1+1 2+2 2+2 1+1 1+1 2+2 1+1 1+1 1+1 1+1 1+1 2+2 2+2 1+1 1+1 2+2 1+1 2+2 2+2 1+1 2+2 1+1 1+1 2+2 1+1 1+1 1+1 1+1 1+1 1+1 2+2 1+1 2+2 1+1 1+1 1+1 1+1 2+2 2+2 2+2 2+2
1001 1101 801 901 1201 701 7011210 710901 7101201 000 1221 1210 9111210 9101211 7101221 710 1220 7011010 910 910 7101210 720 7101220 1810 710910 710910 1010 610 7201210 1110 6101210 1710 1610 7101010 610710 7301210 410 000 710 1220 910 000 710 910 1220
band type
band origin
relative
A A B B A
39074 39244 39271 39512 39526 39640 39872 39900 39919 40046 40056 40300 40358 40377 40431 40437 40568 40618 40640 40640 40682 40831 40945 40973 41022 41025 41047 41057 41070 41140 41310 41314 41416 41444 41448 41461 41482 41556 41947 42060 42137 42230 42622 42725 42759
-972 -802 -775 -534 -520 -426 -174 -141 -126 0 +10 +254 +312 +331 +385 +391 +522 +572 +594 +594 +637 +785 +899 +927 +977 +979 +1001 +1011 +1024 +1094 +1264 +1268 +1370 +1398 +1402 +1415 +1436 0 +391 +504 +581 0 +392 +495 +529
B A A A A B A A B A C B A A A A C C A A C C A A
a The estimated uncertainty for the band origins is (2 cm-1, except for sequence and hot bands for which it is (4 cm-1.
We now return to the weak bands visible in the 39000-41000 cm-1 wavenumber region of the 1 + 1 REMPI spectrum (Figure 3a) of allyl produced by flash pyrolysis. A weak band appears at 40056 cm-1, which had earlier been assigned to the B˜-state electronic origin, being active due to a proposed out-of-plane distortion of the allyl radical in the 3s Rydberg excited state.8 The observation of that band had been critical to the previous interpretation of the 1 + 1 REMPI spectrum.6,7 This band is absent in the 1 + 1 REMPI spectrum of rovibrationally cold allyl radicals (Figure 3b), and we here reassign it to the B˜ 1212 sequence band. We also observe the B˜ 1210 hot band at 39526 cm-1 (-520 cm-1). This agrees nicely with the fundamental wavenumber of 518 cm-1 for the ν12 vibration reported earlier using resonance Raman spectroscopy.35 The B˜ 910 hot band is tentatively assigned to a band at -534 cm-1, which agrees well with the fundamental wavenumber of 536 cm-1 calculated ab initio; see Table 2. These values, however, are in poor agreement
Figure 3. The 1 + 1 REMPI spectra of the allyl radical in the 38000-41000 cm-1 wavenumber range recorded using (a) the pyrolysis and (b) the photolysis radical sources.
with ν˜ 9 ) 549 cm-1 reported in ref 25 using resonance Raman spectroscopy. We only observe the allyl radical CH2 oop bending mode ν8 as a hot band at -775 cm-1 in the 1 + 1 REMPI spectrum, in good agreement with both the fundamental wavenumber of 778 cm-1 calculated ab initio (Table 2) and ν˜ 8 ) 775 cm-1 observed in experiments performed in Ar matrix.36 Hot bands involving the ν10 and ν11 vibrational modes appear at -972 and -802 cm-1, respectively, in the 1 + 1 REMPI spectrum. Both these assignments are in good agreement with earlier experiments and also with our ab initio calculations. Hirota et al. reported ν˜ 11 ) 802 cm-1 using laser-diode spectroscopy in a molecular jet expansion37 and Nandi et al. measured a fundamental wavenumber of 983 cm-1 for the CH2 oop bending mode ν10 in Ar-matrix spectroscopy.36 We also identified numerous other transitions originating from hot ground state allyl radicals and the band positions, and their assignments are listed in Table 1. A list of all fundamental wavenumbers observed in this report appears in Table 3. Finally, we focus on the 40300-41550 cm-1 wavenumber region of the 1 + 1 REMPI spectrum of the allyl radical where a large number of bands appear that we assign to vibronically allowed transitions to vibrational levels of the B˜ state. Two prominent type A bands appear at +1001 and +1094 cm-1 in the 1 + 1 REMPI spectrum that we assign to the B˜ 101 and B˜ 111 state, respectively. The 1 + 1 REMPI spectra of these bands scanned at high spectral resolution are displayed in Figure 5 and Figure 6. This assignment agrees with the energetic ordering of the fundamental vibrational frequencies for ν10 and ν11 ˜ state; see Table 2. We also recently predicted ab initio for the B measured the 1 + 1′ PFI-ZEKE photoelectron spectrum via both of these intermediate states and observed intense ∆ν ) 0 transitions into the corresponding cationic state, supporting these revised assignments.22 In the 40300-41550 cm-1 wavenumber region we also identified three type C bands with Γve′ ) B2
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Gasser et al. TABLE 2: Calculated Anharmonic Vibrational Frequencies in cm-1 of the Allyl Radical for the Ground Electronic State and for the Ground State of the Allyl Cation22 Obtained at the HCTH147/TZ2P Level of Theorya
mode
description
˜ X ( 2A 2 )
B˜ (2A1)
ν˜ /cm-1 ˜ C˜ D (2B2) (2A1)
ν1 ν2 ν3 ν4 ν5 ν6 ν7 ν8 ν9 ν10 ν11 ν12 ν13 ν14 ν15 ν16 ν17 ν18
iph CH2 stretch CH2 stretch CH stretch CH2 scissors CH2 rock CCC stretch CCC bend CH2 oop bend CH2 twist CH oop bend CH2 oop bend CH2 twist CH2 stretch CH2 stretch CH2 scissors CH bend CCC stretch CH2 rock
3106 3046 3030 1455 1220 986 426 778 536 975 806 517 3104 3031 1449 1375 1193 911
3158 3030 3169 1503 1265 1007 402 1055 599 960 1050 305 3171 3037 1569 1394 1251 915
3168 3036 3145 1506 1248 1009 418 1065 593 951 1066 317 3177 3039 1591 1417 1272 910
3152 3024 2935 1514 1264 1019 431 1064 618 965 1064 283 3138 2995 1565 1398 1152 922
E˜ (2B1)
˜+ X (1A1)
3201 3086 3147 1519 1269 1017 428 1026 490 928 1026 265 3198 3086 1602 1411 1254 921
3103 2990 3049 1517 1262 1022 427 1116 571 1011 1111 304 3100 2989 1546 1399 1265 937
a The harmonic vibrational frequencies in cm-1 of the Rydberg states obtained at the MR-CISD/DZP++ level of theory are scaled by a factor of 0.94.
Figure 4. The 1 + 1 REMPI spectra of the B˜ (2A1) 1210 band (type A) of the allyl radical and a simulation of the absorption spectrum for (a) Trot ) 264 K and (b) for Trot ) 5.5 K. See text for more details.
symmetry. Our ab initio calculations predict fundamental vibrational frequencies of 915 cm-1 (ν18), 1251 cm-1 (ν17), and 1394 cm-1 (ν16) for the three lowest frequency vibrational modes of b2 symmetry in the B˜ state; see Table 2. The three type C bands appear at +927, +1268, and at +1370 cm-1 in the 1 + 1 REMPI spectrum and we assign these to the B˜ 181, the B˜ 171, and the B˜ 161 states based on the good agreement of their fundamental wave numbers with the ab initio calculations. Noteworthy is in particular the B˜ 1601 band (cf. Figure 7) and the B˜ 1801 band (cf. Figure 2) that have not been previously observed in the 1 + 1 REMPI spectrum of allyl radicals produced by flash pyrolysis because these bands were buried beneath the extended rotational contours of more intense vibronic bands at a similar transition wavenumber.6,22 In addition to the fundamental vibrational levels, we also observe combination bands involving the bending mode (ν7) in the 1 + 1 REMPI spectrum. A short but prominent progression in ν7 appears in the 2 + 2 REMPI spectrum in agreement with the calculated Franck-Condon factors,16 which is not surprising as the bond angle in allyl changes strongly upon electronic ˜ state.6 In the 1 + 1 REMPI spectra displayed excitation to the B in Figure 6 through Figure 8, we observe three type A bands that we assign to a prominent progression of ν7 in combination ˜ 71121 state with ν12. The first member of that progression, the B
appears at +637 cm-1, the B˜ 72121 state at +1024 cm-1, and the B˜ 73121 state at +1415 cm-1. We also identified other combination bands involving the ν7 and ν12 vibrational modes, and their band positions and assignments are listed in Table 1. ˜ (2B2) 3py Rydberg State. We locate the electronic 4.2. The C origin of the 2B2 r 2A2 band system at 41566 cm-1 in the 1 + 1 REMPI spectrum in agreement with the original assignment by Blush et al.6 We recently also measured the 1 + 1′ PFIZEKE photoelectron spectrum via this intermediate state, now ˜ 00 intermediate state, and the observed newly designated as the C intensity distribution and rotational contour of the 00 band in the photoelectron spectrum agreed with predictions made in the realm of an orbital ionization model,22 confirming the original symmetry assignment.6 Three bands observed in the 1 + 1 ˜ REMPI spectrum can be assigned to vibrational levels of the C -1 state; see Figure 2. A band appears at +391 cm that is assigned to the C˜ 71 state.6 We observe two other bands at +504 cm-1 and +581 cm-1, which we assign to the C˜ 122 state and the C˜ 91 state, respectively. Schultz et al.13 reported that the excitedstate lifetimes continuously decrease from 22 ps for the B˜ 00 state down to 9 ps for the C˜ 71 state. The short excited-state lifetimes together with spectral congestion precludes the unambiguous identification of the band type for other vibronic bands in this wavenumber range and makes further assignments ambiguous. ˜ (2A1) 3pz Rydberg State. In the 2 + 2 REMPI 4.3. The D spectrum we observe a previously unknown weak band system with a vibronic structure very similar to that of the B˜ state starting at 42230 cm-1. Those vibronic bands could in principle correspond to transitions to vibrational levels of the B˜ state, but no vibrational levels are expected to be active 2184 cm-1 ˜ state.16 High level ab initio above the electronic origin of the B 25 2 calculations predicted a state of A1 symmetry lower in energy than the B˜ (2A1) 3s Rydberg state. We also measured a 2 + 2 REMPI spectrum (not shown) in the wavenumber range from ˜ state origin band at 40046 cm-1 without 33600 cm-1 up to the B observing a new band system that could be assigned to the
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TABLE 3: Summary of all Experimental Fundamental Vibrational Frequencies for the Electronic Ground State and the 3s, 3py, and 3pz Rydberg Statesb ν˜ /cm-1 ˜ (2A2) X
B˜ (2A1) 3s
C˜ (2B2) 3py
˜ (2A1) 3pz D
˜ + (1A1) X
CH2 scissors CCC stretch CCC bend
426
1436 1011 391
391
392
433
ν8 ν9
CH2 oop bend CH2 twist
775 534
594
581
603
ν10 ν11 ν12
CH oop bend CH2 oop bend CH2 twist
972 802 520
1001 1094 254
252a
1009 1111 283
ν16 ν17 ν18
CH2 scissor CH bend CH2 rock
mode
description
ν4 ν6 ν7
a1
a2 b1 265a
b2
a
1370 1268 927
1276
Value calculated from the wavenumber of the 122 level. b The experimental allyl cation vibrational frequencies are also given.22
missing 2A1 state. Therefore, we assign the band at 42230 cm-1 to the electronic origin of the 3pz (2A1) Rydberg state. A band appears 392 cm-1 above the electronic origin that we assign to ˜ 71 state. In the B˜ state this vibration has a fundamental the D
wavenumber of 391 cm-1. Two more bands are visible in the 2 + 2 REMPI spectrum at +495 and +529 cm-1 that we ˜ 122 state. Given ˜ 91 state and the D tentatively assign to the D the very small wavenumber differences between these two vibrational levels, their assignment remains uncertain. The bands
Figure 5. The 1 + 1 REMPI spectrum of the allyl radical B˜ (2A1) 710910 band (type B), the 1010 band (type A), and the 7201210 band (type A).
Figure 7. The 1 + 1 REMPI spectrum of the allyl radical B˜ (2A1) 1610 band (type C) and the 7101010 band (type A). The band system centered at 41465 cm-1 consists of two overlapping bands of type A, and the one to lower wavenumber is tentatively assigned to 7301210.
Figure 6. The 1 + 1 REMPI spectrum of the allyl radical B˜ (2A1) 1110 band (type A), the partially overlapping 6101210 band (type A), and 1710 band (type C). The relative intensities of the two bands systems were adjusted to reproduce the amplitudes observed in the overview spectrum shown in Figure 2.
Figure 8. The 1 + 1 REMPI spectrum of the allyl radical B˜ (2A1) 910 band (type B) and the B˜ (2A1) 7101210 band (type A). The relative intensities of the two bands was adjusted to reproduce the amplitudes observed in the overview spectrum shown in Figure 2.
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˜ state appearing in the 2 + 2 REMPI spectrum are of the D ˜ about one order of magnitude less intense than those of the B state, possibly because of shorter excited state lifetimes. The ˜ state, however, have origin bands of both the B˜ state and the D a similar full width at half-maximum (fwhm) that amounts to ˜ state ∼25 cm-1 indicating that the weaker intensity of the D band system may arise from a smaller cross section for twophoton excitation. ˜ (2B1) 3px Rydberg State. A broad and continuous 4.4. The E absorption starts near 43300 cm-1 and extends up to at least 45000 cm-1 in the UV/UV-depletion spectrum displayed in Figure 2c. On top of this continuous absorption appear several sharp bands with a fwhm that amounts to ∼20 cm-1. Our partially rotational state-selected UV/UV-depletion spectrum of jet-cooled allyl radicals with Trot ) 5.5 K strongly resembles the absorption spectrum reported by Callear and Lee obtained by flash photolysis of allylic compounds in the gas phase.2,3 The first of these sharp bands appears centered at 43322 cm-1 in the UV/UV-depletion spectrum, in good agreement with the band observed at 43314 cm-1 of “medium” intensity in absorption spectroscopy.2,3 We also observe a somewhat broader band centered at 44457 cm-1, which agrees nicely with the “very strong” band observed at 44469 cm-1 by Callear and Lee. None of these bands appear prominently in the 1 + 1 REMPI spectrum displayed in Figure 2b, indicating that the excited-state lifetimes of the rovibronic states contributing to the UV/UV-depletion spectrum are too short for efficient 1 + 1 REMPI using pulsed nanosecond dye lasers. Both Callear and co-workers38 as well as Nakashima et al.39 determined the oscillator strength of the transition giving rise to those bands and found fosc ) 0.14 and fosc ) 0.24, respectively. In the UV/UV-depletion spectrum displayed in Figure 2c we also observe two very sharp bands with a fwhm that amounts to ∼3 cm-1 at 41556 and at 42136 cm-1 also visible in the 1 + 1 REMPI spectrum, which correspond to the C˜ 00 state and the C˜ 91 state. Ab initio calculations predict that the oscillator ˜ (2A2) transition is fosc ) 0.013 and strength of the C˜ (2B2) r X that fosc is 0.113 for the transition to the second state of 2B1 symmetry.24 Even though the signal-to-noise ratio in the UV/ UV-depletion spectrum displayed in Figure 2c precludes an estimate of the integrated oscillator strength for the C˜ (2B2) r ˜ (2A2) transition, it is clear that the transition giving rise to X the bands starting near 43300 cm-1 has a much larger oscillator ˜ strength. We thus assign this band system to the E˜ (2B1) r X (2A2) transition to the short-lived 3px Rydberg state. The assignment of the sharp bands on top of the continuous absorption remains unclear. The first three wavenumber intervals relative to the band appearing at 43322 are +104, +218, and +363 cm-1, and no such low-frequency vibrations are expected in the 3px Rydberg state. 5. Computational Results The calculated excitation energies at the MR-CISD level of theory of the first five electronic excited states of the allyl radical are listed in Table 4. For the B˜-state our calculated excitation energy is in good agreement with the prediction made by Matsika and Yarkony.25 These calculated excitation energies, however, are ∼0.3 eV lower than the experimental values of 4.97 eV. Preliminary ab initio MR-CISD calculations with larger basis sets40 reveal that the excitation energies of the 3s and 3p Rydberg states increase compared to the values listed in Table 4 and yield T0 ) 5.02 eV for the 3s Rydberg state in good agreement with the experimental value for the B˜ state. The energetic ordering of the 3p Rydberg states calculated at the
Gasser et al. TABLE 4: Experimental and Calculated Excitation Energies for the Five Lowest Doublet Excited States of the Allyl Radical in eVd state ˜ ( B1) (Val.) A B˜ (2A1) (3s) C˜ (2B2) (3py) ˜ (2A1) (3pz) D E˜ (2B1) (3px) 2
a
expt 3.04 4.97 5.15 5.24 ∼5.5 b
a
Tv
T0
Teb
Tvc
foscc
3.32 4.68 5.29 5.25 5.46
2.96 4.70 5.31 5.21 5.47
3.10 4.66 5.26 5.17 5.45
3.32 5.11 5.76 5.65 5.73
6.4 × 10-4 0.013 0.113
c
From ref 21. CI2 in ref 25. MSCASPT2 from ref 24. d Also listed are the calculated oscillator strengths.
MR-CISD level of theory in this work and ref 25 differs from the predications made using the MSCASPT2 method.24 MRCISD predicts that the 3px Rydbergs state has the highest excitation energy, which nicely agrees with our experimentally derived energetic ordering of the Rydberg states. The E˜ (2B1) state appears at ∼5.5 eV in the UV/UV-depletion spectrum and ˜ (2A2) transition carries most of the oscillator the E˜ (2B1) r X strength, in agreement with the results from the MSCASPT2 method.24 Our MR-CISD calculations predict vertical excitation energies for the two “in-plane” 3py and 3pz Rydberg states differing only by 0.04 eV. The experimental difference in ˜ state is only excitation energy between the C˜ state and the D 0.09 eV. Because the 3py (2B2) and 3pz (2A1) Rydberg states ˜ state have different symmetry, we can assign them to the C ˜ and D state, respectively. The energetic ordering of the 3py and 3pz Rydberg states predicted with MR-CISD, however, is reversed compared to experiment. 6. Discussion and Conclusions Resonance-enhanced multiphoton ionization combined with electronic ground-state depletion spectroscopy of jet-cooled allyl radicals provides information on the vibronic structure of the 3s and 3p Rydberg states. Comparing the REMPI spectra of rovibrationally cold and warm allyl radicals and simulation of the vibronic band envelopes yield band origins and allow identification of transitions from the vibrationless ground state. ˜ (2A1) 3s Rydberg state is located The electronic origin of the B -1 at 40046 cm following two-photon excitation, in agreement with previous studies.4,5,8 We reassign a band observed at a similar transition wavenumber following one-photon excitation to a sequence band, which had earlier been assigned to the B˜ state electronic origin.6,7 The 2 + 2 REMPI spectrum of rovibrationally cold (Trot ) 5.5 K) allyl radicals enables for the first time to identify and assign sharp resonances as transitions ˜ state, including to several fundamental vibrational levels of the B -1 the stretching mode (ν˜ 6 ) 1011 cm ) and the CH2 scissors mode (ν4) with a fundamental wavenumber of 1436 cm-1. We reassign the vibronic bands appearing in the 1 + 1 REMPI spectrum in the 40300-41550 cm-1 wavenumber range to vibronically allowed transitions to vibrational levels of the B˜ state. The analysis of the vibronic structure provides the wavenumbers of severals vibrational levels of the 3s Rydberg state for the first time, and they generally agree well with the ab initio predictions made at the MR-CISD level of theory. The wavenumbers of the vibrational levels in the 3s Rydberg state and the anharmonic constants χ12,12 and χ7,7 are very similar to those observed in the cationic ground state,22 as expected because the potential energy surface of the 3s Rydberg state should strongly resemble that of the cationic ground state. We conclude that the 3s Rydberg state must have a planar geometry, consistent with the ab initio predictions and with the results from our recent PFI-ZEKE study of the allyl radical,22 but in
Rydberg States of the Allyl Radical disagreement with the conclusion drawn from the original analysis of the 1 + 1 REMPI spectrum.6-8 We confirm the original assignment of the band at 41556 ˜ (2B2) r X ˜ (2A2) transition, cm-1 to the electronic origin of the C and we observe a previously unknown weak band system in the 2 + 2 REMPI spectrum with a vibronic structure very similar ˜ (2A2) ˜ (2A1) r X to that of the B˜ state that we assign to the D transition to the 3pz Rydberg state with an electronic origin at 42230 cm-1. The electronic origins of the transitions to these “in plane” 3py and 3pz Rydberg states are separated only by 674 cm-1 and Matsika and Yarkony predicted a two-state conical ˜ states that lies just above the intersection between the C˜ and D adiabatic excitation energies of those two states connected to ˜ /C ˜ /D ˜ and C ˜ /D ˜ /E˜) conical intersections.25 seams of three-state (B The last prominent bands observed in the REMPI spectra appear ˜ state electronic origin and 1025 cm-1 529 cm-1 above the D ˜ above the C state, respectively. This suggests that the weak ˜ (2A2) transition observed in the 2 ˜ (2A1) r X intensity of the D + 2 REMPI spectrum could arise from short excited-state lifetimes and also suggests that ultrafast excited-state deactivation processes enabled by conical intersections may play an important role above ∼42600 cm-1. The weak intensity of the ˜ (2A2) transition, however, may simply arise from ˜ (2A1) r X D a smaller cross section for two-photon excitation compared to that to the B˜ state, as the bandwidths of ∼25 cm-1 fwhm for the observed transitions are similar for both Rydberg states indicating similar excited-state lifetimes. Finally, a partially rotational state selected UV/UV depletion spectrum reveals a broad absorption starting at 43300 cm-1 that ˜ (2A2) transition, which carries we assign to the E˜ (2B1) r X most of the oscillator strength of the coupled 3s and 3p Rydberg states, in agreement with predictions from ab initio calculations. Because of the broad and almost unstructured absorption band that is invisible in the 1 + 1 REMPI spectrum, we conclude that this 3px Rydberg state has a very short excited-state lifetime. Rydberg states with short excited-state lifetimes have also been observed in other small molecules and radicals and often arise from perturbations induced by higher lying repulsive valence excited states.41,42 Further theoretical studies are needed to explore the role of possible interactions of valence excited states with the Rydberg states in the allyl radical,43 which could in principle account for the dissociative nature of the 3px Rydberg state. Further investigations are also needed to clarify the dynamical and spectroscopic consequences of two- and threestate conical intersections and their coupling to vibronic levels44 versus the role played by traditional Herzberg-Teller type vibronic coupling. Acknowledgment. The authors thank Professor Dr. Fre´de´ric Merkt and Dr. Anna M. Schulenburg (ETH Zu¨rich), Professor Dr. Martin Jungen (Basel), and Professor Dr. Ingo Fischer (Wu¨rzburg) for fruitful discussions. Mr. Martin Eck contributed to the project in its early stages. This work was supported financially by ETH Zu¨rich and the Swiss National Science Foundation under Project No 200020-115975. References and Notes (1) Currie, C. L.; Ramsay, D. A. J. Chem. Phys. 1966, 45, 488. (2) Callear, A. B.; Lee, H. K. Nature 1967, 213, 693.
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