Measurement of Ionic Resonances in Alkyl Phenyl Ketone Cations via

Oct 23, 2013 - †Center for Advanced Photonics Research, ‡Department of ... Strong Field Adiabatic Ionization Prepares a Launch State for Coherent ...
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Measurement of Ionic Resonances in Alkyl Phenyl Ketone Cations via Infrared Strong Field Mass Spectrometry Timothy Bohinski,†,‡ Katharine Moore Tibbetts,†,‡ Maryam Tarazkar,†,‡ Dmitri Romanov,†,§ Spiridoula Matsika,‡ and Robert Levis*,†,‡ †

Center for Advanced Photonics Research, ‡Department of Chemistry, and §Department of Physics, Temple University, Philadelphia, Pennsylvania 19122, United States ABSTRACT: Strong-field excitation of alkyl phenyl ketone molecules reveals an electronic resonance at 1370 nm in the radical cations upon measuring mass spectra as a function of excitation wavelength from 1240 to 1550 nm. The ratio of the benzoyl fragment ion to parent ion signal in acetophenone increases from 1:1.5 at 1240 nm excitation to 5:1 at 1370 nm (0.9 eV), and back to 1:1 at 1450 nm. Unlike acetophenone and propiophenone, the homologous molecules acetone and ethylbenzene exhibit no wavelength-dependent fragmentation patterns over the range from 1240 to 1550 nm, supporting the hypothesis that the electronic structure of the alkyl phenyl ketone cation enables the one-photon transition. Calculations on the acetophenone and propiophenone radical cations show the existence of a bright state, D2, 0.87 and 0.88 eV, respectively, above the ground-state D0 minimum. Calculations of the potential energy surfaces of the acetophenone radical cation suggest that a D2 → D0 radiationless transition precedes dissociation on D0. Upon population transfer to the D2 surface, the wavepacket motion is directed toward a three-state conical intersection (D0/D1/D2) that facilitates the photodissociation by converting electronic to vibrational energy on the D0 surface.

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INTRODUCTION Radical cations (M•+) play important roles in chemical, physical, and biological processes. For example, the formation of radical cations of DNA nucleobases1 and/or carotenoids2 after radiation damage represents important photoprotection mechanisms. The radical cation of methyl viologen has been investigated as a means to devise new molecular switches.3 Radical cation intermediates have also been proposed to play an important role in strong field control4 and for interpreting tomographic imaging of CO2 using high harmonic generation.5 Radical cations are of particular importance in mass spectrometry, as they are typically the primary product produced by electron impact and photoionization. The spectroscopy and excited-state dynamics of radical cations represent a challenging new field of study. The dynamics of the excited cationic states of azobenzene have been investigated using an intense (∼1013 W cm−2) ultrashort (∼50 fs) laser pulse to prepare the cation followed by a weak field probe pulse.6 Photoionization-induced twisting of the azobenzene cation CNNC phenyl-ring torsional mode resulted in oscillations of the parent and phenyl fragment ion signals. Calculations suggest the formation of a wavepacket on a lower cationic surface initiates vibrational motion along the reaction coordinate. Cycloketones excited in the visible and near-IR7 reveal fragmentation at 394 nm but not at 788 nm. A feature in the cycloketone radical cation photoabsorption spectrum was proposed to account for the enhanced © 2013 American Chemical Society

fragmentation at 394 nm. Observed enhanced fragmentation of Ni(CO)4+ at 1350 nm and Fe(CO)5+ at 800 nm was attributed to corresponding resonances in the cationic energy states observed by photoelectron spectroscopy8 in metal (Ni, Cr, Fe) carbonyl compounds. The enhanced fragmentation of 1,4-cyclohexadiene compared to 1,3-cyclohexadiene was attributed to a resonance at 800 nm in the 1,4-cyclcohexadiene cation that is lacking in the 1,3-cyclohexadiene cation.9 Time-resolved measurements of halogenated methane radical cations prepared using a strong-field 780 nm pump and probed using a weak-field pulse at 780 nm revealed oscillations in the parent and fragment ion signals.4,10 The oscillations were attributed to fragmentation that occurred whenever the groundstate ionic wavepacket encountered a one-photon resonance with an excited dissociative state. The linear response of the fragmentation yield as a function of the probe−pulse intensity is consistent with a one-photon resonance. In subsequent work, a pump−control−probe scheme was also investigated as a means to manipulate the halomethane wavepacket.11 Simulations and calculations qualitatively supported the control of the wavepacket on the excited-state potential energy surfaces, in particular, the importance of one-photon ionic resonances for the dissociation of the molecule. Received: September 5, 2013 Revised: October 22, 2013 Published: October 23, 2013 12374

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Calculation of the relevant excited-state potential energy surface (PES) and conical intersections is crucial to understanding the photophysics and photochemistry of molecular systems.12,13 When two PESs are close in energy, a timedependent wave function can transfer from one surface to the other. Nuclear and electronic modes may couple when the electronic configuration is a function of nuclear motion, thus leading to nonadiabatic processes. The efficiency of a radiationless transition between two states depends on the derivative coupling vector between the states, and this is inversely proportional to the energy difference between the two states. At the conical intersection, the energy difference is zero, and the derivative coupling diverges, providing the most efficient way for radiationless transitions between states.14,15 Conical intersections play a fundamental role in the interaction of light with molecular systems including biological molecules, proteins, and DNA macromolecules.16 For instance, strongfield ionization measurements of the radical cation of uracil, supported by theoretical studies,17,13 suggest that dissociation of the molecular ion proceeds in a stepwise manner on the ground electronic surface of the radical cation. The ab initio calculations suggest that a rapid radiationless decay process transforms the electronic energy to vibrational energy on the ground ionic surface producing the small fragments. A low-lying excited ionic state was recently measured in the radical cation of acetophenone using frequency-resolved, strong-field, near-infrared excitation.18 The experiment exploited tunnel ionization as a means to create molecular ions in the ground state and mass spectrometry to measure the fragmentation distribution as a function of the exciting laser wavelength. Excitation and ionization in the IR suppresses the electrostatic field in a molecule sufficiently that an electron can tunnel through the barrier.19 In principle, tunnel ionization should place little electronic excitation into the ion produced. Monitoring the parent molecular ion and benzoyl fragment ion yields as a function of excitation wavelength revealed an ionic resonance at 1370 nm (0.9 eV) with a marked increase in the ratio of the benzoyl fragment to parent ion yields. Quantumchemical calculations performed at a high level of theory (equation of motion, ionization potential, coupled cluster singles and doubles)20 supported the presence of the corresponding excited state within a one-photon transition from the ground ionic state, D0. This is a bright excited ionic state, D2 (0.87 eV), where rotation of the acetyl group from a planar to nonplanar structure within the pulse duration enables the otherwise forbidden transition of the acetophenone cation. In the present work, we investigate a series of molecules related to acetophenone to ascertain the effects of molecular structure on the existence of a dissociative resonance in radical cations. The mass-spectral responses of acetophenone and propiophenone interacting with a range of excitation frequencies between 1240 and 1500 nm and intensities from ∼1.0 to 8.0 × 1013 W cm−2 are compared with those of acetone and ethylbenzene, which share some, but not all of the same chemical functionality as the alkyl phenyl ketones, as shown in Figure 1. The nonradiative decay mechanism for acetophenone radical cation is investigated by calculating the relevant potential energy surfaces using multiconfigurational selfconsistent field (MCSCF) method.

Figure 1. Molecular structure for (a) acetophenone, (b) propiophenone, (c) acetone, and (d) ethylbenzene.

Figure 2. The regeneratively amplified Ti:sapphire laser used to pump the optical parametric amplifier produced 1 kHz, 1 mJ, 50 fs pulses centered at 790 nm. A 75/25 beam splitter directs ∼750 μJ of the output to a collinear optical parametric amplifier (nc-OPA) based upon the design of Wilson and Yakovlev.21 The signal wavelength is readily tunable from 1150 to 1550 nm with pulse durations from 50 to 100 fs. The excitation beam is directed into the TOF-MS by a plano-convex lens, f = 20 cm. Attenuation of the beam was performed using a circular variable neutral density filter. Mass spectra were measured using a linear 1 m time-of-flight system operating in positive ion mode. A 500 μm slit was placed between the ionization and detection regions to restrict intensity averaging over the focal volume. A digital oscilloscope (LeCroy LT372) averaged 5000 spectra to produce the raw data. Acetophenone, propiophenone, acetone, and ethylbenzene (Sigma-Aldrich) were leaked into the vacuum chamber by a variable leak valve to attain a sample pressure of 4.6 × 10−4 Pa. A second leak valve was used to maintain the xenon pressure in the vacuum chamber at 7.5 × 10−6 Torr. The laser intensity at each wavelength was internally calibrated for each measurement by the Xe ion intensity. The Xe+ signals were fit to ADK calculations for tunnel ionization of a rare gas atom to determine the absolute laser intensity.22 The background vacuum pressure in the chamber was ∼1.32 × 10−6 Pa.

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CALCULATIONS Doublet ionic states for acetophenone were calculated using the multiconfigurational self-consistent field (MCSCF)23 method. Specifically, a state-averaged, complete-active-space self-consistent-field (SA-CASSCF) calculation using an active space of nine electrons in nine orbitals (9,9) was used. The active orbitals included six π-orbitals from benzene and carbonyl, one lone pair orbital from the oxygen atom, and two σ-orbitals for C−CH3 bond. The designation (n,m) is used here for an active space of n electrons in m orbitals. These orbitals are shown in Figure 3. This active space is sufficient to describe the low-lying ionic states since it includes all the valence and lone pair orbitals from which the electron is most likely to be removed during ionization. The inclusion of the σ-orbitals (one bonding and one antibonding) in the active space guarantees that the dissociation process can also be described adequately. The ccpVDZ24 basis set was used for these calculations. To explore the potential energy surface, relaxed reaction path scans for the ground ionic state were carried out at the B3LYP/6-31G(d) level of theory, starting with the D0 minimum geometry and stretching the C−CH3 single bond. The optimized geometries at each point were used for single-point calculations of ground ionic, first, and second ionic excited states (D0, D1, and D2, respectively) at the CASSCF/cc-pVDZ level. Conical intersections were located using SA-CASSCF and the algorithm25 implemented in GAMESS.26 The minimum on the D0/D1 conical intersection seam was located, while searching for the minimum on the D1/D2 conical intersection revealed a threestate conical intersection among D0/D1/D2. The geometry of

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EXPERIMENTAL SECTION A schematic of the apparatus used to perform the measurements of excited electronic states of radical cations is shown in 12375

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Figure 2. Experimental setup and the layout of the OPA and time-of-flight mass spectrometer. The idler output is simply dumped into a beam block.

range of 1240−1550 nm to probe the mechanism of the dissociative ionization reported previously in acetophenone.18 Propiophenone, containing a phenyl ring coupled to a carbonyl group functionalized with an ethyl group, is most chemically similar to acetophenone. In acetone and ethylbenzene, the phenyl ring and carbonyl group, respectively, are eliminated in comparison to acetophenone. Mass spectra were recorded as a function of excitation wavelength and intensity for the series of molecules. Figure 4 shows the raw mass spectra of each

Figure 3. Orbitals used in the active space in the CASSCF calculations: (a) orbitals that are occupied in D0; (b) orbitals that are unoccupied in D0. The geometry shown is for C−CH3 bond distance of 1.7 Å.

Figure 4. Mass spectra as a function of excitation wavelength for (a) acetophenone, (b) propiophenone, (c) acetone, and (d) ethylbenzene. The excitation wavelengths represented in the colored mass spectra at blue, green, and red are 1250, 1370, and 1440 nm, respectively. All mass spectra were taken with a 60 fs pulse at ∼6.0 × 1013 W cm−2.

the ground ionic state of propiophenone was calculated using the B3LYP/6-31G(d) approach. Ionic states at that geometry were calculated using the EOM-IP-CCSD method with the 6311+G(d) basis set. The CASSCF calculations were carried out using the GAMESS suite of programs27 while the constrained optimizations were performed using the Gaussian28 series of programs. The EOM-IP-CCSD calculations were performed using QChem.29 Visualization was rendered with MACMOLPLT.26

molecule at an intensity of 6.0 × 1013 W cm−2 for the excitation wavelengths 1250, 1370, and 1440 nm. The mass spectra of the two alkyl phenyl ketones display a similar wavelength dependence. At 1250 nm both alkyl phenyl ketones have predominantly benzoyl and parent ion peaks in the mass spectra, while at 1370 nm the parent ion is significantly reduced and the benzoyl ion increases. At 1440 nm the mass spectra of the alkyl phenyl ketones display a fragmentation distribution similar to that observed at 1250 nm, albeit with slightly less parent molecular ion. The yields of lower mass fragments of the alkyl phenyl ketones are small at all of the wavelengths

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RESULTS Acetophenone, propiophenone, acetone, and ethylbenzene were subjected to strong-field ionization in the wavelength 12376

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The parent radical cation of acetone carries >95% of the ionization yield with minimal fragmentation into small quantities of methyl and acetyl ions. The parent radical cation of ethylbenzene carries ∼80% of the ionization yield with additional fragmentation into small amounts of ethyl and toluyl ions.

investigated, which is consistent with the low degree of fragmentation typically observed in tunnel ionization.18 Acetone and ethylbenzene show no wavelength dependence in their fragmentation patterns, and their mass spectra are dominated by the respective parent ion with little fragmentation, again consistent with tunnel ionization. A plot of the ion intensities for the parent and fragments for acetophenone and propiophenone in the range of 1240−1550 nm is shown in Figure 5a. At an excitation wavelength of 1240

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DISCUSSION To explore the wavelength dependence of the dissociation of the radical cation of acetophenone using strong field nearinfrared radiation reported previously,18 the wavelengthresolved measurement was repeated on a series of homologous molecules that included propiophenone, acetone, and ethylbenzene. The integrated ion intensities of the parent and fragment ions are plotted in Figure 5a,b as a function of laser excitation wavelength. The similar wavelength dependence of the parent and benzoyl fragment ion yields for both acetophenone and propiophenone, in particular with respect to fragmentation into the benzoyl ion near 1370 nm, supports the hypothesis that there is a one-photon resonance in the alkyl phenyl ketones that leads to benzoyl formation, as discussed previously.18 Here, we propose ionization and dissociation mechanisms to explain the fragmentation processes observed upon excitation with the resonant wavelength. In the 1240−1550 nm excitation wavelength range studied here, acetophenone and propiophenone are proposed to undergo tunnel ionization to populate the ground ionic surface. This population then serves as a launch state for subsequent photochemical reaction. To distinguish tunnel ionization from multiphoton ionization in the initial reaction step, the Keldysh parameter γ may be utilized. This parameter is defined as the ratio of the laser frequency to a characteristic tunneling frequency that depends on the ionization potential and the laser field magnitude.30 If γ ≫ 1, multiphoton ionization is the dominant mechanism, and if γ ≪ 1, field ionization (combination of tunneling and barrier suppression ionization) dominates. In our experiments, the calculated values of the Keldysh parameters for acetophenone range from 0.59 (at the laser wavelength of 1550 nm) to 0.73 (at the laser wavelength of 1240 nm). The observed increased yield of parent molecular ion as compared to excitation at 800 nm (in the multiphoton regime) shows the importance of using tunnel ionization to produce a large population in the cationic ground state.18 At a resonant wavelength, the population of the ground ionic state can be selectively transferred to an excited electronic state of the ion to undergo dissociation provided that there is a nonzero oscillator strength coupling the two states and that the excited state leads to bond cleavage. In the case of acetophenone, dissociation was observed to occur exclusively to the benzoyl ion fragment upon excitation from the D0 state to the D2 state.18 The yield of the smaller fragment ions displayed no wavelength dependence as they were presumably created through another mechanism. The similarity of the wavelength-dependent response for acetophenone and propiophenone suggests that the excited state that is responsible for the resonance resides mainly on the benzoyl portion of the molecules rather than the alkyl functionality. Therefore, we propose that the same low-lying excited ionic state is involved in the one-photon resonance in both molecules. To test whether the benzoyl group is required for the dissociative ionization resonance observed in the alkyl phenyl ketones, spectrally resolved measurements were performed on acetone and ethylbenzene. In contrast to the alkyl phenyl

Figure 5. (a) Normalized, integrated ion intensities for parent, benzoyl, and small fragments in the alkyl phenyl ketones. The parent ions of acetophenone and propiophenone are denoted by the dark blue and cyan lines, respectively. The benzoyl ions of acetophenone and propiophenone are denoted by the red and magenta lines, respectively. The phenyl, acetyl, and methyl ion fragments that originated from acetophenone are shown; the yields of the same fragment ions from propiophenone were similar as a function of wavelength. The ion yields are normalized to that of the respective benzoyl ion at 1370 nm. (b) Normalized, integrated ion signals for parent and fragment ions of ethylbenzene and acetone. The signals are normalized to their respective parent ions at 1370 nm. All measurements were performed at an intensity of ∼6 × 1013 W cm−2 with a pulse duration of 60 fs.

nm, the acetophenone molecular ion is the most abundant peak, whereas the propiophenone molecular ion has an approximately equal intensity to the benzoyl fragment ion. The benzoyl yield is maximal and the parent ion signal is minimal at 1370 nm for both molecules. At longer excitation wavelengths >1400 nm, the benzoyl ion and parent ion yields return to nearly equal intensity. The signal intensities of the lower-mass fragments of acetophenone remain constant over the tuning range. The lower-mass fragments of propiophenone respond similarly to the corresponding acetophenone fragments and are not shown. The integrated parent and fragment yields for acetone and ethylbenzene are shown in Figure 5b. 12377

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the π-benzene ring (giving rise to two A″ states, D1 and D2) or from the lone pair on oxygen (producing the A′ state, D0). Previous calculations18 revealed that the oscillator strength between the states involved is zero. Oscillator strength is proportional to the energy difference of the two states involved,34 and thus a small energy gap between two states will lead to a smaller oscillator strength decreasing the probability for the transition to occur, but not making it forbidden. As the energy gaps increase when the ion evolves toward equilibrium geometry, the oscillator strengths for the transitions D0 to D1 and D0 to D2 reach the value of 0.002 and 0.046, respectively, at the D0 minimum in the potential energy surface. To determine which states are involved in the dissociation of the methyl group in acetophenone, the potential energy surfaces of the three lowest-lying doublet states were calculated as a function of the C−CH3 bond as shown in Figure 7, with all

ketones, the intensities of the parent and fragment ions of the homologous molecules acetone and ethylbenzene, shown in Figure 5b, remain constant over the entire wavelength tuning range, suggesting that there are no low-lying dissociative states for these molecules in the range between 1240 and 1550 nm. In comparison with acetophenone, acetone lacks the phenyl functionality (replaced by a second methyl group), and ethylbenzene lacks the carbonyl functionality (replaced by a methylene group). This implies that the coupled phenyl and carbonyl functional groups are required to create a low-lying dissociative state accessible in the near-infrared region. The fragments observed in acetone and ethylbenzene presumably arise from excitation to higher states, with a lower nonlinear excitation cross section. Previous investigations of acetone31 and ethylbenzene32 helped to elucidate the dissociation mechanisms of polyatomic molecules in the strong field regime at 800 nm and the dissociation distributions of both molecules were explained in terms of field-assisted mechanisms. To elucidate the dissociation mechanism of the acetophenone molecular cation, portions of the potential energy surfaces for the three lowest-lying doublet states were calculated. Figure 6 displays the energy as a function of torsional angle. As noted

Figure 7. Potential energy surfaces of the acetophenone radical cation calculated as a function of the C−CH3 bond length for the three lowest-lying doublet states D0, D1, and D2. Geometries are obtained from a constrained optimization on D0 at the B3LYP level, and energies of D0, D1, and D2 at these geometries are calculated at the SACASSCF level. The red, green, and blue represent the energies of the D0, D1, and D2 surfaces, respectively.

Figure 6. Potential energy surfaces of the acetophenone radical cation calculated as a function of the phenyl−acetyl dihedral angle for the three lowest-lying doublet states D0, D1, and D2. Geometries are obtained from a constrained optimization on D0 at the MP2/6-31G(d) level, and energies of D0, D1, and D2 at these geometries are calculated at the EOM-IP-CCSD/6-311+G(d) level. The red, green, and blue represent the energies of the D0, D1, and D2 surfaces, respectively.

other nuclear coordinates held fixed. The MCSCF calculations indicate that, as the C−CH3 bond length of the parent ion elongates, the energy of D0 increases, while the energies of D1 and D2 decrease to reach a minimum at 1.69 Å. Further elongation to 2.5 Å reveals that the energy of the D1 and D2 increases approximately by 4 eV while the D0 state increases by 0.5 eV in energy. Therefore, direct dissociation on the D2 surface will not occur, while dissociation on the D0 surface is energetically possible. Dissociation is often mediated by nonradiative passage from an excited state to a lower energy state.35−37 Therefore, we explored the potential energy surfaces for the D0, D1, and D2 states to locate conical intersections that can mediate such nonradiative relaxation. Additional calculations at MCSCF/ccpVDZ level of theory reveal conical intersections near torsional angles of 1° and 22°. Figure 8 shows the ground- and excitedstate energies in the acetophenone radical cation versus the geometry change at the S0 minimum, D0 minimum, D0/D1 conical intersection found at 22°, and D0/D1/D2 conical intersection found at 1°. The wavepacket nonradiatively relaxes into the D0 state either directly through the D0/D1/D2 conical intersection or stepwise through two individual two-state conical intersections. The minimum on the D0/D1 seam was

previously, the vertical excitation leads to 0° torsional angle that subsequently rotates to 44° to reach a minimum on the D0 where subsequent excitation can occur.18 Higher-energy excited ionic states were also investigated but were found to be out of range for a one-photon excitation. We anticipate that onephoton processes are important because tunnel ionization occurs at the peak of the pulse, predominantly populating the D0 surface.18 The system then evolves in the torsional coordinate acquiring oscillator strength to reach the excited D1 and D2 states. The time required to reach the minimum on the D0 state is approximately 600 fs period/4 = 150 fs.33 After ionization at the peak of the laser pulse, the intensity subsides on a time scale of 60 fs fwhm/2 = 30 fs, and therefore D1 and D2 are the only states found to be within range of a one-photon absorption in the lower intensity tail of the pulse. Upon vertical ionization, the parent ion has the planar geometry of the neutral molecule and calculations of the ionic states at the S0 geometry indicate that the three ionic states are close in energy. These states originate by removal of the electron either from 12378

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Figure 9. Proposed mechanism of benzoyl formation via tunnel ionization and a one-photon absorption. The first panel shows the mechanism along the C−CH3 bond length and the second panel depicts the mechanism along the C−CH3 dihedral angle. The figure is numerically annotated to aid in the interpretation of the mechanism. The curved orange arrow signifies formation of the parent molecular ion and the straight orange arrow signifies the resonant one-photon transition to D2. Curves were constructed from data points in Figures 6 and 7.

Figure 8. Energy level diagram of the ground ionic and excited ionic states in acetophenone as a function of geometry. The zero of energy is set to the energy of the optimized ground state. Conical intersections for the D0/D1/D2 and D0/D1 states are shown as well as the equilibrium geometries of the neutral and the cation. The red, green, and blue represent the energies of the D0, D1, and D2 states, respectively; the yellow denotes that D0 and D1 energies are equal. The curved orange arrow denotes tunnel ionization from S0 to D0 and the straight orange arrow denotes a one-photon transition from D0 to D2. The ground and excited states for the acetophenone ion at the conical intersection points, D0/D1/D2 and D0/D1, were calculated at the MCSCF/cc-pVDZ level of theory while the energies at S0 minimum and D0 minimum are calculated at the EOM-IP-CCSD/6-311+G(d) level. The S0 and D0 minimum geometries and energies are taken from ref 23.

in the excited state electronic energy is converted to vibrational energy on the ground ionic state. Quantum chemistry calculations performed on the parent molecular ion of propiophenone show the energy gap between the ionic ground state D0 and the first bright excited state D1 at the equilibrium geometry is 0.88 eV. This value is in agreement with measured resonance at 0.9 eV. The calculations showed that upon tunnel ionization the molecular ion emerges in the planar neutral geometry. The geometry optimization calculation reveals that the acetyl group initiates out-of-plane torsional rotation with respect to the phenyl ring, which is very similar to the acetophenone case. This suggests that the mechanism of dissociation of the propiophenone parent ion will be similar to that of the acetophenone parent ion. Finally, the dynamics of tunnel ionization followed by a onephoton transition should be reflected in the shape and width of the mass-spectral resonance feature. In this case the wavelength-dependent dissociation of the parent ion initially in the ground state to the benzoyl fragment can be modeled as a firstorder unimolecular decay initiated by the absorption of a photon. Dipole transitions between D0 and either D1 or D2 are initially forbidden by the selection rules in this geometry (cf., the discussion accompanying Figure 6). As the ion evolves toward equilibrium geometry, the D0−D2 energy gap grows larger and simultaneously the corresponding transition dipole matrix element acquires some nonzero value, thus enabling a one-photon transition. We can model the wavelength-dependent D0−D2 transformation leading to dissociation of the parent ion in the following way. Let the evolution of the transition dipole be given by μ(t) and the D0−D2 energy distance by ℏωAB(t). These functions are expected to change considerably within the duration of the laser pulse envelope E(t), whose characteristic time scale is much longer than the cycle duration 2π/ω. Then, the buildup of the D2 state amplitude B at the expense of the D0 state amplitude A may be approximated as

located at 22°, and the minimum on the D2/D1 seam at 1° leads to the D0/D1/D2 conical intersection. The presence of the D0/D1/D2 conical intersection indicates that the D2/D1 and D1/D0 seams are easily accessible and facilitate nonadiabatic transitions. The torsional angle of the acetyl group is the critical coordinate in both the one-photon excitation to the D2 state and the radiationless relaxation back to the D0 state. The C− CH3 bond length shortens to 1.50 Å for both conical intersection points (D0/D1/D2 and D0/D1). We propose the mechanism for the dissociation of the carbonyl−methyl bond in the acetophenone parent ion summarized in Figure 9. Tunnel ionization (step 1) prepares a launch state in D0. Within the ionizing pulse duration the molecular ion relaxes to its equilibrium geometry through a torsional motion (step 2) finding a minimum when the torsional angle reaches 44°. This geometry allows for the absorption of a 0.9 eV photon which transfers population from the D0 surface to the PES of the bright D2 state (step 3).18 Once the transition is completed, the wavepacket travels down the D2 potential energy surface (step 4) toward the initial 0° angle of the vertical transition state accessed upon tunnel ionization. The wavepacket then proceeds to the ground ionic surface at the 1° torsional angle through a conical intersection involving the D0, D1, and D2 states through a radiationless decay mechanism (step 5). In the ground ionic state, the electronic energy is converted to methyl−carbonyl vibrational energy due to anharmonic couplings (step 6). This kinetic energy can then be used to dissociate the cation, as the 0.9 eV of energy absorbed exceeds the 0.82 eV needed to dissociate the methyl−carbonyl bond.38 The dissociation of the uracil radical cation in strong field experiments36,39 was also consistent with such a radiationless decay mechanism where

dB i = μ(t )E(t ) exp(iωt − i dt 2ℏ

∫ dt ωAB(t ))A

(1)

If the evolving transition frequency ωAB(t) reaches the resonance with the laser carrier frequency within the pulse 12379

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duration, considerable amplitude transfer occurs, leading to depletion of the parent ion. This process is seen in the upper panel of Figure 5, where, for example, A1370 nm ≪ A1240 nm. The relation between the final yields of the benzoyl fragment and the parent ion is determined by the ratio |B(∞)|2/|A(∞)|2. At the onset of the depletion process, the frequency dependence of this ratio can be estimated as the transition probability Pλ =

1 | 4ℏ2

∫0

∞

dt μ(t )E(t ) exp(iωt − i

∫ dt ωAB(t ))|2 (2)

where we assume that the tunnel ionization occurs at the peak of the pulse, at t = 0. Let us consider a Gaussian pulse shape E(t) = E0 exp(−t2/τ2) and simplify the evolution of the transition dipole and the transition frequency by a threshold function μ(t) = μ0Θ(t − t0); ωAB(t) = ω0Θ(t − t0), where t0 signifies the described geometry-evolution delay between the moment when a ground-state ion is produced by tunnel ionization and the moment when it becomes available to onephoton excitation process. Then, eq 2 is evaluated as Pλ =

⎛t ⎛ 1 ⎞ π i ⎞ |μ |2 E0 2 exp⎜ − Δ2 τ 2⎟ erfc⎜ 0 − Δτ ⎟ ⎝ 2 ⎠ ⎝τ 2 ⎠ 16ℏ2 0

Figure 10. Normalized fragmentation outcome as a function of the carrier frequency detuning from the resonance for two different values of the pulse duration τ, as modeled by eq 3: green curve, τ = 60 fs; red curve, τ = 120 fs. The geometry conversion delay parameter is fixed at t0 = 30 fs.

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CONCLUSIONS Excited-state electronic resonances have been observed in a pair of alkyl phenyl ketones, as revealed by the control of the fragmentation of the molecule as a function of excitation wavelength. In contrast, similar homologues show no wavelength dependence in their fragmentation patterns. Supporting calculations help to elucidate the ionization/dissociation mechanism. Following population of the ground ionic state by tunnel ionization, population transfer to the D2 state occurs if the pulse contains resonant photons. Once on the D2 surface the population decays to the D0 surface through a three-state conical intersection that leads to dissociation along the C−CH3 bong length coordinate. The energy gap for D0−D2 in propiophenone was calculated to be 0.88 eV, suggesting that the mechanism of dissociation of the propiophenone parent ion is similar to that of the acetophenone parent ion. Further experiments into the time-resolved dynamics will be useful to elucidate the wavepacket dynamics and can be extended to plausible coherent control schemes.

2

(3)

where Δ = ω − ω0. Equation 3 reveals that the efficiency of this dissociation mechanism is linearly proportional to the laser pulse intensity, while the expected width of the mass-spectral resonance feature is determined by both the pulse duration and the shape of the potential energy surfaces embodied by the parameter t0. Note that in this approximation Pλ is symmetric with respect to Δ→ −Δ. However, if smoother dependence of μ(t) and ωAB(t) is implemented, asymmetry is expected to emerge in eq 3, because transition frequencies ωAB < ω0 with nonzero values of μ will become available. As a result, the laser field frequency having a certain negative value of the detuning, Δ, will be more likely to cause a transition than the laser field frequency having a positive detuning of the same magnitude. Thus, the red-shift side of the mass-spectral peak is expected to be wider than the blue-shift side, which would even better correspond to the experimental curves in Figure 5 and the previous observations.18 Finally, when comparing with the experiment, Pλ should be convoluted with 25 meV rovibrational distribution anticipated from the Boltzmann distribution of the ground-state neutral at room temperature. The dependence of the mass-spectral resonance feature on the laser pulse duration exemplified in Figure 10 is in good agreement with experimental observation reported in ref 18, where change of the laser pulse duration from 60 to 100 fs resulted in the change of the fwhm of the mass-spectral resonance feature of the benzoyl fragment from 70 to 50 meV. This correspondence between the pulse duration and the resolution of the molecular response feature is an additional confirmation of the one-photon character of the resonant fragmentation process. Note, however, that the data for the longer pulse shown in ref 18 reveals significant depletion of the parent ion. In this case, evolution of the amplitude A should be taken into account, and an equation for A should be considered alongside eq 1. As a result, the exact shape of the mass-spectral resonance curve will deviate from that of eq 3 and can only be obtained as a result of numerical integration of the coupled equations for B and A.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We acknowledge the support of the National Science Foundation through grant nos. CHE0957694 and CHE1213614.

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REFERENCES

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