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Systematic Trends in Photonic Reagent Induced Reactions in a Homologous Chemical Family Katharine Moore Tibbetts,† Xi Xing, and Herschel Rabitz* Department of Chemistry, Princeton University, Princeton, New Jersey 08544, United States ABSTRACT: The growing use of ultrafast laser pulses to induce chemical reactions prompts consideration of these pulses as “photonic reagents” in analogy to chemical reagents. This work explores the prospect that photonic reagents may affect systematic trends in dissociative ionization reactions of a homologous family of halomethanes, much as systematic outcomes are often observed for reactions between homologous families of chemical reagents and chemical substrates. The experiments in this work with photonic reagents of varying pulse energy and linear spectral chirp reveal systematic correlations between observable ion yields and the following set of natural variables describing the substrate molecules: the ionization energy of the parent molecule, the appearance energy of each fragment ion, and the relative strength of carbon−halogen bonds in molecules containing two different halogens. The results suggest that reactions induced by photonic reagents exhibit systematic behavior analogous to that observed in reactions driven by chemical reagents, which provides a basis to consider empirical “rules” for predicting the outcomes of photonic reagent induced reactions. jth column Oj of the matrix  are highlighted in pale blue and magenta, respectively. It is desirable to express the reagent and substrate axis indices i and j in terms of known chemical properties, with the axis values ordered in such a way that best reveals their effects on the measured observable values.5 For example, the reactions4 of C = [H2O F− Cl− Br− OH− I− SCN− CN− S2O3−] and S = [CH3F CH3Cl CH3Br CH3I] in water produced systematically varying yields of the observable  = log k , where each element kij denotes the nucleophilic substitution reaction rate between reactant Ci and substrate Sj. Figure 1b shows that the reaction rate increases systematically along both the chemical reagent C and substrate S axes upon ordering the chemical reagents according to their nucleophilic strength6 and the substrates according to their leaving group ability. Linear free energy relationships extracted from the rate data4 indicate that the reaction proceeds through a two-step process with a tight ionpair intermediate formed as the first step, as opposed to the traditional one-step SN2 mechanism.7 The dependence of the reaction rate in Figure 1b on both the reagent nucleophilic strength and substrate leaving group ability illustrates the connection between an appropriately ordered observable matrix  and ultimately mechanistic insights, in this case through linear free energy relationships.

I. INTRODUCTION Ultrafast laser pulses have been widely employed to initiate chemical reactions1 and even control their outcomes.2 The growing field of laser chemistry naturally leads to extending the concept of a chemical reagent to include an ultrafast laser pulse acting as a “photonic reagent”3 that drives a chemical reaction, where the laser−molecule interaction may be considered in analogy to the interaction between chemical reagents and substrates. This notion raises the question of whether a family of photonic reagents can produce systematic responses from a set of chemically related substrates, much like systematically varying reaction yields are observed from homologous families of chemical reagents and substrates. For instance, a large family of nucleophiles can affect systematically varying displacement reaction rates in the chemically related substrates CH3X (X = F, Cl, Br, I).4 In this work, we investigate systematic behavior in dissociative ionization reactions over a set of chemically homologous substrates induced by families of photonic reagents. To illustrate the concept of homologous families of chemical reagents or substrates, consider a reaction between a set of chemical reagents C and substrates S, expressed as vectors of the species involved. Reacting the ith chemical reagent Ci with the jth substrate Sj gives the observable yield Ci + Sj → Oij, where Oij is an element of the product matrix  consisting of reaction yields, rates of product formation, or any other relevant observable. The observable yields for the entire matrix  can be obtained by reacting every combination of C and S, i.e., P + S → . A schematic illustration of these types of experiments is shown in Figure 1a, where the ith row Oi and © 2013 American Chemical Society

Received: April 17, 2013 Revised: June 28, 2013 Published: August 2, 2013 8205

dx.doi.org/10.1021/jp403824h | J. Phys. Chem. A 2013, 117, 8205−8215

The Journal of Physical Chemistry A

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Figure 1. Comparison of reactions induced by chemical reagents C and photonic reagents P interacting with substrates S. (a) Matrix of observables O arising from interaction of vectors of chemical reagents C and substrates S, with the column vector O j highlighted in magenta, row vector Oi highlighted in pale blue, and matrix element Oij highlighted in their overlapping region. (b) Systematically varying matrix of observable yields  = log k , where kij is the reaction rate of the nucleophilic substitution reaction between the ith reagent and jth substrate4 and the chemical reagents and substrates (i.e., labeled by i and j, respectively) make up the two independent variable axes. (c) Analogous experiments with photonic reagents and substrates. The goal of this work is to assess whether systematic trends occur like those in (b) upon interactions P + S → , as indicated by the question mark over the arrow out of (c).

Cl → Br → I. The family of halomethanes encompasses more than 60 molecules containing one through four halogen atoms, of which 11 containing two or three halogen atoms are chosen for the present investigation due to their commercial availability and ease of experimental manipulation: CH2FCl, CH2Cl2, CHCl3, CH2Br2, CHBr3, CH2BrCl, CH2ICl, CH2IBr, CH2I2, CHCl2Br, and CHClBr2. We investigate the ions produced by the cleavage of a carbon−halogen bond C−X through time-offlight (TOF) mass spectrometry. As the apparatus precludes detection of neutral fragments, the contributions of neutral dissociation products are unknown in the present experiments. Nevertheless, previous femtosecond pump−probe studies on CH2ICl, CH2IBr, and CH2I2 indicate that dissociation occurs predominantly on ionic potential energy surfaces.26−28 These results suggest that detection of the ionized photoproducts can capture many of the significant dissociation processes in these and likely other halomethanes. For a halomethane represented by CH2XY, where “X” denotes the less polarizable halogen and “Y” denotes the more polarizable halogen, the products of interest here are methyl halide ions CH2X+, CH2Y+, and halogen ions X+ and Y+. Although many dissociative ionization studies have provided insight into the dissociation processes in individual halomethanes,25−33,46 no associated systematic trends across a broad family of halomethanes (or any other large molecular family) have been previously reported. The present goal of identifying trends in the relative yields of photoproducts across an entire molecular family is central to understanding the action of photonic reagents in the context of reactions with traditional chemical reagents.

Consider the analogous situation where a set of photonic reagents P interacts with a set of substrates S, as illustrated in Figure 1c. The central question considered in this work is whether systematic variation in observable yields analogous to Figure 1b occurs when the chemical reagents are replaced by photonic reagents. Ultrafast laser-induced dissociative ionization reactions using a set of photonic reagents with a fixed substrate or vice versa have been explored for many classes of molecules.8−42 These studies revealed detailed information about the physical mechanisms underlying the dissociation dynamics in individual molecules and/or identified specific photonic reagents that produce a desired yield of some observable, typically a particular photoproduct or ratio of photoproducts. In contrast, less attention has been given to examining families of chemically homologous molecules interacting with families of photonic reagents; previous investigations typically have examined only a few related molecules43−50 or a large set of unrelated molecules.51 The present paper aims to build a generalized framework for understanding the systematics of reactions between a related set of photonic reagents and a homologous family of substrate molecules, analogous to studies of homologous families of “traditional” chemical reagents and substrates.4,5,52−55 We report systematically varying observable yields from photonic reagent induced chemical reactions, using the dissociative ionization reactions in a family of halomethanes as a simple test case. The properties of this family, including chemical reactivity4,56,57 and ion appearance energies,58−66 vary systematically with the halogen polarizability rising from F → 8206



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When considering sets of observable yields from reactions between families of reagents and substrates, suitable plots of the data can aid in revealing systematic patterns.5,52−55 In this regard, an appropriate ordering of the molecular species along their respective axes is important. The ordering may be performed by a good a priori choice of “natural variables” characterizing the (photonic) reagents and substrate molecules, and automated algorithms are available to identify regular patterns in the data which can then result in the discovery of a proper choice of natural variables.5,54,55 For instance, in Figure 1b the nucleophilic strength and leaving group ability act as natural reagent and substrate variables, respectively, giving rise to the indicated ordering. The substrate ordering in the latter case may equivalently be characterized by halogen polarizability or ionization potential, showing substantial freedom in choosing operationally equivalent natural variables. In this work, the photonic reagents are simply characterized by their pulse energy or linear spectral chirp, as they proved sufficient to produce systematically varying reaction yields across the halomethanes. The characterization of the halomethanes was found to be adequate using three natural variables: the ionization energies (IE) of the parent molecules, the appearance energies (AE) of the fragment ions, and the ratios of the carbon−halogen bond strengths in compounds containing two different halogen atoms. These variables are simple and intuitive when considering dissociative ionization experiments, and they provide a basic illustration of systematic behavior in photonic reagent induced reactions as a foundation for future studies between molecular families and shaped laser pulses, with both likely characterized by many more variables. Beyond the halomethanes, dissociative ionization studies of small families of alkylbenzenes49 and alkylphenols50 with transform-limited 800 nm pulses found that the length of the alkyl chain acts as a natural substrate variable dictating the yields of fragment ions. A significant challenge is to achieve a full understanding of the correlations in reaction yields arising from the interaction of photonic reagents with a family of molecules in Figure 1c, and subsequently to deduce the underlying physical mechanisms. In this context, the discovery of systematic trends in reactions67−69 as in Figure 1a and investigations of reaction dynamics mechanisms across families of chemical reagents and substrates70−73 have both involved an intense effort in many laboratories over at least 40 years to the present day. The present work takes a step toward understanding photonic reagent induced dynamics over families of substrates by assessing whether empirical correlations exist between observables and appropriate photonic reagent and substrate variables, analogous to correlations between chemical structure and reactivity permitting the transition from Figure 1a to Figure 1b. Identifying the extent to which systematic correlations exist may facilitate the discovery of broadly applicable mechanisms across the molecular family. To the degree possible, we will infer mechanistic insights from our available experimental data; further analysis including theoretical calculations is beyond the scope of this work. The latter scope of study will address whether an analogous transition can be made from Figure 1c to a graphic like Figure 1b with photonic reagents and chemical substrates. We hope that the success shown in the present venture can form a foundation for future studies, for instance involving complex shaped laser pulses and additional chemical families. In this regard, for reactions between a given photonic reagent and substrate, electronic structure calculations21−27,46,47

have proven invaluable for suggesting mechanisms and possibly may provide insights extending over a family of molecules. The remainder of the paper is structured as follows. Section II describes the experimental apparatus, including the laser, pulse shaper, and time-of-flight (TOF) mass spectrometer for ion detection. Section III considers three particular photonic reagents and all 11 halomethanes as the substrates. In section IV, additional systematic trends across the substrate family of dihalomethanes are identified using families of photonic reagents with systematically varying pulse energy and spectral chirp. Section V presents a discussion of the results with a summary of the observed systematic trends, as well as concluding remarks.

II. EXPERIMENTAL METHODS The experiments employed a Ti:sapphire oscillator and regenerative amplifier (Coherent) producing 1 mJ pulses centered at 800 nm. A gain-flattening filter (ARO, SF640) placed in the amplifier provided a bandwidth full width at halfmaximum of 60 nm and pulse duration of ∼25 fs. The laser pulses were introduced into a pulse shaper with a programmable dual-mask liquid crystal spatial light modulator (SLM) with 640 pixels and 0.155 nm/pixel (CRI, SLM-640) capable of independent phase and amplitude modulation. The output pulse energy from the shaper was 360 μJ. Residual high-order dispersion in the amplifier output was removed by optimizing the two-photon absorption (TPA) signal measured by a twophoton diode (Thorlabs) with a genetic algorithm.74 The resulting transform limited (TL) reference phase was added to all subsequent pulse shapes implemented on the SLM. Phase− amplitude coupling in the SLM was sufficiently small such that varying the pulse energy by amplitude shaping while maintaining the TL reference phase did not significantly lengthen the TL pulse, as measured by frequency-resolved optical gating (FROG). Similarly, placing arbitrary spectral phases on the SLM did not decrease the output pulse energy below ∼355 μJ. The SLM was employed in two ways in our experiments. First, the pulse energy was scanned from 15 to 360 μJ by systematically changing a constant amplitude across the SLM pixels while maintaining the TL spectral phase. Second, the linear spectral chirp was scanned by imparting a quadratic spectral phase Φ(ω) across the SLM pixels: Φ(ω) = A(ω − ω0)2

(1)

where ω0 is the center spectral frequency of the laser radiation, which is aligned with the center pixel on the SLM. The spectral phase of a linearly chirped pulse is equivalent to the secondorder term of a Taylor expansion of the phase, Φ(ω) = Φ(ω0) + Φ′(ω)(ω − ω0) + 1/2Φ″(ω)(ω − ω0)2 + ..., with the coefficient A = 1/2Φ″(ω) expressed in square femtoseconds. The “+” or “−” sign of the coefficient A corresponds to positive chirp (red before blue) or negative chirp (blue before red), respectively. A was varied on the SLM over the range of ±25 000 fs2, which lies within the limits of the maximal chirp magnitude achievable with our pulse shaper resolution. The shaped pulses were passed through a fused silica lens of 20 cm focal length into a vacuum chamber (base pressure 1.0 × 10−8 Torr) to a knife-edge measured focal spot size of 40 μm, producing a maximal intensity of ∼1015 W/cm2 for the TL pulse at an energy of 360 μJ. The ionized photoproducts were detected using a linear time-of-flight (TOF) mass spectrometer 8207



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Table 1. Properties of Halomethanes, Including Ionization Energies (IE), Appearance Energies (AE), and Bond Strengths C−X and C−Ya species CH2FCl CHCl3 CH2Cl2 CHCl2Br CH2BrCl CHClBr2 CH2Br2 CHBr3 CH2ICl CH2IBr CH2I2

IE, M+ 58

11.63 11.4264 11.3360 10.88† 63 10.7760 10.5964 10.5560 10.5164 9.7560 9.6960 9.4260

AE, CH2X+ 58

12.57 11.52† 66 12.12† 66 11.02† 63 11.5060 11.29† 66 10.53† 66 10.8860 10.8160 10.42† 66

AE, CH2Y+ 14.1

AE, X+

C−X

C−Y 349.862

17.4† 59

462.662 320.762 33860 332.860

277.360

58

11.9860 15.5† 59 15.4† 65 11.6660 11.1160 13.2† 59

290.160 27562 328.260 274.560 216.960

217.460 219.260

a

IE and AE are presented in units of eV and bond strengths are presented in units of kJ/mol. All entries come from photoionization studies, except for those marked with a “†”, which are from electron-impact-ionization studies. For species with two distinct halogens, “X” denotes the less polarizable halogen and “Y” denotes the more polarizable halogen.

Figure 2. TOF spectra under excitation with the 360 μJ TL pulse as photonic reagent P1. (a) TOF spectra of each molecule as a function of mass/ charge (m/q) ratio showing fragments up to 160 amu. Selected methyl halide and halogen ions are labeled, as well as the contaminant H2O+. (b) 35 + Cl ion signal as a function of time (μs). (c) 79Br+ ion signal as a function of time (μs). (d) I+ ion signal as a function of time (μs). All ion signals in (b)−(d) have two or three peaks, where the peaks marked with an asterisk (∗) arise from Coulomb explosion of a multiply charged precursor ion, and the peak marked with a number sign (#) arises from a singly charged precursor ion. The additional peak to the right in (c) is HBr+.

(Jordan TOF), with the laser radiation polarized parallel to the TOF axis. Samples of CH2Cl2, CHCl3, CH2Br2, CHBr3, CH2BrCl, CH2ICl, CH2IBr, CH2I2, CHCl2Br, and CHClBr2 were purchased from Sigma-Aldrich, and CH2FCl was purchased from SynQuest Laboratories. The samples were used without further purification and were introduced into the vacuum chamber through an effusive leak valve to produce a pressure of 1.0 × 10−6 Torr. Ions were collected through an extraction grid with a 0.5 mm diameter pinhole to ensure collection of ions only from the laser focal region, which both facilitates interpretation of the mass spectral features13,24,75,76 and reduces the effects of spatiotemporal coupling of the focused laser beam.77,78 Any residual spatiotemporal focusing effects would be normalized over the set of molecules by use of

the same beam alignment and TOF apparatus. The extracted ions passed through a 1 m field-free flight tube to a dual microchannel-plate detector. The resulting signal was recorded using a digital oscilloscope (LeCroy 104MXi) with the TOF spectra averaged over 50 000 laser shots. The yield of a target photoproduct was determined by integrating over the full width of the associated TOF spectral peak. The experiments presented below reveal systematic correlations between photoproduct yields and one of the following natural variables characterizing the substrates: IE of the parent molecule, AE of the fragment ions, and the ratios of the carbon−halogen bond strengths in compounds of the form CH2XY. The literature values reported for these variables are given in Table 1. Although the photonic reagents in our 8208



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same halogen ion upon ascending the ordinate axis. The kinetic energy release (KER) from Coulomb explosion may be estimated from the separation between the two peaks via8

experiments may, in principle, be characterized by more than 103 independent pixel variables, we consider only the pulse energy E and linear spectral chirp coefficient A (cf. eq 1) to describe the photonic reagents because they were found to be sufficient for identifying reactivity trends with respect to the natural chemical substrate variables in Table 1. In section III, three particular photonic reagents Pi (i = 1, 2, 3) are characterized by specific values of E (μJ) and A (fs2), i.e., Pi ≡ P(E,A); the TL spectral phase corresponds to A = 0. The families of photonic reagents in section IV are denoted as vectors characterized by either E or A, i.e., P ≡ P(E) ≡ E or P ≡ P(A) ≡ A.

KER =

q2(Δt )2 (V1 − V2)2 8md 2

(2)

where q is the charge of the daughter ion, Δt is the time separation between the two spectral peaks, V1 and V2 are the voltages placed on the repeller plate and extraction grid, respectively, m is the mass of the daughter ion, and d is the distance between the repeller plate and extraction grid. The increasing separation Δt upon ascending the ordinate in Figure 2b−d therefore indicates increasing KER. As the substrates are ordered in terms of decreasing IE of the parent molecule (cf. Table 1), the KER is negatively correlated to the IE. This trend is quantified by evaluating eq 2 for the halogen ions Cl+ (circles), Br+ (squares), and I+ (triangles) in Figure 3, where

III. REACTIVITY TRENDS FOR ALL ELEVEN HALOMETHANES We first consider all 11 halomethanes with three photonic reagents P1 ≡ P(E=360,A=0), P2 ≡ P(E=140,A=0), and P3 ≡ P(E=360,A=2000). The spectra of all 11 halomethanes upon excitation with P1 are shown in Figure 2a, and the magnified Cl+, Br+, and I+ ion signals are shown in Figure 2, parts b, c, and d, respectively. The TOF spectra share some common features across the entire family. First, the highest peak in all spectra is the fragment ion formed by loss of a halogen atom Y from the parent molecular ion M+, i.e., the species (M − Y)+. This fragment results from the cleavage of one (weaker) carbon halogen bond C−Y from the neutral molecule or M+. The latter feature has been previously reported in TOF spectra of CH2BrCl, CH2ICl, CH2IBr, and CH2I2 obtained from interaction with 800 nm TL pulses.20,21,31,32,46 The only exception is CH2FCl, where the M+ yield is greater than that of the fragment CH2F+. This property arises because the appearance energy for CH2F+ lies much higher above the IE of CH2FCl as compared to other molecules (cf. Table 1), leaving the parent ion more stable. This unique feature of the only fluorine-containing molecule CH2FCl studied here makes its fragmentation behavior quite distinct from the others, which will be further discussed in section IV.2. Second, the highest charge states of the halogen ions are F+, Cl4+, Br5+, and I6+ (these signals are typically too small to see on the scale in Figure 2a), regardless of the parent molecule. The independence of the highest halogen charge state on the parent molecule (e.g., all molecules containing Br have charge states up to Br5+ in the TOF spectra) has been observed for molecules of the form CnH2n+1X.44 The third common feature is that all of the TOF spectral signals from the halogen ions (both singly and multiply charged) have multipeak structures, as shown for the singly charged halogen ions in Figure 2b−d. The central peak marked with a number sign (#) arises from a singly charged precursor (likely M+), while the two outer peaks marked with asterisks (∗) arise from Coulomb explosion of a multiply charged precursor.8,44 The relative height of the central peak as compared to the outer peaks increases going from Cl+ → Br+ → I+, which correlates inversely with the halogen appearance energies. These similarities across the entire set of molecules reflect their chemical homology upon interaction with the TL pulse (photonic reagent P1). However, there are also two systematic trends of varying observable yields over the halomethane family with respect to one of the substrate natural variables, as explained below. The first trend is evident from the magnified halogen ion signals in Figure 2b−d, where the separation in time between the Coulomb explosion peaks can be seen to increase for the

Figure 3. Kinetic energy release (KER) from Coulomb explosion in eV as a function of the parent molecule IE in eV. Circles, Cl+; squares, Br+; triangles, I+. Red symbols: KER from interaction with P1 ≡ P(E=360,A=0), including error bars from estimating Δt from inspection of the plots in Figure 2b−d. Black symbols: KER from interaction with P3 ≡ P(E=360,A=2000); error bars were of similar magnitude to the case for P1. The KER upon interaction with P2 was comparable to that from P3.

the red symbols denote the KER observed from interaction with P1 and the black symbols denote the KER observed upon interaction with P3. The KER from interaction with P2 was comparable to that with P3 (not shown), so the inverse correlation between the KER and IE appears to hold for TL pulses of varying energy, as well as chirped pulses. The KER scales as Cl+ > Br+ > I+ for any value of IE, which is consistent with a study of ethyl halides C2H5X+ (X = Cl, Br, I)43 and simply correlates inversely with the polarizability (or, equivalently, atomic number) of the halogen atom. Another study revealed the trend that KER of X+ (X = Cl, Br) increased for parent molecules going from C2H5X → C3H7X → C4H9X,44 but a full explanation of the trend is not known. The present correlation between KER and IE may appear to arise from the increasing mass of the remaining fragment from dissociation of the doubly charged parent molecular ion because conservation of momentum dictates that the corresponding halogen ion would be released with a higher kinetic energy. However, this does not explain the higher KER of Cl+ from CH2ICl than Cl+ 8209



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from CHClBr2 in the present results, as the mass of CHBr2+ (171 amu) exceeds that of CH2I+ (141 amu). Thus, the origin of this behavior is likely electronic in nature and may be due to greater excess laser energy above the IE, but a full explanation of this trend would require further investigation, possibly aided by electronic structure calculations. Higher charge states of halogen ions follow the same trend, and often show the contribution of two or more distinct Coulomb explosion pathways (not shown), which has also been observed in other alkyl halides.30,43,44 The second trend across the dihalomethanes CH2FCl, CH2BrCl, CH2ICl, and CH2IBr is that the ratio of the photoproduct yields CH2X+/CH2Y+ qualitatively correlates with the ratio of the carbon−halogen bond strengths C−X/ C−Y (with Y denoting the more polarizable halogen) for all three photonic reagents, as shown in Figure 4. CH2ICl has the

have either systematically varying pulse energy, denoted P(E) (where A ≡ 0) or linear spectral chirp, denoted P(A) (where E ≡ 360 μJ). The family of seven dihalomethanes is considered because the ion yields of methyl halide fragments from the trihalomethanes (e.g., CHX2+) were very low from photonic reagents other than the 360 μJ TL pulse. For P(E), the pulse energy was scanned (with the TL spectral phase fixed) by uniformly changing the amplitude across the SLM pixels, and for P(A), the linear spectral chirp was scanned with the pulse energy fixed at ∼360 μJ by varying the spectral phase Φ(ω) using the coefficient A in eq 1. For both scans, the TPA signal was measured for each pulse to estimate the fractional laser intensity I/I0 with respect to the 360 μJ TL pulse producing I0. All reported ion yields are normalized to the yield obtained from the 360 μJ TL pulse; i.e., ion yields from interaction of the ith photonic reagent with the jth substrate are represented by Oij/OTL,j. IV.1. Scanning the Pulse Energy. Scanning the pulse energy P(E) ≡ E over the substrates S revealed a systematic correlation between the fractional laser intensity I/I0 that produces the maximum yield of each fragment ion and the ion’s appearance energy (AE, cf. Table 1). We denote this fractional intensity as Iopt, where “opt” denotes the optimal yield of the associated fragment ion. The quantity Iopt is related to the wellknown saturation intensity Isat, which denotes the laser intensity that corresponds to a unit probability of ionizing the molecule in the laser focus.12,13 In this work, Iopt is more appropriate than Isat to characterize the intensity dependence of the methyl halide and halogen fragment ions because their yields decrease at the highest laser intensities. The yields of methyl halide ions may decrease due to additional fragmentation, as the yields of smaller fragments such as CH2+ increase with laser intensity, while the observation of multiply charged halogen ions in the TOF spectra suggests that the halogen ion yields decrease at high laser intensities due to multiple ionization. Figure 5 shows that Iopt values recorded from the P(E) scan of the methyl halide and halogen ions are linearly correlated with their AE values given in Table 1. The error bars in Figure 5 reflect the uncertainty in determining the exact location of Iopt from plots of ion yield versus laser intensity, as illustrated in the inset for the CH2Cl+ signal from CH2ICl. The slopes of the least-squares-fit lines in Figure 5 corresponding to formation of the two methyl halide products CH2X+ and CH2Y+ are nearly identical, which suggests that the same physical process underlies the formation of both fragments. In contrast, the slope is higher for the halogen ions X+, suggesting that a distinct process may be involved. IV.2. Scanning the Linear Spectral Chirp. Scanning the linear chirp variable P(A) ≡ A was found to produce distinct patterns in the yields of methyl halide and halogen ions, with four associated systematic trends. Figure 6 shows the methyl halide and halogen ion yields as a function of A, normalized to unity at A = 0. For reference, the normalized TPA signal is shown in Figure 6a,c,e by the black dashed line. The variation of the methyl halide ion yields with A in Figure 6a,c,e follows the variation of the TPA signal, except for CH2FCl in Figure 6e. This dependence of the methyl halide ion yields on the laser intensity is expected because the parent ions and large fragments from a variety of small molecules are known to correlate with the laser intensity upon variation of the linear spectral chirp.16,22,37,51 In contrast, the maximum halogen ion yields occur away from the TL pulse for all ions except for F+ from CH2FCl. The lower X+ yields near the TL pulse may

Figure 4. The (unnormalized) ratio of the ion yields CH2X+/CH2Y+ versus the ratio of associated C−X and C−Y bond strengths, for three fixed photonic reagents: P1 ≡ P(E=360,A=0) (red squares), P2 ≡ P(E=140,A=0) (blue circles), and P3 ≡ P(E=360,A=2000) (black triangles). The four substrates are labeled on the plot. Error bars denote the measured standard deviation from the mean ratio.

highest ratio of bond strengths (cf. Table 1), and has the corresponding highest ratio of the product yields CH2Cl+/ CH2I+. CH2IBr produces a slightly lower product ratio than expected based on the relative bond strengths, but does not significantly deviate from the qualitative trend. For the three photonic reagents and all substrates in Figure 4, the TL pulse with reduced energy P2 gives the highest product ratio and a chirped pulse P3 gives the lowest ratio. A forthcoming optimal control study79 shows that the CH2X+/CH2Y+ product ratio is inversely proportional to both pulse duration and energy, which is consistent with the ordering for the photonic reagents of P2, P1, and P3 producing decreasing photoproduct ratios. Since the AE of CH2X+ is always lower than that for CH2Y+ (cf. Table 1), only CH2X+ is observed for a sufficiently low-energy TL pulse, and the ratio becomes very large. These results suggest that the ratio of the carbon−halogen bond strengths drives the fragmentation patterns in these halomethanes upon interaction with any photonic reagent.

IV. INTERACTION OF PHOTONIC REAGENTS WITH VARYING ENERGY AND SPECTRAL CHIRP WITH SEVEN DIHALOMETHANES This section presents the results of reactions between multiple photonic reagents and substrates where the photonic reagents 8210



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Figure 5. Fractional laser intensity Iopt producing the optimal yield of each fragment ion recorded from the P(E) scan, normalized to I0 of P1, versus their appearance energies in Table 1. The CH2X+ fragment denotes either the only methyl halide fragment (for CH2Cl2, CH2Br2, and CH2I2) or the fragment corresponding to cleavage of the weak carbon−halogen bond. CH2Y+ denotes the fragment corresponding to cleavage of the strong carbon−halogen bond. AE values for halogen ions X+ were only available for CH2Cl2, CH2Br2, and CH2I2. Values of the intensity Iopt of all three fragments correlate linearly with the AE, as shown by the least-squares-fit lines. The error bars on the main plot represent the uncertainty in the location of Iopt on the laser intensity axis. The inset shows how Iopt is determined from a plot of ion yield versus laser intensity, in this case CH2Cl+ yield from CH2ICl.

Figure 6. Methyl halide and halogen ion yields as a function of the chirp coefficient P(A) ≡ A from eq 1, normalized to the yield of each ion from the TL pulse with A = 0. (a) CH2X+ yield from molecules CH2X2; (b) X+ yield from molecules CH2X2; (c) CH2X+ yield from molecules CH2XY; (d) X+ yield from molecules CH2XY; (e) CH2Y+ yield from molecules CH2XY; (f) Y+ yield from molecules CH2XY. The TPA yield is denoted by the black dashed line in (a), (c), and (e) for reference. The TPA yield is normalized to 1.0 at A = 0, although this feature is somewhat obscured by the fragment ion yield curves. The x’s in (b), (d), and (f) denote the maximum halogen ion yields at the corresponding values of A (cf. Figure 7).

arise because X+ formed in the high intensity short pulse quickly loses one or more additional electrons, giving rise to the observed multiply charged halogen ions. Another possibility is that the short pulse closes off reaction channels that give rise to X+, including secondary dissociation of CH2X+ into X+ or neutral dissociation of the parent molecule to form X followed by ionization, both of which would intuitively require a longer pulse duration. Discriminating between these two processes experimentally would require the capability to detect neutral species, and simulations would likely be of high value as well. The observed enhanced production of halogen ions with chirped pulses is analogous to that seen in some small fragment ions from other molecules,16,37,51 but has not been previously observed for halogen ions from halomethanes. The distinct behavior of CH2FCl arises due to the unique feature of M+ being the largest peak in the TOF spectrum of CH2FCl in Figure 2. The maximal yields of CH2F+ and CH2Cl+ at small nonzero magnitudes of A arise because the dissociation of M+ enhances production of these fragments, which overwhelms any decreased yield of these species due to the lower peak intensity. At the same time, further dissociation of CH2F+ or CH2Cl+ is relatively difficult due to the large energy requirements involved. A further significant feature of all ion yields in Figure 6 is that they are not symmetric with respect to the sign of A, with enhanced yield at A < 0. The enhanced fragment ion yield with negative chirp as compared to positive chirp suggests that the leading higher frequency (blue) components of the negatively chirped laser field turn on the ionization process, populating multiple ionic states more effectively due to their higher photon energies. Subsequently, the lagging red components drive the dynamics on the ionic surfaces, leading to the observed fragmentation patterns. The lower ion yields from a positively chirped photonic reagent suggest that ionic

states may be populated less effectively with positively chirped pulses. Pump−probe experiments and/or experiments allowing for detection of neutrals could assess these speculations. In contrast, the TPA signal can be seen from Figure 6a to be symmetric. Importantly, the asymmetry of the ion yields with respect to the sign of A demonstrates that the time-ordered spectral structure of the photonic reagent plays a role in the ionization/dissociation processes, thereby suggesting that coherent dynamic processes may be involved.80 Figure 6 reveals two systematic trends for each group of halogen ions in Figure 6b,d,f, i.e., X+ from CH2X2, X+ from CH2XY, and Y+ from CH2XY. First, the maximum observed ion yield for each type of halogen exhibits a negative correlation with the parent molecule’s IE, as shown in Figure 7a. Second, the associated (negative) value of A producing the maximum halogen ion yield correlates inversely with the IE for each type of ion, as shown in Figure 7b. The positive value of A corresponding to the maximum ion yield at A > 0 produced the same trend (not shown). The separate trend for each type of halogen ion suggests that the dissociation processes may depend on whether the halogen ion originates from a molecule of the form CH2X2 or CH2XY. The distinct behavior of the halogen and methyl halide ions upon variation of A indicates that chirped pulses can significantly enhance the ratio of halogen ion/methyl halide ion yields X+/CH2X+, where X denotes the only (or the less 8211



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Figure 7. (a) Maximum halogen ion yield normalized to yield with the TL pulse for X+ from CH2X2 (blue circles), X+ from CH2XY (red squares), and Y+ from CH2XY (green triangles). (b) Value of the photonic reagent variable P(A) ≡ A (in fs2) producing the maximum halogen ion yields in (a) (all values are negative; the corresponding maximum halogen ion yields at A > 0 followed the same trend). Both trends are plotted as a function of the IE of the parent molecule in eV. The value of A was estimated from the ion signals in Figure 6 (marked by the x’s); error bars denote the uncertainty in this estimation.

Figure 8. Ratios of halogen ions X+ to methyl halide ions CH2X+ from Figure 6, normalized to the ratio with the TL pulse. (a) Ratios recorded at each value of P(A) ≡ A, where the x’s denote the maximum yield of this ratio and the associated positive value of A (cf. Figure 9). (b) Ratios at selected positive values of A as a function of both S and A. Similar trends were found for negative values of A (not shown).

Figure 9. (a) Maximum yield of the halogen/methyl halide ion product ratio from each substrate molecule as a function of the IE (cf. Table 1), estimated from the black x’s in Figure 8a. (b) Value of P(A) producing the maximum ratio yield as a function of the IE of the parent molecule; error bars reflect the region of A values producing at least ∼90% of the maximum observable yield.

IE. Thus, this plot is analogous to Figure 1b, where the correlations evident in Figure 8b from a family of systematically varying photonic reagents are analogous to the correlations in Figure 1b from chemical reagents. With the exception of CH2FCl, the same systematic correlation between the X+/ CH2X+ ratio and the IE over all of the dihalomethanes is observed; the distinct behavior of CH2FCl likely arises from its high IE, discussed earlier. In Figures 1b and 8b, one variable was adequate for describing the chemical reagents and photonic

polarizable) halogen atom on the parent molecule. Figure 8a shows the ratio for each substrate as a function of A, normalized to the ratio obtained with the TL pulse. Figure 8b shows the normalized ratio as a function of the substrates S ordered by IE and selected discrete values of A. The values of A were discretized to facilitate inspection of the trends across both S and A with a three-dimensional bar plot. Figure 8b clearly shows the systematic correlation between the ratio X+/CH2X+ and both the photonic reagent variable A and substrate variable 8212



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reagents, respectively. This circumstance has more complex generalizations with chemical reagents characterized by many variables, and will surely also be the case with optimally shaped photonic reagents with additional variables. However, as with chemical reagents, systematic patterns can still arise.79 Two systematic trends between the maximum yield of the ratio X+/CH2X+ and the parent molecule’s IE are evident from Figure 8. First, the maximum ratio is negatively correlated to the IE, as shown in Figure 9a. Second, the associated (positive) value of A producing the maximum ratio is also inversely correlated to the IE, as shown in Figure 9b. This trend may arise for the intuitive reason that the lower IE of the molecules containing more polarizable halogens (Br and I) allows ions to be observed in the TOF spectra at longer pulses with lower peak intensities. Such longer pulses may enhance the observed photoproduct ratio by facilitating processes such as postfragmentation ionization of halogens X to X+. The negative value of A producing the highest ratio exhibited the same trend (not shown). The ability of chirped pules to significantly enhance the relative yields of halogen ions, particularly for molecules with low IE, has important implications for optimal control of these products, as discussed further below.

Collectively, the systematic trends across the halomethane family reflect homologous behavior of these molecules upon interaction with photonic reagents, in analogy to trends observed for this molecular family in other contexts including reactivity with chemical reagents.4,56,57 In particular, the plot in Figure 8b has a qualitative appearance similar to the analogous chemical reagent case in Figure 1b, and thus serves as an illustration of filling in an evident blank left in Figure 1 indicated by the questioned arrow in Figure 1c. This work presents a first step in assessing systematic observable trends combining photonic reagents described by the simple variables of energy and pulse duration with substrates characterized by natural molecular variables that are also simple and intuitive. Future systematic studies of more complex photonic reagents inducing novel reactions in homologous families of substrates will be valuable to expand the scope of such studies and assess whether similar simple variables can explain the resultant behavior. Building on the present work, a forthcoming study will explore optimal control of dissociation channels in the halomethane family to reveal additional systematic trends between halogen composition on the halomethane substrates and control objective yields.79 The identification of clear trends over the halomethanes suggests that systematic behavior under interaction with photonic reagents may be widespread across homologous families of substrate molecules. We hope that this work spurs investigation of other chemical families in order to obtain a broader foundation for understanding the systematics of photonic reagent control of chemical reactions, which would provide a basis to identify systematic “rules” for understanding and possibly predicting the reactivity of families of substrates with photonic reagents, in analogy to such rules in chemical reactions. Furthermore, the identification of systematic trends just using the simple photonic reagent variables of pulse energy and spectral chirp provides a foundation to conduct analogous experiments with specially tailored shaped laser pulses as photonic reagents characterized by many variables. Finally, the observed systematic trends in this work raise many questions about the physical mechanisms underlying the dissociation processes, which should promote further investigation with additional experimental techniques, as well as theoretical calculations, to unravel the origins of the observed behavior.

V. CONCLUSION The halomethanes form a suitable homologous family for exploring systematic trends in dissociative ionization reactions induced by photonic reagents because they share a common simple molecular structure and known systematic variation of their properties with halogen composition. In our experiments, trends in the values of each observable were effectively characterized by one of three natural variables describing the halomethanes: IE of the parent molecule, AE of the fragments, and relative strengths of the carbon−halogen bonds in molecules containing two different halogens. Although our work found that each particular observable was significantly correlated to only one natural substrate variable, in general, observable yields may depend on many natural variables along with many photonic reagent variables (e.g., to describe optimally shaped pulses). Here, the correlation between each observable and its associated substrate natural variable is presented in Table 2, where the correlation is denoted as positive (+) or negative (−), along with the appropriate figure references that illustrate the correlation.

■

AUTHOR INFORMATION

Corresponding Author

Table 2. Summary of the Observed Systematic Trendsa figure Figure 2, Figure 3 Figure 4 Figure 5 Figure 7a Figure 7b Figure 9a Figure 9b

observable

IE

KE of Coulomb explosion for X+

−

ratio CH2X+/CH2Y+ Iopt of ions from P(E) variation max X+ yield P(A) producing max yield of X+ max ratio of X+/CH2X+ P(A) producing max yield of X+/CH2X+

AE

*E-mail: [email protected]. Present Address

C−X/C−Y

†

Department of Chemistry, Temple University, Philadelphia, PA 19122, USA.

+

Notes

The authors declare no competing financial interest.

+ − − − −

■

ACKNOWLEDGMENTS

■

REFERENCES

The authors acknowledge support from the NSF (Contract No. CHE-0718610) and DOE (Contract No. DE-FG0202ER15344). K.M.T. was supported, in part, by an NSF graduate research fellowship.

a

The trends for each observable are shown by the correlations between the associated substrate natural variable and the observable denoted as positive (+) or negative (−). As each observable was found to correlate with only one natural variable, blank spaces under the natural variables indicate that the observable was not significantly correlated with that natural variable.

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