One- and Two-Dimensional Translational Energy Distributions in the

Article pubs.acs.org/JPCA

One- and Two-Dimensional Translational Energy Distributions in the Iodine-Loss Dissociation of 1,2-C2H4I2+ and 1,3-C3H6I2+: What Does This Mean? Tomas Baer,*,† S. Hunter Walker,†,‡ Nicholas S. Shuman,†,§ and Andras Bodi∥ †

Department of Chemistry, University of North Carolina, Chapel Hill, North Carolina 27599-3290, United States Molecular Dynamics Group, Paul Scherrer Institut, Villigen 5232, Switzerland

∥

S Supporting Information *

ABSTRACT: Threshold photoelectron photoion coincidence (TPEPICO) has been used to study the sequential photodissociation reaction of internal energy selected 1,2-diiodoethane cations: C2H4I2+ → C2H4I+ + I → C2H3+ + I + HI. In the first I-loss reaction, the excess energy is partitioned between the internal energy of the fragment ion C2H4I+ and the translational energy. The breakdown diagram of C2H4I+ to C2H3+, i.e., the fractional ion abundances below and above the second dissociation barrier as a function of the photon energy, yields the internal energy distribution of the first daughter, whereas the time-of-flight peak widths yield the released translational energy in the laboratory frame directly. Both methods indicate that the kinetic energy release in the I-loss step is inconsistent with the phase space theory (PST) predicted two translational degrees of freedom, but is well-described assuming only one translational degree of freedom. Reaction path calculations partly confirm this and show that the reaction coordinate changes character in the dissociation, and it is, thus, highly anisotropic. For comparison, data for the dissociative photoionization of 1,3-diiodopropane are also presented and discussed. Here, the reaction coordinate is expected to be more isotropic, and indeed the two degrees of freedom assumption holds. Characterizing kinetic energy release distributions beyond PST is crucial in deriving accurate dissociative photoionization onset energies in sequential reactions. On the basis of both experimental and theoretical grounds, we also suggest a significant revision of the 298 K heat of formation of 1,2-C2H4I2(g) to 64.5 ± 2.5 kJ mol−1 and that of CH2I2(g) to 113.5 ± 2 kJ mol−1 at 298 K.

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reactive system moves from the TS to products.2,3 Comparisons with experiment have been made by initializing an ensemble of trajectories at the TS with a microcanonical ensemble, as assumed by RRKM (Rice, Ramsperger,4 Kassel,5 and Marcus6) theory,7 and then propagating this ensemble to the product limit.8,9 The product energy partitioning depends on kinematic, mass effects in the exit channel and not only on the shape of the PES.9 The other type of reaction is a simple bond rupture dissociation for which no barrier exists for the reverse association reaction. Product energy distributions have recently been reported for such reactions as methyl loss from tert-butyl radicals10 and H loss from allene and propyne.11 Most ionic dissociation reactions fall into this category. The product energy distributions for these simple bond breaking reactions are expected to be more in accord with statistical theories. Different models have been used to relate the product energy

INTRODUCTION The product energy partitioning for a unimolecular dissociation reaction often provides insight into reaction dynamics. Of particular interest is to relate the observed product energy partitioning with the fundamental statistical theory assumption of rapid intramolecular vibrational energy redistribution (IVR), which gives rise to microcanonical ensembles of states for both the reactant molecule and dissociation transition state (TS). This relationship depends on properties of the reaction’s potential energy surface (PES), with two general PES types. Potential energy surfaces associated with one or more bond rearrangement steps give rise to fixed barriers or saddle points. Examples include many neutral reactions, such as C2H5F → HF + C2H4 or the complex dissociation of C2H4OH radicals.1 Such reactions often give rise to nonstatistical product energy distributions, which depend very strongly on the shape of the PES. Approximate treatments using, for instance, impulsive models1 have been used to account for the observed product energy distributions. More sophisticated treatments involve molecular trajectory calculations. Product energy partitioning is then determined by the couplings in the exit channel as the © 2012 American Chemical Society

Received: December 16, 2011 Revised: February 8, 2012 Published: February 13, 2012 2833

dx.doi.org/10.1021/jp2121643 | J. Phys. Chem. A 2012, 116, 2833−2844

The Journal of Physical Chemistry A

Article

of kinetic energy release in the product energy distribution of unimolecular dissociations is particularly important in setting up the energy balance after several sequential dissociation steps. Organometallic compounds, for example, often show numerous sequential ligand losses35−37 and accurate 0 K appearance energies, and, thus, thermochemical information can only be extracted if the energy “lost” in subsequent dissociation steps is modeled accurately.38−41 Two studies have been reported recently, in which assuming two translational degrees of freedom proved inadequate in modeling the product energy distributions. The kinetic energy release in the first Cl atom loss in dichloroethenes was determined by modeling the consecutive loss of a second Cl atom and was found to correspond to one translational degree of freedom.42 In this case, the translational energy distribution is given by P(E) = E−1/2e−E/RT, and the average translational energy would be (1/2)RT. Sequential Cl-atom losses were also studied in S2Cl2+ and in SOCl2+.43 In both sulfur compounds, the breakdown diagram of the second dissociation was used to infer the kinetic energy release distribution. At low kinetic energy release, i.e., close to the second onset energy, where most excess energy is needed for the fragment ion to dissociate further and only few do so, a three-dimensional distribution was found to reproduce the experimental breakdown curve. In contrast, a two-dimensional distribution fitted the experimental data better at high photon energies, i.e., at high excess energies. In this study, we investigate the sequential dissociations of 1,2-diiodoethane and 1,3-diiodopropane ions via

partitioning with the statistical unimolecular dynamics assumed by RRKM theory.7,12,13 One is the loose TS model of phase space theory (PST), for which the dissociation TS is placed in the product asymptotic limit.14,15 The products then have a statistical distribution of energy in accord with the TS’s microcanonical ensemble. The assumption that the TS is in the product limit is quite approximate, and other approaches have also been developed.16−19 In the orbiting TS model of PST,16,17 the interaction potential between the dissociation products is assumed to be isotropic and the TS is placed at the rotational barrier. To calculate product energies, the orbital angular momentum is assumed to be conserved, i.e., adiabatic, as the dissociation system moves from the orbiting TS to products. Other models are based on variational transition-state theory (VTST) to determine the TS structure18 and the statistical adiabatic channel model (SACM). 19 For each model, assumptions must be made concerning the coupling or adiabaticity of modes in moving from the TS to products. One approach to statistical energy partitioning involves the assumption that the various energy sinks have the same temperature, and in 1973 Klots20 proposed that the statistical theory could be stated very simply in terms of average energies as Eex = E tr(T ) + Ero(T ) + E vi(T ) n n = tr RT + ro RT + 2 2

s

σi σ / RT i −1 i=1 e

∑

(1)

−e−

C2H 4I2 + hν ⎯⎯⎯⎯→ C2H 4I2+ →

In this equation, ntr and nro are the number of product translational and rotational degrees of freedom, σi is the vibrational energy spacing of the ith vibrational mode, and s is the total number of vibrational modes in the neutral and ionic products. The average translational and rotational energies are treated classically, whereas the vibrational energy is treated quantum mechanically. The canonical eq 1 brings up the important issue of the translational and rotational degrees of freedom. How many should there be? According to Klots,14 dissociation takes place in a plane so that the translational degrees of freedom should be two. This results in a kinetic energy release (KER) distribution given by a simple exponential in which the most probable translational energy is zero, and the average energy is RT. However, centrifugal barriers intervene in the orbital transitionstate model so that the low translational energies are depleted, as is indeed observed both in experiments14,21−23 and in theoretical treatments.14,21,24 Thus, it has been proposed22,24 that the KER distribution is described by the following function: P(E) = Eαe−E/RT, where α is a parameter between 0 and 1. A two-dimensional (2-D) distribution would correspond to α = 0, whereas α for a three-dimensional (3-D) distribution would be 1/2. The precise value for the exponent, α, which can be obtained from molecular dynamics simulations,24 varies depending on the interaction potential between the product species. In general, centrifugal barriers are low for ionic dissociations, especially in the case of very polarizable departing atoms such as I, so that a KER distribution close to 2-D (α ≈ 0) would be expected, and has indeed been observed many times.25−32 The kinetic energy release in a first dissociation step can be studied by obtaining product ion yields as a function of internal energy in a second, sequential dissociation reaction of internal energy selected parent ions.33,34 A quantitative understanding

C2H 4I+ + I → C2H3+ + I + HI

(2)

−e−

C3H6I2 + hν ⎯⎯⎯⎯→ C3H6I2+ → C3H6I+ + I → C3H5+ + I + HI

(3)

It will be shown that, in the I-atom loss from C2H4I2+, which one might expect to proceed via a simple bond-scission step, the phase space theory prediction of ntr = 2 is not supported. C2H4I2 is an ideal system for such an experimental inquiry. First, in comparison with dichloroethene, the iodine atom has only a single isotope so that the experiment has sufficient mass resolution to permit the use of a low (e.g., 20 V cm−1) extraction field. In addition, the large mass of the leaving I atom means that a large fraction of the translational energy is imparted to the C2H4I+ product ion, thereby providing the means to measure the translational energy released directly by product ion time-of-flight (TOF) peak analysis. In other words, both the internal energy distribution in the C2H4I+ product ion and the average translational energy as a function of the total ion internal energy can be measured. The energetics of the dissociative photoionization of 1,2diiodoethane and 1,3-diiodopropane are also of interest. The 298 K gas-phase heats of formation of 1,2-C2H4I2 and 1,3C3H6I2 have been determined most recently by rotating combustion calorimetrically by Carson et al.44 to be 73.3 ± 2.0 and 45.2 ± 1.5 kJ mol−1, respectively. The heats of formation of the intermediate ions in reactions 2 and 3, C2H4I+ and C3H6I+, are hardly known. On the other hand, the final vinyl daughter ion, C2H3+, with its H-bridged symmetric structure, is easy to calculate at a high level and thus has a wellestablished heat of formation of 1119.9 ± 1.0 kJ mol−1 at 0 2834



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Table 1. Ancillary and Derived Heats of Formation and Thermal Enthalpies (kJ mol−1) ΔfH°0K 1,2-C2H4I2

1,3-C3H6I2 CH4 C2H6 CH3I CH2I2

C2H5I

1,2-C2H4I2+ 1,3-C3H6I2+ C2H4I+ C3H6I+ C2H3+ C3H5+ I2+ HI I

88.7 80.0 ± 2.5 66.9 ± 1.5 −66.56 ± 0.06 −68.2 ± 0.3 24.8 ± 0.3 129 117.0 123.1 ± 2 6.3 ± 1.5 8.9 ± 0.8 8.25 ± 0.56a 992.7 ± 3.0 973.8 ± 5.0 896.4 ± 3.0 908.7 ± 3.0 1119.9 ± 1.0 967.2 ± 2.5 964.4 28.66 107.157 ± 0.002

ΔfH°298K

H298K − H0K

73.3 ± 2.0 75.0 ± 4.0 64.5 ± 2.5 45.2 ± 1.5 −74.55 ± 0.06 −83.8 ± 0.3 15.23 ± 0.3 14.4 ± 1.4 119.5 ± 2.2 107.5 ± 4.5 113.5 ± 2 −9.8 ± 1.5 −7.2 ± 0.8 −7.05 ± 0.56a 978.0 ± 3.0 953.4 ± 5.0 888.3 ± 3.0 894.1 ± 3.0 1115.6 ± 1.0 b 955.5 ± 2.5b 26.48 106.757 ± 0.002

16.8 20.1 10.0 11.6 10.7

13.2 13.1 13.7 14.58 17.5 20.4 17.5 20.6 11.3 12.5 961.1 8.66 6.20

ref Carson et al.44 (298 K) Pedley74 (298 K) this work Carson et al.44 (298 K) Ruscic et al.75 Pedley74 (298 K) Bodi et al.76 Carson et al.77 (298 K) Carson et al.77 (298 K) Lago et al.78 this work Borkar and Sztaray66 Carson et al.44 (298 K) Goos et al.73 this work this work this work this work Bodi et al.42 Shuman et al.46 Wagman et al.57 Wagman et al.57 Stevenset al.79

a

According to B. Ruscic (private communication), this is an interim value. bIon convention is used for 298 K values in which electron is treated as stationary.

K.42,45 Likewise, the 0 K heat of formation of the final allyl product ion for reaction 3, C3H5+, was recently determined to be 967.2 ± 2.5 kJ mol−1 in a PEPICO study by Shuman et al.46 Combined with the 0 K heats of formation of 28.5 ± 0.2 kJ mol−1 (HI) and 107.16 ± 0.04 kJ mol−1 (I) as listed by Chase,47 we conclude that the total 0 K heats of formation of the final products for reaction 2, C2H3+ + I + HI, and reaction 3, C3H5+ + I + HI, are well-established at 1255.8 ± 1.0 and 1103.1 ± 2.5 kJ mol−1, respectively. However, because the loss of an HI in the second step involves breaking and making new bonds, the onset energy will only correspond to the endothermicity of the dissociative photoionization if there is no energy maximum along the reaction coordinate or if it is deeper lying than the total barrier. By confirming this and determining an accurate 0 K onset for the appearance of the I+ HI-loss daughter ion, it is possible to use the known energy of the final products to test the accuracy of the two alkyl iodide heats of formation as well as that of the intermediate ions.

directions. Threshold electrons were collected by velocity focusing optics,51 which directed all electrons with zero velocity perpendicular to the extraction axis to a 1.4 mm aperture where they were detected by a channeltron electron multiplier. Offaxis electrons were also detected by a second channeltron and used to correct the threshold electron signal for hot electron contamination.52 Ions were extracted by a two-stage acceleration region to a final energy of 260 eV in the 34 cm long drift tube, at the end of which they were detected by a multichannel plate detector. The threshold electrons provided the start signal, and the ions, the stop signal for the ion TOF spectrum. Because of the generally low signal levels (e.g., 100 c/s electrons and 2000 c/s ions), a single-start, single-stop (SSSS) coincidence experiment could be employed without significant loss of signal. The photon resolution was about 10 meV and the threshold electron resolution slightly better than that, thus yielding an overall ion energy resolution of about 12 meV. The SLS experiment, with its 10 times better resolution, also has a much higher photon intensity. This higher photon intensity required the use of a multistart−multistop (MSMS)53 setup to avoid losing signal. The hot electron coincidences that contaminated the electron signal at the center of the imaging detector were removed by subtracting the coincidences obtained from a ring surrounding the central image. The iPEPICO experiment also provided for a higher mass resolution by extracting the ions with a 120 V cm−1 electric field and accelerating them to a final drift energy of 1800 eV. In both setups the sample had a thermal energy distribution at a nominal temperature of 300 K. The ion internal energy is thus given by Eion = hν − IE + Eth, where hν is the photon energy, IE is the molecule’s adiabatic ionization energy, and Eth is the initial thermal energy of the sample. The parent and daughter ion fractional abundances in the mass spectra plotted as a function of photon energy yield the breakdown diagram.

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EXPERIMENTAL APPROACH The threshold photoelectron photoion coincidence (TPEPICO)33 experiments, employed to prepare internal energy selected ions, were carried out in Chapel Hill, NC, USA, with a laboratory hydrogen light source,48 and in Villigen, Switzerland, using a synchrotron light source. The Swiss Light Source (SLS) imaging PEPICO experiment disperses bending magnet radiation with a grazing incidence monochromator providing a resolution approaching 1 meV, with suppression of higher harmonics using a gas filter.49 The imaging PEPICO (iPEPICO) experiment50 employs an imaging detector with sub-millivolt resolution for electrons. In the Chapel Hill experiment, a room-temperature gasphase sample was photoionized in an electric field of 20 V cm−1, which extracted the electrons and ions in opposite 2835



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Figure 1. iPEPICO breakdown diagram or fractional ion abundances in the vicinity of the first dissociation of the 1,2-C2H4I2+ ion dissociation. The red line is the threshold photoelectron spectrum (TPES). The solid lines through the data points are the modeled breakdown curves from which we extract a 0 K dissociation limit of 9.573 ± 0.010 eV. The adiabatic IE = 9.46 ± 0.020 eV is determined from the divergence of the calculated and experimental breakdown data.

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THEORETICAL METHODS

that interconnect them. We considered the following four isodesmic reactions:

The data analysis requires computational input in two regards. First, rovibrational densities of states, ρ(E), are needed to calculate the thermal energy distribution of the sample and the product energy distribution after dissociative photoionization even when the dissociation is fast.34 Density functional theory (DFT) with the B3LYP functional and the 6-311G(d,p) basis set was used to obtain rotational constants and harmonic vibrational frequencies, which are then employed in calculating ρ(E). Second, quantum chemical calculations are also useful in order to interpret and confirm appearance energies, as well as in understanding the dissociative photoionization mechanism. Iodine being a fifth-row element, ab initio approaches aiming for chemical accuracy in atomization energies can be prohibitively expensive. In particular, not addressing spin− orbit coupling in open shell calculations is expected to lead to errors as high as 2000 cm−1 (250 meV). In a separate study on halon compounds, several methods have been benchmarked against known interhalogen heats of formation using isogyric reactions,54 and the fc-CCSD/(SDB-)aug-cc-pVTZ//B3LYP/ 6-311++G(d,p) energies were found to agree best with the experimental values. We therefore opted for this method with Stuttgart−Dresden−Bonn (SDB) relativistic effective core pseudopotential (ECP) on iodine to obtain relative energies at stationary points, as well as carrying out B3LYP/6-311+ +G(d,p) constrained optimization scans and reaction path and transition-state calculations with the synchronous transit-guided quasi-Newton (STQN) method.55 The Gaussian09 computational chemistry suite56 was used in these calculations. The thermochemistry of the closed shell neutrals can also be addressed computationally by setting up isodesmic reactions

(a) CH3I → CH2I2 + CH 4 (b) CH2I2 + C2H6 → C2H 4I2 + CH 4 (c) 2 C2H5I → C2H 4I2 + C2H6 (d) C3H6I2 + CH 4 → C2H 4I2 + C2H6

(4)

The ancillary heats of formation are listed in Table 1, where we have used ab initio calculated vibrational frequencies to obtain the thermal energy (H298K − H0K) and have used the elemental thermal energies as listed by Wagman et al.57 The geometry optimizations were carried out with density functional theory with the dispersion corrected ωB97X-D functional58 as well as with second-order perturbation theory (MP2) with the aug-ccpVTZ basis set on C and H and the aug-cc-pVTZ-PP59 basis set with a small core relativistic ECP on I, downloaded from the basis set exchange.60,61 The DFT and MP2 geometries and zero point energies (ZPE) agree quite well, and the DFT results were used in further calculations. The valence electron correlation was taken into account with coupled cluster singles and doubles with or without perturbative triples corrections, CCSD and CCSD(T), respectively. In addition to the triple-ζ aug-cc-pVTZ(-PP), the triple-ζ aug-cc-pVTZ-SDB basis set62 with large-core ECP as well as the quadruple-ζ aug-cc-pVQZ(PP/-SDB) analogues were used with the exception of C3H6I2 for which the CCSD(T)/aug-cc-pVQZ-PP calculations were found to be prohibitively expensive. However, the effect of using a small-core vs large-core ECP was generally small and unchanged when comparing the triple- and quadruple-ζ results. The triples contributions in CCSD(T) were found to be larger, in the 0.9−3.2 kJ mol−1 range for the reaction energies, but they were also converged to within 0.3 kJ mol−1 of the quadruple-ζ value at the triple-ζ basis set. Consequently, we report an effective CCSD(T)/aug-cc-pVQZ-PP reaction energy for (4d) with the contribution of the large-core SDB vs the small-core PP ECP being included with triple-ζ basis sets. The core 2836



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ionization energy, where only initially “hot” neutrals may be ionized. In other words, neutrals with less internal energy than IE − hν will not be ionized and the ion internal energy distribution does not correspond to a Boltzmann distribution in this energy range. Thus, the photon energy below which the observed behavior deviates from the model corresponds to the adiabatic ionization energy.54 On the basis of the breakdown curve, the IE of 1,2-diiodomethane is determined to be 9.46 ± 0.02 eV. The best fit 0 K dissociative photoionization onset energy is 9.573 ± 0.005 eV. Slightly above the first onset at about 9.6 eV, we observed the appearance of the I2+ product ion. The complete breakdown diagram, including the I2+ channel, from 9.4 to 13 eV is shown as Figure S1. The I2+ signal level remains flat with a relative abundance of about 10% up to 12.25 eV, at which energy it goes to zero. No I+ channel is evident, which indicates that the I2+ channel simply shuts off above 12 eV (at which energy it should dissociate to I+ + I). There is also some evidence that the sample is contaminated with elemental I2, a probable decomposition product of 1,2-C2H4I2. We do not fully understand the mechanism for the I2+ formation, especially its constant branching ratio relative to the dominant I-loss channel. This issue is discussed later in connection with the quantum mechanical (QM) calculations that suggest a complex set of rearrangement reactions for both I-loss and I2+ formation. Because the I2+ channel shows up after the onset for I-loss and essentially disappears before the HI-loss channel in Figure 2, we chose not to include this channel in Figures 1 and 2.

correlation and relativistic effects with the Douglas−Kroll− Hess second-order scalar relativistic model are found to have a small, 0.0−0.2 kJ mol−1 effect on the reaction energies obtained in frozen core/all electron CCSD calculations with the ccpVTZ basis set on H, cc-pCVTZ on C,63 and cc-pwCVTZ-PP on I.64 The full point groups of the species were C3v (CH3I), C2v (CH2I2 and C3H6I2), Td (CH4), D3d (C2H6), C2h (C2H4I2), and CS (C2H5I). In C3H6I2, the C1 symmetry minimum with 53° I−C(1)−C(3)−I dihedral angle is 1.1 kJ mol−1 more stable than the C2h minimum at the CCSD(T)/aug-cc-pVTZ-SDB level, which was added as a correction to the (4d) reaction energy. The largest sources of uncertainty in the data set are the 2.6 kJ mol−1 difference between the DFT and MP2 ZPE contributions to (4c), the 3 kJ mol−1 triples contributions (4a), and the 4−5 kJ mol−1 small-core/large-core ECP difference in (4b) reaction energies. Overall, such computed isodesmic reaction energies among closed shell species are assumed to be chemically accurate to within 2−3 kJ mol−1.

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RESULTS 1,2-C2H4I2: Breakdown Diagram for First Dissociation Onset. Figure 1 shows the breakdown diagram for the C2H4I2+ ion in the vicinity of the first I-atom loss obtained with the SLS iPEPICO experiment. The fractional or relative abundances of the parent and daughter ions are obtained by integrating the TOF mass peaks. In addition, we have plotted the threshold photoelectron spectrum (TPES) on this plot. The full TPES up to 14 eV is shown as Figure S1 in the Supporting Information. The ion TOF peaks (not shown) are symmetric, which indicates that the dissociation is fast on the time scale of our experiment (i.e., k > 107 s−1). The solid lines in Figure 1 are the modeled breakdown diagram. Because the reaction is fast, any ion with a total energy of hν + Eth in excess of the dissociation energy, E0, will dissociate and be counted as a daughter ion. The daughter ion signal for a normalized thermal energy distribution P(E) is thus obtained by the simple integral: D(hν) =

∞

∫E − hν P(E) dE 0

D(hν) = 1

for hν < E0 for hν ≥ E0

(5)

The only adjustable parameters in this fit are the assumed sample temperature and the 0 K dissociation energy. If the neutral sample thermal energy distribution upon ionization were transposed faithfully to the ion manifold, the ion sample temperature would be just that of the neutral sample. This assumption is based on the observation with many samples, including ones where the sample temperature was varied over more than 120 K.65,66 This is a result of the fact that Franck− Condon factors for threshold ionization are nearly constant across the thermal energy distribution at any given photon energy. Typically, the ion internal energy distribution is welldescribed with a canonical distribution with a temperature within 10% of the neutral sample temperature. In this case, the optimal temperature, which is reflected in the slope at which the parent ion descends toward the baseline, is 290 K. Another aspect of the breakdown diagram is the region below 9.5 eV, in which the fractional abundances start deviating strongly from the model. This is due to the adiabatic ionization energy of the sample, which was reported to be 9.50 eV.67,68 The shape of the breakdown curve is predicted on the basis of the assumption that the whole internal energy distribution contributes to either the parent or the daughter signal. This is not the case below the

Figure 2. iPEPICO breakdown diagram in the vicinity of the HI-loss channel. Points are experimental, while the two lines represent the expected breakdown diagram for the 1-D (solid) and 2-D (dashed) translational energy distributions. The four arrows show the thermochemical onsets based on the heats of formation from the literature, 12.096 eV (light green), the 2-D fit result, 12.149 eV (dashed red), the dissociative photoionization energy based on our revised heats of formation, 12.186 ± 0.025 eV (dark green), and the 1D fit result of 12.225 ± 0.020 eV (dark blue).

1,2-C2H4I2: Breakdown Diagram for Second Dissociation Onset. Figure 2 shows the breakdown diagram in the vicinity of the sequential HI-loss, C2H4I+ → C2H3+ + HI. This second onset, between 12 and 12.4 eV, is analyzed by taking into account the additional broadening caused by the departing I atom in the first reaction.34 In addition to the thermal energy distribution of the starting compound, the first I atom departs with a distribution of translational energy, which results in additional broadening of the C2H4I+ ion internal energy 2837



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73.3 ± 2.0 kJ mol−1, reported by Carson et al.,44 this onset from the parent molecule should be 12.096 ± 0.020 eV, shown by the light green arrow in Figure 2. However, when the dissociation onset was optimized in fitting the data for the 2D and 1-D models, the optimized onset energies were 12.149 and 12.225 ± 0.020 eV, respectively. Thus, the 1-D model fits the breakdown diagram quite well, but yields an onset that is apparently 0.11 eV too high, while the 2-D model fails to fit the experimental breakdown diagram but yields an onset that is closer to the literature value based on the Carson experiment. It is possible that either the heat of formation of the C2H4I2 molecule reported by Carson et al. in 1994 is too high by 10.6 kJ mol−1 or their determination of the heat of sublimation is in error. The other possibility is that there is a 100 meV barrier for HI loss, although all of our calculations suggest that this is not the case. Because of these issues, we decided to search for additional information by analyzing the time-of-flight peak shapes for the C2H4I+ ion as a function of the photon energy. In addition, we will return to the question of the C2H4I2 heat of formation using high-level ab initio calculations using a selfconsistent reaction network. 1,2-C2H4I2: TOF Peak Analysis for Translational Energy Release. The breakdown curves in Figure 2 measure directly the internal energy distribution of the C2H4I+ ion, which is produced in the first reaction. We can also look at the complementary data, namely, the translational energy of this ion from the widths of the TOF distributions as a function of the photon energy. These data can be collected over the energy range between the I-loss and the HI-loss dissociation channels, that is, between 9.6 and 12 eV. Figure 4 shows how the C2H4I+

distribution. The C2H4I+ internal energy distribution, P(E), expected from a purely statistical partitioning of the available energy can be obtained in the microcanonical formalism using eq 6, where ρ(E) is the density of states.7 In particular, ρtr(E) is the translational density of states of the departing fragments. PC H I+(E) = 2 4

ρC H I+(E) ρtr(hν − E0 − E) 2 4 hν− E0

∫0

ρC H I+(y) ρtr(hν − E0 − y) dy 2 4 (6)

The density of states of the ion is obtained from the vibrational frequencies and thus contains no adjustable parameters. However, as pointed out above, there is some ambiguity about the model for the translational energy distribution. In Figure 2, we show the results for both the one- [ρ(E) ∝ E−1/2] and the two-dimensional [ρ(E) = constant] translational energy distributions. Clearly, the 1-D distribution fits the data far better than the 2-D model. The C2H4I+ internal energy distributions obtained from eq 6 assuming 1- and 2-D translational distributions are shown in Figure 3 together with the 1- and 2-D translational energy distributions.

Figure 3. Initial parent ion internal energy distribution based on the 298 K internal energy distribution of the neutral is shown in blue. It is the room-temperature thermal energy distribution shifted to 12.33 eV by the photoionization process. The ion energy is relative to the 1,2C2H4I2+ ion ground state at 9.46 eV. The calculated product ion distributions, associated with the 1-D and 2-D translational energy distributions, are shown by the solid blue and dashed red lines, respectively. The experimental points are obtained from the derivative of the C2H3+ data in the breakdown curve of Figure 2.

Figure 4. C2H2I+ time-of-flight distributions at three energies between the I- and HI-loss onsets of C2H2I2+ ions obtained with the Chapel Hill TPEPICO apparatus. The solid lines are Gaussian functions, whose full widths at half-maxima are shown. The broadened peak widths are a result of translational energy release and can be converted to the average translational energy.

Figure 3 also shows the experimental internal energy distribution, which was determined by taking the derivative of the breakdown diagrams in Figure 2, as recently described in detail by Baer et al.69 The derivative was obtained by using a nine point smoothing routine in the Savitzy−Golay 70 procedure. The experimental distribution is approximate because the energy partitioning changes with photon energy. However, since the crossover in the breakdown diagram is confined to a very small energy range, the approximation is certainly within the scatter in the derivative of the breakdown curve. An interesting aspect of the data analysis in Figure 2 is the dissociation limit to the final products, C2H3+ + I + HI. According to the heat of formation, ΔfH°298K(1,2-C2H4I2) =

TOF distribution widths, obtained with the Chapel Hill TPEPICO apparatus, increase as the excess energy increases. The Chapel Hill apparatus was better suited for these studies because the 20 V cm−1 extraction field results in larger product ion peak widths than the 120 V cm−1 used in the iPEPICO apparatus, thereby providing more accurate energy release information. The average translational energy can be readily extracted by the Stockbauer−Stanton−Monahan method32,71 from the full 2838



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1,3-C3H6I2: Breakdown Diagram and Translational Energy Release. To test our method against another system, we chose the related molecule, 1,3-C3H6I2. The molecular ion also dissociates by I-atom loss in the first step, followed by an HI loss at higher energies. The breakdown diagram with the modeled breakdown curves is shown in Figure 6, and the

width at half-maximum of the fragment ion peak. In this approach, one assumes that the translational energy is released in the form of a 3-D Maxwell−Boltzmann distribution for a sample with a room-temperature distribution of translational energies. The average translational energy imparted to the fragment ion, ⟨Etr⟩, is then given by ⟨E tr⟩ =

M 3 m [qεT1/2]2 − ⟨E th⟩ (M − m)m 16 ln 2 M−m (7)

In eq 7 M and m are the parent and fragment ion masses, respectively, q is the electronic charge, ε is the electric field in the first acceleration region, and T1/2 is the full width at halfmaximum of the fragment ion time-of-flight peak. In this equation, time is expressed in seconds, ε in V m−1, mass in kilograms, and q = 1.6 × 10−19 C. Etr and Eth are then given in electronvolts. The last term, involving the average thermal translational energy of the sample, takes into account the TOF peak width in the absence of any translational energy released in the reaction, so that the ⟨Etr⟩ is only due to the kinetic energy release. Unfortunately, it is not possible to derive closed form expressions for the peak shape resulting from a thermal sample with its 3-D translational energy distribution combined with either a 1-D or a 2-D energy release. However, the error is probably small. The conversion of these peak widths into average translational energies is shown in Figure 5. The expected average

Figure 6. Overall breakdown diagram of 1,3-diiodopropane in the 9− 11.5 eV photon energy range obtained by the Chapel Hill TPEPICO apparatus. Points are experimental, while the continuous lines represent the modeled breakdown diagram assuming a two-dimensional translational energy distribution in the first I-loss step. The first two onset energies are experimental, while the last one (green) is the calculated onset using known thermochemistry for the 1,3-C3H6I2 → C3H3+ + I + HI onset.

results for the kinetic energy release in the I-loss reaction for this ion are shown in Figure 7. The 2-D distribution fits both

Figure 5. Average translational energy release from the peak widths analysis for the indicated reaction. The solid and dashed lines are calculated using the Klots eq 1 for the case of a one- and twodimensional translational energy release. The lower axis lists the energy in excess of the first dissociation limit (9.573 eV), while the upper axis indicates the effective temperature of the dissociating system.

Figure 7. Average translational energy release from the peak widths analysis for the indicated reaction. Data below 0.25 eV were not available because the peaks were asymmetric due to the slow reaction rates. The solid lines are calculated using Klots eq 1 for the case of a one- and two-dimensional translational energy release.

energies using the Klots eq 1 are shown as solid or dashed lines. For the 1-D distribution, we simply use (1/2)RT as a measure of the translational energy and reduce the rotational contribution to zero. The reason for eliminating the rotational energy is that if the translational energy is one-dimensional, then there can be no rotational energy imparted to the products. That is, the reverse association reaction must have zero impact parameter. However, even if we include the rotations, the calculated ⟨Etr⟩ changes by less than 5%. For the 2-D distribution, we use RT for both the translational and rotational energies. Clearly, the 1-D distribution fits perfectly, in agreement with the results of Figure 2.

the breakdown diagram and the average translational energy release quite well. As already pointed out, this is in accord with a number of other studies done on a variety of ionic dissociation reactions. In addition, the measured onset energy (E0 = 10.724 ± 0.015 eV) for the reaction C3H6I2 → C3H5+ + I + HI agrees quite well with the known thermochemistry (10.739 ± 0.015 eV) for this reaction (see Table 1). 2839



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has brought to our attention that CCSD energies at geometries obtained with DFT could be meaningless, so these are not reported for the I-loss path. The reported DFT energies also suffer from the neglect of spin−orbit coupling. On the left-hand energy scale, ΔE is shifted by the experimental adiabatic ionization energy of C2H4I2, i.e., the energies are relative to the neutral, whereas on the right-hand axis, ΔE′ = 0 at the computed C2H4I2+ ion energy. In the first step, the two I atoms move in a concerted fashion over the transition state [2]⧧ to form the bridged C2H4I+ product ion to which the leaving I atom is coordinated from the other side of the C−C bond, [3]. From this isomerized structure [3], the reaction pathway is proposed to branch in two. First, the weaker bound I atom may leave in one step, i.e. [3] → [6], which would mean that the rotating motion turns into a linear stretch. The second reaction pathway branch was suggested by Hase et al.72 on the basis of MP2 trajectory calculations. The rotating motion in [1] → [3] proceeds until after an almost complete turnaround; I2 is coordinated to the C−C bond in structure [5]. The I-loss reaction is again possible by a bend in the reaction coordinate, in which the rotation is converted into an I−I bond stretch. The intermediate I2···C2H4+ ion [5] is calculated to be more stable than the parent ion and appears to be the global minimum on the ion potential energy surface. Recall that the experimental appearance energy is 9.57 eV, and the calculated E0, 9.93 eV, is too high by about 360 meV, although DFT predicts no overall reverse barrier to the process. A reverse barrier to the dissociation would result in enhanced kinetic energy release in the I-loss step, which is incompatible with KER results in Figures 4 and 5. Notwithstanding the difficulty in carrying out reliable calculations on such a large open shell system, we conclude that the I-atom loss takes place not along a purely attractive potential energy curve, as is often the case for unimolecular dissociations in cations, but via several minima and transition states along the way to dissociation. The reaction coordinate also changes character, as it starts out as a concerted rotation of the I atoms along the C−C bond and ends as a bond stretch coordinate. Such bends in the reaction coordinate may facilitate the statistical re-distribution of the internal energy, as the original rotational energy in the reaction coordinate is turned into internal rotation of the I...C2H4+ product, and the reaction turns to proceed along a constrained, 1-D stretch coordinate. The experimental data offer further insight into the dissociation mechanism. The I2 coordinated structure 5 is quite stable, i.e. the corresponding phase space volume is large, and I atom loss from this structure is a simple bond breaking along a purely attractive potential energy curve. If it were a true, deep, and statistically populated minimum along the dissociation path as calculations predict, this structure should be the determining reactant in the dissociation with two consequences. The kinetic energy release would then be expected to correspond to a 2-D distribution, since the system would have enough time to forget about the “bend” in the reaction coordinate. More importantly, C2H4 loss yielding I2+ is only 55 meV higher in energy than I-atom loss, its predicted onset being E0 = 9.64 eV. The corresponding transition state should be equally loose as that of I loss, so that at high energies C2H4 loss should effectively compete with I loss. Apart from the wellresolved peaks in the I2+ signal assigned to threshold photoionization of I2 as shown in Figure S1, the I2+ abundance levels off at around 8−9% in the 10−11.9 eV photon energy region. It was not possible to reproduce the intensity of the I2+

The onset energies in the breakdown diagram of Figure 6 are based in part on the fitting of the time-of-flight distributions. While the smaller 1,2-C2H4I2+ ion, with a first dissociation barrier of only 0.11 eV, dissociated on a time scale less than 10−7 s, the larger 1,3-C3H6I2+ ion with a first dissociation barrier of 0.42 eV, dissociated considerably more slowly so that the fragment ion TOF distributions were asymmetric. This asymmetry is a result of ions dissociating throughout the time they are being accelerated in the first extraction region. Modeling these asymmetric TOF distributions34 provides more stringent criteria for fitting the breakdown diagram. In particular, we found that the data could only be fitted by assuming a loose transition state in which the entropies of activation, evaluated at 600 K, were 60 and 69 J mol−1 K−1 for the I- and HI-loss reactions, respectively. This confirms that there are no barriers for the I- and HI-loss reactions in this 1,3C2H6I2+ ion dissociation. The metastable ion TOF distributions (Figures S2 and S3) and their modeled fits are shown as Supporting Information. In addition, the RRKM dissociation rate constants are shown in Figure S4.

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DISCUSSION

Iodine Atom Loss Mechanism from 1,2-C2H4I2+ and Translational Energy Release. As is shown by both the breakdown diagram (Figure 2) and the TOF peak analysis (Figures 4 and 5), the I-loss reaction from 1,2-C2H4I2+ proceeds with a distribution of translational energies that can be described by a one-dimensional translational energy distribution (Figure 3). One implication of such a 1-D distribution is that the reverse association reaction has a small impact parameter so that this reaction proceeds along a potential energy surface that is highly channeled and thus very nonisotropic. It also implies that the transitional C−I bending modes, which normally are assumed to convert into orbital angular momentum, are not free to participate in the dissociation but instead are highly constrained. This means that the dissociation cannot proceed via a simple C−I bond rupture from the original 1,2-C2H4I2+ geometry along a nonsymmetric geometry. Ab initio calculations can shed light on this reaction. Figure 8 shows the I-loss mechanism in C2H4I2+ as obtained with density functional theory. A consistent description of the reaction path could not be obtained with the UCCSD method. A reviewer

Figure 8. Minimum energy path for the doublet 1,2-C2H4I2+ → I...C2H4+ + I obtained at the B3LYP/6-311++G(d,p) level. The experimental dissociation energy is 9.57 eV. 2840



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yield with a statistical model that assumes structure 5 in Figure 8 as the precursor to both I and C2H4 loss, and we have consequently disregarded this minor channel in the modeling of the sequential reaction. While the observation of the I2+ signal proves that an I−I bond is sometimes formed in the first dissociation step, this leveling off makes a statistical population of structure 5 somewhat unlikely. Isodesmic Reaction Energies and Enthalpies of Formation. Despite the good fit of the statistical models to the experimental breakdown diagrams in Figures 2 and 6, the second onset in the 1,2-C2H4I2 reaction (I + HI loss) does not agree with the literature heat of formation of the 1,2-C2H4I2. We return thus to the possibility that the reported heat of formation for this molecule is in error. The ab initio isodesmic reaction energies using the methods outline above for reactions 4a−d are 4.5, −43.8, 0.0, and 12.9 kJ mol−1, respectively, and are expected to be accurate within 2−3 kJ mol−1. On the basis of the published enthalpies of formation (see Table 1 where we use the Carson et al.44 values for 1,2-C2H4I2 and 1,3-C3H6I2, the Active Thermochemical Tables value of Goos et al.73 for C2H5I, and the Lago and Baer45 value for CH2I2), the same reaction energies are calculated to be 0.8, −26.7, 4.0, and 20.2 kJ mol−1, respectively, suggesting a significant discrepancy between at least two literature enthalpies of formation and the ab initio reaction energies. When enthalpies of formation were systematically varied to minimize the sum of squares of the differences between enthalpy of formation based and ab initio calculated isodesmic reaction energies, it became evident that changing the CH2I2 and C2H4I2 formation enthalpies are most effective in decreasing the error. The error can be further decreased by relaxing ΔfH(C2H5I), which leads to an iodoethane enthalpy of formation consistent with the most recent experimental result of Borkar and Sztáray66 (6.3 ± 1.5 kJ mol−1). In their work, the dissociative photoioinization onset for C2H5I + hν → C2H5+ + I was measured, and ΔfH(C2H5I) is anchored to the C2H5+ heat of formation, now well-established at 915.6 ± 1.4 kJ mol−1.66 Even though the error bars overlap, this leads us to support the ΔfH(C2H5I) value of 6.3 ± 1.5 kJ mol−1 instead of the more precise Active Chemical Tables value of 8.25 ± 0.56 kJ mol−1 in our network. As a result, we propose to revise the ΔfH for CH2I2 and C2H4I2 by +6.1 and −8.7 kJ mol−1, respectively (see Table 1), which decreases the error function in the overall network from 423 to 14 kJ2 mol−2. The new 0 K thermochemical value of 80.0 ± 2.5 kJ mol−1 for 1,2-C2H4I2 predicts an onset energy for the 1,2-C2H4I2 → C3H5+ + I + HI of 12.186 ± 0.025 eV, which now agrees with the predictions of the 1-D model in the breakdown diagram of Figure 2. Potential Energy Surface for the Sequential HI Loss from C2H4I+. The discrepancy in the C2H3+ + I + HI onset energy assuming the Carson heat of formation of 1,2-C2H4I2 can be accounted for either by a revised 1,2-C2H4I2 heat of formation or by the presence of a reverse barrier for the final HI loss. Although our ab initio calculations suggest that the Carson value is indeed too high by 8.7 kJ mol−1, this discrepancy is so significant that we must also establish that there is no exit channel barrier associated with the rearrangements required for HI loss. Because only closed shell species are involved in this dissociation step, the reaction energy curve is expected to be more reliable than for I atom loss. The stationary points along the HI-loss minimum energy path, obtained with the STQN method, are shown in Figure 9, together with zero-point energy corrected closed shell CCSD energies. On the left-hand side,

Figure 9. Minimum energy path for the singlet C2H4I+ → C2H3+ + HI obtained at the B3LYP/6-311++G(d,p) level. The CCSD/(SDB-)augcc-pVTZ energies at the B3LYP/6-311++G(d,p) stationary points and with the B3LYP zero point energy corrections are also plotted. The CCSD reaction energy of 11.9 eV is slightly below the experimental value of 12.2 eV.

the energy scale is shifted by the experimental E0 for I loss so that a direct comparison with the breakdown diagram becomes possible. The right-hand axis shows energies relative to the C2H4I+ minimum. The first H-transfer step involves a tight transition state, [7]⧧, after which the iodine is bound to a single carbon and the H−I bond is formed in 8. This transition state, however, lies at least 500 meV below the final barrier. As we go further out and the HI···C2H3+ induced dipole/ion complex is formed, the H migration takes place without an apparent barrier. The breaking of this long-range interaction leading to C2H3+, [9], is not expected to involve an energy maximum. As a result, in the absence of an overall reverse barrier, the onset energy of HI loss is expected to agree with the dissociative photoionization energy. The general agreement between the DFT and CCSD calculations and the reasonable agreement between the predicted onset of 11.9 eV (CCSD) and the experimental onset of 12.2 eV provides some confidence that these calculations and the conclusion that there is no barrier are valid.

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CONCLUSIONS

The sequential I- and HI-loss reactions for 1,2-C2H4I2+ and 1,3C3H6I2+ ions, as measured by photoelectron photoion coincidence experiments, proceed with very different translational energy distributions. The former ion loses the I atom with a one-dimensional translational energy distribution, while the latter ion does so with the more usual two-dimensional distribution. These results are qualitatively interpreted in terms of an I-loss channel from a highly symmetric isomerized structure of 1,2-C2H4I2+, which favors a zero impact parameter trajectory of the departing I atom. Classical trajectory calculations are currently underway to explain these results quantitatively.72 The derived onset energies for the final HI loss channels have confirmed the experimental literature value for the 1,3C3H6I2 heat of formation. However, they indicate that this same calorimetric study resulted in a 1,2-C2H4I2 heat of formation that is about 8.7 kJ mol−1 too high. Ab initio calculations using a series of isodesmic reactions support the new heat of formation and also warrant a revision of the CH2I2 heat of formation. 2841



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ASSOCIATED CONTENT

S Supporting Information *

Figures S1−S4 showing the complete breakdown diagram for 1,2-C2H4I2, ion time of flight distributions for 1,3-C3H6I2+, and calculated RRKM rate constants. This information is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*

Present Addresses ‡

Department of Chemistry, North Carolina State University, Raleigh, NC 27695. § Air Force Research Laboratory, Space Vehicles Directorate, 3550 Aberdeen Ave. SE, Kirtland Air Force Base, NM 871175776. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We are very grateful to Bill Hase for not only suggesting the complicated mechanism for this “simple” bond fission reaction but also for helpful discussions. We thank the U.S. Department of Energy and U.S. National Science Foundation for support of this work. Part of the experimental work was carried out at the vacuum-ultraviolet beamline of the Swiss Light Source of the Paul Scherrer Institut.

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REFERENCES

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