Temperature and Pressure Dependences of the Reactions of Fe+ with

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Temperature and Pressure Dependences of the Reactions of Fe with Methyl Halides CHX (X = Cl, Br, I): Experiments and Kinetic Modeling Results 3

Shaun G Ard, Nicholas S. Shuman, Oscar Martinez, Nicholas R. Keyes, Albert A Viggiano, Hua Guo, and Juergen Troe J. Phys. Chem. A, Just Accepted Manuscript • Publication Date (Web): 10 May 2017 Downloaded from http://pubs.acs.org on May 11, 2017

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The Journal of Physical Chemistry

Temperature and Pressure Dependences of the Reactions of Fe+ with Methyl Halides CH3X (X = Cl, Br, I): Experiments and Kinetic Modeling Results

Shaun G. Ard,1 Nicholas S. Shuman,1 Oscar Martinez Jr.,1 Nicholas R. Keyes2, Albert A. Viggiano,1* Hua Guo,2 and Jürgen Troe3

1

Air Force Research Laboratory, Space Vehicle Directorate, Kirtland AFB, Albuquerque,

NM 87117, USA 2

Department of Chemistry and Chemical Biology, University of New Mexico, Albuquerque,

NM 87131, USA 3

Institut für Physikalische Chemie, Universität Göttingen, Tammannstrasse 6, D-37077

Göttingen, Germany and Max-Planck-Institut für Biophysikalische Chemie, D-37077 Göttingen, Germany *

Corresponding author, [email protected]

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ABSTRACT The pressure and temperature dependence of the reactions of Fe+ with methyl halides CH3X (X = Cl, Br, I) in He were measured in a selected ion flow tube over the ranges 0.4 – 1.2 Torr and 300 – 600 K. FeX+ was observed for all three halides and FeCH3+ for the CH3I reaction. FeCH3X+ adducts (for all X) were detected in all reactions. The results were interpreted assuming Two State Reactivity with spin-inversions between sextet and quartet potentials. Kinetic modeling allowed for a quantitative representation of the experiments and for extrapolation to conditions outside the experimentally accessible range. The modeling required quantum-chemical calculations of molecular parameters and detailed accounting of angular momentum effects. The results show that the FeX+ products come via an insertion mechanism, while the FeCH3+ can be produced from either insertion or SN2 mechanisms, but the latter we conclude is unlikely at thermal energies. A statistical modeling cannot reproduce the competition between the bimolecular pathways in the CH3I reaction indicating that some more direct process must be important.


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I.

INTRODUCTION

The reactions of Fe+ with methyl halides CH3X (X = Cl, Br, I) offer the opportunity to study aspects of bond activation in a systematic manner. Two bimolecular channels are possible: Either CH3 can transfer to Fe+ to make FeCH3+, Fe+ + CH3X → FeCH3+ + X,

(1)

or the halide can add, Fe+ + CH3X → FeX+ + CH3.

(2)

Alternatively, adduct formation can happen, Fe+ + CH3X (+ M) → FeCH3X+ (+ M).

(3)

Experiments using ion cyclotron reasonance mass spectrometry (ICRMS)1-3 near room temperature observed FeBr+ as the only product in the CH3Br-reaction, while FeI+ and FeCH3+ were detected with nearly equal yield in the CH3I reaction. Not only ground state 6

Fe+, but also excited 4Fe+ was investigated in the guided ion beam mass spectrometry

(GIBMS) experiments of ref. 4. The use of a large energy range (up to 7 eV) allowed for the observation of both bimolecular products in reactions with all three methylhalides. The FeCH3+ product channel in both the CH3Cl and CH3Br reactions, however, had energy thresholds indicating endothermic processes. 4Fe+ reacted faster than 6Fe+ in the CH3Cl and CH3Br reactions for both channels. In the CH3I reaction, the excited state produced FeI+ more rapidly, but the opposite was observed for FeCH3+ production. The competition between the bimolecular reactions was further elucidated in the quantum-chemical calculations of ref. 5 where the FeCH3+ channel was calculated to come from an SN2 mechanism and the FeX+ channel from an insertion



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mechanism. However, we show later that both products can come from an insertion mechanism, and that the SN2 mechanism is unlikely to contribute at thermal energies.

A deeper understanding requires both extended studies of kinetic properties and their evaluation in terms of rate theories. Both are addressed in the present work. In particular, previous experiments were done at low pressure and adduct formation was not investigated. Here we studied the reactions in selected ion flow tube (SIFT) experiments at both elevated pressures and temperatures. The kinetic modeling required energetics, vibrational frequencies, and rotational constants of reactants, products, intermediate adducts, and transition states. Therefore, we extended the quantum-chemical calculations of ref. 5. As we have demonstrated previously (e.g., refs. 6-10), kinetic modeling of temperature, translational energy, and pressure dependences of rate constants and branching fractions provides deeper insight into the dynamics of bond activation by transition metal cations. Under the condition that statistical intrinsic dynamics is approached, statistical rate theory provides an alternative to classical trajectory calculations. It also allows one to cover larger ranges of conditions, in particular to inspect pressure dependences. The study of pressure effects introduces a “collisional clock” which leads to information on lifetimes of intermediates. By evaluating these in terms of the statistical theory of complexforming bimolecular reactions,11,12 conclusions about the intrinsic mechanism can be drawn. We find that the competion between bimolecular reaction and adduct formation in the CH3Cl and CH3Br reactions follows the same pattern as observed in our earlier study of the reaction of Fe+ with CH3OCH3.10 This is consistent with the GIBMS work from ref. 4. In contrast to these systems, the results for the CH3I reaction could not be interpreted in a similar way. One aspect of our kinetic modeling should be emphasized. The considered reactions proceed from loose “entrance” structures of the reactants to loose “exit” structures of the products, 4 ACS Paragon Plus Environment

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passing through compact intermediate adduct structures and transition states. In this situation wide ranges of angular momenta (quantum numbers J), arising from the orbital motion of the reactants, contribute to the reaction. This markedly influences the reactivity and requires particular attention to the energy (E)- and angular momentum(J)- dependences of specific rate constants k(E,J) for the intrinsic dynamics. Neglecting the J-dependence leads to incorrect conclusions. This confirms the results from ref. 10 on the reaction of Fe+ with CH3OCH3. The successful kinetic modeling of the SIFT data finally allows us to extrapolate pressure- and temperature-dependences of the rates and branching ratios to conditions outside the range accessible in the SIFT experiments. The present work demonstrates this for the CH3Cl- and CH3Br-reactions.

II.

EXPERIMENTAL METHOD AND RESULTS

All measurements were performed on the Air Force Research Laboratory’s variable temperature selected ion flow tube instrument which has been described elsewhere,13 however several recent additions will be described in detail here. Fe+ ions were created using either an electron ionization source in the presence of a 10% mixture of Fe(CO)5 in He, or a recently added glow discharge source (with identical kinetic results). The latter source, based on a design by Armentrout et al,14 consists of a ¼” rod of the target metal (1045 carbon steel in the present case) biased to negative 1-2 kV and centered within a 3” diameter grounded cylindrical can. A flow of 1-5 std. L min-1 of an Ar/He gas mixture varied between 10/90 and 80/20 passes over the rod resulting in pressures on the order of 1 Torr. These conditions are sufficient to form a discharge of 20-40 mA between the rod and grounded can, producing Ar+ ions which then bombard the metal rod at high energy. This bombardment results in expulsion of neutral metal atoms and ions, with some of the neutrals subsequently also ionized by Ar+. This mixture is carried downstream by the flow and ions are extracted through a truncated 5 ACS Paragon Plus Environment


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nose cone to a differentially pumped region and injected into a quadrupole mass filter. Here Fe+ is mass selected and the ions are focused and introduced to a laminar flow tube via a Venturi inlet. Roughly 104 to 105 collisions with a He buffer gas thermalize the ions and carry them downstream. Potential production of excited electronic states of Fe+ was found to have minimal effect on the subsequent measurements as determined by the observation of linear kinetic decays on a semi-logarithmic scale over 1-2 orders of magnitude. The temperature (accuracy of about ±5 K) of the flow tube is variable over a large range either using resistive heating devices (300 – 600 K) or pulsing chilled methanol (200 – 300 K) or liquid nitrogen (100 - 300 K). Operating pressures of 0.4 – 1.2 Torr of He are maintained in the flow tube channels. The neutral reagents, here methyl halides, are added 59 cm upstream of the end of the flow tube, with typical reaction times on the order of 3-10 ms, dependent on helium buffer flow (varied from 10-13 std. L min-1), pressure, and temperature. At the terminus of the flow tube, the flow is sampled through a 3 mm diameter orifice in a rounded nosecone into a differentially pumped chamber containing a rectilinear quadrupole ion guide, which transports ions to the entrance of an orthogonally accelerated reflectron time-of-flight mass spectrometer (TOF). The output of the TOF z-stack microchannel plate detector is analyzed in counting mode employing a time to digital converter (FastComTec). Mass spectra are accumulated at 104 Hz to accumulate 103 or greater initial ion counts. At each pressure and temperature condition, mass spectra are collected as a function of methyl halide concentration, and ion signals determined by integrating over the appropriate mass peaks. Total rate constants are determined by the decay of the Fe+ signal with increasing methyl halide concentration with typical uncertainties of ± 25% absolute and ±15% relative between conditions. Product branching fractions, and subsequently partial rate constants, are determined by monitoring product ion formation at low methyl halide concentrations, such


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that secondary chemistry is minimized. Typical uncertainty is ±0.1 for a product branching fraction of 0.5. The measured total rate constants ktot = k1 + k2 + k3

(4)

and partial rate constants k1 (for reaction (1)), k2 (for reaction (2)), and k3 (for reaction (3)) are summarized in Table 1 for Fe+ + CH3Cl, Table 2 for Fe+ + CH3Br, and Table 3 for Fe+ + CH3I. A few details should be noted. For the CH3Cl-reaction, the increase of ktot with increasing pressure P is accompanied by a decrease of k2/ktot (with k1/ktot being unobservably small under our conditions); at a given P, ktot decreases with increasing T. For the CH3Brreaction, similar trends are identified, again with k1/ktot being unobservably small. For the CH3I-reaction, within our accuracy no pressure dependence of ktot was observed; however, adducts were only identifiable at 300 K with small yield of 3(±2)%. For this system, both k1/ktot and k2/ktot could be measured, with k1/ktot decreasing with increasing temperature (and the corresponding k2/ktot increasing with T). The results will be interpreted by kinetic modeling in sections IV – VI after a description of our quantum-chemical calculations is given in section III.

III.

QUANTUM-CHEMICAL CALCULATIONS

Like in the earlier quantum-chemical calculations of ref. 5, the ORCA quantum chemistry program of ref. 15 was used to determine energies, frequencies, and rotational constants of the sextet and quartet stationary points on the potentials of the reactions (however, in contrast to ORCA 2.8 in ref. 5, we used the version ORCA 3.0.3). The values given below were calculated using the B3LYP functional16-19 and the def2-SVP basis set.20 This level of theory



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was chosen because of its favorable behavior in the considered reactions and to keep our work in line with ref. 5.

The geometry optimizations were carried out with tight convergence criteria (∆E < 10-6 Hartree) and a tight self-consistent field (SCF) (∆E < 10-8 Hartree). Geometry optimizations were limited to no more than 50 steps, while SCF convergence was allowed up to 2500 iterations during optimization. Stationary points were found to converge typically in less than 50 steps. After identifying an optimized geometry, harmonic vibrational frequencies were calculated. For saddle points, only one imaginary frequency was found. The rotational constants at all stationary points were computed using the corresponding geometries. Sextet- and quartet-potential energies (zero point energy - corrected) for the three reaction systems and the relevant SN2 (FeCH3+ only) and insertion (FeCH3+ and FeX+) pathways are shown in Figs. 1 – 3. Table 4 summarizes the energies of the relevant stationary points. The corresponding frequencies and rotational constants are given in Section S1 of the Supporting Information (SI). On the way from the reactants to the products crossing of the potentials opens the possibility for spin-inversion, i.e. for Two-State-Reactivity (TSR).21 Furthermore, entrance wells (RC) and exit wells (IM) are separated by transition states (TS). In all cases the quartet TS are lower in energy than the sextet TS. Analyzing Figs. 1 – 3, one should be aware of the fact that the figures correspond to zero overall angular momentum. The energies of the intermediate structures between reactants and products may considerably increase when rotational energies from non-zero angular momenta are added. Rotational contributions to the energies of the intermediate structures RC , TS, and IM in the figures will be much larger than for the reactants and products such that “rotational channel switching” may occur,12 see below.


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IV.

ANGULAR MOMENTUM EFFECTS IN THE KINETIC MODELING

In the following, high pressure limiting values ktot,∞ of the total rate constants ktot are first compared with ion-molecule capture rate constants kcap. A suitable starting point for this is the Su-Chesnavich (subscript SuCh) equation for ion-dipole capture,22 given by kcap,SuCh/kL = 0.4767 xSuCh + 0.6200

for xSuCh ≥ 2

(5)

for xSuCh ≤ 2

(6)

and kcap,SuCh/kL = (xSuCh + 0.5090)2/10.526 + 0.9754 where xSuCh = µD/(2α kBT)1/2

(7)

The Langevin rate constant kL is given by kL = 2πe(α/µ)1/2

(8)

(µ denotes the reduced mass of the collision pair, µD is the dipole moment and α the polarizability of CH3X). It also appears useful to consider capture rate constants from phase space theory (PST) which are given by the “locked-dipole” rate constant23 kcap,PST = kL + kD

(9)

where kD = 2πeµD(2/πµkBT)1/2

(10)

Table 5 compares experimental values (at the highest applied pressures) of ktot with kcap,SuCh and kcap,PST (calculated with µD/D = 1.896, 1.820, and 1.641 and α/10-24 cm3 = 5.35, 5.87, and 7.97 for CH3Cl, CH3Br, and CH3I, resp.24). kcap,SuCh is smaller than kcap,PST, because the latter 9 ACS Paragon Plus Environment


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neglects the anisotropy of the ion-dipole potential, whereas the former accounts for its anisotropy. The observation of ktot < kcap,SuCh can be attributed to two possibilities: (i) there is back-dissociation of the adducts RC to the reactants; (ii) the adduct never forms due to anisotropy of the potential being more pronounced than in the ion-dipole potential. The latter would also reduce ktot,∞ to values below kcap,SuCh. The experimental observation of relatively efficient reactions, see Tables 1 and 2, clearly suggests that possibility (i) applies. This, however, does not rule out possibility (ii) which may also contribute. Unfortunately the pressure range is too small to accurately predict ktot,∞ by extrapolation. However, the kinetic modeling presented below shows that the assumption ktot,∞ ≈ kcap,SuCh is roughly consistent with the experimental observations and only minor reductions of ktot,∞ are necessary. Next, we examine the effects of angular momenta (quantum numbers J) of the adducts, RC, formed by encounter of the reactants. If the ion-dipole potentials were isotropic, i.e. of “locked-dipole” form, the centrifugal maxima would be given by23 E0(J) = 0

for J < J0

(11)

and E0(J) = [J(J+1)-J0(J0+1)]2ħ4/8µ2e2α

for J > J0

(12)

where J0(J0+1) =2µeµD/ħ2

(13)

(note that the zero level of the energy scale throughout this article is placed at the energy of the separated reactants in their electronic sextet ground states at 0 K). Solving eq. (13) one finds J0 ≈ 268, 303, and 306 for CH3Cl, CH3Br, and CH3I, respectively. This calculation shows that large ranges of angular momenta contribute to the reaction. However, because of the absence of anisotropy in the PST potential, this model might underestimate the centrifugal 10 ACS Paragon Plus Environment

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barriers E0(J) and, therefore, overemphasize the role of angular momenta. The Statistical Adiabatic Channel Model (SACM)25 is used to clarify this. In particular, it provides access to the centrifugal barriers E0(J) of an anisotropic ion-dipole potential. For the range J < J0, instead of E0(J) = 0 one now has25 E0(J) ≈ Bhc/2 (1-G)

(14)

where G = J(J+1)/J0(J0+1)

(15)

(see eq. (3.2) of ref. 25; B is the rotational constant of the dipole). The corresponding thermal J-distribution, being proportional to (2J+1) exp(-Bhc/2kBT[1-G]), is peaked near J = J0 such that similarly large ranges of J-values need to be considered as suggested by the locked-dipole PST model of eqs. (11) – (13). For simplicity, we focus our analysis on J of the order of J0. One consequence of large angular momenta is “rotational channel switching”.12,26 Adding rotational energy to the energies shown in Figs. 1 – 3 considerably changes the energies of the comparably compact structures RC, TS, and IM relative to the energies of the loose “entrance” and “exit” structures. Denoting the entrance threshold energies by E0(J) and the transition state energies by E0≠(J), there may be a switching from a situation with E0(J) > E0≠(J) at small J to E0(J) < E0≠(J) at large J. This effect is encountered when E0≠(J=0) is not much smaller than E0(J=0) (which is chosen to be zero in Figs. 1 – 3), and it is responsible for part of negative temperature coefficients of ktot.6-10 As an example, Fig. 4 shows E0(J) and E0≠(J) for the sextet and quartet energiesof the insertion pathway in the CH3Cl-system. For the quartet and sextet surfaces, E0≠(J) exceeds E0(J) for J ≥200 and J ≥ 85, respectively (note that at much higher J > J0 , E0(J) again grows larger due to the the centrifugal barriers increasing as ~J4). Similar effects are observed for the insertion pathway in the CH3Br and CH3I reactions. The situation is different for the SN2 pathway of the CH3I reaction (Fig. 3) 11 ACS Paragon Plus Environment


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where rotational channel switching in the quartet state takes place at much smaller J than in the quartet insertion processes.

V.

KINETIC MODELING OF PRESSURE EFFECTS IN THE CH3Cl- AND CH3Br-REACTIONS

Although the experimental data base is limited, the observed pressure dependences of the rate constants lead to insight into the intrinsic dynamics. We start with the CH3Cl and CH3Br reactions for which insertion yielding FeX+ (k2) and substantial adduct formation (k3) were observed. We employ the simplified approach to complex-forming bimolecular reactions from ref. 11, such as applied before to the reaction of Fe+ with CH3OCH3.10 The Supporting Information summarizes the formalism. Our analysis is limited by the fact that the data do not allow for an accurate experimental determination of ktot,∞. For this reason, we identify ktot,∞ with kcap,SuCh, but eventually allow for a minor reduction in this parameter due to valence anisotropies of the potential. Using this ktot,∞, experimental yields YAss (here identified with k3/ ktot,∞) and YCA (here identified with k2/ ktot,∞) are determined and included in Table 1 and Table 2. Following the formalism of ref. 11 (summarized in section S2 of the SI), the subscript Ass stands for collision-induced association, while the subscript CA stands for chemical activation processes such as insertion or SN2 reactions; one should note that the latter processes may also be influenced by collisions, but lead to products such as in reactions (1) and (2). Using the experimental values of YAss and YCA , with eq. (SI1) of the SI one obtains the limiting low pressure insertion rate constant kCA,0 ≈ 1.9 x 10-10(T/300 K)-0.8 cm3 s-1

(16)


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for the CH3Cl system (kCA,0 ≈ 4.2 x 10-10 (T/300 K)-0.2 cm3 s-1 for the CH3Br-system). If ktot,∞ would be ten times smaller than kcap,SuCh, the derived kCA,0 would increase only slightly, at maximum by a factor of 1.5 in both reactions. An interpretation of the absolute value and the temperature dependence of kCA,0 is given below. Decoupling adduct formation (i.e. “association”) and the insertion reaction (i.e. one possibility of “chemical activation”) is done with eqs. (SI2) and (SI3) of the Supporting Information. The corresponding YAss* and YCA* are included in Tables 1 and 2, where the asterisk denotes the value of that quantity that would be expected in the absence of the competing channel. One realizes that YAss* is only slightly larger than Yass, while YCA* markedly exceeds YCA. The values of Yass* ≈ Yass are approximately proportional to the pressure (apart from the values at 600 K which must suffer from experimental artifacts), indicating that adduct formation here is close to the low pressure limit of a recombination process and can be analyzed by standard unimolecular rate theory.27 Using the molecular parameters from the present quantumchemical calculations, this calculation is straight-forward, leading to modeled values of kAss,0*. The experimentally derived values of kAss,0*/[He] ≈ 9.1 x 10-27 at 300 K and 3.1 x 10-27 at 500 K for CH3Cl (values in cm6 s-1; 1.6 x 10-26 at 300 K and 8.0 x 10-27 at 500 K for CH3Br), then are compared with theoretical results for several possible intrinsic mechanisms. We analyze this three ways. First we assume that spin-inversion does not take place (i.e. that TSR does not apply) and association leads into the first sextet well. For the CH3Cl reaction we obtain kAss,.0*/[He] ≈ 1.6 x 10-27 at 300 K and 3.5 x 10-28 at 500 K. Second we assume curve crossing occurs (TSR applies) and the quartet adduct RC is efficiently formed. This leads to kAss,0*/[He] ≈ 3.0 x 10-27 at 300 K and 6.5 x 10-28 at 500 K. Finally, we assume that TSR applies and the adduct 4RC rapidly isomerizes via 4TS to the intermediate 4IM, i.e. the most stable adduct is formed. One then finds kAss,0*/[He] ≈ 2 x 10-26 at 300 K and 4 x 10-27 at 500 K. Only the latter scenario appears compatible with the experimental values. Some caution comes from the fact 13 ACS Paragon Plus Environment


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that the theoretical modeling involves the estimate of an average energy transferred per collision. Here, /hc ≈ -100 cm-1 was chosen, being of typical magnitude such as derived experimentally in refs. 28 and 29. Vibrational anharmonicity was neglected. We then conclude adduct formation is likely to occur via a TSR mechanism - sextet reactants→ quartet RC → quartet IM adducts. This is consistent with the earlier conclusion that a mechanism involving sextet reactants → sextet RC adducts can be ruled out on the basis of angular momentum arguments. For CH3Br similar conclusions can be reached. We predict (1) that the sextet-sextet mechanism without TSR yields kAss,0*/[He] ≈ 4.4 x 10-27 at 300 K and 8.4 x 10-28 at 500 K; (2) the TSR sextet-quartet RC mechanism yields 1.0 x 10-26 at 300 K and 1.9 x 10-27 at 500 K; and (3) the TSR sextet-quartet IM mechanism gives 5.2 x 10-26 at 300 K and 9.8 x 10-27 at 500 K. The experimental data for the CH3Br-reaction, therefore, also clearly favor the TSR mechanism with rapid transition from RC to IM. The conclusion about quartet IM adduct formation is further supported by the calculation of specific rate constants k(E) for the 4RC → 4IM isomerization. Fig. 5 shows k(E) for going from the 4RCi entrance well to the adduct exit well 4IMi of the insertion pathways for both the CH3Cl and CH3Br reactions. The values are obtained using rigid activated complex RRKM theory.30 Average thermal internal energies E0≠ of the adducts are indicated by arrows. Comparing k(E0≠) with the collision frequenciesof the excited molecules under the present conditions indicates that 4RC and 4IM equilibrate long before collisional stabilization of the adduct becomes substantial. Furthermore, the concentration of 4IM by far exceeds that of 4RC. The modeling also predicts larger values of kAss,0* (at a given temperature) for the CH3Br reaction compared to the CH3Cl reaction which is in line with the experimental data. This supports the validity of the interpretation. After kAss,0* and ktot,∞ are determined, kAss* in the intermediate range of the falloff curves of the association reactions are derived from standard unimolecular rate theory, e.g. in the form given by refs 27, 30, and 31. 14 ACS Paragon Plus Environment

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The experimental values of the decoupled chemical activation YCA* should be compared with the modeling of the chemical activation process 4IMi → FeCl+ + CH3 and its pressure dependence. The analysis requires knowledge of the specific rate constants k(E,J) for this process and the rates of rovibrational collisional energy transfer of highly excited 4IMi. In contrast to k(E) for the process 4RC→ 4IM, the J-dependence of the specific rate constant is of central importance. Fig. 6 shows k(E,J) for this process such as calculated with PST (for linear plus spherical top reaction products, see ref. 32). The calculated k(E,J) show both strong E- and J-dependencies. At the thermal energies of the reactants and J of the order of J0, they are of the same magnitude as the collision frequencies at pressures where YCA* starts to decrease. Symbolically this may be represented by33 YCA*≈ [ 1 + c(E,J) Z [He] / < k(E,J)> ]-1

(17)

where c(E,J) is a chemical activation collision efficiency, Z is a collision frequency, and is an average specific rate constant of the relevant dissociation process, i.e. here 4IMi → FeCl+ + CH3 . Unfortunately, there is not enough known on rovibrational collisional energy transfer of excited molecular ions to allow for a more quantitative evaluation of eq. (17). However, employing the approximate method of ref. 33 , at least a semi-quantitative modeling can be made when the collision efficiency c(E,J) is estimated with eq. (SI7) of the SI, see below. For practical use, the empirical expression from refs. 11, 34, and 35, YCA*≈ [ 1 + ktot,∞ [He] / kCA,∞*]-1

(18)

is fitted to the CH3Cl experiments with a temperature dependent parameter kCA,∞*given by kCA,∞*=5.0 x 107(T/300 K) s-1

(19)



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Eqs. (18) and (19) are used to extrapolate the experimental data to conditions outside the experimental range (kCA,∞*= 5.5 x 107(T/300 K)2 s-1 was derived for the CH3Br-reaction; chemical activation broadening factors11 in eq. (18) were neglected). The comparison of the experimental ktot,∞ / kCA,∞* of eqs.(18) and (19) with the modeled c(E,J) Z / then leads to . With the properties of k(E,J) from Fig 6, Z = 5.4 x 10-10 cm3s-1 and c ≈ 0.6, one obtains ≈ 107 s-1 (for 300 K). At ≈ 10 kJ mol -1, this is just what one would expect for ≈ J0 = 268 (see above). The modeling thus appears consistent with the earlier conclusions about the mechanism and its statistical dynamics. Although the described modeling at the present stage can only be semi-quantitative, it confirms the importance of angular momentum effects. The neglect of angular momentum effects, i.e. working with k(E,J=0), would have required orders of magnitude larger experimental pressures to generate a decrease of YCA*. This conclusion is quite analogous to that drawn in our analysis of the reaction of Fe+ with CH3OCH3.10 We finally consider the limiting low pressure chemical activation constants kCA,0 from eq. (16). We note that its value is about one order of magnitude smaller than kcap,SuCh.This observation could be explained in two ways: either there is marked “back-dissociation” by rotational channel switching of the adducts at the quartet barrier 4TS or the competition between the “back-dissociation” 4IM → Fe+ + CH3Cl and the “forward-dissociation” 4IM → FeCl+ + CH3 markedly favors back-dissociation. This question can be answered by comparing k(E,J) for back- and forward- dissociation of 4IM. For this purpose, Fig. 6 compares k(E,J) for the two processes (from PST calculations with atom plus spherical top reactants and linear rotor plus spherical top products, respectively32). Obviously, forward-dissociation wins over back-dissociation, such that the small value of kCA,0 is explained by rotational channel switching, generated by large angular momenta raising the energy of 4TS. The situation thus is similar to that of the reactions which we analyzed previously, see refs. 6 – 10. 16 ACS Paragon Plus Environment

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The relevant parameters determining YAss* and YCA* such as derived by comparing experiments and kinetic modeling are given in section S3 of the SI. These parameters are the limiting low pressure (kAss,0*) and high pressure (ktot,∞) rate constants for the association reaction and the limiting high pressure rate parameter (kCA,∞*) for collisional quenching of the chemical activation process. These quantities are used for rate extrapolations below. In order to do this, the collisional association and chemical activation must be coupled, i.e. one must derive YAss and YCA from YAss* and YCA* by means of eqs. (SI4) and (SI5) of the SI. A comparison of the results with the experimental data then illustrates the quality of the procedure (a minor fine-tuning of the parameters appeared appropriate, see section S3 of the SI). Tables 1 and 2 include the resulting rate constants for the CH3Cl and CH3Br reactions. Within the experimental scatter, the agreement between kinetic modeling and the experimental data appears quite satisfactory (although a few inconsistencies in the measurements are noted). One should emphasize that the kinetic modeling results are consistent with statistical rate theory in these two reactions, leading to clear conclusions about the dominant intrinsic mechanism. Beyond the comparison of modeled and experimental data in Tables 1 and 2, the modeling of the YAss and YCA can be further used for rate extrapolations. Figs. 7 and 8 illustrate the results for a pressure range of 0.1 – 10 Torr and the temperatures of the present experiments. The figures show the transition between chemical activation- and collisional association-determined reactions. The shift of these transition pressures to higher values with increasing temperatures corresponds well to the expectations for falloff curves of collisional association and chemical activation reactions such as given by statistical unimolecular rate theory.

VI.

RATE CONSTANTS OF THE CH3I-REACTION



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The CH3I reaction differs from the CH3Cl and CH3Br reactions in several ways. The energy diagram of Fig. 3 suggests that both insertion and SN2 pathways are energetically accessible under the present SIFT conditions and that the insertion pathway can lead to either FeCH3+ or FeX+. However, a TSR mechanism with spin-inversion would be required to circumvent the barriers 6TSi, 6TSs. Both of these barriers, as well as 4TSs, would considerably increase with increasing J. After spin-inversion to 4RCs, large angular momenta would still close the SN2 pathway, because the barrier 4TSs is not far below zero. Therefore, only adducts with small angular momenta would be able to proceed on the SN2 pathway. This is different for the insertion pathway where the low 4TSi barrier allows for a fast transition from 4RCi to 4IMi and for the formation of products. For successful modeling, three observations of the present experiments would have to be explained: (i) the similar magnitude of the rate constants k1 and k2, (ii) the overall reaction rate constants, which are much closer to ion-dipole capture rates than in the CH3Cl and CH3Br reactions, (iii) the much smaller adduct yields than in the CH3Cl and CH3Br reactions. At present we are not in a position to provide unique answers by statistical rate theory and only speculations can be made. (i) As explained above, the pathways with 6TS barriers are inaccessible and only low J-encounters between Fe+ and CH3I can overcome the 4TSs barrier to form FeCH3+ products from the SN2 pathway. High J-encounters would lead to backdissociation to the reactants. This is in contradiction to the observed product branching, as seen in Fig. 9. Furthermore, the temperature dependence of the product branching is consistent with both products dissociating from the same complex. Calculations of the energetics, carried out at the same level of therory as before, have verified that 4IMi can dissociate into either product channel without a potential barrier. The FeI+ + CH3 channel would be increasingly preferred with temperature as a molecule plus molecule dissociation can reasonably be expected to be entropically preferred to an atom plus molecule dissociation. 18 ACS Paragon Plus Environment

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What is inconsistent with this picture, however, is the amount of FeCH3+ observed, as the FeI+ channel is both energetically and entropically preferred. A statistical interpretation of the pathways is simply unable to account for the observed product branching. This is documented in Fig. 10 which compares k(E;J) for dissociation of 4IM into the two dissociation products. No adjustment to the relative energetics of these channels within the established uncertainty could account for the amount of FeCH3+ observed. (ii) The exothermic energetics of the two products appears responsible for the large magnitude of the overall rate constant. As the SN2 pathway is only viable in a small part of the reaction encounters (those with very low J), the vast majority of the observed reactivity takes place on the insertion pathway. Near capture control can then be checked by comparing the specific rate constants k(E,J) for the processes of 4IMi leading forwards to FeI+ + CH3 or I + CH3Fe+ and backwards to Fe+ + CH3I. The corresponding PST calculations in Fig. 10 show that indeed the forward process is orders of magnitude faster than the backward process. (iii) Kinetic modeling analogous to the CH3Cl and CH3Br reactions shows that collisional stabilization of adducts under the present conditions is only efficient on the insertion pathway where the 4IMi adduct has a sufficiently long lifetime for collisional stabilization to occur. In the CH3I reaction, modeling of the decoupled process Fe+ + CH3I + He → 4RCs + He leads to kAss,0*/[He] ≈ 1.2x10-29 (T/300 K)4.7

cm6s-1 while modeling of the process Fe+ + CH3I + He → 4IMi + He gives kAss,0*/[He] ≈

7.5x10-26 (T/300 K)-3.4 cm6s-1 . The former process thus is much less probable to contribute to adduct stabilization than the latter process. Coupling of collisional stabilization and chemical activation introduces the ratio of forward- over back-dissociation into the association yield. Inspecting Fig. 10, one realizes that this ratio for the relevant energies and angular momenta in the CH3I reaction is about one order of magnitude more in favor of forward dissociation of 4

IMi than in the CH3Cl and CH3Br reactions. This explains why the adduct yield in the CH3I

reaction is about one order of magnitude smaller than in the CH3Cl and CH3Br reactions.



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According to the proposed mechanism, the decrease of k1 with increasing T as usual can be attributed to a decreasing part of the J-distribution being able to overcome the 4TSs.

VII.

CONCLUSIONS

We showed that the properties of the insertion reactions of Fe+ with CH3Cl and CH3Br can be explained by kinetic modeling using statistical unimolecular rate theory. The pressure dependences of these reactions follow the same pattern as observed earlier in our analysis of the reaction of Fe+ with CH3OCH3.10 The simplified approach to complex-forming bimolecular reactions from ref. 11, in combination with statistical unimolecular rate theory,27 again proved useful. In particular, extrapolations of the experimental results of the present SIFT work over wide ranges of conditions outside the experimental range became possible. In contrast to the CH3Cl and CH3Br reactions, results for the reaction of Fe+ with CH3I could not be explained uniquely. The formation of adducts by collisional stabilization could be attributed to the insertion channel within statistical theory, and a statistical picture is consistent with the temperature dependance of the product channels if they were to both dissociate from the same intermediate, 4IMi. The large amount of FeCH3+ produced, however, could not be explained within this approach. A more direct pathway to the FeCH3+ product, preventing statistical dynamic behavior, could explain the experiments. Explorations of the potential energy surfaces for this reaction in greater detail appear necessary to arrive at a quantitative interpretation of the experimental results for the Fe+ + CH3I reaction. In addition, one would have to explore dynamical effects as well as accounting for spininversion processess.

ASSOCIATED CONTENT 20 ACS Paragon Plus Environment

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Supporting Information (S1)

Frequencies and rotational constants of stationary points on the potential energy

surfaces. (S2)

Simplified decoupling of chemical activation and adduct stabilization.

(S3)

Modeled parameters for decoupled chemical activation and adduct stabilization.

Acknowledgments

The AFRL authors are supported by the Air Force Office of Scientific Research under AFOSR award 13RV02COR. S.G.A. acknowledges support of Boston College Institute of Scientific Research under Contract No. FA9453-10-C-0206. J. T. acknowledges support by the EOARD Grant Award No. FA9550-17-1-0181 and help by A. Maergoiz and G. Marowsky. The UNM team acknowledges the Air Force Office of Scientific Research for funding (Grant No. AFOSR-FA9550-15-1-0305) and the UNM Center for Advanced Research Computing (CARC) for computational resources used in this work. NRK acknowledges a Space Fellowship for supporting a summer internship at the AFRL.



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REFERENCES

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(9) Ard, S. G.; Johnson, R. S.; Melko, J. J.; Martinez Jr, O.; Shuman, N. S.; Ushakov,V. G.; Guo, H.; Troe, J.; Viggiano, A. A. Spin-Inversion and Spin-Selection in the Reactions FeO+ + H2 and Fe+ + N2O. Phys. Chem. Chem. Phys. 2015, 17, 19709 – 19717. (10) Ard, S. G.; Johnson, R. S.; Martinez Jr, O.; Shuman, N. S.; Guo, H.; Troe, J.; Viggiano, A. A. Analysis of the Pressure Dependence of the Complex-Forming Bimolecular Reaction CH3OCH3 + Fe+.. J. Phys. Chem. A 2016, 120, 5264 – 5273. (11) Troe, J. Simplified Representation of Partial and Total Rate Constants of ComplexForming Bimolecular Reactions. J. Phys. Chem. A 2015, 119, 12159 – 12165. (12) Troe, J. The Colourful World of Complex-Forming Bimolecular Reactions. J. Chem. Soc. Faraday Trans. 1994, 90, 2303 – 2317. (13) Viggiano, A. A.; Morris, R. A.; Dale, F.; Paulson, J. F.; Giles, K.; Smith, D.; Su, T. Kinetic Energy, Temperature, and Derived Rotational Temperature Dependences for the Reactions of Kr(P3/23) and Ar with HCl. J. Chem. Phys. 1990, 93, 1149 – 1157. (14) Schultz, R. H.; Crellin, K. C.; Armentrout, P. B. Sequential Bond Energies of Fe(CO)x+ (x = 1-5): Systematic Effects on Collision-Induced Dissociation Measurements. J. Am. Chem. Soc. 1991, 113, 8590-8601 (15) Neese, F. The ORCA Program System. WIREs Comput. Mol. Sci. 2012, 2, 73-78. (16) Becke, A. D. Density- Functional Thermochemistry. 3. The Role of Exchange. J. Chem. Phys. 1993, 98, 5648 – 5652. (17) Lee, C.; Yang, W.; Parr, R. G. Development of the Colle-Salvetti Correlation-Energy Formula into a Functional of the Electron Density. Phys. Rev. B 1988, 37, 785 – 789.



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(18) Vosko, S. H.; Wilk, L.; Nusair, M. Accurate Spin-Dependent Electron Liquid Correlation Energies for Local Spin Density Calculations: a Critical Analysis. Can. J. Phys. 2011, 58, 1200 – 1211. (19) Stephens, P. J.; Devlin, F. J.; Chabalowski, C. F.; Frisch, M. J. Ab Initio Calculation of Vibrational Absorption and Circular Dichroism Spectra Using Density Functional Force Fields. J. Phys. Chem. 2002, 98, 11623 – 11627. (20) Weigend, F.; Ahlrichs, R. Balanced Basis Sets of Split Valence, Triple Zeta Valence and Quadruple Zeta Valence Quality for H to Rn: Design and Assessment of Accuracy. Phys. Chem. Chem. Phys. 2005, 7, 3297-3305. (21) Schröder, D.; Shaik, S. ; Schwarz, H. Two-State Reactivity as a New Concept in Organometallic Chemistry. Acc. Chem. Res. 2000, 33, 139 – 145. (22) Su, T.; Chesnavich, W. J. Parametrization of the Ion – Polar Molecule Collision Rate Constants by Trajectory Calculations. J. Chem. Phys.1982, 76, 5183 – 5185. (23) Troe, J. Statistical Adiabatic Channel Model of Ion – Neutral Dipole Capture Rate Constants. Chem. Phys. Lett. 1985, 122, 425 – 430. (24) Lide, D. R. Handbook of Chemistry and Physics. 85th edn. (CRC Press, BocaRaton, 2004). (25) Troe, J. Statistical Adiabatic Channel Model for Ion – Molecule Capture Rate Processes. II. Analytical Treatment of Ion – Dipole Capture. J. Chem. Phys. 1996, 105, 6249 – 6262. (26) Troe, J. Rotational Effects in Complex – Forming Bimolecular Reactions.: Application to the Reaction CH4 + O2+. Int. J. Mass Spectrom. Ion Phys. 1987, 80, 17 – 30. 24 ACS Paragon Plus Environment

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(27) Troe, J. Predictive Possibilities of Unimolecular Rate Theory. J. Phys. Chem. 1979, 83, 114 – 126. (28) Fernandez, A. I.; Viggiano, A. A.; Miller, T. M.; Williams, S.; Dotan, I.; Seeley, J. V.; Troe, J. Collisional Stabilization and Thermal Dissociation of Highly Vibrationally Excited C9H12+-Ions from the Reaction O2+ + C9H12 → O2 + C9H12+. J. Phys. Chem. A 2004, 108, 9652 – 9659. (29) Fernandez, A. I.; Viggiano, A. A.; Maergoiz, A. I.; Troe, J.; Ushakov, V. G.Thermal Decomposition of Ethyl Benzene Cations (C8H10+): Experiments and Modeling of Falloff Curves, Int. J. Mass Spectrom. 2005, 241, 305 – 313. (30) Baer, T.; Hase, W. L. Unimolecular Reaction Dynamics. Theory and Experiments (Oxford University Press, New York and Oxford, 1996). (31) Troe, J.; Ushakov, V. G. Representation of “Broad” Falloff Curves for Dissociation and Recombination Reactions. Z. Phys. Chem. 2014, 228, 1 – 10. (32) Olzmann, M.; Troe, J. Rapid Approximate Calculation of Numbers of Quantum States W(E,J) in the Phase Space Theory of Unimolecular Bond Fission Reactions. Ber. Bunsenges. Phys. Chem. 1992, 96, 1327 – 1332. (33) Troe, J. Approximate Expressions for the Yields of Unimolecular Reactions with Chemical and Photochemical Activation. J. Phys. Chem. 1983, 87, 1800 – 1804. (34) Larson, C. W.; Stewart, P. H.; Golden, D. M. Pressure and Temperature Dependence of Reactions Proceeding via a Bound Complex. An Approach for Combustion and Atmospheric Chemistry Modelers: Application to HO + CO → [HOCO] → H + CO2. Int. J. Chem. Kinet. 1998, 20, 27 – 40.



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(35) Miller, J. A.; Klippenstein, S. J. The Reaction Between Ethyl and Molecular Oxygen. II: Further Analysis. Int. J. Chem. Kinet. 2001, 33, 654 – 668. (36) Troe, J. Theory of Unimolecular Reactions at Low Pressures: Solutions of the Master Equation. J. Chem. Phys. 1977, 66, 4745 – 4757.


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Fig.1

Fig.2



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Fig.3


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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure captions

Fig. 1

Energy diagrams (at J=0) for the Fe+ + CH3Cl reaction from quantum-chemical

calculations of this work, for the SN2 pathway (dashed lines), and the insertion pathway (full lines). Both the sextet curves for reaction of 6Fe+ (red lines) and quartet curves for reaction of 4Fe+(blue lines) are indicated. The lines connecting the stationary points are meant to guide the eyes, rather than accurate potentials.

Fig. 2

As Fig. 1, but for the reaction Fe+ + CH3Br.

Fig. 3

As Fig. 1, but for the reaction Fe+ + CH3I. 32 ACS Paragon Plus Environment

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Fig. 4

Threshold energies E0(J) for the reaction Fe+ + CH3Cl → FeCl+ + CH3 (horizontal

line starting at zero: ion-dipole potential for Fe+ + CH3Cl, eqs. (11) – (13), labeled curves: sextet and quartet transition states TSi from quantum-chemical calculations, see text).

Fig. 5

Specific rate constants k(E) for the transition from adduct 4RCi to adduct 4IMi in the

reactions of Fe+ + CH3Cl → FeCl+ + CH3 and Fe+ + CH3Br → FeBr+ + CH3, see Figs. 1 and 2 (the arrows denote average thermal energies in the CH3Cl-reaction, see text; note that E = 0 corresponds to the energy of the reactants at 0 K).

Fig. 6

Specific rate constants k(E,J) in the CH3Cl-reaction for back-dissociation 4IMi → Fe+

+ CH3Cl (light curves at the right-hand side of the figure) and forward-dissociation 4IMi → FeCl+ + CH3 (heavy curves at the left-hand side of the figure).

Fig. 7

Rate constants for the chemical activation reaction Fe+ + CH3Cl (+He) → FeCl+ +

CH3 (+ He) (k2, decreasing with pressure P, full lines) and for the adduct formation Fe+ + CH3Cl (+He) → FeCH3Cl+ (+He) (k3, increasing with pressure P, dashed lines) (curves from top to bottom for T/K = 200, 300, 400, 500, and 600; selected experimental points for k2 (filled circles) and k3 (open circles) at 300 K (red) and 500 K (green) ).

Fig. 8

As Fig. 7 for the CH3Br-reaction.

Fig. 9

Experimental branching fractions k1/ktot (Fe+ + CH3I → FeCH3+ + I, red squares),

k2/ktot (Fe+ + CH3I → FeI+ + CH3, blue circles), and k3/ktot (for the adduct formation Fe+ + CH3I → FeCH3I+, green diamond, 0.4 Torr).

Fig. 10

Specific rate constants k(E,J) in the CH3I-reaction for back-dissociation 4IMi → Fe+

+ CH3I (light curves at the right-hand side of the figure), forward-dissociation 4IMi → FeI+ +



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CH3 (heavy curves at the left-hand side of the figure), and forward-dissociation 4IMi → I + CH3Fe+(dashed curves).

Table Captions

Table 1 Rate constants k2 for the reaction Fe+ + CH3Cl → FeCl+ + CH3 and k3 for the association reaction Fe+ + CH3Cl (+ He)→ FeCH3Cl+ (+ He) (left-hand columns: experimental results, right-hand columns: kinetic modeling results, see text); experimental yields YAss (defined by k2/ ktot,∞) and YCA (defined by k3/ ktot,∞) expressedwith the limiting high pressure association rate constants ktot,∞ ≈ kcap,SuCh ;after decoupling chemical activation and association, YCA* and YAss* are derived from YCA and YAss, using the relationships given in section S2 of the SI.

Table 2 As Table 1, but for the Fe+ + CH3Br reaction.

Table 3 As Table 1, but for the Fe+ + CH3I reaction (without kinetic modeling results)..

Table 4 Calculated energies of stationary points (in kJ mol-1, see text).


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Table 5 Maximum experimental total rate constant ktot = k1 + k2 + k3 (in cm3 s-1) for Fe+ + CH3X in comparison to capture rate constants kcap,SuCh from the Su-Chesnavich equation (anisotropic ion-dipole model) and kcap,PST from phase space theory (locked-dipole model); values in cm3 s-1, see text.

Table 1 T/K 300

400

500

600

P/Torr 0.40 0.80 1.20 0.40 0.80 1.20 0.44 0.84 1.20 0.44 0.80

k2 / 10-10 cm3 s-1 1.68 1.75 1.66 1.65 1.71 1.54 1.27 1.46 1.34 1.43 1.31 1.41 1.18 1.24 1.17 1.23 1.18 1.22 0.97 1.08 1.24 1.08

k3 / 10-10 cm3 s-1 1.07 1.20 1.84 2.22 2.62 3.17 0.39 0.46 0.70 0.76 1.07 1.02 0.24 0.21 0.35 0.35 0.61 0.46 0.65 0.11 0.36 0.18

YCA 0.081 0.080 0.082 0.067 0.071 0.069 0.067 0.066 0.068 0.058 0.075

YCA* 0.610 0.480 0.400 0.770 0.660 0.550 0.830 0.770 0.660 0.600 0.770

YAss 0.051 0.088 0.126 0.021 0.037 0.057 0.014 0.020 0.035 0.039 0.022

YAss* 0.056 0.095 0.136 0.022 0.040 0.061 0.015 0.021 0.037 0.041 0.024

k2 / 10-10 cm3 s-1 3.58 3.81 3.46 3.45 3.42 3.02 3.73 3.84 3.47 3.75 3.71 3.67 3.73 3.74 3.19 3.70 3.70 3.67 3.88 3.63 3.57 3.61

k3 / 10-10 cm3 s-1 1.64 1.66 3.07 3.18 3.71 5.01 0.67 0.53 0.95 0.88 1.27 1.21 0.48 0.23 0.75 0.38 0.60 0.50 0.18 0.11 0.07 0.19

YCA 0.201 0.194 0.192 0.230 0.214 0.229 0.245 0.210 0.229 0.269 0.248

YCA* 0.690 0.530 0.480 0.850 0.790 0.750 0.890 0.810 0.860 0.960 0.980

YAss 0.092 0.172 0.208 0.041 0.059 0.078 0.032 0.049 0.039 0.013 0.005

YAss* 0.114 0.214 0.258 0.053 0.073 0.100 0.040 0.062 0.052 0.016 0.007

Table 2. T/K 300

400

500

600

P/Torr 0.40 0.80 1.20 0.41 0.80 1.20 0.43 0.80 1.20 0.46 0.80

Table 3



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T/K 300 400 500 600

k1 / 10-10 cm3 s-1 5.2 4.68 4.34 3.53

P/Torr 0.4 0.4 0.4 0.4

k2 / 10-10 cm3 s-1 3.93 5.07 5.76 5.53

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k3 / 10-10 cm3 s-1 0.27 -

Table 4 Fe+ + CH3Cl

Fe+ + CH3Br

6

Reactants RCs 6 TSs 6 IMs SN2 Products 4 Reactants 4 RCs 4 TSs 4 IMs

0 -3.11 84.77 56.96 64.93 26.95 -36.69 69.57 54.7

0 -12.09 49.18 -12.5 25.46 26.95 -45.32 34.98 19.53

0 -28.37 2.15 -28.09 -17.26 26.95 -63.53 -10 -25.61

-97.16 -12.92 -126.14 -14.43 -120.88 -61.24 -146.34

-112.33 -35.88 -155.8 -42.83 -142.49 -91.12 -173.43

-116.83 -14.35 -168.91 -28.78 -149.91 -111.05 -180.49

6

6

Rci TSi 6 IMi Ins. Products 4 RCi 4 TSi 4 IMi 6

Fe+ + CH3I

Table 5.

CH3Cl

CH3Br

CH3I

T/K 200 300 400 500 600 300 400 500 600 300 400 500 600

ktot 7 4.3 2.4 1.8 1.6 7.1 5 4.3 3.6 9.1 9.8 10.1 9.1

kcap,SuCh 24 20.8 18.9 17.6 16.6 17.8 16.2 15.2 14.4 15 13.7 12.8 12.1

kcap,PST 31.2 27.4 25.2 23.6 22.5 23.7 21.8 20.5 19.5 19.9 18.3 17.2 16.4


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Fig. 1 Energy diagrams (at J=0) for the Fe+ + CH3Cl reaction from quantum-chemical calculations of this work, for the SN2 pathway (dashed lines), and the insertion pathway (full lines). Both the sextet curves for reaction of 6Fe+ (red lines) and quartet curves for reaction of 4Fe+(blue lines) are indicated. The lines connecting the stationary points are meant to guide the eyes, rather than accurate potentials. 224x154mm (150 x 150 DPI)

ACS Paragon Plus Environment


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Fig. 2. As Fig. 1, but for the reaction Fe+ + CH3Br 229x154mm (150 x 150 DPI)


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Fig. 3. As Fig. 1, but for the reaction Fe+ + CH3I 230x154mm (150 x 150 DPI)



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Fig. 4 Threshold energies E0(J) for the reaction Fe+ + CH3Cl → FeCl+ + CH3 (horizontal line starting at zero: ion-dipole potential for Fe+ + CH3Cl, eqs. (11) – (13), labeled curves: sextet and quartet transition states TSi from quantum-chemical calculations, see text). 284x199mm (300 x 300 DPI)


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Fig. 5 Specific rate constants k(E) for the transition from adduct 4RCi to adduct 4IMi in the reactions of Fe+ + CH3Cl → FeCl+ + CH3 and Fe+ + CH3Br → FeBr+ + CH3, see Figs. 1 and 2 (the arrows denote average thermal energies in the CH3Cl-reaction, see text; note that E = 0 corresponds to the energy of the reactants at 0 K). 284x199mm (300 x 300 DPI)



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Fig. 6 Specific rate constants k(E,J) in the CH3Cl-reaction for back-dissociation 4IMi → Fe+ + CH3Cl (light curves at the right-hand side of the figure) and forward-dissociation 4IMi → FeCl+ + CH3 (heavy curves at the left-hand side of the figure). 284x199mm (300 x 300 DPI)


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Fig. 7 Rate constants for the chemical activation reaction Fe+ + CH3Cl (+He) → FeCl+ + CH3 (+ He) (k2, decreasing with pressure P, full lines) and for the adduct formation Fe+ + CH3Cl (+He) → FeCH3Cl+ (+He) (k3, increasing with pressure P, dashed lines) (curves from top to bottom for T/K = 200, 300, 400, 500, and 600; selected experimental points for k2 (filled circles) and k3 (open circles) at 300 K (red) and 500 K (green) ). 284x199mm (300 x 300 DPI)



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Fig. 8

As Fig. 7 for the CH3Br-reaction. 284x199mm (300 x 300 DPI)


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Fig. 9 Experimental branching fractions k1/ktot (Fe+ + CH3I → FeCH3+ + I, red squares), k2/ktot (Fe+ + CH3I → FeI+ + CH3, blue circles), and k3/ktot (for the adduct formation Fe+ + CH3I → FeCH3I+, green diamond, 0.4 Torr). 284x199mm (300 x 300 DPI)



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Fig. 10 Specific rate constants k(E,J) in the CH3I-reaction for back-dissociation 4IMi → Fe+ + CH3I (light curves at the right-hand side of the figure), forward-dissociation 4IMi → FeI+ + CH3 (heavy curves at the left-hand side of the figure), and forward-dissociation 4IMi → I + CH3Fe+(dashed curves). 284x199mm (300 x 300 DPI)


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TOC figure 338x190mm (96 x 96 DPI)


Temperature and Pressure Dependences of the Reactions of Fe+ with

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