Theoretical Study of the Pair-Correlated F + CHD3(

Article pubs.acs.org/JPCA

Theoretical Study of the Pair-Correlated F + CHD3(v = 0,ν1 = 1) Reaction: Effect of CH Stretching Vibrational Excitation Joaquin Espinosa-Garcia,*,† Laurent Bonnet,‡ and Jose C. Corchado† †

Departamento de Química Física and Instituto de Computatión Científica Avanzada, Universidad de Extremadura, 06071 Badajoz, Spain ‡ CNRS, Institut des Sciences Moleculaires, UMR 5255, 33405 Talence, and Université de Bordeaux, Institut des Sciences Moleculaires, UMR 5255, 33405 Talence, France ABSTRACT: The F + CHD3(v) reaction is a benchmark system in polyatomic reactions. Theoretical/experimental comparisons have been reported in recent years that present some controversies, specifically the role of the reactant CH stretching vibrational excitation, CHD3(ν1 = 1), on the reactivity of both isotope channels, DF(v) + CHD2(v′) and HF(v) + CD3(v′). However, in many cases, these comparisons are not made on an equal footing. Previous theoretical studies were concerned with overall reactivity of each isotope channel, while fine velocity map imaging experiments provided results in a product pair-correlated manner. In order to shed some light on these controversies, we perform here a pair-correlated theory/experiment comparison for the title reaction, using quasi-classical trajectory calculations on a full dimensional potential energy surface. When these calculations are analyzed in a quantum spirit, i.e., by discarding those trajectories whose results do not meet quantum-mechanical requirements and aiming to reproduce stringent experimental constraints, some of the discrepancies on overall reactivity and the effect of the CH vibrational excitation are now resolved. Agreement with the available experimental studies, though still qualitative in some aspects, has noticeably improved.

1. INTRODUCTION The gas-phase F + CHD3(v) reaction involves two channels, DF(v) + CHD2(v′) and HF(v) + CD3(v′), and its dynamics study presents controversies between theory and experiment, specifically regarding the effect of reactant CH stretching vibrational excitation, CHD3(ν1 = 1) on the reactivity of both channels. Experimentally, Liu and co-workers1−5 studied the F + CHD3(v = 0, ν1 = 1) reaction at low collision energies, < 4 kcal mol−1; they found first that the CH excited reaction suppresses overall reactivity and yields more DF than HF products, which is counterintuitive since CH stretching excitation should favor the HF channel, and second that the CHD2(ν1 = 1) product in the DF(v) + CHD2(v′) channel is not the only detectable product state. Recently, Yang and co-workers6,7 also studied this problem at higher collision energy, 9 kcal mol−1. They found too that the overall reaction rate is suppressed by the CH stretching excitation, by 34 and 26%, for the DF(v) + CHD2(v′) and HF(v) + CD3(v′) channels, respectively. Moreover, they found that four additional CHD2(v′) vibrational states appeared in the excited reaction, which were absent in the ground-state reaction, and finally, that all product CHD2(v′) vibrational states are strongly hindered in the CH excited reaction with respect to the ground-state reaction. Theoretically, this problem has also deserved a lot of attention8−16 and in general the results obtained do not reproduce the experiments, especially the effect of CH © XXXX American Chemical Society

stretching vibrational excitation on reactivity. In a theoretical study, the choice of both the dynamical method and the potential energy surface (PES) are important. Ideally, one would like to calculate the dynamics quantum mechanically (QM) and exactly. However, the reaction at hand involves 12 degrees of freedom, and a large number of rotovibrational states are available to the products. In such a case, exact QM calculations become prohibitive for the present time. An economical alternative is the quasi-classical trajectory (QCT) calculations, which work with full-dimensionality and in a classical spirit, i.e., they classically move the nuclei in the field of the PES. In recent years, three different PESs (and some modifications) have been developed by different groups for this system and its isotopic variants: PES-200617 is an analytical fulldimensional surface developed by our group, with a valencebond/molecular mechanics (VB/MM) functional form, which improved previous surfaces for this system, PES-199618 and PES-2005.19 In 2011, Czako and Bowman12 developed a fulldimensional surface using their permutational invariant polynomials method and including spin−orbit (SO) corrections, fitted to ∼20 000 high-level ab initio calculations, which improved their previous CSBB surface.20 Manthe’s group also developed a series of surfaces describing this system,13,21,22 Received: March 22, 2017 Revised: May 9, 2017 Published: May 10, 2017 A

DOI: 10.1021/acs.jpca.7b02665 J. Phys. Chem. A XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry A

computational details, and the constraints to better comply with the VMI restrictions in the QCT analysis are detailed. In Section 3, the QCT results are reported and compared with the experimental information at collision energies of 1.2, 3.6, and 9.0 kcal mol−1. Finally, the conclusions are summarized in Section 4.

including SO corrections and based on a high number of ab initio calculations: PWEM surfaces. Thus, while PES-2006 is a VB-based surface, CSBB and PWEM are molecular orbital (MO)-based surfaces. Recently, using QCT calculations we performed an exhaustive comparison14 of these three surfaces and compared the results with the experimental evidence at different collision energies. We found, first, that the three PESs increase overall reactivity when the CH stretching mode is vibrationally excited by one quantum, this effect being more pronounced in the MO-based surfaces, in contradiction with experiments, especially at low collision energies. Second, when both channels are independently analyzed and PES-2006 is used, CH vibrational excitation decreases reactivity for the DF(v) + CHD2(v′) channel, thus reproducing the experiment, but increases it for the HF(v) + CD3(v′) channel, in strong contrast with the experiment. However, using MO-based surfaces, reactivity increases in both channels with CH excitation, contrary to the experiment in both cases. The recent Nobel prize-winner Arieh Warshel drew attention to this point, stating that23 “It is more physical to calibrate surfaces that reflect bond properties (i.e., valence bond (VB) based surfaces) than to calibrate surfaces that reflect atomic properties (i.e., MO-based surfaces)”. In sum, QCT calculations based on the three different surfaces only qualitatively reproduce some experimental results and are contrary to the suppression of reactivity when the CH stretching mode is excited. Recently, two studies appeared on this reaction.15,16 In the first, using QCT calculations on the PWEM-SO surface, a state-to-state study was performed at collision energy of 9.0 kcal mol−1. The calculated vibrational state resolved differential cross sections reproduce the Yang’s group experiment.6,7 Note, however, that pair-correlated speed distributions, i.e, velocity distribution for a given vibrational quantum state, were not reported. In the second work, a reduced-dimensional 8D-QM study was performed on this PES, concluding that 8D-QM (and QCT) results on the same PES deepen the theory-experiment controversy. These theory/experiment discrepancies motivated the present study. A priori, these discrepancies could be due to the theoretical approximations (QCT/PES) or to experimental difficulties, but there is a third possibility, namely, that the physical properties measured in both cases are different, i.e., the theoretical/experimental comparison is made on a different footing. This seems to be the case in the present study: while experimentally a product pair-correlated study is performed, theoretically all product states are simultaneously considered without restrictions. For polyatomic reactions, velocity map imaging (VMI)24−29 permits accurate measurements of angle-velocity distribution for a given quantum state of one of the two products, the socalled pair-correlated angle-velocity distribution. VMI permits probing of the dynamics of polyatomic reactions at an amazing level of detail, but lead to serious constraints in the theoretical calculations. One of the main aims of the present work is to show that theoretical/experimental discrepancies can be significantly reduced when a few constraints are taken into account in the analysis of the QCT results. In the present study, the title reaction is revisited, with the focus on the theoretical description of the pair-correlated vibrational (PCVD), speed (PCSD), and angular (PCAD) distributions in the F + CHD3(v = 0,ν1 = 1) reactions, and on the role of reactant CH stretching vibrational excitation. The paper is organized as follows: In Section 2, PES-2006 is briefly presented together with the QCT

2. COMPUTATIONAL DETAILS A. Potential Energy Surface. The first step in the theoretical description of a reactive system is the development of the corresponding PES. In 2006 we developed the analytical full-dimensional surface for the F + CH4 reaction and its isotope analogues, named PES-2006,17 which presents analytical gradients. It has high exothermicity, ΔER = −28.22 kcal mol−1 (ΔHR(0 K) = −31.30 kcal mol−1), a low barrier height, 0.35 kcal mol−1, and complexes in the entrance and exit channels, stabilized by 0.13 and 2.70 kcal mol−1 with respect to reactants and products, respectively, reproducing the topology of a practically barrierless and very exothermic reaction. B. Trajectories. The second step consists of moving nuclei on the PES-2006 by using the QCT method as implemented in the VENUS code.30,31 To analyze the role of reactant CH stretching vibrational excitation on the F + CHD3(v = 0,ν1 = 1) reactions, 106 trajectories were run for each reactant vibrational state at three collision energies, 1.2, 3.6, and 9.0 kcal mol−1, for direct comparison with experiments. In total, more than 6 million trajectories were calculated. Note that in our previous paper14 only 50 000 trajectories were run for each reaction, CHD3(v = 0) and CHD3(ν1 = 1). The reactant CHD3 rotational energy was chosen by thermal sampling at 10 K, to ensure very low rotational excitation and to reproduce the initial experimental conditions. For the ground-state and the CH vibrational excited reactions, the maximum impact parameters, bmax, are, respectively: Ecol = 1.2 kcal mol−1: 3.6 and 3.8 Å; Ecol = 3.6 kcal mol−1: 3.0 and 3.2 Å, and Ecol = 9.0 kcal mol−1: 2.9 and 3.1 Å. For the three collision energies, the integration step was 0.01 fs, with an initial separation between the F atom and the CHD3 molecule center of mass of 8.0 Å. For these reactions and collision energies, Table 1 lists the Table 1. Number of Reactive Trajectories by Channel and Reactant CH Vibrational Excitation, for Different Collision Energies (kcal mol−1) F + CHD3(v = 0)

F + CHD3(ν1 = 1)

Ecol

DF(v) + CHD2(v′)

HF(v) + CD3(v′)

DF(v) + CHD2(v′)

HF(v) + CD3(v′)

1.2 3.6 9.0

101773 217260 311111

42720 86460 116361

101602 198616 276404

64530 104812 126640

number of reactive trajectories by channel. Clearly the reactivity increases with the collision energy. Note that given the high reactivity, the statistical errors are practically negligible ( 1 kcal mol−1 [EHFrot (v = 3) ≥ 1 kcal mol−1] and an inverse v/r progressive series chosen to simulate the experiment.

3. RESULTS AND DISCUSSION As the VMI experiments have been reported at three different collision energies, we analyze the QCT results in three different sections. 3.1. QCT Calculations at Ecol = 1.2 kcal mol−1. We begin by analyzing product energy distribution. The QCT/PES2006 results for the CHD2(v = 0) and CD3(v = 0) states are listed in Table 4, together with the experimental data3 for comparison.

Figure 4. Theoretical CHD2(v) (panel a) and CD3(v) (panel b) vibrational distributions computed using the PES-2006 surface for the vibrational ground-state (blue bars) and CH stretching excited (red bars) reactions. Only the populations ≥2% are represented. The state (0,0,1,0) presents a population HF, reproducing again the experiment, by a factor 1.82, slightly lower than the statistics factor. In our previous study on the role of the CH stretching excitation14 we find that this extra

Experimental values from ref 3. bf R = 1 − f V − f T and contains the rotational energy for both products in each channel. a

The theory/experiment agreement is good, with the largest fraction deposited in the vibrational mode of the diatomic molecule (DF or HF depending on the channel), and with errors ≤5%. Experimentally, the rotational fraction contains the contribution from both products, although theoretically we obtain the independent contributions: f R(DF): 7%, f R(CHD2): 1%, and f R(HF): 9%, f R(CD3): 1%. Experimentally, Liu’s group1−5 reported the following vibrational states for the vibrational ground-state reaction, F + CHD3(v = 0): CHD2(v = 0, ν2 = 1, ν3 = 1, ν5 = 1) and CD3(v = 0, ν1 = 1, ν2 = 1,2, ν3 = 1, ν4 = 1), while for the CH excited reaction, F + CHD3(ν1 = 1), the CHD2(ν1 = 1) state also appears, which was anticipated from the spectator model, i.e., the CH excited bond maintains the excitation along the reaction path. The QCT/PES2006 results show a larger number of states and populations, in special the bending mode appears more excited, CHD2(ν4) and CD3(ν2). Figure 4 plots the product vibrational states, CHD2(v) (panel a) and CD3(v) (panel b) for the ground-state and CH excited reactions. We observe 14 and 10 vibrational states, respectively, F


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a steric effect due to the fact that this vibrational motion is orthogonal to the reaction coordinate, and diminishes reactivity. On the other hand, it is well-known that vibrational excitation produces weakening of the reactant CH bond, increasing reactivity. Thus, the final result will be a delicate balance between these two effects. In both cases, pair-correlated and all-states, clearly the second effect is the same, and its result is to increase overall reactivity. However, the first effect is very different. Taking Figure 3 as a reference, we observe that in the pair-correlated reaction all product vibrational states present an “early” barrier [more important in the series (4,0) → (0,0) or (3,0) →(0,0), depending on the channel], and its result is to inhibit overall reactivity. As was shown experimentally and theoretically (present work), the first effect dominates over the second, and the final result is suppression of overall reactivity. However, in the all-states study,14 up to 20/28 vibrational states (DF/ HF) are observed with populations ≥1% [Figure 4 (panel a) shows some of these states for the CHD2(v) product], and as is seen in Figure 1, example DF(v) + CHD2(ν1 = 1) channel, the exothermicity for each vibrational state diminishes, the reaction is less “early” or more “late”, and consequently, reactivity is more favored by the vibrational excitation, reinforcing the second effect, with the final result that overall reactivity is increased or unaltered (depending on the weight of the different pair-correlated vibrational states), as was reported in our previous study.14 This comparison shows again that theory/ experiment comparisons need to be performed in similar conditions, otherwise erroneous results may be obtained. The DF(v) branching ratios in the DF(v) + CHD2(v = 0, ν1 = 1) channel for the vibrational ground-state and CH stretching vibrational excited reactions are listed in Table 5 and compared

Figure 5. Same as Figure 4, but including only the vibrational states experimentally reported.

Table 5. DF(v) Branching Ratios (in Percentage) for the Pair-Correlated CHD3(v = 0) → CHD2(v = 0) and CHD3(ν1 = 1) → CHD2(ν1 = 1) Reactions at Ecol = 1.2 kcal mol−1

energy practically does not affect the reactivity of the DF(v) + CHD2(v′) channel, but it increases it for the HF(v) + CD3(v′) channel, thus contradicting the experimental evidence, the net effect being that CH stretching vibrational excitation barely modifies overall reactivity. A priori, these discrepancies might be attributed to deficiencies of the QCT calculations and/or lack of accuracy of PES-2006. However, it is important to note that in that previous study, all rotational and vibrational states of the products were considered, i.e., these results were obtained in conditions very different from the experimental VMI measurements. In the present study, however, we find a better agreement with the experiment when a few constraints are added to the analysis of the QCT results to better cope with the VMI conditions, in other words, when a “quantum spirit” is included in the analysis of the classical QCT calculations. Therefore, these results emphasize the necessity to perform theory/experiment comparisons on an equal footing. To shed more light on these discrepancies and to reconcile these two (apparently) contradictory results with reactant CH vibrational excitation, i.e., suppression of overall reactivity in the pair-correlated study and a negligible effect when all vibrational states are analyzed, we follow the arguments already reported in previous studies on the role of vibrational excitation on different reactions.14,57 Basically, the vibrational excitation of the reactant CH stretching mode, CHD3(ν1 = 1) shows two opposite effects: on the one hand, this very exothermic reaction presents an “early” barrier, i.e., the transition-state is reactantlike, and following Polanyi’s rules58 vibrational excitation creates a bottleneck in the entrance channel, i.e., it produces

CHD3(v = 0) → CHD2(v = 0)

a

CHD3(ν1 = 1)→CHD2(ν1 = 1)

DF(v)

theo

expa

theo

exp

v=2 v=3 v=4

4 37 59

5 43 52

4 51 45

8 64 28

Experimental values from ref 3.

with the only experimental results reported at this collision energy.3 The QCT PCVDs reproduce the experimental evidence, where the most populated states are DF(v = 4) and DF(v = 3) for the ground-state and CH excited reactions, respectively. Note that these values are normalized to the common reported experimental values, although theoretically we obtain higher populations; DF(v > 4): 5 and 3%, respectively, which represents an overestimation of the QCT method, always ≤5%. In sum, the populations of vibrational states DF(v) are p2,0 = 0.04, p3,0 = 0.37, and p4,0 = 0.59 for the ground-state reaction and p2,1 = 0.04, p3,1 = 0.51, and p4,1 = 0.45 for the CH excited reaction. In the analysis of pair-correlated speed distribution, Pn,n′(v) denotes the contribution of the pair-correlated states DF(n = (v) + CHD2(n′ = 0) in the ground-state reaction or the contribution of states DF(n = (v) + CHD2(n′ = 1) in the CH excited reaction, to the PCSD, P(v). Following the previous developments, G


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7) to be compared with the experiment (upper panel in Figure 7). As was previously noted, these individual distributions show

P(v) = p2,0 ·P2,0(v) + p3,0 ·P3,0(v) + p4,0 . P4,0(v), for the ground‐state reaction

(10)

or P(v) = p2,1 ·P2,1(v) + p3,1 ·P3,1(v) + p4,1 ·P4,1(v), for the CH excited reaction

(11)

,where P2,0(v), for instance, represents the contribution of the pair-correlated DF(v = 2) + CHD2(0,0,0,0,0,0) states to the speed distribution, P(v). Like pn,n′, Pn,n′(v) is better calculated in a quantum spirit, taking into account the VMI constraints previously analyzed. In order to illustrate the Pn,n′(v) calculation, we first focus on the most populated state, DF(v = 4), and calculate P4,0(v), i.e., correlated with the polyatomic coproduct CHD2 in its vibrational ground-state. The resulting GB distribution, normalized to unity, is represented in Figure 6.

Figure 6. Contribution of the state DF(v = 4) to the pair-correlated speed distribution for the DF(v) + CHD2(v = 0) channel. Blue curve: P4,0(v) obtained from QCT calculations and the SB procedure. Red curve: same as previously, but obtained with the GB procedure. Black curve: corresponding experimental distribution of Liu et al. (see Figure 2b in ref 5). All distributions are normalized to unity for a direct comparison.

In addition, standard binning (SB) distribution is also included, together with the experimental distribution for comparison. Clearly the SB distribution is much broader than the GB one, reaching greater velocities. However, the procedure taking into account the VMI constraints still shows widening of the P(v) distribution, which is due to the fact that, although the vibrational motion is pseudoquantized through the GB procedure, the rotational constraints have been taken “ad hoc”, and an overestimation of the rotational population has been observed (Table 4). However, note that this problem is not exclusive to the QCT calculations, and it also occurs in the VMI experiments, because the collision energy and the reactant rotational motion are not fully defined. In addition, the theoretical PCSD is shifted slightly to greater velocities, 0.45 versus 0.35 km s−1, which is related with the “ad hoc” constraints imposed on the rotational analysis of the DF(v = 4) −1 state, Erot DF ≤ 1 kcal mol , which is experimentally unknown. Thus, if greater DF rotational energy had been considered in the constraints, lower translational energies (and velocities) would be expected, in better agreement with experiment. The pair-correlated speed distributions for the other less populated DF(v) vibrational states, P2,0(v) and P3,0(v), are obtained in the same way, and with this information we obtain the P(v) distributions (eqs 10 and 11) (lower panel in Figure

Figure 7. Pair-correlated speed distributions for the DF(v) + CHD2(v = 0) channel at Ecol = 1.2 kcal mol−1. Lower panel: weighted GB distributions from the DF vibrational sates (see eqs 10 and 11). Middle panel: final theoretical result obtained from a convolution of the sum of the previous quantities (see eq 12). Upper panel: experimental distribution from Liu et al. (ref 5). All values are normalized to unity. Blue line from the reactant vibrational groundstate and red line from the CH excited reaction.

a widening (both theoretically and experimentally) due to rotational overestimation, leading to overlapping of states, and this problem has been taken into account in our analysis through the Gaussian convolution, Pc(v) =

∫

dv′

⎡ ⎛ v′ − v ⎞ 2 ⎤ ⎟ ⎥P(v′) exp⎢ −⎜ α π ⎣ ⎝ α ⎠⎦ 1

(12)

where α is chosen at 0.03 to reproduce the experimental speed distribution at the threshold and cutoff as satisfyingly as possible. The final distributions are also shown in Figure 7 H


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Figure 8. Pair-correlated angular distributions for the DF(v) + CHD2(v = 0,ν1 = 1) channel at Ecol = 1.2 kcal mol−1. Lower panel: Theoretical GB results fitted to a six degree polynomial. Upper panel: experimental values from ref 5. All values are normalized to unity.

a rough approximation to real behavior, although the trends are clearly revealed. We remember that for the DF(v) + CHD2(v = 0, ν1 = 1) pair-correlated states, the range [0,π] is divided into intervals of 5°, and we count the reactive trajectories in each channel taking into account the VMI constraints. This discontinuous representation is fitted to a six degree polynomial to obtain a continuous curve to be compared with the experiment. The QCT/PES-2006 results for the vibrational ground-state and the CH excited reactions are plotted in Figure 8, together with the experimental data for comparison. Theoretically the PCADs of the ground-state and the CH excited reactions show few differences, reproducing the experimental behavior: in both cases, scattering distribution is forward−backward, the former due to the DF(v = 4) state, associated with a stripping mechanism, and the latter due to the DF(v = 3) contribution, associated with a rebound mechanism. The QCT calculations clearly show the shift from backward to forward scattering with the increase of the DF vibration, which reproduces the experiment. Finally, note that the backward scattering is less pronounced in theory than in the experiment, due to the lesser backward character of the DF(v = 3) state as compared with the experiment. 3.2. QCT Calculations at Ecol = 3.6 kcal mol−1. In 2009, Liu’s lab reported a series of VMI experiments analyzing the role of CH stretching excitation on the dynamics of the F + CHD3(v) reaction.5 The QCT/PES-2006 results presented in this section are compared with those experiments following the

(middle panel). Note that the PCSDs for the CH stretching excited reaction, DF(v) + CHD2(ν1 = 1), also appear in Figure 7, as red lines. First, the peaks from the vibrational ground-state and the CH excited reactions practically coincide. Experimentally (higher panel), however, while the peaks for the DF(v = 3) state coincide, for the DF(v = 4) state, the excitation of the reactant CH vibration shifts the peak to lower velocities. Second, in accordance with the DF(v) branching ratios (Table 5), DF(v = 4) > DF(v = 3) in the ground-state reaction, while the inverse ratio is obtained for the CH excited reaction, reproducing (at least qualitatively) the experimental tendency. We finish this section devoted to the study of the results at Ecol = 1.2 kcal mol−1 by analyzing product correlated angular distribution, PCAD: DF(v = 3,4) + CHD2(v = 0, ν1 = 1) (note that the number of weighted reactive trajectories from the DF(v = 2) state is too low to provide accurate statistics). However, it is important at this point to raise a note of caution on this dynamics property using the very rigorous VMI criteria. In a recent paper59 on the OH/OD + CH4 reactions we drew attention to the very high computational cost needed to perform accurate PCADs in polyatomic reactions. Following Truhlar and Blais’ arguments,60 it is necessary to run about 10 million trajectories in the present reaction to obtain a sufficient number of reactive trajectories to achieve statistical significance, and the application of the very stringent VMI constraints do not help. Therefore, in the present paper with 1 million trajectories run by channel, the results should be considered as I


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The Journal of Physical Chemistry A arguments presented in the previous section at Ecol = 1.2 kcal mol−1. Product energy distribution is an average property that provides us with distribution of the available energy in rotation, vibration and relative translation of the products. The paircorrelated theoretical values for both channels, DF(v) + CHD2(v = 0) and HF(v) + CD3(v = 0) are listed in Table 6 Table 6. Product Energy Distribution for the CHD2(v = 0) and CD3(v = 0) States at Collision Energy of 3.6 kcal mol−1 Applying the VMI Constraints (Values in Percentages) DF+CHD2(v = 0)

HF+CD3(v = 0)

theo

expa

theo

exp

80 13 1 6

80 15 5

79 12 1 8

85 10 5

f V(FD,HF) fT f R(CX3) f R(XF)

a Experimental values from ref 3. f R = 1 − f V − f T and contains the rotational energy for both products in each channel.

together with the experimental data3 for comparison. First, we note that, unlike Table 3, Table 6 reports theoretical results applying the VMI constraints, where the rotational contribution has diminished, and the vibrational contribution has augmented. This analysis shows the importance of constraints analyzed in the present paper for direct comparison with the experiment. Second, as in the previous case at Ecol = 1.2 kcal mol−1, agreement with experiment is good, with differences ≤5%. The energy is mostly deposited as vibration of the diatomic product, DF(v) or HF(v), with a ratio of ∼80%, and to a lower extent as relative translation. Therefore, this property does not change with the collision energy. Now we analyze the DF(v) + CHD2(v = 0, ν1 = 1) paircorrelated branching ratios for the vibrational ground-state and the CH excited reactions. The QCT/PES-2006 results together with the experimental data3 are listed in Table 7. For both

Figure 9. Theoretical CHD2(v) (panel a) and CD3(v) (panel b) vibrational distributions computed using the PES-2006 surface for the vibrational ground-state (blue bars) and CH stretching excited (red bars) reactions, including only the vibrational states experimentally reported.

reducing the population of all the vibrational states of the products, with the exception, obviously, of the CHD2(ν1 = 1) state, thus reproducing the experiment and resolving the previous theory/experimental controversy. Quantitatively, the reaction cross section diminishes from 0.032 to 0.011 Å2 and from 0.0068 to 0.0045 Å2 for the DF(v) + CHD2(v = 0) and HF(v) + CD3(v = 0) channels, upon CH stretching excitation. This implies that reactant CH excitation inhibits overall reactivity by 66 and 34%, respectively, again only in qualitative agreement with experiment, ∼ 90%. In addition, the DF channel is favored with CH excitation, DF > HF, factor 2.44, which is practically the statistical factor. Finally, it is important to note that in addition to the reported common vibrational states in Figure 7, a larger number of vibrational states were theoretically found in both channels. Thus, we observed 13 vibrational states with populations ≥2% in both channels, and up to 20 and 28 vibrational states with populations ≥1% in the case of the CHD2(v) and CD3(v), respectively. Therefore, only when the same pair-correlated conditions are analyzed is possible to reproduce the experimental tendency. This agreement is nowadays possible with reliable potential energy surfaces and at a huge computational cost, millions of trajectories using QCT methods in a quantum spirit and/or exact quantum mechanical calculations. Product pair-correlated speed distribution is one of the most sensible dynamics properties to check the accuracy of the theoretical tools used in the analysis, because very fine

Table 7. DF(v) Branching Ratios (in Percentage) for the Pair-Correlated CHD3(v = 0) → CHD2(v = 0) and CHD3(ν1 = 1) → CHD2(ν1 = 1) Reactions at Ecol = 3.6 kcal mol−1 CHD3(v = 0) → CHD2(v = 0)

a

CHD3(ν1 = 1) → CHD2(ν1 = 1)

DF(v)

theo

expa

theo

exp

v=2 v=3 v=4

3 38 59

3 40 57

4 40 56

5 45 50

Experimental values from ref 3.

reactions, the DF(v = 4) state is the most populated (> 50%), thus reproducing the experiment. As in the previous case at Ecol = 1.2 kcal mol−1, theoretically, an overestimation of the vibrational populations is obtained, with DF(v > 4): 6% in both reactions, and so the values in Table 7 are those normalized to the common experimental populated states. The most debatable point in the theoretical/experimental controversy, the effect of reactant CH stretching vibrational excitation on the dynamics of the F + CHD3(v) reaction, is subsequently analyzed using the same pair-correlated reactions as the experiment.5 The CHD2(v) (panel a) and the CD3(v) (panel b) vibrational populations from the CHD3(v = 0, ν1 = 1) reactions are plotted in Figure 9. For both channels, CH stretching vibrational excitation inhibits CH bond cleavage, J


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(middle panel), together with the experimental values (higher panel). At this collision energy, theory/experiment agreement is better than at the lower collision energy. Again, the effect of the reactant CH excitation is small, with a slight shift of the maximum at lower velocities, thus reproducing the experiment. With respect to the experiment, the theoretical results are slightly shifted at low velocities, especially the peak corresponding to the DF(v = 3) state. Obviously, these shifts with respect to the experiment are related with the constraints in the product rotational energies, which are experimentally unknown. In sum, the very sensitive experimental PCSDs are reproduced theoretically when the QCT results are analyzed in a quantum spirit. We finish this Section by analyzing the PCADs at Ecol = 3.6 kcal mol−1 for the F + CHD3(v = 0, ν1 = 1) → DF(v) + CHD2(v = 0, ν1 = 1) reactions, which permits us to study the effect of reactant CH vibrational excitation on this property. Figure 11 plots the theoretical results together with the experimental measurements.5 First, as in the previous case at Ecol = 1.2 kcal mol−1, it is necessary to take into account that due to the stringent constraints imposed on the pair-correlated VMI experiment, the theoretical results must be taken as a first approximation to real behavior. Second, for both reactions, angular distribution varies from backward at low DF(v) vibrational states to forward at high DF(v), which reproduces the experiment, with the total PCAD being forward. Thus, the effect of reactant CH vibrational excitation is small or negligible. Third, however, the backward contribution theoretically obtained overestimates the experimental evidence, especially the lower DF(v) state, which presents the lowest number of reactive trajectories fulfilling VMI constraints. This behavior could be a consequence of the polynomial fitting used, which tends toward oscillatory behavior, which is not experimentally reported. 3.3. QCT Calculations at Ecol = 9.0 kcal mol−1. In the two previous sections we analyzed the dynamics and the effect of reactant CH stretching vibrational excitation in the title reaction at low collision energies, Ecol HF upon CH stretching excitation by a factor 5. Using the same arguments and constraints as previously, the PCSD is calculated using eqs 10 and 11: M


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Figure 12. Pair-correlated translational energy distributions for the DF(v) + CHD2(v = 0) (left panel) and HF(v) + CD3(v = 0) (right panel) channels at Ecol = 9.0 kcal mol−1. Lower panel: final theoretical result obtained from a Gaussian convolution (see eq 12) of the sum of the weighted GB distributions from the DF/HF vibrational sates (see eqs 10 and 11). Upper panel: experimental distribution from Yang and co-workers (refs 6, 7). All values are normalized to unity. Blue line from the reactant vibrational ground-state and red line from the CH excited reaction.

individual DF(v) vibrational contributions, thus correcting the negative effect of widening due to the rotation in QCT calculations, and consequently, to approximate the theoretical results to the experimental data.

these vibrational distributions permit us to obtain the error in the QCT calculations: ≤ 10%. 3. The effect of reactant CH stretching vibrational excitation, F + CHD3(ν1 = 1), on reactivity has presented the largest theory/experiment controversy in the literature. While experimentally CH excitation inhibits overall reactivity, the contrary effect was theoretically reported previously. This controversy is resolved in the present paper when a quantum spirit is included in the analysis of the QCT calculations, and the same paircorrelated reactions are considered in theory and experiments, i.e., when the theory/experiment comparison is performed on the same footing. In this paircorrelated analysis the QCT/PES-2006 theoretical results reproduce the experimental evidence that CH stretching excitation suppresses overall reactivity. Quantitatively, the agreement is best at the highest collision energy. 4. At all collision energies, CH stretching excitation favors the DF(v) channel to the detriment of the HF(v) one. At

4. CONCLUSIONS In the pair-correlated study of the F + CHD3(v = 0, ν1 = 1) reactions, and considering all collision energies, we conclude that 1. The largest amount of available energy is deposited as DF(v) and HF(v) vibrational energy, ∼70−80%, with a small amount as relative translational energy, ∼10−20%. The vibrational energy diminishes and the translational energy increases with the collision energy. Reactant CH stretching vibrational excitation by one quantum practically does not change this distribution. 2. The excited DF(v) and HF(v) vibrational states appear with high populations at all collision energies. Compared with the maximum available energy in each reaction, N


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Figure 13. Pair-correlated angular distributions for the DF(v) + CHD2(v = 0) (left panel) and HF(v) + CD3(v = 0) (right panel) channels at Ecol = 9.0 kcal mol−1. Lower panel: Theoretical GB results fitted to a six degree polynomial. Upper panel: experimental values from refs 6 and 7. All values are normalized to unity.

states analyzed, CHD2(v = 0) and CD3(v = 0). We assume that a statistical or quasi-statistical ratio would be found when all vibrational states are considered, this ratio being larger with the collision energy.14 Again, this analysis drew our attention to the fact that theory/ experiment comparisons should be performed under the same conditions. 5. At the three collision energies analyzed, the product paircorrelated speed distributions, PCSD, reproduce, at least qualitatively, the experimental measures from two independent laboratories, with a clear separation of the peaks associated with the different vibrational states. In general, the effect of reactant CH excitation on this property is small, the maximum of each peak shifting at lower velocities, in accordance with the experiment. However, the theoretical distributions are broader and this effect is associated with the treatment of the rotational energies in reactant and products to reproduce the VMI constraints, which are “ad hoc” conditions in the present study. 6. Finally, the analysis of the pair-correlated angular distribution, PCAD, shows how it changes from a forward−backward distribution at the lower collision energy (Ecol = 1.2 kcal mol−1) to a forward distribution when this energy increases. This behavior is associated with the influence of the valley in the entrance channel, greater at lower energies. In the pair-correlated reactions analyzed, the effect of the reactant CH excitation is again small. With respect to the behavior of each DF(v) and HF(v) vibrational state, we found that at low collision energies while the low vibrational states (v = 2,3) show a backward scattering tendency, associated with a rebound mechanism and low impact parameters, the highest vibrational state, v = 4, presents forward distribution,

Figure 14. Translational energy distribution for the DF(v) + CHD2(v = 0) channel, where all the unweighted reactive trajectories are considered, and therefore, the quantization of the vibrational energy, and VMI constraints are not imposed.

low collision energy, Ecol < 1.5 kcal mol−1, Czako and Bowman10 proposed that due to the presence of a deep well in the entrance channel in the CSBB surface,18 reactant CH excitation steers the fluorine atom to one of the CD bonds, although later the same authors,12 with a modified PES including spin−orbit corrections, found that this effect was dampened. Using our PES-2006 surface, which presents a less deep well, 45 versus 363 cm−1, we did not find this effect of orientation. This fact, together with the fact that at the higher collision energy, 9.0 kcal mol−1, the effect of the reactant well is negligible although the DF > HF ratio is maintained, leads us to suspect that this ratio is found in these pair-correlated experiments due to the limited number of vibrational O


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(14) Espinosa-Garcia, J. A Quasiclassical Trajectory Study on the Role of CH Stretching Vibrational Excitation in the F(2P) + CHD3(v1=0,1) Reactions. J. Phys. Chem. A 2016, 120, 5−13. (15) Xie, Ch.; Jiang, B.; Yang, M.; Guo, H. State-to-State Mode Specificity in F + CHD3 →HF/DF + CD3/CHD2 Reaction. J. Phys. Chem. A 2016, 120, 6521−6528. (16) Qi, J.; Song, H.; Yang, M.; Palma, J.; Manthe, U.; Guo, H. Mode Specific Quantum Dynamics of the F + CHD3 →HF + CD3 Reaction. J. Chem. Phys. 2016, 144, 171101. (17) Espinosa-Garcia, J.; Bravo, J. L.; Rangel, C. New Analytical Potential Energy Surface for the F(2P) + CH4 Hydrogen Abstraction Reaction: Kinetics and Dynamics. J. Phys. Chem. A 2007, 111, 2761− 2771. (18) Corchado, J. C.; Espinosa-Garcia, J. Theoretical Study of the CH4 + F → CH3+ FH Reaction. II. Semiempirical Surfaces. J. Chem. Phys. 1996, 105, 3160−3167. (19) Rangel, C.; Navarrete, M.; Espinosa-Garcia, J. Potential Energy Surface for the F(2P3/2,2P1/2) + CH4 Hydrogen Abstraction Reaction. Kinetics and Dynamics Study. J. Phys. Chem. A 2005, 109, 1441−1448. (20) Czakó, G.; Shepler, B. C.; Braams, B. J.; Bowman, J. M. Accurate Ab initio Potential Energy Surface, Dynamics, and Thermochemistry of the F + CH4 → HF + CH3 Reaction. J. Chem. Phys. 2009, 130, 084301. (21) Westermann, T.; Eisfeld, W.; Manthe, U. Coupled Potential Energy Surface for the F(2P) + CH4 → HF + CH3 Entrance Channel and Quantum Dynamics of the CH4 · F− Photodetachment. J. Chem. Phys. 2013, 139, 014309. (22) Westermann, T.; Kim, J. B.; Weichman, M. L.; Hock, C.; Yacovitch, T. I.; Palma, J.; Neumark, D. M.; Manthe, U. Resonances in the Entrance Channel of the Elementary Chemical Reaction of Fluorine and Methane. Angew. Chem., Int. Ed. 2014, 53, 1122−1126. (23) Olsson, M. H. M.; Mavri, J.; Warshel, A. Transition State Theory can be Used in Studies of Enzyme Catalysis: Lessons from Simulations of Tunnelling and Dynamical Effects in Lipoxygenase and other Systems. Philos. Trans. R. Soc., B 2006, 361, 1417−1432. (24) Chandler, D. W.; Houston, P. L. Two-dimensional Imaging of State-selected Photodissociation Products Detected by Multiphoton Ionization. J. Chem. Phys. 1987, 87, 1445−1446. (25) Eppink, A. T. J. B.; Parker, D. H. Velocity Map Imaging of Ions and Electrons Using Electrostatic Lenses: Application in Photoelectron and Photofragment Ion Imaging of Molecular Oxygen. Rev. Sci. Instrum. 1997, 68, 3477−3484. (26) Lin, J. J.; Zhou, J.; Shiu, W.; Liu, K. Application of Time-sliced Ion Velocity Imaging to Crossed Molecular Beam Experiments. Rev. Sci. Instrum. 2003, 74, 2495−2500. (27) Townsend, D.; Li, W.; Lee, S. K.; Gross, R. L.; Suits, A. G. Universal and State-Resolved Imaging of Chemical Dynamics. J. Phys. Chem. A 2005, 109, 8661−8674. (28) Chichinin, A. I.; Kauczok, S.; Gericke, K.-H.; Maul, C. Imaging Chemical Reactions − 3D Velocity Mapping. Int. Rev. Phys. Chem. 2009, 28, 607−680. (29) Lee, S. K.; Lin, Y. F.; Lingenfelter, S.; Fan, L.; Winney, A. H.; Li, W. Communication: Time- and Space-sliced Velocity Map Electron Imaging. J. Chem. Phys. 2014, 141, 221101. (30) Hu, X.; Hase, W. L.; Pirraglia, Y. Vectorization of the General Monte Carlo Classical Trajectory Program VENUS. J. Comput. Chem. 1991, 12, 1014−1024. (31) Hase, W. L.; Duchovic, R. J.; Hu, X.; Komornicki, A.; Lim, K. F.; Lu, D-h.; Peslherbe, G. H.; Swamy, K. N.; Van de Linde, S. R.; Varandas, A. J. C.; et al. VENUS96: A General Chemical Dynamics Computer Program. QCPE Bull. 1996, 16, 43. (32) Corchado, J. C.; Espinosa-Garcia, J. Product Vibrational Distributions in Polyatomic Species Based on Quasiclassical Trajectory Calculations. Phys. Chem. Chem. Phys. 2009, 11, 10157−10164. (33) Bonnet, L. Classical Dynamics of Chemical Reaction in a Quantum Spirit. Int. Rev. Phys. Chem. 2013, 32, 171−228. (34) Bonnet, L.; Rayez, J. C. Quasiclassical Trajectory Method for Molecular Scattering Processes: Necessity of a Weighted Binning Approach. Chem. Phys. Lett. 1997, 277, 183−190.

associated with a stripping mechanism and high impact parameters. At the higher collision energy, however, both analyzed states, v = 3 and 4, present forward distributions, related with the larger available energy in this case. 7. In sum, although the agreement with the experiment is not yet quantitative, very fine experimental measurements are reproduced when accurate potential energy surfaces are used and the QCT calculations are analyzed in a quantum spirit.

AUTHOR INFORMATION

ORCID

Joaquin Espinosa-Garcia: 0000-0002-0058-8727 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was partially supported by Gobierno de Extremadura, Spain (Project No. GR15015). Many calculations were carried out on the LUSITANIA computer at Computaex (Spain).

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REFERENCES

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Theoretical Study of the Pair-Correlated F + CHD3(

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