A Theoretical Study on the Dynamics of the Reaction of CH Radicals

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A Theoretical Study on the Dynamics of the Reaction of CH Radicals with Water Molecules Elham Mazarei, and Seyed Hosein Mousavipour J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.7b05504 • Publication Date (Web): 26 Sep 2017 Downloaded from http://pubs.acs.org on September 27, 2017

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The Journal of Physical Chemistry

A Theoretical Study on the Dynamics of the Reaction of CH Radicals with Water Elham Mazarei and S. Hosein Mousavipour* Department of Chemistry, College of Science, Shiraz University, Shiraz, Iran

Abstract Quasi-classical trajectory (QCT) and RRKM-SSA calculations are carried out to gain insight into the dynamics of the title reaction. The barrier-less initiation step in this system is governed by the capture probability in the entrance channel to form an energized adduct once the centrifugal barrier is surmounted. The dynamics of the title reaction on its lowest doublet electronic state is studied at the DFT level of MPWB1K/6-31++g(2df,2p). An iteratively modified Shepard interpolation technique implemented in the GROW program suite was used to construct a global potential energy surface for the title reaction. The total and individual cross sections for the main products and corresponding reaction probabilities as a function of initial collision energy ranging from 0.4 kJ mol-1 to 52.5 kJ mol-1 are calculated. These data are used to calculate the total rate constant for the title reaction by means of collision theory. Our calculated QCT rate constant is compared with the calculated rate constant from RRKM-SSA method at the CCSD(T)/Aug-ccpVTZ//MP2/6-31++g(2df,2p) level. The energy partitioning for the main products CH2O + H and HCOH + H and also for the reactants after non-reactive collisions as a function of initial collision energy are discussed.

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Introduction CH(X2II) radical is a main reactive species in hydrocarbon combustion and atmospheric processes.1-3 This radical is highly reactive due to the presence of an occupied molecular orbital with one electron and one vacant non-bonding molecular orbital localized on the carbon atom, that allows addition of π-bonds and insertion of σ-bonds with no barrier.4 Reactions of CH radical are of importance in determining the NOx levels during the combustion processes and is one of the few species that is reactive enough to cleave the triple bond in nitrogen molecule.5 Water molecule is one of the key molecules that reacts with CH 1

radical in combustion processes and in remote atmosphere. H2O( A) is one of the major reservoirs for interstellar oxygen and plays a vital role in the chemistry and physics of the universe. In the interstellar medium6, an important channel of water formation is the reaction of atoms on the surface of dust grains as Jing et al. in an experimental study reported as the initial stages of formation of water on the surface of amorphous silicates.6 Water has been shown to catalyze the reactions between neutral species due to its ability to decrease the intrinsic barriers. Few reactions of water molecule itself with neutral species are considered in astrochemical databases given its low inherent reactivity below room temperature.8,9 Experimental and computational works are reported on the reactivity of CH radical with CH4, CD4, H2, N2, H2O, O2, NO, NH3 and CH2O species in gas phase.5,10-20 A few theoretical and experimental study on the kinetics of the title reaction to predict the total rate constant and reaction mechanism are reported to date that show a large divergence of the reported rate constants.1,8,20-25 Zabarnick et al.20 in a photolysis experiment investigated the temperature and pressure dependence of the title reaction. They reported the measured rate constant is independent of the total pressure over a range of 20 to 300 Torr at room temperature and with negative temperature dependency as k (T ) = (5.7 ± 0.05) × 109 exp(380 ± 20) K / T L mol-1 s−1 over a temperature range of 298-669 K. They suggested two path ways for the title reaction, insertion reaction

CH + H 2O → CH 2OH and direct hydrogen abstraction reaction CH + H 2O → CH 2 + OH , with the insertion channel as the major path. The same results for the pressure and temperature dependencies with different rate expression in a laser flash photolysis/laser-induced fluorescence 2


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(LIF) experiment is reported by Blitz et al.1 They have also studied the isotope effect (CH, CD, H2O and D2O) on the kinetics of the title reaction. They reported vibrational excitation of CH(υ=1) and CD(υ=1,2) enhances the rate coefficient. Wang et al.21 in a theoretical study proposed a potential energy surfaces (PES) for the reaction of CH(X2II) radical with H2O, NH3, HF molecules using ab initio calculations at the UHF /6-31G(d), UMP2/3-21G, and UMP2/6-31G(d,p) levels of theory. They reported formation of a pre-reaction intermediate HC···OH2 following the insertion reaction to form H2COH. Low temperature kinetics of the title reaction (296 K down to 50 K) is investigated by Hickson et al.7 using CRESU apparatus.22 They reported the reaction initially proceeds through formation of a pre reaction complex HC···OH2. Statistical RRKM-Master equation solving method23 was used to predict the rate constant for the formation of main product H2COH. This energized adduct could easily convert to energetically accessible sets of products H + H2CO or H2 + HCO Daranlot24 and co-workers pointed out the apparent rate for the formation of H + H2CO and H2+ HCO is governed by the competition between re-dissociation of the CH---OH2 complex to the reactants, its isomerization to CH2OH, or collisional stabilization at low temperatures. A survey on the reported mechanism and rate constants for the title reaction in the literature indicates a diverse result that demands for more accurate study on the kinetics and dynamics of the title reaction. In this paper, we present the results of a theoretical study on the kinetics and dynamics of 1

the barrier less reaction of CH(X2II) radicals with H2O( A) molecule over the lowest doublet potential energy surface. To the best of our knowledge, no theoretical study on the dynamics of the title reaction is reported to date. In this study we utilized quasi-classical trajectory calculations to look at the dynamics of the title reaction and find out the reaction probabilities and reactive cross sections for the formation of possible products as a function of initial collision energy in order to calculate the rate constants at the DFT level. The energy partitioning for the main products and also reactants after non-reactive collisions are investigated. We have also calculated the rate constant for the formation of the main product of the title reaction at the CCSD(T) level using RRKM-SSA25 method to compare with the one calculated from QCT calculations at the DFT level. 3



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METHODS Ab Initio calculations All electronic structure calculations were carried out by means of Gaussian03 program suite.

26

Construction and having an accurate PES is a key element to study the kinetics or

dynamics

of

a

reaction.

Single

point

CCSD(T)/Aug-cc-pVTZ//MP2/6-31++g(2df,2p)

calculations was carried out to obtain accurate energies of the stationary points along the PES (Table 1) to be used in RRKM-SSA calculations. Since it is crucial to use a method that is both rationally accurate and computationally cost-effective for constructing a global PES, MPWB1K/6-31++g(2df,2p) method was chosen to construct the lowest electronic PES (Figure 1) to study the dynamics of the title reaction. Harmonic vibrational term values for all the stationary points were examined in order to characterize stationary points as local minima or first-order saddle points and exploring the nature of the transition states. Vibrational term values and moments of inertia for all of the stationary points are listed in Supporting Information Table S1. In order to investigate the connectivity of each saddle point to the corresponding minima along the reaction coordinates, the intrinsic reaction coordinate (IRC) calculations were carried out. Scheme 1 shows the suggested mechanism for the title reaction where w is the collisional stabilization rate constant. Schematics of relative energies of the stationary points in this system at the CCSD(T) and MPWB1K levels of theory are shown in Figure 1. The quoted energies in Figure 1 are corrected for the zero point energies. In Table 1 the relative calculated energies at the MPWB1K/6-31++g(2df,2p) level are compared with those calculated at the CCSD(T)/aug-cc-pVTZ level. The results from ab initio calculations are used to calculate the rate constants by means of RRKM calculations along with the steady state approximation for the formation and consumption of the energized intermediates (RRKM-SSA).25 The results are compared with the rate constant calculated from quasi-classical trajectory calculations at the MPWB1K level in this work and reported rates in the literature.

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Features of the Potential Energy Surface and Reaction Mechanism. The PES within the Born-Oppenheimer approximation for the title reaction at the CCSD(T)/aug-cc-pVTZ//MP2/6-31++g(2df,2p) and MPWB1K/6-31++g(2df,2p) levels of theory are shown in Figure 1. Our suggested PES consists of two main energized intermediates INT* and CH2OH* radical, along with H2, H, HCO, HOC, CO, CH3O, CH2, OH, and CH2O species as the feasible products. Formation of HCO, HOC, and H2, and CO have not been reported by Wang et al.21 while, Bergeat et al.23 have just reported formation of HCO + H2, HOC + H2, CH2OH, and CH2O+H species but not CO, CH3O, CH2, and OH as the products of the title reaction. As shown in Figure 1, the most probable initiation step in this system is the barrier less association reaction R1 to form a chemically activated intermediate INT*(HC---OH2*) that its energy is 33.6 kJ mol-1 lower than the total energy of the reactants at the CCSD(T)/aug-ccpVTZ//MP2/6-31++g(2df,2p) level of theory in excellent agreement with the value reported by Xu et al.27 at the CCSD(T)/aug-cc-pVTZ//CCSD/aug-cc-pVTZ level of theory. Our reported relative stability of INT* is 14.4 kJ mol−1 less than the value reported by Bergeat et al.23 at the B3LYP/cc-pVQZ level of theory and 26.2 kJ mol−1 less than the value reported by Wang et al.21 at the UMP2/6-31G(d,p). The calculated relative stability of INT* is -44.5 kJ mol-1 at the MPWB1K level in agreement with the value reported by Bergeat et al.23 As soon as energized pre-reaction complex INT*(HC--OH2*) is formed three possible channels may compete to each other, collisional stabilization (w), isomerization reaction R2 to form CH2OH by passing over saddle point TS2 with 31.7 kJ mol−1 barrier height at the CCSD(T)/aug-cc-pVTZ//MP2/6-31++g(2df,2p) level, or dissociation reaction R12 to form transHCOH + H by passing over saddle point TS12 with 112.4 kJ mol−1 barrier height at the CCSD(T)/aug-cc-pVTZ//MP2/6-31++g(2df,2p) level of theory. The energy of CH2OH radical lies 352.6 kJ mol-1 below the reactants’ energy at the CCSD(T)/aug-cc-pVTZ//MP2/6-31++g(2df,2p) level of theory that means this product is highly energized. Our calculated relative stability of CH2OH at the CCSD(T)/aug-cc-pVTZ//MP2/631++g(2df,2p) level of theory is 3.9 kJ mol−1 more stable than the value reported by Xu et al.28 at the CCSD(T)/aug-cc-pVTZ//CCSD/aug-cc-pVTZ level of theory, 62.1 kJ mol−1 less stable than 5



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the value reported by Wang et al.21 at the UMP2/6-31G(d,p) level of theory and about 22.5 kJ mol−1 less stable than the value reported by Bergeat et.al23 at the B3LYP/cc-pVQZ level of theory. The energized CH2OH* radical could either undergoes rearrangement process in reaction R3 to form CH3O radical by surmounting of saddle point TS3 with 160.8 kJ mol−1 barrier height in agreement with the value of 159.3 kJ mol-1 reported by Xu et al.28 at the CCSD(T) level of theory or dissociates to HOC radical and H2 molecule in reaction R7 by passing over saddle point TS7 with 346.9 kJ mol-1 barrier height at the CCSD(T) levels of theory, about 7.6 kJ mol-1 less than the value reported by Xu et al.28 at the CCSD(T) level of theory. Other possible paths for energized CH2OH* are dissociation reaction to form CH2 and OH radicals or CH2O + H species in reactions R6 and R11, respectively, with no saddle point. Energized CH2OH* can dissociate to trans or cis-HCOH + H in reactions R9 or R10, respectively. The HCO molecule could undergo rearrangement process in reaction R8 to form HOC molecule by passing over saddle point TS8 with 94.5 kJ mol−1 barrier height at the CCSD(T) level of theory. The barrier height for isomerization of trans-HOCH to cis-HOCH was found to be 111.7 kJ mol−1 at the CCSD(T) level of theory, reaction R13. In reaction R15, trans-HOCH isomerizes to CH2O by passing over transition state TS15 with a barrier height of 129.8 kJ mol−1 at the CCSD(T) level of theory. Our calculated relative stability shows that CH2OH is 34.9 kJ mol-1 more stable than CH3O at the CCSD(T) level of theory. The reported value for the stability of CH2OH relative to CH3O lies in a range of 17.1 kJ mol-1 to 37 kJ mol-1 in the literature.28-32 The produced CH3O radical either dissociates to CH2O + H species in reaction R5 or to CH3 + O species in reaction R4 As shown in Figure 1, there are three possible paths for the formation of CH2O; dissociation of CH3O (reaction R5), dissociation of CH2OH (reaction R11), and isomerization reaction of trans-HCOH (reaction R15). The results from QCT calculations indicate dissociation reactions R11 and R5 are the most probable paths for the formation of CH2O molecule, in 6


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accordance with our reported PESs. Our calculated barrier height for reaction R17 (CH2O + H → HCO + H2) was found to be 20.4 kJ mol−1 at the CCSD(T) level of theory. Constructing the PES Chemical reaction can be described as the motion of the nuclei on a PES.33 In order to characterize such processes, an accurate PES for all the relevant nuclear configurations should be constructed that can be as large as a 3N-6 dimensional configuration space for a system of N atoms. In the present study, GROW program package34 was used to calculate the energies, gradients and matrixes of second derivatives of different geometries over the whole regions of the PES. The GROW program uses an iteratively interpolation technique to construct the PES using a small number of initial geometrical data sets along the possible channels of the reaction. The program defines Rk ={R1, R2,…….,R10} to represent interatomic distances between the atoms present in a system. The potential energy at a configuration, R, in the vicinity of a data point, R(i), can be expanded as a Taylor series, Ti (the T is the second order Taylor series expansions for the energy around each data point). k =10

Ti ( Z ) = V ( Z (i)) + ∑ ( Z k − Z k (i )) k =1

dV dZ k

Z = Z (i )

+

1 k =10 j =10 d 2V ( − ( )) × ( − ( )) Z Z i Z Z i ∑∑ k k j j 2! k =1 j =1 dZ k dZ j

Z =Z (i)

(1)

V ( Z (i )) is the value of the potential at Z(i) (=1/Ri) and the derivatives are taken with respect to the inverse of distances Z(i). The expansions are truncated at the second order terms. The required energy and derivatives have been evaluated at a number of molecular configurations, Ndata, called data points and a modified Shepard interpolation35,36 technique is used to give the total potential energy at any configuration Z as a weighted average of the Taylor series about all Ndata data points and their symmetry equivalents:37 N data

E (Z ) =

∑ ∑W

g∈G i =1

g oi

( Z )T g oi ( Z )

(2)

In equation 2 the sum over i iterates over the Ndata data points which ab initio or DFT calculations have been performed to evaluate the potential energy and its first and second derivatives. The quantity W is a normalized weight function38 and Wg oi is defined in equation 3. 7



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The sum over G means that all permutationally equivalent geometries are included in the expansion, so the interpolated potential obeys the underlying permutation symmetry. Data points spatially ‘‘close’’ to Z will have larger weights than those at large ‘‘distances’’. This is achieved by using the unnormalized weight function, νi(Z) W g oi ( Z ) =

ν i (Z )

(3)

Nd

∑∑ν

g oi

(Z )

g∈G k =1

ν i (Z ) =

1 Z − Z (i )

(4)

2p

To start the PES construction, an initial set of data points is selected to define the possible paths for the reaction. Then reaction path in the vicinity of the stationary points is defined by equation 2 and classical trajectories are evaluated by relying on initial conditions that are defined for the reaction. All the molecular configurations generated during these trajectory calculations are recorded. Among these configurations, one is chosen to be as a new data point, where energy, gradient, and second derivative are evaluated at that point and the data point is added to the set, generating a new description of the PES. Two methods are used in GROW program to choose a new data point after performing the trajectory calculations:38 variance sampling method, [root mean square (rms) sampling], σ v2 [Z ] , and the H-weight sampling method, h[Z ] .38,39 The variance method places data points at configurations where the uncertainly in equation 2 is highest, while the H-weight method attempts to place data in regions where the trajectories often visit, but where few data points are already present.40 Adding of new data points will be repeated to grow data set on associated PES. The process normally is terminated when the classical trajectories show that the observable parameters does not change with increasing data set size or convergence of the dynamical observables can be verified.38,41 In the present study, initially 500 data points along the reaction coordinates from DFT calculations for the formation of different products were introduced as initial input. The interpolated PES was grown up to 2000 set of data points from the 500 initial set of data points.

Quasi Classical Trajectory Calculations 8


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In this study GROW classical trajectory code was used to generate reaction probability and reactive cross sections. A standard velocity-Verlet integrator was used to calculate the classical equations of motion for the atoms with a time step of 0.01 fs, which yields a conservation of the total energy better than 1 in 105. A Markov walk was used to generate a microcanonical distribution of initial atomic positions and velocities for the classical trajectories. The number of Markov chain steps per trajectory and Markov step length for all fragments were set at 500 and 0.02 Å, respectively. The initial center of mass separation of the reactants was set to 4.2 Å with the impact parameter selected from a linear distribution of the N(N-1)/2 reciprocal bond lengths with a maximum impact parameter of up to 2.6 Å (depends on the relative translational energy). The maximum value of the impact parameter, bmax, was determined at each initial translational energy in the range of 0.4 kJ mol-1 to 52.5 kJ mol-1 by computing batches of 2000 trajectories at fixed values of b. To find the maximum value of b, systematically the size of b increased until no reaction was observed in the batches of 2000 trajectories. The molecular fragments were initially randomly oriented and given zero rotational angular momentum. The reactive cross section at each translational energy is defined as;

σ (Etr) = π (bmax) 2 Pr

(5)

that Pr is the ratio of the number of reactive trajectories to the total number of trajectories (Nr/NT). In calculating the reaction probability Pr, a FORTRAN program was used to select those structures that their geometries were close to the geometry of one of the stable stationary points. To avoid of trapping the reaction into the CH2OH* potential well with -384 kJ mol-1 energy at the DFT level most of the trajectories were initialized with energized intermediate CH2OH* to increase the number of reactive trajectories and obtain the global PES for the title reaction. The internal energy of this intermediate was set to 471.5 kJ mol-1 (sum of its zero-point energy of 87.4 kJ mol-1 plus energy released in CH2OH* formation of 384.1 kJ mol-1). One of the interesting aspects of such strategy is characterizing the behavior of an energized intermediate in a multichannel reactive system. The initial relative translational energy of CH radical and H2O molecule (Etrans) was fixed for each trajectory ensemble at a value in a range of 0.4 to 52.5 kJ 9



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mol-1. The GROW program evaluates a random initial velocities and configurations for the reactants by means of a modified efficient microcanonical sampling method.42 In the present study, we also calculated the rate constant for the formation of main product by means of RRKM-SSA method25 that is based on a strong collision assumption for the energy transfer, and the results are compared with the calculated rate constant from QCT calculations.

Results and Discussion Batches of 2000 trajectories at different initial collision energy were run to determine the dynamics quantities. The PES is taken to be converged when the calculated cross sections do not change significantly by increasing the number of data points. Figures 3 and 4 show the total reaction cross section and cross section for the formation of CH2OH*, respectively, as a function of data point at initial relative translational energy of 23.6 kJ mol-1. These figures show that adding the final several hundred data points (out of the total of 2000 data points) did not alter the calculated cross section within the estimated uncertainly. Figure 5 shows a typical total probability of the reaction as a function of impact parameter at three different initial relative translational energies. It is noted that the maximum of total reaction probability is decreased by increasing the initial relative translational energy. No trajectory with zero-point leakage in our simulations was observed at low or high translational energies. Figure 6 shows the total reaction cross section as a function of initial relative translational energy. Since the entrance channel of the CH + H2O reaction to form the energized intermediate INT* is a barrier less channel, higher reactivity can be predicted at lower energies (temperatures) which is in perfect agreement with the reaction probability results. As expected for barrier less association reactions, the reactive cross section decreases by increasing the initial collision energy and reaction probability decreases by increasing the impact parameter of the reaction. The data in Figure 6 was fitted to equation 6 to find an expression for the total cross section (σtotal(E)) as a function of initial relative translational energy with 0.98 regression coefficient. 10


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-4

σ total ( E ) = ( A + B exp(bE )) = (0.46 + 24.41e -8.14×10 E )

Å2

(6)

The values of impact parameters, probabilities of the reactions, and reactive cross sections at different values of initial relative translational energy are summarized in Tables 2 and S2 to S8 in the Supporting Information, respectively. The rate constant for the reaction of CH(X2II) radical with H2O(1A) molecule was calculated by inserting the total reactive cross section expression (6) into the rate expression (7) from collision theory: 1

k (T ) = g e (T )(

∞ 8 −E ) 2 ∫ Eσ ( E ) exp( )dE 3 0 K BT πµ ( K B T )

(7)

Here g e is the ratio of electronic partition function. g e (T ) =

2 ( 2 + 2e

−38.82

T

)(1 + e

−77365.62

T

(8) )

The total rate expression after integration was found as;

k total (T ) = 4.61 × 10 6 × g e × T 0.5 × (31.8 +

24.41 ) (0.12 + 0.0008T ) 2

L mol −1 s −1

(9)

Equation 9 was used to sketch the Arrhenius plot for the title reaction in Figure 7 over the temperature range of 100-1000 K. A nonlinear least squares fitting to the QCT rate constant in Figure 7 gave the following rate constant expression: k total (T ) = 1.42 × 1011 T −0.51e

0.31kJmol −1

L mol −1 s −1

RT

(10)

In Figure 7, our calculated QCT rate constant for the title reaction is compared with the reported rate constants in the literature and also our calculated rate constant using RRKM-SSA method at the CCSD(T)/Aug-cc-pVTZ level of theory that will be discussed in the next section.

RRKM-SSA Rate Constant calculations As shown in Figure 1, the first step of the title reaction is the formation of chemically energized CH2OH*. To calculate the rate constant by means of RRKM-SSA method, a program from Hase et al.43 was used to calculate k(E) at the CCSD(T)/aug-cc-pVTZ level of theory. For the formation of energized intermediates INT* no saddle point was found. Microcanonical 11



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variational RRKM method44 was used to locate the position of the bottleneck for the reverse reaction of barrierless channel R1. As expected, for barrier-less reactions there is considerable variability in the location of the transition state, as available energy decreases the optimal transition state generally occurs at larger separations where the two reacting fragments are only weakly interacting. Thus, a general treatment of such reactions must employ state counting procedures that are appropriate over a wide range of separations.45 The reaction path is generally determined by starting at fairly large separation and propagating into shorter separation of the transition state. Implementation of the reaction path approach have tended to employ rigid-rotor harmonic oscillator assumption with occasional corrections based on separable torsional assumption. While the rigid-rotor harmonic oscillator assumption may be valid at short separation, where the interactions are quite strong, at larger separations the inter fragments modes transform to free rotors and harmonic vibrator assumption are clearly inappropriate. In such case, the implementation of separable hindered rotor assumptions for some of the modes can alleviate such failures.46 Furthermore, anharmonic effect for the inter-fragment modes should be particularly important. Reaction takes place whenever the system is captured by the potential, if the kinetic energy is larger than the centrifugal barrier (the centrifugal potential was vanished at very large distances), the colliding partners are able to enter the inner part of the PES, and strongly interact, leading to reaction. The rotational and vibrational modes of the separate fragments are generally termed the transitional modes, since they transform their character during the reaction process.46 In this study, the number of states from rotational and vibrational modes of the fragment is evaluated as a direct sum over the rotational and vibrational numbers along with one internal degree of freedom was treated as internal rotation.47

Microcanonical variational RRKM calculations are carried out to locate the bottleneck for the entrance channel. Table 3 shows the results of such calculations for reaction R1. As shown in Table 3, the position of the bottleneck decreases as the available energy to the reaction increases. Our calculations indicate that at lower temperature/energy the long range interactions are more important, while at higher temperatures short range interactions become more important.

12


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RRKM calculations were used to calculate corresponding k(E)s for unimolecular dissociation of this energized intermediate to reform the reactants or the main products CH2O + H. In calculating k(E)s, the energy step size (∆E#) was set to 1 kJ mol-1 up to 500 kJ mol-1. N2 was chosen as bath gas and a value of 0.2-0.5 was selected for the collision efficiency (βc).48 The calculated values of k(E)s along with the assumption of steady state approximation for the formation and consumption of energized intermediate INT* and CH2OH* were used to calculate the value of k(T) for the formation of main products CH2O + H in a wide range of temperature. Our results indicated that the rate of other channels in this system are negligible compare to the rate of formation of CH2O. The result is shown in Figure 7. As expected for a barrier less reaction, no pressure dependence was observed for the calculated rate constant over the pressure range of 10 Torr to 2000 Torr in agreement with Zabarnick et al.20 and Blitz et al.1 reports. A nonlinear least squares fitting to the RRKM-SSA data in Figure 7 gave the following rate constant expression:

k RRKM (T ) = 3.9 × 1011 T −0.66 e

0.62 kJmol −1

L mol −1 s −1

RT

(11)

In Figure 7, we have compared our calculated QCT total rate constant with the one from RRKM-SSA method. The difference between the two rate constant should be due to the differences in the PESs from MPWB1K in our QCT calculations with the one from CCSD(T) that was used in our RRKM-SSA calculations. A comparison between our calculated PES from MPWB1K method in Figure 1(b) with the one from CCSD(T) calculations in Figure 1(a) reveals that the barrier height for reaction R11 (formation of main products CH2O + H) is 129.5 kJ mol-1 at the MPWB1K level, while this value is 124.7 kJ mol-1 at the CCSD(T) level (less than 4%) to cause a higher values of calculated k(T) from RRKM-SSA calculations. It should also be noted that the energized CH2OH* well at the MPWB1K method is 31.5 kJ mol-1 deeper than that at the CCSD(T) level. It has been noted that a significant number of trajectories (around 6% to 20% depends on the relative kinetic energy) fall into this deep well of CH2OH* in the potential energy surface and remain there for a long period of time (on average remain there up to 1.6 × 106 steps at lower relative energies to 4.8 × 105 steps at higher relative energies) to cause a decrease in calculating the rate constant for the formation of products at lower temperature. It should also be 13



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noted that the title reaction is important at higher temperatures in hydrocarbon combustion process and at lower temperatures in dark and cold interplanetary spaces. Our calculated QCT and RRKM-SSA rate constant are compared with the reported rate constants in the literature. Our QCT rate constant values are smaller than the experimental values reported by Hickson et al.7, Zabarnick et al.20 and Boslani et al.49. Shannon et al.50 have attributed the reason to the formation of a hydrogen bonded complex (INT) prior to hydrogen abstraction reaction at temperatures lower than room temperature. The rate constant for the barrierless reaction of CH with H2O is controlled by long range interactions to form a pre reaction complex INT* prior to hydrogen abstraction reaction R2, as shown in Figure 1.44,50-53

Products Energy Partitioning The modality of the energy distribution in reactions has a large influence on the extent of chemical systems especially for those barrierless reactions involving the formation of chemically energized species.54-58 The total energy release in the chemical reactions can be partitioned into the relative translational energy and ro-vibration excitation of the products. The energy distribution in HCOH + H (the products of reactions R9, R10, R12 and R13) and CH2O + H (the products of reactions R5, R11 and R15) are investigated in the dynamics part of the present study. Wang et al.59 suggested angular momentum distribution for exothermic reactions is governed by two factors: character of the PES (attractive, repulsive, or mixed,) and mass combination. They noted for heavy heavy-light (H H-L) mass combination, distribution is almost independent to the surface and mass combination plays a key role in angular momentum distribution. In order to produce HCOH and CH2O, the OH fragment should be separated from H2O reactant. Since HC and OH fragments are heavy versus light H atom, the distribution of angular momentum is expected to be the same in both products HCOH + H and CH2O + H. The rotational quantum number j might be obtained from J = [ j (j + 1)]1/2 ħ, where J is the classical value of the rotational angular momentum derived from the output of GROW package. 14


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The obtained J values are rounded to the nearest integer.60 The HCOH and CH2O can be considered as near prolate symmetric top with A >B ≈ C and their rotational energies can be obtained by equation 12.

Erot ( j , K ) = Bj ( j + 1) + ( A − B) K 2

K = j , ( j − 1) ⋅ ⋅ ⋅ ⋅0 ⋅ ⋅ ⋅ ⋅(− j )

(12)

where K is the projection of j values on the principal axis of the molecule. The calculated value for A, B and C are 285.8, 37.2 and 32.9 GHZ for HCOH and 287.2, 39.8 and 35.0 GHZ for CH2O at the MPWb1K/6-31++g(2df,2p) level of theory. Figure 8 presents the distribution of rotational angular momentum in CH2O and HCOH fragments among the trajectories as a function of initial collision energies. For instance, the average angular momentums of CH2O and HCOH and are 34.1 ħ and 30.1 ħ at 0.4 kJ mol-1 collision energy, respectively, equivalent to the rotational energies of 15.3 kJ mol-1 and 12.7 kJ mol-1, respectively. The maximum of total angular momentum for CH2O fragment varies from approximately 34.1ħ at 0.4 kJ mol-1 initial collision energy to 13.9ħ at 52.5 kJ mol-1 initial collision energy, see Figure 8(a). The maximum of total angular momentum for HCOH fragment varies approximately from 30.1ħ at 0.4 kJ mol-1 initial collision energy to 10.0ħ at 52.5 kJ mol-1 initial collision energy, see Figure 8(b). The trend of angular momentum distribution become smaller and broader as initial collision energy increases, see Figure 8. For the sake of clarity, summary of angular momentum distribution from figures 8(a) and 8(b) are listed in Tables S9 and S10 in Supporting Information. Figure 9(a) and 9(b) shows the average angular momentum for the formation of HCOH and CH2O at different initial collisional energies. Figure 9(a) and 9(b) show that increasing the initial collision energy enhances the rotational energy in R9 and R11 reaction. Braunstein and Conforti61 reported the same trend for the study of angular momentum distribution in abstraction reaction product HO + OH in H2O + O reaction. According to the PES, the available energy for the formation of HCOH + H (mainly from reaction R9) and CH2O+H (mainly from reaction R11) are 36.6 and 254.6 kJ mol-1, respectively. The total available energy for each product is the sum of the energy released during an 15



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exothermic reaction plus initial internal energies and relative translational energy. So, the total available energy for HCOH and CH2O are 421.2 and 639.2 kJ mol-1 at initial collision energy of 0.4 kJ mol-1, respectively. Figure 8 shows that average angular momentum of the CH2O and HCOH products are 34.1 ħ and 30.1ħ, respectively, at 0.4 kJ mol-1 collision energy, respectively. Based on equation 12, the rotational energies of CH2O and HCOH are 15.3 and 12.7 kJ mol-1, respectively. Therefore, 15.3 kJ mol-1 of 639.2 kJ mol-1 and 12.7 kJ mol-1 of 421.2 kJ mol-1 total available energy is liberated to rotational energy levels of CH2O and HCOH (approximately 2.4% and 3.0% of the total available energy, respectively). Figure 10 shows the relative translational energy distribution for the formation of HCOH + H and CH2O + H products as a function of initial collisional energy. Figure 11(a) and 11(b) present average relative translational energy of trans and cis-HCOH + H and CH2O + H products as a function of initial collisional energy. Obviously, the relative translational energies of the products increases with increasing the initial collisional energy of the reactants in both channels. It declares that the average relative translational energies of CH2O +H and HCOH+H are 101.0 and 119.0 kJ mol-1 at 0.4 kJ mol-1 initial collision energy, respectively. Therefore, 101.0 kJ mol-1 of 639.2 kJ mol-1 and 119.0 kJ mol-1 of 421.2 kJ mol-1 total available energy releases into the relative translational energy of CH2O + H and HCOH + H products at 0.4 kJ mol-1 collision energy, respectively, (approximately 15.8% and 28.2% of the total energy, respectively). Based on the distribution of rotational and translational energies for CH2O and HCOH, it was found that approximately 81.8% and 68.7% of the total available energy transfers into the internal degrees of these two products at 0.4 kJ mol-1 initial collisional energy, respectively. It means that CH2O and HCOH products are highly vibrationally excited. That is the reason for no ZPE leakage observation during the simulation. This result is in accordance with our PES that the vibrationally excited products CH2O and HCOH can easily dissociate through reactions R14 and R16, formation of CO + H2.

16


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Tables 4 and 5 present the fraction of vibration, translation and rotation( < f vib > , < f trans > and < f rot > ) for CH2O and HCOH products at the collision energies studied. The

fraction of the total available energy transfers into translation, < f trans > , can be written as: < f trans >=

Et

(13)

E av

Et is translational energy and Eav is total available energy. The same calculated was used to obtained < f vib > and < f rot > . The pattern of energy distribution in the main products does not change significantly as the collision energy increases. Our products energy distributions are based on MPWB1k/631++G(2df,2p) PES. In Figure 2, we have compared the structure of the stationary points at two levels of theory, i.e. MP2/6-31++G(2df,2p) and MPWB1K/6-31++G(2df,2p). Insensitivity of the products' state distributions with regard to the internal excitation of the reactants is proposed by Zhao et al.62. They suggested the products' energy disposal should be controlled by the position and structure of transition state. The geometrical consistency of the transition states at the two levels of theory imply that the products’ energy disposal should not be basically affected by the method that is used as the geometrical structures of the important stationary points are very close in two methods. Similar calculations are performed to obtain the distribution of ro-vibrational and translational energy levels for HCOH and CH2O at other initial collisional energies studied in this work. Our results indicate that distribution of ro-vibrational energy is around 71.8% to 65.6 % for HCOH and 84.2% to 81.9% for CH2O and amount of energy release to translational energy are approximately 28.2% to 34.4% of the total available energy for HCOH and approximately 15.8% to 18.1% for CH2O over the initial collisional energy range of 0.4 kJ mol-1 to 52.5 kJ mol-1, respectively.

Inelastic scattering The energy partitioning in non-reactive collisions is also investigated in order to examine the rotational energy distributions of the reactants H2O and CH after non-reactive collisions. In our QCT calculations, the initial states for the trajectories were selected from the irrotational microcanonical ensemble for each fragment at a specific initial collisional energy. It 17



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was found that CH radical and H2O molecule are rotationally excited and gain orbital angular momentum after non-reactive collisions. Batches of 2000 trajectories have been run at initial collision energy of 23.6 kJ mol-1. As shown in Figure 5, the probability of reaction decreases to approach zero as the impact parameter of the reaction increases, approximately 5 Å, where the nonreactive trajectories start to become important. Figure 12 shows the calculated final average classical angular momentum of the reactants as a function of number of data points, at large impact parameters, over a range of 5 Å to 11 Å. Figure 12 indicates that after collisions the average angular momentum of reactants (H2O and CH) converges as the size of data sets increases. As shown in Figure 12, the average final angular momentum reduces with increasing the impact parameter. This trend is in good agreement with the reported results by Ramazani et al.63 for inelastic collision investigation. The final angular momentum of reactants remains non-zero even at impact parameters greater than 11 Å. That means even when the impact parameter is greater than 11 Å, collisions happen but these collisions are non-reactive and only energy transfer is occurring. The average angular momentum values at impact parameter of 11 Å is 1.5 ħ and 1.2 ħ for H2O and CH reactants, respectively. Figure 13 presents the calculated cross sections for angular momentum transfer to the initially irrotational H2O(1A) molecule and CH radical as a function of data set size. In H2O molecule and CH radical, the calculated cross sections were converged as more data points are added. As expected, the non-reactive cross sections in Figure 13 are much larger than those in reactive collisions shown in Figure 6. There are, however, no experimental determinations of rotational cross section for 1

H2O( A) molecule and CH radical and we have relied exclusively on theoretical predictions. The reference method is the Coulomb–Born approximation.64 This theory assumes that the collisional excitation rates can only be determined by long-range interactions. Faure65 showed that the widely used Coulomb–Born approximation is valid for ∆j=1 transitions when the molecular ion has a dipole greater than about 2D and transitions with ∆j>1 are found to have appreciable rates and are found to be entirely dominated by short range interactions.

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Conclusions Quasi-classical trajectory calculations along with RRKM-SSA calculations have been performed to study the dynamics of the reaction of CH(X2II) + H2O(1A) at the DFT and CCSD(T) levels of theory, respectively. In QCT calculations an interpolated PES generated from GROW package at the collision energy range from 0.4 kJ mol-1 to 52.5 kJ mol-1 at the MPWB1K/6-31++g(2df,2p) level of theory was used. The reaction precedes quantum mechanically over the lowest doublet potential surface. The reaction probability and reactive cross section during the simulation at several collisional energies were obtained to calculate the total reactants consumption rate constant. The calculated relative energies at the MPWB1K level are compare with those calculated at the CCSD(T) level of theory. The CCSD(T) energies were used to calculate the rate constant using RRKM-SSA method for the formation of main product that is almost equal to the total rate. The new rate constants expression from QCT calculations at the MPWB1K level and RRKM-SSA method at the CCSD(T) level of theory are introduced to be compared with the available data in the literature. The lower rate constant at lower temperatures from QCT calculations should be raised from the difference in the depth of CH2OH* well at the MPWB1K’s PES relative to that at the CCSD(T)’s PES, while at higher temperatures (energies) the rate constants from both methods coincide. At MPWB1K level it has been noted that the CH2OH* well is about 31.5 kJ mol-1 more deeper than that at the CCSD(T) level to cause CH2OH* stay there for a longer period of time to decrease the rate constant at lower energies (temperatures). It can be suggested that the newly formed O-C stretching vibration in H2COH could particularly well couple to the other vibrational modes in this energized radical. It should be noted that the main purpose of the dynamics part in this study was to investigate the energy partitioning in CH2O + H and cis or trans-HCOH products. It seems that the results for that part should be acceptable as in Table 1 our calculated ∆E values for reactions R11 or R5 to form CH2O + H and reactions R9 and R10 to form cis or trans-HCOH at the MPWB1K level are relatively comparable with ∆Ho(273K) values reported in the literature. Comparison of the enthalpies indicates that despite of relatively large differences in calculated ∆E values at two levels of MPWB1K and CCSD(T), the energy depositions in reactions R5 or 19



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R11 and R9 or R10 at the MPwB1K are not that much off. The error in the total energy deposition relative to the reported values of ∆Hs in the literature was found to be about 7.0 kJ mol-1 for reaction R9 and 11.0 kJ mol-1 for reactions R5 or R11, which means only 4% error for reactions R5 or R11, while 23% error for reaction R9. Our results indicate that in this system reactions R5 or R11 for the formation of CH2O + H are much more important than reactions R9 or R10 for the formation of cis or trans-HCOH. The average energy partitioning from QCT calculations at different initial collision energies (0.4 up to 52.5 kJ mol-1) was found to be as; 12.7-1.4 kJ mol-1 and 15.3-2.6 kJ mol-1 for the rotational energies of HCOH and CH2O, respectively, 119.0-162.9 kJ mol-1 and 101.0-125.2 kJ mol-1 for the relative translational energies of HCOH + H and CH2O + H products, respectively, and approximately 289.5-309.2 kJ mol-1 and 522.4-563.4 kJ mol-1 for the internal degrees of freedom of HCOH and CH2O products, respectively.

Supporting Information Rotational moments of inertia and harmonic wave numbers calculated at the MPWB1K/631++g(2df,2p) level of theory are listed in Table S1. Summary of the maximum impact parameter, probability, and reactive cross section as a function of initial collision energy for the formation of different products are shown (see Tables S2 to S8). Summary of the maximum of angular momentum for CH2O and HCOH as a function of initial collision energy are included (see Tables S9 and S10). AUTHOR INFORMATION Corresponding Author *E-mail: [email protected]. Notes The authors declare no competing financial interest. ACKNOWLEDGMENTS The financial support from the Research Council of Shiraz University is acknowledged.

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Shannon, R. J.; Caravan, R. L.; Blitz a, M. A.; Heard, D. E. A Combined Experimental and

Theoretical Study of Reactions between the Hydroxyl Radical and Oxygenated Hydrocarbons Relevant to Astrochemical Environments. Phys. Chem. Chem. Phys 2014, 16, 3466-3478.

25



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

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Fuente, A.; Rodriguez-Franco2, A.; Garcia-Burillo, S.; Martin-Pintado, J.; Black, J. H.

Observational Study of Reactive Ions and Radicals in PDRs. Astron. Astrophys 2003, 406, 899– 913. 55

Smith, M. A.; Schlemmer, S.; Richthofen, J. V.; Gerlich, D. HOC+H2 Isomerization Rate 25

K: Implications for the Observed [HCO+]/ [HOC+] Ratios in the Interstellar Medium. J. Astrophys 2002, 576, 78- 90. 56

Barker, J. R. Energy Transfer in Master Equation Simulations: A New Approach. Int. J. Chem.

Kinet 2009, 41, 748 – 763. 57

Liu, C. L.; Hsu, H. C.; Lyu, J. J.; Huang, C, L.; Ni, C. K. Energy Transfer of Highly

Vibrationally Excited Azulene: Collisions Between Azulene and Krypton. J Phys. Chem 2006, 124, 054302-054309. 58

Barker, J. R.; Yoder, L. M.; King, K. D. Vibrational Energy Transfer Modeling of Non

equilibrium Polyatomic Reaction Systems. J Phys. Chem. A 2001, 105, 796–809. 59

Wang, M. L.; Han, K. L.; He, G. ZH. Product Rotational Polarization in the Photo initiated

Bimolecular Reaction A+BC→AB+C on Attractive, Mixed and Repulsive Surfaces. J. Chem. Phys 1998, 109, 5446-5454. 60

Castillo, J. F.; Aoiz, F. J.; Banares, L.; Collins, M. A. The H +N2O→ OH +N2 Reaction

Dynamics on an Interpolated QCISD Potential Energy Surface. A Quasi Classical Trajectory Study. J. Phys. Chem. A 2004, 108, 6611- 6623. 61

Braunstein, M.; Conforti, P. F. Classical Dynamics of State-Resolved Hyperthermal O(3P) +

H2O( 1A1) Collisions. J. Chem. Phys 2013, 138, 074303-074319. 62

Zhao, B.; Sun, Zh.; Guo, H. Communication: State-to-State Dynamics of the Cl + H2O → HCl

+ OH Reaction: Energy Flow into Reaction Coordinate and Transition State Control of Product Energy Disposal. J. Chem. Phys. 2015, 142, 241101-241105.

26


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63

Ramazani, Sh.; Frankcombe, T. J.; Andersson, S.; Collins, M. A. The Dynamics of the

H2+CO+ Reaction on an Interpolated Potential Energy Surface. J. Chem. Phys 2009, 130, 244302-244309. 64

Dickinson, A. S.; Flower, D. R. Electron Collisional Excitation of Interstellar Molecular Ions.

Mon. Not. R. Astr. Soc 1981, 196, 297-304. 65

Faure, A.; Tennyson, J. Electron-Impact Rotational Excitation of Linear Molecular Ions. Mon.

Not. R. Astron. Soc 2001, 325, 443–448.

27



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

Page 28 of 41

Table 1. Comparison of the Corrected Relative Energies for Zero-Point Energies of Various Species at Three Different Levels of Theory in kJ mol-1. Species

∆Ho(298K)27

MPWb1K/6-

CCSD(T)/Aug-

31++g(2df,2p)

cc-pVTZ//MP2/631++g(2df,2p)

CH+ H2O

0.0

0.0

INT

-44.5

-33.6

TS2

-8.5

-2.0

TS12

58.3

78.8

TS13+H

63.2

99.5

TS8

-46.9

-35.5

TS15+H

99.2

117.6

TS3

-224.9

-191.8

TS17

-236.9

-207.5

TS7

-33.7

-5.7

TS16+H

101.0

112.9

TS14+H

187.2

202.9

HOCH2

-384.1

-352.6

HCO+H2

-318.5

-302.1

HOC+H2

-148.5

-130.0

CH3O

-360.0

-317.7

CH2O+H

-254.6

-227.9

-243.2

Cis-HCOH+H

-16.7

6.0

-9.68

Trans-HCOH+H

-36.6

-12.2

-28.16

OH+ CH2

109.7

110.6

CH3+O

289.6

249.7

CO+H2+H

-245.1

-237.0

28


Page 29 of 41

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


CH + H2O

k1 k-1

INT*

R1 w k2

INT

Rw

CH2 OH

R2

k3

CH3O

R3 k4

CH3+O

R4

CH2O+H

R5

k5 k6 k7

CH2+OH

R6

HOC+H2

R7

k8

R8

k9

trans-HCOH+H

R9

k10

cis-HCOH+H

R10

k11 k12

HCO+H2

CH2O+H

R11

trans-HCOH+H

R12

k13

cis-HCOH+H k14

k15

R13 CO+H2+H

CH2O+H k16 k17

R15 CO+H2+H

R16

HCO+H2

R17

Scheme 1. The proposed mechanism for the reaction of CH(X2II) radicals with H2O(1A) molecule.

29


R14


CH3+O 249.6

TS14+H

(a)

202.9

R14

-1 Relative Energy(kJ.mol )

TS15+H TS13+H 99.5

TS12 78.8

R12

0

CH+H2O

-33.6

TS16+H

110.6

112.9

R13 -12.2

TS7 -5.7

cis-HCOH+H

trans-HCOH+H

R2

R16

R6

5.9

TS2 -2.0

0.0 R1 INT

CH2+OH

117.6

R15

TS8+H2 -35.5

R8

R7

-130.0 HOC+H2

R10 R9

R4

TS3 -191.8

TS17 -227.9

R3

CO+H2+H

-207.5

CH2O+H

R11

-352.6

-237.0 HCO+H2

R17

R5

-317.7

-302.1

CH3O

CH2OH

0

Reaction Coordinate

CH3+O

(b)

289.6 TS14+H

200

187.2

R14 TS15+H

-1

Relative Energy(kJ.mol )

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

Page 30 of 41

R12

0

CH+H2O 0.0 R1

58.3

R13

R2

-16.7

-33.7

cis-HCOH+H

trans-HCOH+H

-44.5

101.0

R16

-36.6

-8.5

TS16+H

109.7

63.2

TS2 INT

CH2+OH

99.2

R15

TS13+H

TS12

TS8+H2

TS7

-46.9

R8 -148.5

R10

-200 R9

R3

R7

HOC+H2

-224.9 TS3

-254.6 CH2O+H

R4

R17

R6 R11 -384.1

-400

TS17

CH3O -360.0

R5

CO+H2+H

-236.9

-245.1 HCO+H2 -318.5

CH2OH

Reaction Coordinate

Figure 1. The relative energies of the stationary points, at the CCSD(T)/Aug-cc-pVTZ//MP2/6-31++g(2df,2p) (a) and MPWB1K/6-31++g(2df,2p) (b) levels of theory.

30


10 9.7 H (10 1.10 0.95(0.96) O 0.95(0.96) H H 6 [91.2] ( 1 . . 9) C 08) [0.96] H + [1.11] 92.0(92.6) 0.95(0.96) [95.2] 1.11(1.10) H 1.18(1.12) H O 106.9(105.7) C 1.77(1.75) ) 0.95(0.96) 5 . [1.86] 98 H [0.96] 2( CH + H2O . 9 9

[9 8. 3]

4.1) 4(10 105.

H

98.2(98.9) 1.09(1.09) C

H

0.96(0.97)

O

(65

1.69(1.76)

INT* H

.5 64

) .8 00 (1 3.6 10

5(9 0.7

)

.4)

1.24(1.26) C

1.12(1.10)

87.

1.31(1.35)

1.10(1.10) H

H TS2

1.16(1.16) O

H 1.30(1.32)

C O 100.4(99.6) 1.36(1.40) 0.95(0.97) H TS12 109.2(107 .4) H 1.29(1.31) 0.95(0.96) C O + H 1.1(1.1) 102.5 (102.2 ) H trans-HCOH+H

1.28(1.31)

.7) 13 (1 5.0 11

116 .0(1 17.9 H ) 1.32(1.35) 0.95(0.96) O C 1.11(1.11) 109.5(104.4)

TS15+H

H

H 1.07(1.08)

TS13+H

H

10 6.9 (1 06 .6

)

O 1.35(1.36) 0.85(1.38) 1.29(1.31) 1.52(1.51) 121.07(121.1) C ) ) O C . O 1.8 3 + H 2 3 1 1.18(1.21) 1.11(1.11) 0.96(0 ) 0.95(0.96) 8( .7( H . 1.08(1.08) 3 ) 1 3 . .97) 2 3 3 + H C 4.3 C 1 11 1 1.36(1.38) ( H 1 H H ( H 0.3 1.09(1.10) 11 1.09(1.10) 5.9 11 1.33(1.35) 6.2 11 (1 CH2OH H 16 H cis-HCOH+H 0.95(0.96) O .4 ) TS7 H CH O+H 2

1.08(1.08) C H

114 C .3(1 12.2 1.26(1.27) ) O H2 + H 0.97(0.97)

1.18(1.22) 67.7(68.0)

H

1.25(1.23) 1.08(1.08)

HOC+H2

H

O 1.17(1.18) C

1.10(1.11)

TS3

H O 61.8(63.1)

H 11 3 .0 (1 12

O

1.30(1.30)

.5) 1.35(1.37)

1.09(1.09) H

C

1.09(1.09) H ) 1.4 1.09(1.09) 1 (1 6.6 0 H 1 CH3O

1.26(1.29) 0) 179 H 1.05(1.0 .9(1 79.7 H )

TS17

1.12(1.12) 1.25(1.27) + H2 C TS8

1.21(1.27) O 66.1(70.2) H ) .4) 03.2 .7(1 .7(120 1 0 1 125 66.5(63.3) C H 1.35(1.30)

1.17(1.13)

1.36(1.37)

11 3. 9( 11 2. 6)

O

9) (1.0 1.06

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


10 2.6 (11 5.8 ) 12 6.7 (13 0 .8 )

Page 31 of 41

TS14+H

) H .27 1.09(1.09) 5(1 2 . 1 C + H H 1.63(1.64) ) 9 . 1.15(1.17) 62 .1(1 162 O

TS16+H O 1.16(1.18) 124.8(124.0) C H 1.11(1.11)

+ H

H 0.74(0.74)

HCO+H2

1.12(1.13) C O + H0.74(0.74) H + H CO+H2+H

Figure 2. Optimized geometries of the stationary points at the MPWb1K/6-31++g(2df,2p) level. In INT*, angles and

31



bonds are compared with the reported values by Wang et al.21 at UMP2/6-31G(d,p) level of theory that is given in bracket. The calculated values, in this work, at UMP2/6-31++g(2df,2p) level of theory is given in parentheses (bonds are in angstrom and angles are in degree). 3.55 3.54 3.53 2 Total Reaction Cross Section(Å )

3.52 3.51 3.50 3.49 3.48 3.47 3.46 3.45 1000

1200

1400

1600

1800

2000

2200

Number of Data Point

Figure 3. The calculated total reactive cross section of the title reaction as a function of data points size at initial collision energy of 23.6 kJ mol-1.

CH2OH

0.075

Cross Section of CH2OH Formation(Å2)

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

Page 32 of 41

0.050

0.025

0.000

-0.025

-0.050 1000

1200

1400

1600

1800

2000

2200

Number of Data Point

Figure 4. The calculated cross section for the formation of CH2OH as a function of data points size at initial collision energy of 23.6 kJ mol-1.

32


Page 33 of 41

-1

52.5(kJmol ) -1 5.2(kJmol ) -1 0.4(kJmol )

1.2

Total Probability of Reaction

1.0

0.8

0.6

0.4

0.2

0.0 0

1

2

3

4

5

Impact Parameter for the Reaction(Å)

Figure 5. Reaction probability as a function of impact parameter for the collisions of CH radicals with H2O molecules at different initial collision energies.

25

2

Å

)

20

Total Reaction Cross Section(

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


15

10

5

0

0

10

20

30

40

50

60

-1 Translational Energy(kJ mol )

Figure 6. Total reaction cross section as a function of initial collisional energy.

33



Table 2. Summary of the Trajectory Calculations of the Reaction of CH(X2II) radical with H2O(1A) Molecule. E(kJ mol-1)

T(k)

bmax(Å)

Pr

σ(Å2)

52.5

4210.6

0.53

0.89

0.78

26.3

2105.3

0.53

0.89

0.78

23.6

1894.8

0.53

0.90

0.79

21.0

1684.2

0.53

0.91

0.79

18.4

1473.7

0.53

0.93

0.81

15.7

1263.2

0.53

0.93

0.81

5.2

421.1

1.06

0.95

3.33

1.6

126.3

1.59

0.98

7.74

0.5

42.1

2.12

0.99

13.91

0.4

21.1

2.65

0.99

21.83

26.0 25.5 25.0 24.5 -1 ln k(L mol-1 s )

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

Page 34 of 41

24.0 23.5 23.0 22.5 22.0 21.5 21.0 20.5 20.0 0

2

4

6

8

10

1000/T(K)

Figure 7. Comparison of calculated total rate constants in the present work with those reported in literatures for CH + H2O reaction. () and () lines from ref. 23 (TS2 energy is -16.2 or -7.2 kJ mol-1 relative to the reactants energy, respectively), ( ̶ ̶ ) and () and () from ref. 1, () and () from ref. 7 with Ar or SF6/N2 as bath gas, respectively, () from ref. 49, () from ref. 20, (

) and (

) from RRKM-SSA or QCT calculations in the

present work, respectively.

34


Page 35 of 41

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


Table 3. Microcanonical variational RRKM results for unimolecular dissociation reaction R1. R*(Å)a Eb(ν,j) E0c Nd(ν,ј)×102 Ge(E*)×104

k(E)×1011(1/s)

3.77

47.2

42.9

0.276

0.009

0.99

3.73

49.3

42.6

0.328

0.045

4.01

3.72

51.4

42.4

0.387

0.116

9.01

3.67

53.5

42.3

0.454

0.235

15.54

3.54

57.6

41.7

0.620

0.818

39.60

3.48

61.9

41.5

0.833

1.909

68.71

3.42

63.9

41.5

0.961

2.763

86.14

2.98

68.1

33.0

1.269

5.084

120.10

2.96

70.2

32.9

1.451

6.465

133.61

2.92

76.5

32.4

2.139

12.540

175.82

2.51

82.8

20.3

3.088

22.521

214.61

2.48

84.8

19.3

3.475

26.212

226.12

2.46

86.9

19.1

3.903

30.363

233.21

2.44

89.0

18.3

4.376

35.021

239.83

2.43

91.1

17.8

4.896

40.191

246.14

2.41

93.2

17.3

5.471

45.972

251.90

2.40

95.3

16.8

6.105

52.484

257.71

2.38

97.4

16.5

6.802

59.592

262.64

2.36

99.5

15.9

7.566

67.430

267.20

2.34

101.6

15.1

8.405

76.071

271.33

2.33

103.7

14.8

9.325

85.563

275.11

2.31

105.7

14.5

10.321

95.961

a

b

278.80 -1

Position of the bottleneck in angstrom. Total available energy to the system in kJ mol . c Classical energy difference between the reactant and the transition state. d Density of states in cm-1. e Sum of states.

35



52.5(kJ mol-1)

18

16

CH2O

14

(a)

% Trajectory

12 10 8

8 6 4 2

0

0

-2 30

40

50

60

70

80

90

100

0.4(kJ mol-1)

10

2

20

15.7(kJ mol-1)

12

4

10

23.6(kJ mol-1)

HCOH (b)

14

6

0

26.3(kJ mol-1)

16

% Trajectory

-1 52.5(kJmol ) -1 26.2(kJmol ) -1 23.6(kJmol ) -1 21.0(kJmol ) -1 18.3(kJmol ) -1 15.7(kJmol ) -1 5.2(kJmol ) -1 1.6(kJmol ) -1 0.4(kJmol )

18

0

110

10

20

30

40

50

60

70

80

Rotational Angular Momentum(h/2π)

Rotational Angular Momentum(h/2π)

Figure 8. Abundance of rotational angular momentum distribution of CH2O (a) and HCOH (b) products among the trajectories at different initial collision energies with the bin size of 4 ħ.

HCOH (b)

35 34

34

CH2O (a)

33

32

Average Angular Momentum(h/2π)

32 Average Angular Momentum(h/2π)

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

Page 36 of 41

30

28

26

24

22

31 30 29 28 27 26 0

0

10

20

30

40

50

10

20

30

40

50

60

60

-1 Initial Collisional Energy(kJmol )

-1 Initial Collisional Energy(kJmol )

Figure 9. The average angular momentum of the CH2O (a) and HCOH(b) products as a function of initial collision energy.

36


Page 37 of 41

-1 52.5(kJmol ) -1 26.2(kJmol ) -1 18.3(kJmol ) -1 15.7(kJmol ) -1 1.6(kJmol ) -1 0.4(kJmol )

13 -1 52.5(kJmol ) -1 26.2(kJmol ) -1 23.6(kJmol ) -1 21.0(kJmol ) -1 18.3(kJmol ) -1 15.7(kJmol ) -1 5.2(kJmol ) -1 1.6(kJmol ) -1 0.4(kJmol )

H CO+H 2

% Trajectory

(a)

10

12

HCOH+H

(b)

11 10 9

% Trajectory

15

8 7 6 5 4

5

3 2 1 0

0

0

100

200

300

400

-1 Relative Translational Energy(kJmol )


Figure 10. Relative translational energy distribution for formation of CH2O (a) and HCOH (b) at different initial collision energies with the bin size of 10 kJ mol-1. CH2O+H

120

HCOH+H

(a)

(b)

115

150 145 -1 Relative Translational Energy(kJmol )


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


110

105

100

95

140 135 130 125 120 115 110

0

10

20

30

40

50

60 0

-1 Initioal Collisional Energy(kJmol )

10

20

30

40

50

60

-1 Initioal Collisional Energy(kJmol )

Figure 11. The average relative translational energy of the CH2O + H (a) and cis and trans-HCOH + H (b) products as a function of initial collision energy.

37



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

Page 38 of 41

Table 4. Summary of the energy partitioning data for the CH+ H2O reaction at different collision energies have been seen in the trajectories for CH2O. E(kJ mol-1)

< f rot >

< f trans >

< f vib >

52.51 26.26 23.63 21.00 18.38 15.75 5.25 1.6 0.4

0.004 0.001 0.001 0.003 0.010 0.019 0.024 0.024 0.024

0.181 0.18 0.17 0.17 0.17 0.16 0.16 0.16 0.16

0.82 0.82 0.83 0.83 0.82 0.82 0.82 0.82 0.82

Table 5. Summary of the energy partitioning data for the CH+ H2O reaction at different collision energies have been seen in the trajectories for HCOH. E(kJ mol-1)

< f rot >

< f trans >

< f vib >

52.51 26.26 23.63 15.75 0.4

0.002 0.006 0.010 0.015 0.03

0.344 0.339 0.318 0.297 0.282

0.654 0.655 0.672 0.688 0.688

.

38


Page 39 of 41

8

Average of Angular Momentum(h/2π)

11 10

Average of Angular Momentum(h/2π)

9 8

H2O

7

(a)

6

2067 data points 1905 data points 1433 data points 762 data points

9

2067 data points 1905 data points 1433 data points 762 data points

12

5 4 3

7 HCOH (b)

6 5 4 3 2

2

1

1

0

0 4

5

6

7

8

9

10

11

4

5

6

7

8

9

10

11

Impact Parameter(Å)

Impact Parameter(Å)

Figure 12. The final average angular momentum of H2O (a) and CH (b) in nonreactive collisions as a function of the impact parameter at initial collision energy of 23.6 kJ mol−1. Results are shown for QCT calculations on PESs interpolating at the different data points. j=1 j=2 j=3 j>3

180 160 140

H2O(a)

120 100 80 60 40 20

j=1 j=2 j=3 j>3

140 2 Total Rotationally Inelastic Cross Section(Å )

2 Total Rotationally Inelastic Cross Section(Å )

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


120 100

CH(b) 80 60 40 20

0

0

1200

1400

1600

1800

2000

2200

1200

Number of Data Points

1400

1600

1800

2000

2200

Number of Data Points

Figure 13. Total rotationally inelastic cross sections as a functions of the data set size for different final values of J(H2O) (a) and J(CH) (b) at initial collision energy of 23.6 kJ mol−1.

39



TOC Graphic

CH3+O 249.6

TS14+H

R14

202.9

TS15+H


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

Page 40 of 41

0

TS13+H 99.5

TS12 78.8

R12 CH+H2O

-33.6

TS16+H

110.6

112.9

R13 -12.2

TS7 -5.7

cis-HCOH+H

trans-HCOH+H

R2

R16

R6

5.9

TS2 -2.0

0.0 R1 INT

CH2+OH

117.6

R15

TS8+H2 -35.5

R8

R7

-130.0 HOC+H2

R10 R9

R4

TS3 -191.8

TS17 -227.9

R3

-207.5

CO+H2+H

CH2O+H

-352.6

R11

-317.7

R5

CH3O

CH2OH

0

Reaction Coordinate

40


-237.0

R17

HCO+H2 -302.1

Page 41 of 41

Quasi-classical trajectory and RRKM-SSA calculations are carried out to study the dynamics of the reaction of CH + H2 O. Energy partitioning in reactive and non-reactive collision over the initial collision energy from 0.4 kJ mol-1 to 52.5 kJ mol-1 is investigated.

CH3+O 249.6

TS14+H

R14

202.9

TS15+H


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


0

TS13+H TS12

CH+H2O

TS16+H

110.6

112.9

R13 -12.2

TS7 -5.7

cis-HCOH+H

trans-HCOH+H

R2

R16

R6

5.9

TS2 -2.0

0.0 Rw INT -33.6

99.5

78.8

R12

CH2+OH

117.6

R15

TS8+H2 -35.5

R8 R7 -130.0 HOC+H2

R10 R9

R4

TS3 -191.8

TS17 -227.9

R3

-207.5

CO+H2+H

CH2O+H

-352.6

R11

-317.7

R5

CH3O

CH2OH

0

Reaction Coordinate


-237.0

R17

HCO+H2 -302.1

A Theoretical Study on the Dynamics of the Reaction of CH Radicals

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