Direct Chemical Dynamics Simulations of H3+ + CO Bimolecular

Subscriber access provided by University of Sunderland

A: Kinetics, Dynamics, Photochemistry, and Excited States 3+

Direct Chemical Dynamics Simulations of H + CO Bimolecular Reaction Erum Gull Naz, Sumitra Godara, and Manikandan Paranjothy J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.8b08671 • Publication Date (Web): 11 Oct 2018 Downloaded from http://pubs.acs.org on October 12, 2018

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 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

The Journal of Physical Chemistry

Direct Chemical Dynamics Simulations of H3+ + CO Bimolecular Reaction Erum Gull Naz, Sumitra Godara, and Manikandan Paranjothy∗ Department of Chemistry, Indian Institute of Technology Jodhpur, Jodhpur 342037 Rajasthan, India E-mail: [email protected] Phone: +91 291 280 1306. Fax: +91 291 251 6823

1

ACS Paragon Plus Environment

The Journal of Physical Chemistry 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

Abstract The proton transfer reaction H3+ + CO −−→ HCO+ /HOC+ + H2 has gained considerable attention in the literature due to its importance in interstellar chemistry. The reaction products - formyl cation (HCO+ ) and isoformyl cation (HOC+ ) are known to initiate multiple chemical reaction networks resulting in complex molecules found in space. Several experimental and theoretical studies probing the structure and energetics of the [H3 CO]+ system, HCO+ /HOC+ product branching ratios, reaction mechanisms, etc., have been reported in the literature. In the present work, we investigated the H3+ + CO bimolecular reaction in the gas phase using direct dynamics methodology. The simulation conditions were chosen to mimic a recently reported velocity map imaging experiments on the same reaction. The calculations were performed using density functional PBE0/aug-cc-pVDZ level of electronic structure theory. Internal energy and scattering angle distributions of reaction products found from the simulations are in qualitative agreement with the experiment. However, the product branching ratios at low collision energies were in contrast with the experimental predictions. Interesting dynamical features were observed in the simulations and detailed atomic level mechanisms are presented.

Introduction During the past several decades numerous cationic, anionic, and neutral molecules containing few atoms to polycyclic aromatic hydrocarbons have been identified in the interstellar media and the chemistry of these species has received considerable attention in the literature. 1–4 Ionmolecule reactions occurring in the interstellar media play an important role in determining the molecular abundances in space. 5,6 The most widely distributed ionic species in space is the H3+ molecular ion 7–9 which is highly reactive due to its tendency to lose proton easily and is known to initiate several chemical reaction networks. 10–12 The proton transfer reaction between H3+ and another abundant molecule CO is particularly important since the reaction

2


Page 2 of 25

Page 3 of 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


products - the stable formyl cation (HCO+ ) and the metastable isoformyl cation (HOC+ ) are precursors for several complex molecules found in space. 13 Stability of formyl cation is due to the partial negative charge on the carbon atom in CO molecule. These two ions initiate different reaction chains and thus an understanding of their relative abundance in the interstellar environment is essential. There are many studies available in the literature 14–20 on this subject wherein HCO+ /HOC+ ratios ranging from 360 to 6000 have been reported depending upon the region of observation. Several experimental and theoretical investigations of the [H3 CO]+ system probing the − → structures and energetics, reaction mechanisms, product branching ratios, and HCO+ − ← − − HOC+ isomerization have been reported. 21–34 We mention here only a few studies that are relevant to the present work. Detailed electronic structure calculations at the benchmark CCSD(T)/CBS level of theory characterizing the potential energy surface and various reaction pathways of the [H3 CO]+ system have been reported. 28 A weak temperature dependence of the rate constants for the H3+ + CO reaction was found in an ab initio molecular dynamics study. 30 Further, 26 % and 8 % of HOC+ formation was predicted at 298 K and 20 K temperatures, respectively, in the same work. Trajectory simulations of H3+ + CO collision dynamics on an interpolated analytic potential energy surface were performed by Le et al. 32 They reported 40 - 43% of HOC+ formation at temperatures 75 - 300 K for a range of collision energies. Klippenstein et al., 31 combined high level electronic structure methods with statistical rate constant calculations and predicted 38 % and 19 % of HOC+ formation at T = 300 K and 20 K, respectively. + + + − → The HCO+ − ← − − HOC isomerization reaction may influence the observed HCO /HOC

abundance. Highly accurate electronic structure calculations characterizing the energy profiles of these reactions are available in the literature. 28,35,36 Li et al., 28 found that HCO+ isomer is stable by 37.7 kcal/mol with respect to HOC+ at the benchmark CCSD(T)/CBS level of theory. Further, they reported 77.1 and 36.9 kcal/mol energy barriers for the forward (HCO+ −−→ HOC+ ) and the backward reactions, respectively. Hence, these reactions

3



require large activation energies. However, in presence of a catalyst the barrier for these reactions reduce and even vanish in presence of certain molecules such as HF and N2 . 24,37 These studies have shown that the catalyst molecules act as carriers of proton transporting it from C to O end and vice versa. Due to the abundance of hydrogen molecule in space, the H2 assisted isomerization reaction H2 + HOC+ −−→ H2 + HCO+ has been considered as a source of depletion of the isoformyl cation in the interstellar media. 25,29 However, smaller rate constants have been reported for this reaction under 100 K temperatures. 23 Note that a roaming mechanism for the H2 catalyzed HOC+ isomerization reaction has been proposed. 33 Carrascosa et al., 34 have reported a crossed beam velocity map imaging study of the H3+ + CO reaction. The dynamics of this reaction was studied for a range of collision energies (Erel = 0.2 - 4.3 eV) and the product branching ratios were estimated by fitting a sum of two distribution functions to product internal energy distributions measured in experiments. Less than 10 % of HOC+ formation was predicted at low collision energies and a maximum of 24 % was estimated at Erel = 1.8 eV. For Erel greater than 1.8 eV, + − → the measured product internal energies were above the HCO+ − ← − − HOC isomerization

barriers and a distinction between the isomer populations could not be performed. Further, a high degree of product internal energy excitation was observed in the experiments. In the present work, we report classical chemical dynamics simulations performed for the H3+ + CO bimolecular reaction. The simulation conditions were set to mimic the aforementioned crossed beam experiments. 34 The objectives of the present work are to investigate atomic level reaction mechanisms, HCO+ /HOC+ branching ratios as a function of Erel , product internal energy (Evib + Erot ) distributions, etc. The simulations were carried out using the direct dynamics 39–41 methodology i.e., on-the-fly integration of classical equations of motion using potentials and gradients computed from a chosen electronic structure theory. The article is organized as follows. Computational details and potential energy surface are discussed in the next Section. This is followed by a detailed Results and Discussion and a brief Summary of the article. Supporting Information containing details of the electronic

4


Page 4 of 25

Page 5 of 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


structure calculations, trajectory snapshots, etc., is also provided.

Computational Methodology The direct dynamics simulations were performed using the density functional PBE0/aug-ccpVDZ level of electronic structure theory and this was decided based on the relatively less computational time requirements for density functional theory. Further, stationary point energies on the [H3 CO]+ potential energy surface computed using the chosen level of theory were close to those reported using the benchmark CCSD(T)/CBS method. 28 The detailed potential energy profile for the H3+ + CO −−→ HCO+ /HOC+ + H2 reaction is presented in Figure 1(a) wherein the energies are given in units of kcal/mol without zero point energy corrections. A comparison of the potential energy profiles computed using the PBE0/augcc-pVDZ and the CCSD(T)/CBS methods is given in Supporting Information. The proton transfer from H3+ to CO results in either formyl or isoformyl cation. These reactions are barrierless and exoergic (due to the low proton affinity of H2 ) and proceed via a transition state that lies 4.9 kcal/mol below the reactants. Without zero point energy correction, the H2 + HCO+ and H2 + HOC+ products have energies -40.4 and -0.9 kcal/mol, respectively, with reference to the separated reactants. Reaction pathways incorporate weak product complexes (H2 ... HCO+ and H2 ... HOC+ ) which dissociate as final products. The formyl cation is stable by 39.5 kcal/mol with respect to the HOC+ ion. The isomerization reaction HCO+ −−→ HOC+ has an energy barrier of 75.4 kcal/mol and the reverse reaction has a + − → barrier of 35.9 kcal/mol. Energy profile for the HCO+ − ← − − HOC isomerization reaction

is given in Figure 1(b). The electronic structure calculations discussed here were performed using the package NWChem. 42 Details of the dynamics simulations are briefed here. For the trajectory initial conditions, normal mode vibrational energies and thermal rotational energies for the H3+ molecule were chosen from a 300 K Boltzmann distribution. 43 To the diatomic CO molecule, zero point

5



vibrational energy (v = 0) and zero rotational energy was added. Initial center-of-mass separation between H3+ and CO molecules were kept at 10.0 Å and the impact parameter for the collisions was randomly chosen between 0.0 and 4.0 Å. This maximum value was selected based on reactivity observed in trajectories and it was sufficient for all collision energies except at the lowest value. However, we chose the above mentioned range of impact parameters uniformly at all energies. The reactants H3+ and CO were randomly oriented in each trajectory. At five different collision energies Erel = 0.2, 0.6, 1.8, 2.7, and 4.3 eV, an ensemble of trajectories were generated. These initial conditions were chosen in accordance with the crossed beam experiments on the H3+ + CO reaction by Carrascosa et al. 34 The trajectories were propagated to 2.0 ps or until reaction products were separated by a minimum distance of 12.0 Å. Trajectory integrations were carried out using a 6th order Symplectic integrator 44,45 with a step size of 0.5 fs. The trajectory calculations were performed using the general chemical dynamics program VENUS 46,47 coupled with the NWChem 42 electronic structure theory package. (a)

0

E (kcal/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 6 of 25

-20

-40

(b)

(0.0) 0.0 + H3 + CO

+

(-3.6) -4.9 +# [H3...CO]

(-2.4) -0.9 + H2 + HOC (-17.6) -19.0 + H2...HOC (-44.3) -47.0 + H2...HCO

(72.3) 75.4

75

[HCO]

(38.3) 39.5 + HOC

50 (-40.7) -40.4 + H2 + HCO

+#

25 0

(0.0) 0.0 + HCO

Figure 1: Potential energy profiles for (a) the bimolecular reaction H3+ + CO −−→ + − → HCO+ /HOC+ + H2 and (b) HCO+ − ← − − HOC isomerization reaction. Energies given are in units of kcal/mol and without zero point energy corrections. Also, zero point corrected energies are given in brackets. The calculations were performed using density functional PBE0/aug-cc-pVDZ level of theory.

6


Page 7 of 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


Simulation Results A total of 5000 trajectories (1000 trajectories at a given Erel ) were generated. Total energy (Etot ) in the trajectories was conserved within Etot ±1.0 kcal/mol during the integration. The trajectories were analyzed for reaction mechanisms, branching ratios, energy distributions, and scattering angles. Detailed discussions of the trajectory results are presented below. NHCO+/NHOC+

4

750

2

0

500

0

4

2

Nr NHCO+ NHOC+

250

0 0

4

2 Erel (eV)

Figure 2: Number of reactive trajectories (black circles), trajectories resulting in HCO+ + H2 (red squares), and HOC+ +H2 (blue triangles) as a function of relative energy Erel . The inset (black diamonds) shows branching ratios between HCO+ and HOC+ products as a function of Erel .

Reactivity and Branching Ratio Table 1 and Figure 2 show summary of observed trajectory events. Overall reactivity was dependent on the collision energy and decreased with increase in Erel . The H3+ +CO reaction is barrierless and exoergic (see Figure 1) and does not need activation. At the lowest Erel (0.2 eV), 80.0 % of the trajectories were reactive and at the highest Erel (4.3 eV) reaction occurred only in 19.1 % of the trajectories. At high Erel values, the reactants do not spend sufficient amount of time in close proximity for the proton transfer to take place - they fly off of each other (except at very low impact parameters). Reactivity enhances at low collision 7



Page 8 of 25

energies as seen from Figure 2. The reactive trajectories were classified as either HCO+ or HOC+ trajectory (listed as NHCO+ and NHOC+ in Table 1) depending upon which isomer it + − → resulted upon collision. The subsequent HCO+ − ← − − HOC auto-isomerization, if happened

in a trajectory, was ignored while classifying the trajectory. Note that only at the highest collision energy, an appreciable fraction of trajectories (≈ 10 %) showed isomerization. The high energy HOC+ isomer resulted in less number of trajectories in comparison to the HCO+ isomer as shown in Table 1. For Erel = 0.2, 0.6, 1.8, 2.7, and 4.3 eV, the computed branching ratios (NHCO+ /NHOC+ ) were 1.9, 3.1, 2.5, 2.8, and 2.4, respectively. At all energies, HCO+ dominated over HOC+ and the branching ratios did not show any particular trend with Erel .

Table 1: Summary of Trajectory Events Following H3+ +CO Bimolecular Collisions. NHCO+ (c)

NHOC+ (d)

NHCO+ NHOC+

800

527(65.9±1.7%)

273(34.1±1.7%)

1.9

0

1000

561

425(75.8±1.8%)

136(24.2±1.8%)

3.1

0

1.8 eV

1000

318

228(71.7±2.5%)

90(28.3±2.5%)

2.5

1

2.7 eV

1000

250

184(73.6±2.8%)

66(26.4±2.8%)

2.8

4

4.3 eV

1000

191

135(70.7±3.3%)

56(29.3±3.3%)

2.4

19

Erel

N(a)

Nr (b)

0.2 eV

1000

0.6 eV

Niso (e)

(a)

number of trajectories generated at a given Erel

(b)

number of reactive trajectories

(c)

number of trajectories forming H2 + HCO+ . The quantity in brackets is (NHCO+ /Nr )× 100% and

the associated error bar (d)

number of trajectories forming H2 + HOC+ . The quantity in brackets is (NHOC+ /Nr )× 100% and

the assiciated error bar (e)

+ − → number of trajectories showing HCO+ − ← − − HOC isomerization

8


Page 9 of 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


Product Energy Distributions From the trajectories, vibrational (Evib ) and rotational (Erot ) energies of the reaction products were computed by two different methods. In the first method, all the reactive trajectories were included while calculating the product energies without using any zero point energy (ZPE) constraint. In the second, only those trajectories satisfying a "soft" ZPE constraint 48,49 were used. According to this constraint, trajectories in which the sum of product vibrational energies was greater than the total zero point energies of the products were to be considered. Total ZPE of HCO+ + H2 and HOC+ + H2 products are 0.66 eV and 0.61 eV, respectively. Internal energy Eint (= Evib + Erot ) distributions of the HCO+ and HOC+ isomers are presented in Figure 3 wherein first row shows Eint distributions of HCO+ and HOC+ products computed using all the reactive trajectories. Second row presents similar data computed from those trajectories which satisfied the ZPE constraint. In the third row, normalized and ZPE constrained energy distributions are shown for only HCO+ isomer and the fourth row shows similar data for HOC+ . Each column corresponds to a given Erel . Energy distributions without the ZPE constraint (first row) are presented for comparison only and for discussion purposes the ZPE constrained data are used. Internal energy distributions shown in Figure 3 agree qualitatively with the experimental distributions (Figure 1 of reference 34). Energy distributions from the simulations are peaked at slightly lower values in comparison to the corresponding experimental data. Nonetheless, simulations indicate a high degree of internal excitation in agreement with the experimental work. Such high internal energy transfers were observed in a few other proton transfer reactions also. 50,51 Energy distributions of HCO+ and HOC+ products shown in the second row of Figure 3, are essentially monomodal in agreement with experiments. It was proposed in the experimental work 34 that the monomodal distribution was a result of overlapping energy distributions of HCO+ and HOC+ isomers. One can observe from Figure 3 that the individual isomer energy distributions (shown in third and fourth rows) when combined and normalized result in the observed monomodal energy distributions. The experimentally observed width of the Eint 9



distributions was ascribed to the intrinsic reaction dynamics i.e., varying energy partitioning among the degrees of freedom of the reaction products for different collision events rather than experimental factors such as the uncertainty in Erel . This prediction also agrees with our calculations. Clearly, the spread observed in the experimental plots are also seen in the simulation results presented in Figure 3. This spread increases with increase in Erel and is a result of multiple pathways by which the available energy was distributed among the translational, vibrational, and rotational degrees of freedom of the reaction products. 0.6 eV

0.2 eV

Probability

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 10 of 25

2.7 eV

1.8 eV

4.3 eV

0.9

0.9

0.9

0.9

0.9

0.6

0.6

0.6

0.6

0.6

0.3

0.3

0.3

0.3

0.3

0

0

0

0

0

0.9

0.9

0.9

0.9

0.9

0.6

0.6

0.6

0.6

0.6

0.3

0.3

0.3

0.3

0.3

0

0

0

0

0

0.9

0.9

0.9

0.9

0.9

0.6

0.6

0.6

0.6

0.6

0.3

0.3

0.3

0.3

0.3

0

0

0

0

0

0.9

0.9

0.9

0.9

0.9

0.6

0.6

0.6

0.6

0.6

0.3

0.3

0.3

0.3

0.3

0

0 0

1

2 3 Eint(eV)

4

5

0 0

1

2

3

4

5

0 0

1

2

3

4

5

0 0

1

2

3

4

5

0

1

2

3

4

Figure 3: First row shows normalized internal energy (Eint = Evib +Erot ) distributions of HCO+ and HOC+ products computed using all the reactive trajectories. Second row shows normalized Eint distributions from only those trajectories satisfying the soft ZPE constraint. Third row shows normalized and ZPE constrained Eint distributions for only HCO+ isomer and the fourth row shows similar data for only HOC+ isomer. x-axes ranges are identical in all the plots and Erel is fixed for a given column.

A qualitative understanding about which rovibrational modes of the reaction products are excited can be achieved by analyzing the Erot and Evib of both ionic (HCO+ and HOC+ ) and neutral (H2 ) products. Trajectory averaged Eint , Erot , and Evib of the HCO+ and HOC+ 10


5

Page 11 of 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


isomers are presented in Figures 4(a) and (b), respectively. The insets in these figures show similar data for the associated H2 product. Clearly, internal energy transfer is substantial for the ionic products and minimum for the neutral product H2 irrespective of Erel . Further, HCO+ and HOC+ are vibrationally more excited than the rotational degrees of freedom. Specifically, the bending modes were excited as observed from visualization of the trajectories. Fraction of energy transfer to the rovibrational degrees of freedom of HCO+ and HOC+ was computed from the trajectories. A quantity fint defined as the trajectory averaged ratio of Eint of HCO+ and HOC+ and the available (kinetic) energy is plotted in Figure 4(c) as a function of Erel . This figure can be compared directly with the experimental data given in Figure 2 of reference 34. Though the fractions computed from the simulations are slightly lower in comparison to experiments, the qualitative behavior remains the same i.e., fint decreases slowly with increase in collision energy. Further, the quantity fint was computed for specific ranges of product scattering angles θ and plotted in Figure 4(c) (a discussion about product scattering angle distributions is given in the next Section). In Figure 4(c), red squares, green squares, and blue diamonds correspond to the θ ranges (0-20◦ ), (30-50◦ ), and (60-80◦ ), respectively. Clearly, the trend of decrease in fint with Erel remains nearly the same for different ranges of scattering angles in agreement with experiments 34 which indicates that the internal energy transfer is independent of scattering angle. As discussed in the next section, the scattering angle distributions computed from the trajectories showed that forward scattering was dominant at all Erel except at the lowest value at which the distribution had a forward-backward symmetry. We computed the quantity fint from trajectories undergoing backward scattering (θ >90◦ ) and it is almost same as fint estimated from forward scattering trajectories for Erel = 0.2 eV.

Scattering Angles The product scattering angles θ and their distributions P(θ) were computed from the trajectories. The definition of θ (shown in Figure 5) is such that small values of θ indicate forward 11



(a)

(b)

Eint Evib

3

Evib

3

Erot

2

Total o θ = 0-20 o θ = 30-50 o θ = 60-80

(c)

Eint

Erot

E (ev)

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 12 of 25

0.9

fint

2

0.6 1

1

0.3

+

HCO

0 0

2

Erel (eV)

4

+

HOC

0 0

2

Erel(eV)

4

0 0

2

Erel(eV)

4

Figure 4: (a) Trajectory averaged HCO+ rotational energy (Erot , blue squares), vibrational energy (Evib , red triangles), and internal energy (Eint , black circles) are plotted as a function of Erel (b) similar data for HOC+ . The insets in (a) and (b) show similar data for H2 . (c) Trajectory averaged fraction (fint ) of total energy being transferred as internal energy to the ionic reaction products (HCO+ and HOC+ ) is plotted as a function of Erel . The quantity fint is given for all scattering angles θ (black), trajectories with θ = 0-20◦ (red), θ = 30-50◦ (green), and θ = 60-80◦ (blue).

scattering (in the direction of incoming CO molecule) and large values indicate backward scattering. Figure 5 shows normalized scattering angle distributions computed from HCO+ trajectories, HOC+ trajectories, and all the reactive trajectories in the first, second, and third columns, respectively. Each row corresponds to a given Erel . In general, forward scattering was dominant except at the lowest Erel (first row) wherein an approximate forward-backward symmetry can be observed. With increase in collision energy, forward scattering becomes dominant (in agreement with experiments 34 ) with a major fraction of trajectories having θ ≤ 30◦ . These fractions are 15±1.3%, 32±1.9%, 39±2.7%, 46±3.2%, and 36±3.5%, at Erel = 0.2, 0.6, 1.8, 2.7, and 4.3 eV, respectively. These small θ values indicate a stripping type of mechanism by which the CO abstracts a proton from the H3+ molecule. This was verified by visual inspection of the trajectories.

Discussion Carrascosa et al., 34 carried out crossed beam velocity map imaging experiments on the H3+ + CO −−→ HCO+ /HOC+ + H2 reaction and predicted product ratios by fitting a sum 12


Page 13 of 25

+

+

HCO 0.2 eV

HOC

+

+

90

180

HCO + HOC

0.6 eV

1.8 eV

2.7 eV

4.3 eV

0.9

P(θ)

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


0.6 0.3 0 0

90

θ

180 0

90

180 0

Figure 5: Normalized product scattering angle distributions computed from HCO+ trajectories, HOC+ trajectories, and total reactive trajectories are shown in first, second, and third columns, respectively. Erel is the same in a given row. Respective axes ranges are same in all the plots.

13



Page 14 of 25

of two distribution functions to the measured Eint distributions. It was assumed that the relative energy loss for both the isomer channels is same in this fitting procedure. They estimated a maximum of 24 % of HOC+ formation at Erel = 1.8 eV and less than 10 % at the two lower Erel values. The fitting was not done at higher collision energies as the reaction products had Eint greater than the isomerization barriers and a distinction between the two isomers was not possible. 34 In our simulations, 34.1, 24.2, 28.3, 26.4, and 29.3 % of HOC+ formation was observed at Erel = 0.2, 0.6, 1.8, 2.7, and 4.3 eV, respectively (see Table 1). Larger fractions of the high energy HOC+ isomer formation at low Erel was observed in simulations in contrast to experimental predictions. Such high fractions of HOC+ have been reported in previous theoretical studies. Le et al., 32 predicted 40 - 43 % of HOC+ in a classical trajectory study of the H3+ + CO reaction on an interpolated potential energy surface. This study was performed at temperatures 75 - 300 K and with relative collision energies below 0.2 eV. Further, 26 % of HOC+ was predicted 30 in an ab initio molecular dynamics study performed at 298 K temperature and 38 % was reported by Klippenstein et al., 31 based on electronic structure theory and statistical rate constant calculations. To investigate further this discrepancy between the experimental and computed branching ratios at low Erel values, we tested the assumption used in the fitting procedure in the experimental work. 34 It was assumed that the relative energy loss for the two isomer +

+

+

+

+

HCO HCO HOC HOC HCO channels is same i.e., < Eint > /Emax =< Eint > /Emax where < Eint > and +

+

HOC HCO > are average internal energies taken from Figure 4 and Emax = Erel −(−1.75 eV) < Eint HOC and Emax

+

= Erel − (−0.04 eV). Here, -1.75 and -0.04 eV are the exoergicities of the

HCO+ and HOC+ isomer formation pathways, respectively (see Figure 1). Results of these calculations are summarized in Table 2 which shows that the assumption may not be valid at low collision energies. With increase in Erel , relative energy loss for both the isomer channels are becoming roughly equivalent. Note that at Erel = 1.8 eV, simulations show 28.3 % of HOC+ while the experimental prediction is 24.0 %. It is possible that the branching ratios found from simulations and experiment might be similar at the high collision energies (2.7

14


Page 15 of 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


and 4.3 eV) though branching ratios were not reported in the experiment for these energies.

Table 2: Relative Energy Loss for the two Isomer Channels. +

+

Erel

HCO >

Direct Chemical Dynamics Simulations of H3+ + CO Bimolecular

Recommend Documents