Quasiclassical Study of the C(3P)

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Quasiclassical Study of the C(P) + NO(X#) and O(P) + CN(X#) Collisional Processes on an Accurate DMBE Potential Energy Surface Marcelo Vieira Alves, Cayo Emilio Monteiro Goncalves, Joao Pedro Braga, Vinícius C. Mota, António J.C. Varandas, and Breno R. L. Galvão J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.9b03860 • Publication Date (Web): 29 Jul 2019 Downloaded from pubs.acs.org on July 29, 2019

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The Journal of Physical Chemistry

Quasiclassical Study of the C(3P ) + NO(X 2Π) and O(3P ) + CN(X 2Σ+) Collisional Processes on an Accurate DMBE Potential Energy Surface M. V. Alvesa , C. E. M. Gon¸calvesa , J. P. Bragaa , V. C. Motab , A. J. C. Varandasc,d * and B. R. L. Galvãoe *∗ a

Departamento de Qu´ımica, Universidade Federal de Minas Gerais, 31270-901, Belo Horizonte, Brazil

b

Departamento de F´ısica, Universidade Federal do Esp´ırito Santo, 29075-910 Vitória, Brazil

c

School of Physics and Physical Engineering, Qufu Normal University, 273165 Qufu, China

d

Coimbra Chemistry Centre and Chemistry Department, University of Coimbra, 3004-535 Coimbra, Portugal.

e

Centro Federal de Educa¸cão Tecnológica de Minas Gerais, CEFET-MG, Av. Amazonas 5253, (30421-169) Belo Horizonte, Minas Gerais, Brazil. E-mail: [email protected](A.J.C.V.),[email protected](B.R.L.G.)

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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 predicted rate constants for C + NO and O + CN collisions in three potential energy surfaces (PESs) for the 2 A0 state of the CNO molecule are compared using quasiclassical trajectories. Different temperature dependencies are obtained for the C+NO reaction, which are explained in terms of the long range properties of the PESs. Recommended values and mechanistic details are also reported. For O+CN collisions, a better agreement between the theoretical results is found, except for temperatures below 100 K.

1

Introduction

Gas phase reactions involving second-row elements of the periodic table are widely observed in atmospheric, combustion and interstellar conditions. Specifically, carbon, nitrogen and oxygen are abundant in such environments, and hence a potential energy surface (PES) describing the interaction of these three atoms is important for quantitatively predicting their reaction dynamics. In fact, the CNO PES describes very important reactions, with all involved diatomic molecules (NO, CO, CN) playing key roles in chemistry. Nevertheless, only a few global PESs are available for the CNO molecule, 1–7 and there is no agreement on their calculated properties. Indeed, only in 2018 have PESs been modeled for the title reactions from accurate multireference calculations. 6,7 Recently, 7 we reported a global ab-initio based PES for the 2 A0 state of CNO 7 from the double many-body expansion 8–11 (DMBE) method, hereinafter denoted as GGMBV from the authors’ initials, using highly accurate explicitly correlated multireference configuration interaction (MRCI-F12 12–14 ) calculations and the cc-pVQZ-F12 basis set. Since most reactions described by this PES occur without a reaction barrier, an accurate description of long range-interactions is mandatory for the dynamics studies. This has been explicitly taken into consideration by describing the involved electrostatic and dispersion interactions within the DMBE formalism. 2


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In this work, we elaborate further one the above topic by reporting a comparative study of the title collisional processes using the three most recent 2 A0 PESs, namely the one of Andersson, Markovic and Nyman 3 (AMN) based on CASPT2 energies, that of Koner, Bemish and Meuwly 6 (KBM) based on MRCI/aug-cc-pVTZ data, and our own 7 (GGMBV) based on MRCI-F12/cc-pVQZ-F12 calculations (which shows an overall root mean squared error of 0.99 kcal mol−1 ). The quasiclassical trajectory (QCT) method is employed for the endeavour, with the neglect of quantum effects being justified by the large masses of all atoms involved. Indeed, it has been shown that QCT successfully reproduces the results of quantum mechanical calculations for the title system. 6 The paper is organized as follows. Section 2 gives details on the QCT approach. The results for the C+NO collisional process are in section 3, while section 4 provides the O+CN ones. The concluding remarks are in section 5.

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Quasiclassical trajectories

We have employed the QCT 15,16 method for integrating trajectories at selected temperatures. Each batch consisted of 25000 trajectories, with the sampling of the relative atom-diatom translational energy, as well as the rovibrational quantum state of the diatomic reactant determined from the appropriate distribution at the fixed temperature. The integration employed a time step of 0.2 fs, and the maximum value of the impact parameter (bmax ) has been chosen by trial and error for each temperature. Accordingly, the Monte-Carlo integrated rate coefficient for each process assumes the form k(T ) = ge (T )

8kB T πµ

1/2

N πb2max

r

N

(1)

where kB is the Boltzmann constant, µ is the reduced mass of the reactants, and N r /N is the fraction of reactive trajectories. In turn, ge (T ) is the electronic degeneracy factor which is specific for each collision being studied, while the 68 % error bar associated with 3



the trajectory sampling is given by ∆k = k

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N −N r 1/2 . r NN

For the C(3 P )+NO(X 2 Π) collisional process the electronic degeneracy factor is extracted from the partition functions Q as ge (T ) = QC−NO /QC(3 P ) QNO(2 Π) , leading to:

ge (T ) =

1 + exp (−23.6/T ) [1 + 3 exp (−23.6/T ) + 5 exp (−62.4/T )] [2 + 2 exp (−172.4/T )]

(2)

In turn, for O(3 P )+CN(X 2 Σ+ ), QO−CN = 1 and QCN(X2 Σ+ ) = 1, with such a factor commonly assuming the simpler form:

ge (T ) =

1 5 + 3 exp (−228/T ) + exp (−326/T )

(3)

To elucidate the contributions of the NCO and CNO isomers in the mechanisms of each reaction, we have monitored the geometry and potential energy at each integration step along the trajectories that have been run. First, to ensure that only bound regions are counted, we consider to have formed a complex only whenever the potential energy of the aggregate is less than 2 kcal mol−1 below the lowest asymptotic channel. If such a criterion is met, it is certain that we are either at the NCO or CNO basins of attraction, with subsequent differentiation between the two forms then carried out via geometric parameters. Specifically, if the NO distance is larger than the CO one, a NCO complex is considered to have been formed, otherwise CNO is formed instead. Two representative trajectories for C+NO collisions are illustrated in Fig. 1, which employs a relaxed triangular plot 17 in scaled hyperspherical coordinates, β ? = β/Q and γ ? = γ/Q: 







1  Q   1 1     β  =  0 √3 −√3       γ 2 −1 −1

R12



      R2   2    R32

(4)

where Q is a variable that relates with the perimeter of the triangle formed by the three atoms, and β ? and γ ? define the shape of the molecular triangle. 4


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Figure 1: Relaxed hyperspherical plot of the GGMBV PES using the coordinates of Eq. 4. The zero of energy is set as the highest lying dissociation channel (C+NO). Solid lines correspond to energies below this limit while dashed ones are above. Contours are spaced by 0.2 eV, starting at ±0.1 eV (the plus sign refers to positive contours, while the minus sign refers to negative ones). Two trajectories are ploted, C+NO→O+CN (black) and C+NO→N+CO (red).

3

Collisions of ground state C atoms with NO

Trajectories have been integrated from 15 to 10000 K, with the numerical values of all calculated rate constants given in the Supporting Information (SI). A graphical comparison between the reaction rate constants predicted from the three most recent PESs 3,6,7 (all using the electronic degeneracy factor of Eq. 2) is given in Fig. 2. As can be seen, all results agree in that C+NO→O+CN is the dominant reactive channel, even though formation of N+CO is energetically favored. This happens because the C+NO interaction leads barrierlessly to the deep CNO minimum, from which N+CO cannot be formed directly. This reaction can only happen via CNO ↔ NCO isomerization (see illustrative isomerizing trajectory in Fig. 1) or by overcoming the barrier via a direct abstraction mechanism through the CON region. Note that the isomerization barrier lies lower in energy than the C+NO limit, and hence this channel is open for whatever temperature. Despite the agreement in favor of the C+NO→O+CN channel, the numerical values of the rate coefficients and its temperature dependence differ largely among the three PESs. 5



Specifically, the AMN PES 3 shows a strong increase in the rate coefficient for low temperatures, a behavior similar to that displayed by the KBM PES 6 although less compelling. On the other hand, the results from the GGMBV PES 7 show no significant temperature dependence (upper panel in Fig. 2). It has been shown in Ref. 6 (Fig.7) that the KBM results overestimate the experimental rate constants 18 at low temperatures, which appears to support the findings here reported. All PESs seem to agree on the high temperature limit.

In order to understand the above discrepant results, the features of the PESs must be compared. Consider first the C+NO→O+CN reactive channel. As can be seen from Fig. 3 (panels a, b and c), no entrance barrier is present in the three PESs when the C atom approaches the N atom side of NO, with the acceptance cone being similar in all them. Therefore, the magnitude of the rate constant will depend largely on the long range (electrostatic and dispersion) behavior of the PES at intermediate and large separations. Note that the GGMBV PES 7 explicitly incorporates electrostatic (R−4 and R−5 ) and dispersion energy terms (R−6 , R−8 and R−10 ) in the functional form. For modeling these terms, dipolar polarizabilities as well as quadrupolar and dipolar moments were calculated at the MRCIF12/cc-pVQZ-F12 level as a function of the internuclear distance of the diatomic molecules, and modeled (reliably, albeit approximately) using the DMBE formalism. 7 Similar energy terms were employed in the AMN PES, 3 but they were apparently used to generate points for a subsequent polynomial fit, thus not including R−n explicitly. In turn, the KBM PES, 6 was interpolated with the reproducing kernel Hilbert space (RKHS) method, which smoothly decays to zero as R−6 . The different temperature dependence observed on the rate constants for the C+NO→O+CN reaction for the GGMBV PES may therefore be largely ascribed to the different and more precise treatment of the long range interactions included in this PES.

Fig. 4 shows a more quantitative view of the aspects described in the previous paragraph by comparing the GGMBV PES 7 with AMN. 3 This plot shows also ab initio energies calcu-

6


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8.0 C+NO → O+CN 6.0 4.0 2.0 0.0 1.8

k(T)/10−11 cm3 s−1

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


C+NO → N+CO this work Anderson et al. Koner et al.

1.2

0.6

0.0 9.0 C+NO → products 6.0

3.0

0.0 1.0

1.5

2.0

2.5

3.0

3.5

4.0

log10(T/K) Figure 2: Rate coefficients for the two channels of C(3 P )+NO(X 2 Π) collisions on the 2 A0 electronic state and their sum (lower panel), on three different analytic potential energy surfaces 3,6,7

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KBM (2018)

GGMBV (2018)

AMN (2000) (b)

(c)

(d)

(e)

(f)

(g)

(h)

(i)

O+CN

C+NO

(a)

N+CO

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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Figure 3: Contour plot for an atom moving around a diatom fixed at equilibrium bond distance on three PESs of the 2 A0 state 3,6,7 . Red contours correspond to energies below the dissociation limit (set as zero) while blue ones correspond to positive energies. As in Figure 1, both are spaced by 0.2 eV and start at ±0.1 eV. The left panel was adapted from Ref. 6

8


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lated at the MRCI/aug-cc-pVTZ level of theory (employed in the KBM PES), and MRCIF12/cc-pVQZ-F12 (employed in GGMBV.) As seen, the AMN PES has a very heavily tailed long range term, which may explain its very large rate coefficients for lower temperatures (at which the long-range interactions are most relevant). Although the main plot shows the potential energy for a collinear approach, which is the minimum energy path, the isotropic and leading anisotropic terms in a Legendre expansion of the atom-diatom interaction potential are also relevant; these are shown as inset in Fig. 4, where the heavy tail trend of the AMN PES is shown to persist both in the isotropic and anisotropic components of the interaction.

energy/kcal mol

−1

0

−20

−40

0 −3 −6 −9

(a)

−12

−1

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Vn/kcal mol

energy/kcal mol−1

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−60

6

7

8

V0

−5

AMN (2000) GGMBV (2018) −10 GGMBV long range MRCI−F12/cc−pVQZ−F12 MRCI/aug−cc−pVTZ

−80

5

0

V2

4

(b)

5

6

7

8

−100 2

3

4

5

6

7

RC−NO/a0

Figure 4: Collinear profile for a C atom attacking NO via the N atom for GGMBV 7 and AMN 3 PESs. Inset (a) shows a zoom at the long-range part, and inset (b) the isotropic (V0 as solid lines) and leading anisotropic (V2 in dashed) components of the C-NO interaction potential.

Regarding the C+NO→CO+N channel (middle panel in Fig. 2), it can happen via two mechanisms: (i) isomerization (C+NO→CNO→NCO→N+CO) as illustrated in Fig. 1 or (ii) direct abstraction with the C atom attacking the O end of the diatom (C+ON→CO+N). In the latter case, there is a small barrier (named SP3 in Ref. 7) to overcome, which lies 0.13 eV above reactants on the GGMBV PES, and 0.03 eV on the AMN one. This can be seen in Fig. 3 for the GGMBV and KBM PESs (blue contours near x ≈ 5 a0 ) but is absent in the

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AMN PES (its height is lower than the first shown positive contour of the plot). Due to this barrier, mechanism (ii) must be closed for low temperatures, and should open only when the collision energy becomes enough for overcoming it: this should happen around kT = 0.13 eV, which corresponds to a temperature of about 1500 K. This may be seen from the middle panel of Fig. 2, where the two slopes can be clearly distinguished, each corresponding to a different mechanism. The temperature at which path (ii) opens corroborates the above prediction and has apparently not been pointed out before. For a more quantitative view of this aspect, we have separated the portion of the total C+NO→N+CO rate constant that corresponds to trajectories that entered both CNO and NCO wells (mechanism (i)) from the ones that entered none of them [mechanism (ii)]. The results are shown in Fig. 5, which clearly indicates that the overall rate constant can indeed be decomposed in the above two contributions. Since mechanism (ii) involves a reaction barrier while (i) does not, it is expected to show a stronger temperature dependence, a trend that is also visible from this Figure.

This plot shows also that for temperatures higher than 3600 K, mechanism (ii) is

even dominant over mechanism (i). 1.20

C+NO → N+CO 1.00

k(T)/10−11 cm3 s−1

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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mechanism (i): C+NO → CNO →NCO→ N+CO 0.80

mechanism (ii): C+NO → N+CO (no energy minimum) mechanism (i) + mechanism (ii)

0.60 kT=0.13eV

0.40

0.20

0.00 1.0

1.5

2.0

2.5

3.0

3.5

4.0

log10 (T/K)

Figure 5: Contributions to the rate constant from trajectories that passed all or none CNO and NCO complexes, as discussed in the text, section 2.

A final remark is now made on the direct mechanism (ii). Although the SP3 barrier 10


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occurs for a collinear C-ON attack, for bent configurations (∠CON angle of 120◦ ) this barrier gives rise to a conical intersection between ground and excited 2 A0 states, which shows as a cusp in the adiabatic potentials. In normal and smooth PESs, this is usually modeled as a maximum (second order saddle point). However, we have developed a scheme for accurately embedding the cusp caused by such intersections, 19,20 with our PES being the only one that describes it explicitly; its impact on the PES can be seen in Fig. 6 and its location is given in Fig. 1 (green dot). Due to the presence of such a cusp, the GGMBV PES should provide a more realistic adiabatic form for describing mechanism (ii), specially for temperatures above 1500 K, where the trajectories have enough energy to reach this region of the PES.

R

Figure 6: Attack of a C atom to a NO molecule fixed at its equilibrium geometry along a valence angle of 120◦ . Clearly visible is the conical intersection between the ground and excited 2 A0 states. Recall that the GGMBV PES is fitted using a method that allows for a correct description of the cusp behavior, a feature commomnly smoothed out in most adabatic potentials, as illustrated in the plot for the AMN PES.

Note that the AMN PES predicts larger rate constants in the low temperature region, where the CNO→NCO isomerization mechanism is dominant. This can be explained by the high probability of trajectories forming the CNO structure (which must happen in this mechanism) as expected from the very strong long range tail in the AMN PES (see Fig. 4).

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4

Collisions of ground state O atoms with CN

In the work of Koner et al., 6 the rate constants for this collisional process on the KBM surface have not been reported, and hence we have only compared the results from the AMN PES 21 with our own in GGMBV (numerical values are included in the SI). It can be seen from Fig. 7 that both PESs yield very similar results from 100 to 3000K, decreasing with temperature in this range as expected in a reaction without a potential energy barrier. Both PESs show a maximum on the rate coefficients around 100K, with a sharper peak occurring for the AMN PES. The major differences between the two sets of results is therefore in the low temperature limit, with our results displaying a significantly larger reactivity. The features of both PESs can be seen in Fig. 3 (panels e and f). 8 GGMBV (This work) AMN

O+CN → products 7

k(T)/10−11 cm3 s−1

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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6

5

4

3

2 0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

log10 (T/K) Figure 7: Rate coefficients for O(3 P ) + CN(X 2 Σ+ ) collisions on the 2 A0 electronic state GGMBV 7 and AMN 3 PESs.

For these collisions, significant recrossing rates have been predicted by Frankcombe et al. 22 which could be reducing the overall reactivity. Unlike the collisions described in the previous sections, the direct formation of NCO and CNO complexes are available (see Fig. 1 for a global perspective on the mechanisms). If the CNO minimum is reached first, it 12


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will likely recross according to O+CN→CNO→O+CN, because C+NO formation is highly endothermic. Therefore the main reactive channel is likely to be O+CN→NCO→N+CO, which was confirmed by analyzing the number of trajectories that occurred through each minimum. This is shown in Fig. 8, from where it can be seen that this mechanism is dominant over the whole temperature range. It can also be seen from this plot that trajectories that go only through the CNO complex (blue points) do not contribute to reaction, as they will recross as argued above. In fact, recrossing becomes very important after 1000 K. An isomerization mechanism O+CN→CNO→NCO→O+CN is also available (green points) but, as can be seen from this Figure, its contribution is lower than formation via a direct path. 7

O+CN 6

k(T)/10−11 cm3 s−1

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


5 4

reactive via NCO

3

reactive via NCO and CNO (isom.) reactive via CNO recrossing (nonreactive)

2 1 0 0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

log10 (T/K)

Figure 8: Rate constants for O+CN reaction through different paths and recrossing rate constant. See section 2 for the definition of each path.

Differently from the results of the previous section, both GGMBV and AMN PESs agree quite well on the long range behavior for NCO formation (the preferred mechanism), which can be seen in Fig. 9. This is true both for the collinear path shown in inset (a), as well as for the isotropic and anisotropic contributions of inset (b). The differences in rate constants for the low temperature region are then likely to be due to the fact that the AMN PES shows a stronger preference for the O+CN→CNO→CN+O recrossing path. This preference for the CNO formation can be appreciated in the right hand side of panels e and f of Fig. 3 13



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−80 −100

−10

AMN (2000) −20 GGMBV (2018) MRCI−F12/cc−pVQZ−F12 4.5 MRCI/aug−cc−pVTZ

−120

5.5

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V0 V2 (b) 5.5

6.5

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−140 2

3

4

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8

RNC−O/a0

Figure 9: Collinear profile for NCO formation on the GGMBV 7 and AMN 3 PESs. As in Fig. 4, inset (a) shows a zoom of the long-range regions, while inset (b) shows the isotropic (V0 as solid lines) and leading anisotropic (V2 , in dashed) components of the O-CN interaction potential.

5

Concluding remarks

Using the quasiclassical trajectory method, we have predicted the rate constants for C+NO and O+CN collisions on a new DMBE potential energy surface. The results for the C+NO→O+CN reaction show no temperature dependence, in sharp contrast with previous results. This is explained in terms of the features of the PESs, with special attention to their long-range behavior. Our results also predict larger rate constants for the low temperature limit on O+CN collisions. The mechanisms and reaction details are discussed. Finally, we note that the GGMBV PES is fitted to ab initio energies employing a higher level treatment of the electronic correlation, a larger basis set, and its functional form explicitly incorporates electrostatic and dispersion energy terms (from accurately calculated dipolar polarizabilities and quadrupolar and dipolar moments), features that are known to play a key role when describing barrierless reactions such as the title ones. Supporting Information: The numerical values of the rate constants calculated in this work are available for both C+NO and O+CN collisions.

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Acknowledgments This study was financed in part by the Coordena¸cão de Aperfei¸coamento de Pessoal de N´ıvel Superior - Brasil (CAPES) - Finance Code 001, Conselho Nacional de Desenvolvimento Cient´ıfico e Tecnológico (CNPq), grants 403352/2016-9 and 305469/2018-5, and Funda¸cão de Amparo à Pesquisa do estado de Minas Gerais (FAPEMIG), grant CEX - APQ-00071-15. BRLG is also thankful to Rede Mineira de Qu´ımica (RQ-MG), while VCM acknowledges the support of Edital 2015 do Programa institucional de Fundo de Apoio a` Pesquisa da Universidade Federal do Esp´ırito Santo and also the Edital Universal FAPES 2018. This work has also the support of Foundation for Science and Technology, Portugal, and Coimbra Chemistry Centre, Portugal, through the project UID/QUI/00313/2019. AJCV thanks also China’s Shandong Province “Double-Hundred Talent Plan” (2018).

References (1) Halvick, P.; Rayez, J.; Rayez, M.; Duguay, B. Three-atom indirect exchange reactions. II. Dynamical behaviours explained by a simple model. Chemical physics 1987, 114, 375–387. (2) Simonson, M.; Marković, N.; Nordholm, S.; Persson, B. Quasiclassical trajectory study of the C+ NO reaction on a new potential energy surface. Chemical physics 1995, 200, 141–160. (3) Andersson, S.; Markovic, N.; Nyman, G. Quasi-classical trajectory simulations of C + NO crossed molecular beam experiments. Chem. Phys. 2000, 259, 99–108. (4) Andersson, S.; Markovic, N.; Nyman, G. An improved potential energy surface for the C + NO reaction. Phys. Chem. Chem. Phys. 2000, 2, 613–620. (5) Abrahamsson, E.; Andersson, S.; Markovic, N.; Nyman, G. A new reaction path for the

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C+NO reaction: dynamics on the 4 A00 potential-energy surface. Phys. Chem. Chem. Phys. 2008, 10, 4400–4409. (6) Koner, D.; Bemish, R. J.; Meuwly, M. The C(3 P) + NO(X2 Π) O(3 P) + CN(X2 Σ+ ), N(2 D)/N(4 S) + CO(X1 Σ+ ) reaction: Rates, branching ratios, and final states from 15 K to 20000 K. J. Chem. Phys. 2018, 149, 094305. (7) Gon¸calves, C. E. M.; Galvão, B. R. L.; Mota, V.; Braga, J. P.; Varandas, A. J. C. Accurate Explicit-Correlation-MRCI-Based DMBE Potential-Energy Surface For GroundState CNO. J. Phys. Chem. A 2018, 112, 4198–4207. (8) Varandas, A. J. C. A General Approach to the Potential Energy Function of Small Polyatomic Systems: Molecules and vdW Molecules. J. Mol. Struct. Theochem. 1985, 21, 401–424 (The article has been published as part of Vol. 120 of the same journal). (9) Varandas, A. J. C. Intermolecular and Intramolecular Potentials: Topographical Aspects, Calculation, and Functional Representation via a DMBE Expansion Method. Adv. Chem. Phys. 1988, 74, 255–338. (10) Varandas, A. J. C. In Lecture Notes in Chemistry; Laganà, A., Riganelli, A., Eds.; Springer: Berlin, 2000; Vol. 75; p 33. (11) Varandas, A. J. C. In Conical Intersections: Electronic Structure, Dynamics & Spectroscopy; Domcke, W., Yarkony, D. R., Köppel, H., Eds.; Advanced Series in Physical Chemistry; World Scientific Publishing, 2004; Vol. 15; Chapter 5, p 205. (12) Shiozaki, T.; Werner, H. J. Explicitly Correlated Multireference Configuration Interaction With Multiple Reference Functions: Avoided Crossing and Conical Intersections. J. Chem. Phys. 2011, 134, 184104. (13) Shiozaki, T.; Knizia, G.; Werner, H. J. Explicitly correlated multireference configuration interaction: MRCI-F12. J. Chem. Phys. 2011, 134, 034113. 16


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(14) Shiozaki, T.; Werner, H. J. Multireference Expicitly Correlated F12 Theories. Mol. Phys. 2013, 111, 607–630. (15) Hase, W. L.; Duchovic, R. J.; Hu, X.; Komornicki, A.; Lim, K. F.; Lu, D.; Peslherbe, G. H.; Swamy, K. N.; Linde, S. R. V.; Varandas, A. J. C. et al. VENUS96: A General Chemical Dynamics Computer Program. QCPE Bull. 1996, 16, 43. (16) Peslherbe, G. H.; Wang, H.; Hase, W. L. Monte Carlo Sampling for Classical Trajectory Simulations. Adv. Chem. Phys. 1999, 105, 171–201. (17) Varandas, A. J. C. A Useful Triangular Plot of Triatomic Potential Energy Surfaces. Chem. Phys. Lett. 1987, 138, 455. (18) Chastaing, D.; Picard, S. D. L.; Sims, I. R. Direct kinetic Meansurements On Reactions Of Atomic Carbon, C(3 P), With O2 and NO at Temperatures Down to 15K. J. Chem. Phys. 2000, 112, 8466. (19) Galvão, B. R. L.; Mota, V. C.; Varandas, A. J. C. Modeling Cusps in Adiabatic Potential Energy Surfaces. J. Phys. Chem. A 2015, 119, 1415–1421. (20) Galvão, B. R. L.; Mota, V. C.; Varandas, A. J. C. Modeling cusps in adiabatic potential energy surfaces using a generalized Jahn-Teller coordinate. Chem. Phys. Lett. 2016, 660, 55–59. (21) Andersson, S.; Marković, N.; Nyman, G. Computational Studies of the Kinetics of the C + NO and O + CN Reactions. J. Phys. Chem. 2003, 107, 5439–5447. (22) Frankcombe, T. J.; Andersson, S. An Adiabatic Capture Theory and Quasiclassical Trajectory Study of C + NO and O + CN on the 2 A0 , 2 A00 , and 4 A00 Potential Energy Surfaces. J. Phys. Chem. 2012, 116, 4705–4711.

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O

CN O+

N+ CO

NCO

CN

N CO

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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C+NO Figure 10: Table of contents (TOC) graphic

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Quasiclassical Study of the C(3P)

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