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Computational Study of the Reaction of P+ with Acetylene: Does Spin-Crossing Play a Significant Role? Á lvaro Cimas,*,† Víctor M. Rayón,‡ and Antonio Largo‡ †

Centro de Investigaçaõ em Química, Departamento de Química e Bioquímica, Faculdade de Ciências, Universidade do Porto, 4169-007 Porto, Portugal ‡ Departamento de Química Física y Química Inorgánica, Facultad de Ciencias, Universidad de Valladolid, 47005 Valladolid, Spain S Supporting Information *

ABSTRACT: A computational study of the reaction of P+(3P) with acetylene has been carried out. The only exothermic products correlating with the reactants are PCCH+(2Π) + H(2S). Two different pathways leading to these products that are apparently barrier-free have been found. Both pathways involve isomerization into open-chain intermediates followed by direct elimination of a hydrogen atom. The possibility of spin-crossing has been considered because the species on the singlet surface are considerably more stable than those on the triplet one. On the singlet surface, there are other possible channels for the reaction, namely, cyclic PC2H+(2A′) + H(2S) and CCP+(1Σ) + H2 (1Σg+). A computational kinetic study shows that, in agreement with the experimental evidence, the major products are PCCH+(2Π) + H(2S) at all temperatures. Only at very high temperatures is CCP+(1Σ) + H2 (1Σg+) formed in non-negligible amounts. Therefore, only PCCH+ should be formed in the interstellar medium.

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INTRODUCTION The astrochemistry of phosphorus is rather interesting, especially after the detection of different phosphorus-containing molecules in astronomical sources. So far, three diatomic molecules have been detected, namely, PN,1,2 PC,3 and PO.4 Furthermore, the observation in space of PCH has also been reported.5 Looking for phosphorus compounds in the interstellar medium has already been addressed by Lattelais et al. for CHxOP [x = 1,3,5] isomers.6 The most recent phosphoruscontaining interstellar species is C2P.7 As can be seen, phosphorus−carbon chemistry seems to be particularly relevant in astrochemistry. The phosphapropynylidyne radical, C2P, has been observed in laboratory experiments through laser-induced fluorescence spectroscopy8 and rotational spectroscopy.9 These experiments confirmed a linear CCP structure with a 2Π electronic ground state, as previously predicted by theoretical calculations.10−12 An important point is how this kind of compounds could be formed in space. It is thought that ion−molecule reactions could play an important role for many interstellar compounds because cosmic rays are able to ionize many species.13 Following this idea, we have previously carried out preliminary theoretical studies of several ion−molecule processes that could lead to the production of interstellar phosphorus compounds.14−19 In the particular case of the interstellar production of C2P, Millar20 and Halfen et al.7 have proposed that a © 2012 American Chemical Society

plausible ion−molecule synthetic route could be initiated by the reaction of P+ ions with acetylene P+ + C2H2 → C2PH+ + H followed by dissociative recombination

(1)

C2PH+ + e → C2P + H (2) Dissociative recombinations are usually fast and therefore are not usually bottlenecks in this kind of process. In fact, it is estimated21 that reaction 2 could have a rate coefficient of ∼10−7 cm3 s−1. Reaction 1 has been studied in laboratory experiments22,23 through the selected ion flow tube (SIFT) technique. The experiments have shown that reaction 1 is rapid, with a rate coefficient of 1.3 × 10−9 cm3 s−1 at 300 K, and that the branching ratios are 0.95 for the production of C2PH+ and 0.05 for the formation of the adduct PC2H2+. In these experiments, the isomeric identity of the products cannot be determined. In our previous theoretical work19 on this reaction, we found that the most favorable C2PH+ isomer is a linear PCCH+ species with a 2Π ground state, which should be the precursor of ground-state CCP through dissociative recombination. However, a cyclic isomer PC2H+ with a 2A′ electronic state Received: December 22, 2011 Revised: February 21, 2012 Published: February 21, 2012 3014

dx.doi.org/10.1021/jp2123604 | J. Phys. Chem. A 2012, 116, 3014−3022

The Journal of Physical Chemistry A

Article

Due to the complexity of the reaction, the kinetic calculations have been carried out in the framework of the statistical theories. Such an approach, despite its intrinsic limitations,46 basically provides the unique tool for addressing at a semiquantitative level mechanistically complicated reactions, such as the one under study. For the kinetic calculations concerning the formation of the initial intermediate, 3I1, because we considered that the reactants are in thermal equilibrium and, in that case, the canonical variational transition-state theory rate constant for the association process can be obtained using the microcanonical theory, as well as for those processes where no transition structure (i.e., first-order saddle point) was found, we adopted the microcanonical variational transition-state theory (μVTST) in its vibrator formulation.47,48 More specifically, the potential energy paths were first scanned at the B3LYP/ cc-pVTZ level of theory due to the known deficiencies of MP2 for describing this kind of process. To be able to build an appropriate unrestricted wave function in the case of the singlet surface hydrogen atom eliminations, we used the keyword guess=mix, and we checked the stability of the wave function at each point of the scan. Subsequently, at each point of the scan, the Hessian matrices describing the modes orthogonal to the reaction path were evaluated according to the standard procedure of Miller et al.,49 and then, the sum of states was minimized to obtain the location of the loose TS. For the unimolecular reactions involving all of the intermediates, the microcanonical rate coefficients have been calculated employing the following usual equation of RRKM theory:50

lies quite close in energy. In principle, given the triplet ground state of the phosphorus cation, it is expected that the reaction takes place initially on the triplet surface. However, in our theoretical study,19 we found that the singlet PC2H2+ species are much more stable than the corresponding triplet ones. Therefore, it is conceivable that if spin-crossing is efficient, the singlet surface could play an important role, and finally, other products could be formed. We should mention that in other similar reactions, spin-crossing has been shown to be important. For example, the reactions of S+ and C(3P) with acetylene24−26 are clear examples of the importance that spin-forbidden processes can play in spin-allowed reactions. However, we also point out that spin-forbidden products have not been observed for the reaction of acetylene with Si(3P) atoms.27 In the present work, we carry out a computational study of the reaction of P+ with acetylene, taking into account the possibility of spin-crossing. Therefore, both triplet and singlet surfaces will be involved in our study.

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COMPUTATIONAL METHODS Geometrical optimizations were carried out employing secondorder Møller-Plesset (MP2)28 theory with the Dunning’s tripleζ cc-pVTZ basis set.29,30 The nature of the stationary points on the respective potential surface was checked through computation of vibrational frequencies at the MP2/cc-pVTZ level. These calculations also allow an estimate of the zero-point energy (ZPE). Several minima and transition states (TSs) were also optimized at the CCSD level of theory to assess the performance of the MP2 method for this reaction. We have found that both methods provide geometries in good agreement to each other. Thus, MP2 should provide reliable potential energy surfaces for this reaction. In order to have more accurate energetic predictions, electronic energies were further refined at the CCSD(T) level (coupled-cluster single and double excitation model augmented with a noniterative triple excitation correction31) with the aug-cc-pVTZ basis set (thus including diffuse functions). The G03 package of programs32 was employed for these ab initio calculations. The minimum-energy crossing points (MECPs), that is, the minimum of the hyperline of intersection33−38 between the singlet and triplet surfaces, were located by employing two computational levels. An accurate optimization39−42 was carried out by employing second-order Møller-Plesset perturbation theory (MP2) with the cc-pVTZ basis set and subsequently refined at the CCSD(T)/aug-cc-pVTZ//MP2/cc-pVTZ level, where the latter notation denotes coupled cluster energies in conjunction with MP2 analytical gradients (the correlated consistent aug-cc-pVTZ and cc-pVTZ basis sets of Dunning29,30 were employed). We have, as well, estimated the curvature of the seam,41,43 and therefore, the zero-point vibrational energies at the MECPs were roughly determined. The approximate monoelectronic44 spin−orbit coupling Hamiltonian matrix, which provides an estimation of the magnitude of the coupling between the two surfaces,33,34 has been calculated for the MECP structures using first-order configuration interaction (FOCI) wave functions constructed using the natural orbitals from a state-averaged CASSCF (complete active space self-consistent field) calculation carried out with the cc-pVTZ basis set. All of these calculations have been carried out using the GAUSSIAN 0332 and GAMESS US45 packages. An IRC-like procedure has been carried out to know which minima are actually interconnected through the MECPs.

k(E , J ) = σ

N # (E , J ) hρ(E , J )

(3)

where σ is the reaction symmetry factor, N#(E,J) is the number of states at the TS, and ρ(E,J) is the density of the states at the minimum. The density and sum of states were estimated through the Forst algorithm50,51 using the corresponding frequencies and moments of inertia. The possibility of tunneling was accounted for in terms of a monodimensional probability according to the generalized Eckart potential.52 The nonadiabatic version of the RRKM theory33,43 was employed for the treatment of the spin-forbidden processes. In such cases, the unimolecular rate coefficients are computed as k(E , J ) =

2 hρ(E , J )

∫0

E MECP

ρ

(E − Eh , J )P(Eh , J ) dEh (4)

where Eh is the fraction of the nonfixed energy reversed in the coordinate orthogonal to the seam and ρMECP(E − Eh,J) is the density of the states at the MECP. In the above formula, P(Eh,J) represents the surface hopping probability calculated as (1 + P)(1 − P), in which (1 − P) and P(1 − P) are, respectively, the probability of hopping on the first passage and the probability of not hopping on first crossing. For evaluating P, that is, 3015



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Figure 1. Geometrical parameters at the MP2/cc-pVTZ level for the most relevant intermediates and TSs located on the PC2H2+ triplet surface. Bond distances are given in angstroms and angles in degrees.

P(E,J), we used the monodimensional model proposed by Delos53−55 2 ⎛ 2μH ⎞ P(E , J ) = 4π 2V12 ⎜ 2 ⎟ ⎝ ℏ F ΔF ⎠

2/3

We have omitted the information about other species that are less stable and do not play a significant role on the studied reaction. An interesting point is that the production of the most stable isomer of PC2H+, namely, linear PCCH+, is only slightly exothermic by 1.6 kcal/mol at the CCSD(T) level of theory. On the other hand, the next isomer in stability, cyclic PC2H+(2A′), is slightly endothermic (1.9 kcal/mol at the CCSD(T) level of theory). The formation of other possible products, such as C2P+(3B2) + H2(1Σg+), is clearly endothermic and therefore does not seem feasible under interstellar conditions. Initially, the interaction of P+ with acetylene results in the cyclic intermediate I1, which lies about 60 kcal/mol below the reactants. Direct elimination of a hydrogen atom from I1 implies a small barrier because it involves transition state TS1‑H which is located about 3 kcal/mol above the reactants. It is interesting to point out that this process from I1 implies opening the ring and results in the linear PCCH+ species. Consequently, the cyclic isomer PC2H+ is not formed on the triplet surface. Nevertheless, there are other possibilities for the evolution of I1. In the first place, a hydrogen shift toward a carbon atom results in intermediate I2, with the two hydrogen atoms bonded to the same carbon atom. This is the most stable species on the triplet surface, lying 67 kcal/mol below the reactants. In addition, hydrogen shift toward phosphorus gives intermediate I3, which is located higher in energy than I1. Both hydrogen migrations involve TSs clearly located below reactants. Furthermore, hydrogen atom elimination from both I2 and I3 seems to proceed without any net barrier. We must point out that it is possible to locate a TS for hydrogen atom elimination from I2 at the MP2 level, but at higher correlated levels, this TS seems to disappear. At the CCSD(T) level, it is located 4.8 kcal/mol below the reactants. In summary, production of PCCH+ seems to be the only feasible channel on the triplet surface and should proceed through previous isomerization of the initially formed species, I1, into either I2 or I3. The former one should be favored on energetic arguments. We now turn to the analysis of the singlet surface. The intermediates and TSs characterized on the singlet surface are depicted in Figure 3, whereas in Figure 4, a schematic representation of such a surface is provided. The singlet states of I1, I2, and I3 were obtained. In addition, we also provide in

⎡

⎢ Ai 2⎢(E − EMECP ⎢⎣

⎛ 2μ ΔF 2 ⎞1/3⎤⎥ − Erot(J ))⎜⎜ H2 4 ⎟⎟ ⎥ ⎝ ℏ F ⎠ ⎥⎦

(5)

where F and ΔF are, respectively, the geometric mean and the difference of the norms of the gradients on the two surfaces at the crossing point, Ai is the Airy function, μH is the reduced mass for movement along the direction orthogonal to the seam, 2 and V12 is the square of the electronic matrix element for the coupling of the two surfaces (essentially, the spin−orbit coupling in the present case). All of the kinetic calculations were carried out with our own routines, employing the CCSD(T)/cc-pVTZ electronic energies and the MP2/ccpVTZ geometries and vibrational frequencies. It should be pointed out that in the kinetic calculations, we have not considered pressure effects. The reason is that we are interested in the interstellar conditions, not in the particular conditions of the reactions in terrestrial experiments, and in the interstellar medium, the reaction should proceed at a very low pressure.

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RESULTS AND DISCUSSION The reaction of ground-state P+ with acetylene has been studied experimentally.22,23 The product observed in the experiments is PC2H+ +

P+(3P) + C2H2(1Σg ) → PC2H+ + H(2S)

(6)

PC2H has a linear ground state corresponding to a 2Π electronic state, and there is also a low-lying cyclic isomer with a 2A′ electronic state. Therefore, the products correlate with the reactants, and the reaction should take place initially on the triplet surface. The geometries of the minima and TSs characterized on the triplet surface are shown in Figure 1, whereas the energy profile on that surface is schematically represented in Figure 2. +

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Figure 2. Energy profile (in kcal/mol) for the reaction of P+(3P) with acetylene on the triplet surface. Relative energies have been computed at the CCSD(T)/aug-cc-pVTZ level including MP2/cc-pVTZ ZPE corrections.

their counterparts on the triplet surface. However, the stability order is not the same for both potential surfaces. Whereas I2 is the most stable species on the triplet surface, on the singlet one, the global minimum is I1. It is also worth mentioning that the TSs connecting the different intermediates on the singlet surface lie, in general, higher in energy than their counterparts on the triplet surface, reflecting the fact that isomerization between singlet species involves higher barriers than that between triplet intermediates. An important characteristic of the singlet surface is that formation of ground state PCC+ is now possible. In fact, the channel PCC+(1Σ) + H2(1Σg+) is the most exothermic one because these products lie more than 2 kcal/mol below PCCH+(2Π) + H(2S). However, the production of PCC+(1Σ) can only take place from I2 or I4. In both cases, isomerization from I1 is necessary, and the corresponding transition states, TS12 and TS14, lie much higher than I1. Furthermore, elimination of a hydrogen molecule from either I2 or I4 involves also significant barriers, as suggested by the relative energies of the associated transition states TS2‑H2 and TS4‑H2, respectively. In the case of formation of PCC+ from I2, the TS is still slightly lower in energy than the P+(3P) + C2H2(1Σg+) reactants, but in the case of I4, the TS is clearly above the reactants. Elimination of a hydrogen atom from I1 leads to the cyclic isomer, PC2H+(2A′). Nevertheless, this process is slightly endothermic because the products lie nearly 2 kcal/mol above P+(3P) + C2H2(1Σg+). Linear PCCH+(2Π) can be obtained from either I2 or I3 through hydrogen atom elimination. Again, the CCSD(T) results suggest that there are no barriers associated with these processes. As mentioned before, the PCCH+(2Π) + H(2S) channel is slightly exothermic by 1.6 kcal/mol. The key point to ascertain whether the singlet surface is important in the reaction of the ground-state phosphorus cation with acetylene is the probability of spin-crossing.

Figure 3. Geometrical parameters at the MP2/cc-pVTZ level for the most relevant intermediates and TSs located on the PC2H2+ singlet surface. Bond distances are given in angstroms and angles in degrees.

Figure 3 the geometrical parameters of I4, a bent intermediate with a hydrogen atom bonded to phosphorus. The energies given in Figure 4 are relative to P+(3P) + C2H2(1Σg+), in order to make direct comparisons with the energy values provided in Figure 2. As expected, the different intermediates on the singlet surface are much more stable than 3017



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Figure 4. Energy profile (in kcal/mol) for the reaction of P+(3P) with acetylene on the singlet surface. Relative energies have been computed at the CCSD(T)/aug-cc-pVTZ level including MP2/cc-pVTZ ZPE corrections.

We have searched for MECPs connecting the triplet and singlet surfaces. Two different MECPs were characterized, one of them connecting 3I1 with 1I1 (MECP1−1) and the other one (MECP2−2) for the 3I2 → 1I2 conversion (in what follows, the left superscript will denote the spin multiplicity of the corresponding species, in order to distinguish between triplet and singlet structures). Their geometrical parameters, at both MP2 and CCSD(T) levels, are provided in Figure 5. Whereas MECP1−1 maintains the C2v symmetry, MECP2−2 has Cs symmetry. Nevertheless, in both cases, the geometry is closer to the triplet intermediates than to the singlet ones. Their relative energies at the CCSD(T) level, taking P+(3P) + C2H2(1Σg+) as the reference, are −61.3 (MECP1−1) and −58.7 (MECP2−2) kcal/mol. Therefore, both MECPs lie much lower in energy than the TSs located on the triplet surface. For example, it can be seen in Figure 1 that the TS for the 3I1 → 3I2 conversion (TS12) lies −48.2 kcal/mol below the reactants. The spin−orbit coupling matrix elements at the MECPs take the following values: 124.1 cm−1 for MECP1−1 and 114.0 cm−1 for MECP2−2. In principle, these are moderate values, but their role on the overall process should be based on a full kinetic treatment. In order to perform such kinetic treatment, we have developed a mechanistic model for the reaction of P+(3P) with acetylene, which is shown in Scheme 1. In this model, we have taken into account not only the pathways on the triplet surface but also those reaction pathways that are opened after a possible crossing to the singlet surface. Therefore, we have included three different channels, (a) formation of linear

Figure 5. Geometrical parameters at the MP2/cc-pVTZ and CCSD(T)/aug-cc-pVTZ levels for the minimum-energy crossing points (MECPs) connecting the triplet and singlet PC2H2+ surfaces. Bond distances are given in angstroms and angles in degrees. 3018



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Scheme 1. Mechanistic Model for the Kinetic Study of the P+(3P) + C2H2(1Σg+) Reactiona

a

Relative energies (in kcal/mol) have been computed at the CCSD(T)/aug-cc-pVTZ level employing MP2/cc-pVTZ vibrational frequencies.

PCCH+(2Π) + H(2S), (b) production of linear CCP+(1Σ) + H2 (1Σg+) and (c) formation of cyclic PC2H+(2A′) + H(2S). Note that channel b, CCP+(1Σ) + H2 (1Σg+), is a spin-forbidden process, and therefore, it should imply hopping to the singlet surface. On the other hand, channel c, PC2H+(2A′) + H(2S), is spin-allowed, but in practice, there is no pathway on the triplet surface leading to these products. Therefore, the only way to obtain the products in channel c involves also the singlet surface. The steady-state solution of the master equation derived from Scheme 1 leads to the following expression of the overall rate coefficient: koverall = ka + k b + kc

where A = k−22 + k−12S + k2aS + k2bS k B = k−11 + k12S + k13S + k14S + k1cS − 12S A k−13Sk13S k−14Sk14S − − k−13S + k3aS k−14S + k4bS k k k C = k12T + −22 12S 11 AB k k D = k−12T + k22 + k2aT − −22 22 A k−22k12Sk−12Sk22 − A2B C E= D

(7)

where a, b, and c denote the channels leading to PCCH+(2Π) + H(2S), CCP+(1Σ) + H2 (1Σg+), and PC2H+(2A′) + H(2S), respectively. The individual rate coefficients are given by the following expressions: ka = k1aTG + k2aTEG + k3aT

k13T G k−13T + k3aT

⎧k k k k k E⎫ k E + k2aS⎨ 12S 11 + 22 + 12S −212S 22 ⎬G ⎩ AB ⎭ A AB ⎧ ⎛ k13S k k E⎞G ⎫ ⎜k11 + −12S 22 ⎟ ⎬ + k3aS⎨ ⎠B⎭ A ⎩ k−13S + k3aS ⎝

F = k−captk12Tk13Tk11 − k−12TE −

G=

(8)

⎧k k k k k E⎫ k E k b = k2bS⎨ 12S 11 + 22 + 12S −212S 22 ⎬G ⎩ AB ⎭ A AB ⎧ ⎛ k14S k k E⎞G ⎫ ⎜k11 + −12S 22 ⎟ ⎬ + k4bS⎨ ⎠B⎭ A ⎩ k−14S + k4bS ⎝

F (11)

The above expressions were subsequently thermally averaged, according to the Boltzmann distribution, in order to obtain the final canonical rate coefficients. As the intermediates cannot be collisionally stabilized, their internal energy always remains equal to the collision energy plus the energy of chemical activation, where the energy of chemical activation is the relative energy of the particular intermediate with respect to the reactants but opposite in sign.

(9)

⎛ k k E⎞G kc = k1cS⎜k11 + −12S 22 ⎟ ⎝ ⎠B A

k k k E k k − −11 11 − −11 −12S 12S B AB kcapt

k−13Tk13T k−13T + k3aT

(10) 3019



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Table 1. Rate Coefficients (cm−3 s−1 molecule−1) for the Different Channels and the Overall Process Reported at Different Temperatures (K) T/K

ka

100.0 150.0 200.0 250.0 300.0 350.0 400.0 450.0 500.0

1.928 4.737 7.373 9.544 1.122 1.248 1.342 1.414 1.472

× × × × × × × × ×

kb 10−11 10−11 10−11 10−11 10−10 10−10 10−10 10−10 10−10

1.071 2.137 9.622 9.896 4.872 1.561 3.801 7.676 1.357

× × × × × × × × ×

kc 10−21 10−18 10−17 10−16 10−15 10−14 10−14 10−14 10−13

Table 2. Product Molar Ratios Reported at Different Temperatures (K) PCCH+(2Π) + H(2S)

C2P+(1Σ) + H2(1Σg+)

PC2H+(2A′) + H(2S)

100.0 150.0 200.0 250.0 300.0 350.0 400.0 450.0 500.0

1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.999 0.999

0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.001 0.001

0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

× × × × × × × × ×

kTotal 10−22 10−19 10−18 10−16 10−16 10−15 10−15 10−15 10−14

1.928 4.737 7.373 9.544 1.122 1.248 1.343 1.415 1.474

× × × × × × × × ×

10−11 10−11 10−11 10−11 10−10 10−10 10−10 10−10 10−10

difference of the norms of the gradients at MECP1−1 are 4.755034 × 10−2 and 0.1383711 au/Bohr, respectively. Therefore, our results do not change essentially the role of the reaction of P+(3P) with acetylene in the context of interstellar chemistry. At low temperatures, such as in the interstellar medium, only the PCCH+ isomer should be effectively formed. Upon dissociative recombination, this cation would lead to linear CCP, the most stable isomer and the species detected in space. However, we think that our theoretical results are relevant for the interpretation of the experiments in terrestrial laboratories. In the experiments,22,23 the observed product at 300 K, apart from residual amounts of the adduct, is PC2H+. However, the isomeric identity of this species remains unknown because the identification through mass spectrometry does not allow identification of the precise molecular structure of the formed species. Our results suggest that the observed product should be the most stable isomer, namely, linear PCCH+. Another interesting point is the role of spin-crossing in the reaction of P+(3P) with acetylene. Despite the fact that the hopping probability into the singlet surface is moderate according to the theoretical calculations, once the system is on the singlet surface, there is a pathway for the production of CCP+(1Σ) + H2 (1Σg+) through hydrogen molecule elimination from 1I2 involving a high barrier. Due to this fact, only at high temperatures is the most exothermic channel, CCP+(1Σ) + H2 (1Σg+), formed in non-negligible amounts.

In Table 1, the overall and individual canonical rate coefficients at different temperatures are provided. The computed value at 300 K for the global rate coefficient is 1.12 × 10−10 cm3 s−1 molecule−1, about 1 order of magnitude smaller than the measured rate coefficient in the SIFT experiments,21,22 namely, 1.3 × 10−9 cm3 s−1 molecule−1. Bearing in mind the accuracy achieved by the computational levels of theory, this discrepancy is not totally unexpected. One should be aware that an error in the estimate of a barrier height in a chemical reaction of nearly 1 kcal/mol would produce an error of roughly 1 order of magnitude. Besides, our theoretical calculation assumes a collisionless regime, and this might introduce another source of discrepancy with the experimental results. Nevertheless, the most important aspect of the theoretically predicted rate coefficients in the present work is their relative magnitude. It is clear from Table 1 that the dominant channel at every temperature is channel a, namely, PCCH+(2Π) + H(2S). The channel leading to CCP+(1Σ) + H2 (1Σg+), channel b in Scheme 1, has a very small contribution at all temperatures. Finally, channel c, which corresponds to the formation of a cyclic isomer PC2H+(2A′), has a negligible contribution to the global process at all temperatures. The resulting branching ratios for the different channels are shown in Table 2.

T/K

1.195 2.271 9.813 1.003 5.075 1.711 4.453 9.709 1.864

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CONCLUSIONS

A computational study of the reaction of P+(3P) with acetylene has been carried out. Given the spin multiplicity of the reactants, the reaction initially takes place on the triplet surface. The interaction of the reactants gives a cyclic intermediate, 3I1, which is quite stable (about 60 kcal/mol below the reactants). The only exothermic products (−1.6 kcal/mol) correlating with the reactants are PCCH+(2Π) + H(2S). We have found two different pathways leading to these products that are apparently barrier-free. Both pathways involve isomerization into openchain intermediates, 3I2 and 3I3, followed by direct elimination of a hydrogen atom. We have considered the possibility of spin-crossing because the species on the singlet surface are considerably more stable than those on the triplet one. Two different MECPs have been characterized, and the probability for surface hopping has been estimated. Once the singlet surface is reached, there are other possible channels for the reaction. Apart from the production of PCCH+(2Π) + H(2S), formation of another isomer, namely, cyclic PC2H+(2A′) + H(2S), is also feasible, although slightly endothermic (1.9 kcal/mol). In addition, formation of

The branching ratio for cyclic PC2H+(2A′) + H(2S) is virtually zero at all temperatures. The contribution of CCP+(1Σ) + H2 (1Σg+) is negligible at temperatures lower than 300 K and only approaches very small values (always lower than 0.01) at higher temperatures. We point out that, in addition to the moderate value of the hopping probability, the small contribution of this reaction channel is also due to a nonfavorable orientation of the relative gradients on both surfaces; the geometric mean and the 3020



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CCP+(1Σ) + H2 (1Σg+), which are, in principle, spin-forbidden products, seems now feasible and in fact constitutes the most exothermic channel (−4.2 kcal/mol). However, the last channel involves elimination of a hydrogen molecule, and this process involves energy barriers. On the other hand, elimination of a hydrogen atom leading to either PCCH+(2Π) or cyclic PC2H+(2A′) seems to proceed without any other barrier apart from its endothermicity. A computational kinetic study, within the context of statistical theories, has been carried out. In this treatment, the possibility of spin-crossing has been included, and different temperatures within the interval of 100−500 K have been considered. Our theoretical results are fully compatible with the experimental observation because the major products are PCCH+(2Π) + H(2S) at all temperatures, whereas the channel leading to cyclic PC2H+(2A′) has no significant contribution at any temperature. We have observed that the channel leading to CCP+(1Σ) + H2 (1Σg+), the most exothermic products, has also no significant contribution at low temperatures. Only at high temperatures are they formed in non-negligible amounts. Therefore, our theoretical study does not change the implications of the reaction of P + with acetylene in astrochemistry because the interstellar medium is characterized by a very low temperature. Nevertheless, the present theoretical study allows identification of the nature of the observed products in the laboratory experiments. Furthermore, the present theoretical study shows that spin-crossing takes place in this reaction, although it leads mainly to the formation of the same products formed on the triplet surface, namely, PCCH+(2Π) + H(2S).

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ASSOCIATED CONTENT

S Supporting Information *

Detailed data on the individual rate coefficients for all of the steps involved in the reaction and potential energy curves for the direct hydrogen atom eliminations from the singlet surface. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Thanks are due to the Fundaçaõ para a Ciência e a Tecnologia, FCT, Lisboa, Portugal, and FEDER for finantial support and ́ Centro de Investigaçaõ en Quimica de Universidade do Porto. A.L. and V.M.R. thank the Ministerio de Educación y Ciencia of Spain (Grant CTQ2010-16864) and the Junta de Castilla y León (Grant VA040A09).

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REFERENCES

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