Does the Gaseous Aniline Cation Isomerize to Methylpyridine Cations Before Dissociation?

Abstract

We have explored the potential energy surface for the isomerization of the aniline (AN) radical cation to the 2-, 3-, and 4-methylpyridine (picoline, MP) radical cations using G3 model calculations. The isomerization may occur through the 1H-azepine (7-aza-cycloheptatriene) radical cation. A quantitative kinetic analysis has been performed using the Rice-Ramsperger-Kassel-Marcus theory, based on the potential energy surface. The result shows that isomerization between $AN^{+\bullet}$ and each $MP^{+\bullet}$ hardly occurs before their dissociations.

Introduction

The kinetics and mechanisms of isomerizations and dis-sociations of aromatic molecular ions have been extensively studied using several experimental and theoretical techni-ques. The toluene radical cation is one of the most famous research targets.12 It is well known that the formation of the benzylium ion by direct H• loss from the toluene cation competes with the formation of the tropylium ion by H• loss after a ring expansion to the seven-membered cyclohep-tatriene radical cation. Similar six to seven-membered ring expansions of radical cations of toluene analogues and its derivatives, such as phenylsilane,3 anilne (AN),4 methylpyri-dines (picolines, MPs),5 phenylphosphine,6 phenylarsane,7 phenol,8 thiophenol,9 and halotoluenes10-15 have been investigated to understand their dissociation mechanisms. Several theoretical studies showed that ring contractions to five-membered intermediates played important roles in the dissociations of those cations, including the N, O, and P atoms.

Recently, dissociations of the AN4 and 2-, 3-, and 4- methylpyridine (2-MP, 3-MP, 4-MP)5 radical cations have been investigated in this laboratory. The HNC loss is the main channel in the dissociation of AN+•, which occurs though isomerizations to the 5-iminocyclohexa-1,2-diene (IC) cations and five-membered intermediates, according to theoretical molecular orbital calculations.4 The rate constant calculated based on the dissociation pathways agreed well with the previous experimental photoelectron-photoion coincidence result.16 In experimental and theoretical study on the isomeric MP cations,5 we have proposed the reaction pathways for the main dissociation channels, such as the losses of H•, C2H2, and HCN. In these two studies, however, we have not examined whether AN+• isomerizes to one of the isomeric MP cations before dissociation and vise versa, even though it has been proposed that they isomerize to a common seven-membered intermediate, the 1H-azepine (7-aza-cycloheptatriene, 1H-AZ) radical cation. The fact that the main dissociation channels are different for the AN and MP cations suggests that their interconversion does not occur effectively before dissociation. On the other hand, in a photodissociation study of neutral AN and 4-MP by Tseng et al.,17 it has been proposed that more than 23％ of AN and 10％ of 4-MP produced from the excitation by 193 nm photons isomerize to seven-membered ring intermediates, followed by the H migration in the seven-membered ring, and then isomerize to both MP and AN before dissociation. This is reflected in the experimental observation that the photodissociation channels of AN and 4-MP are very similar, even though the fragment relative intensities are very different. In this work, we examined the isomerization between the radical cations of AN and MP. Based on the potential energy surface constructed from quantum chemical calculations, a kinetic analysis was performed to predict whether such an isomerization occurs before dissociation.

 

Computational Methods

In our previous studies, the potential energy surface for the dissociation of AN+• was constructed from single point energy calculations at the B3LYP/6-311+G(3df,2p) level, with the optimized geometries at the B3LYP/6-31G(d) level,4 whereas the energies obtained from G3 theory calculations using the B3LYP density functional method (G3//B3LYP) were used for the construction of the potential energy surface for the dissociation of MP cations.5 Therefore, the energies for the species in the reaction pathways starting from AN+• were re-calculated with the G3//B3LYP method using the Gaussian 09 suite of programs.18

The Rice-Ramsperger-Kassel-Marcus (RRKM) expression was used to calculate the rate-energy dependences for some reaction steps of interest as follows:19

Here, E is the internal energy of the reactant, E0 is the critical energy of the reaction, N‡ is the sum of the TS states, ρ is the density of the reactant states, σ is the reaction path degeneracy, and h is Planck’s constant. N‡ and ρ were evaluated through a direct count of the states using the Beyer-Swinehart algorithm.20 The E0 values for the individual steps were obtained from the G3//B3LYP calculations. Each normal mode of vibration was treated as a harmonic oscillator. The vibrational frequencies obtained from the B3LYP/6-31G(d) calculations were scaled down by a factor of 0.9614.21

 

Results and Discussion

The pathways for the loss of HNC and H• from AN+• and for the formation of 1H-AZ+• are shown in Scheme 1 with the G3//B3LYP energies including the zero point vibrational energies. The relative G3//B3LYP energies of most of the species agree with those calculated at the B3LYP/6-311+G(3df,2p)//B3LYP/6-31G(d) level within ± 10 kJ mol−1.4 1H-AZ+• may undergo the loss of C2H2 or isomerizations to 2-, 3-, and 4-MP+•, of which details were described in the previous study.5

Figure 1 shows a simplified potential energy diagram for the isomerizations of AN+• to 2-, 3-, and 4-MP+• and dis-sociations to form the cations of cyclopentadiene (CP), pyrrole (PR), phenyl aminium (PA), and 7-aza-tropylium (AT) by the loss of HNC, C2H2, H•, and H•, respectively. 1H-AZ +• is the most stable among the intermediates for the isomerizations of AN+• to isomeric methylpyridine cations. The isomerization AN+• → 1H-AZ+• occurs through several steps, as shown in Scheme 1, but we simplify them as two steps. The first is the 1,3-H shift of the NH2 group of AN+• to eventually form IC+•, and the second is the ring expansion to form 1H-AZ+•. Because the first step occurs by two different pathways with similar barrier: AN+• → 2a → IC+• and AN+• → 6a → 2a → IC•, we will consider these as a doubly degenerated pathway for simplicity in rate calculations. The highest barrier in the isomerization IC+• → 1H-AZ+• corre-sponds to the step (E = 320 kJ mol−1) for the formation of a bicyclic intermediate. The several steps for IC+• → CP+• + HNC are simplified by two steps: the formation of the five-membered isomer and the dissociation step. The highest barrier in the former corresponds to the ring-closure step (E = 312 kJ mol−1) occurring through a tight transition state. Even though the barrier for the dissociation step is the same, the ring-closer step is the rate-determining step because the dissociation step occurs much faster through a loose transi-tion state. 1H-AZ+• can lose C2H2 to form PR+• through several steps, which are simplified as one step with the rate-determining isomerization step, for forming the bicyclic inter-mediate (see Figure 10 of Ref. 5). For the isomerizations to three isomeric MP cations, the H-ring walk should be requir-ed to form 3H-AZ+• (8d), for which the barrier is higher than those for the loss of C2H2 and H•.

Scheme 1.The isomerization and dissociation pathways of the aniline (AN) radical cation obtained from G3//B3LYP calculations. The calculated relative energies given in kJ mol−1 are shown in the parentheses and next to the arrows for the stable species and transition states, respectively. Species numbering follows the notation of Choe et al.4

The dissociation kinetics of AN+• and three isomeric MP cations were investigated in detail previously without con-sidering the isomerizations between AN+• and each MP cation.45 Briefly, AN+ → CP+• + HNC is the predominant channel at low energies in the dissociation of AN+•, and the loss of H• to form PA+ or AT+ is competitive only at high energies. In the dissociations of three isomeric MP cations, the formation of the pyridylmethylium ion, CP+•, and the 1,2,4-pentatriene radical cation by the loss of H•, C2H2, and HCN, respectively, are the main channels. The loss of CH3 • from each of three isomeric MP cations is possible only at high energies. To check the occurrence of the isomerizations of AN+• to each MP cation before dissociation, the rate constants for important reaction steps were calculated with the RRKM formalism (Eq. 1).

The most stable intermediate in the isomerization between AN+• and each MP cation is 1H-AZ+•, as mentioned above. The isomerization AN+• → 1H-AZ+• occurs through the intermediate IC+•. After the formation of IC+•, it can dissociate to CP+• + HNC, isomerize to 1H-AZ+•, or return to AN+•.

The corresponding rate constants, k2 – k4, were calculated on the basis of the potential energy surface in Figure 1. For reaction 2, the final step (E = 312 kJ mol−1) in the isomeri-zation to the five-membered intermediate was taken as the rate-limiting step. The reaction path degeneracies of 2, 2, and 4 were used in the calculations for k2 – k4, respectively. For k4, the two different pathways to AN+• were considered as a doubly degenerated pathway as mentioned above. The RRKM rate constants thus calculated are shown in Figure 2 as a function of the internal energy of AN+•. k2 is much larger than the other two at the whole energies investigated, indicating that most of the formed IC ions undergo dissocia-tion to CP+•. Because these three reactions are competitive, the portion of the isomerization to 1H-AZ+• among the reactions of IC+• is estimated from k3/(k2 + k3 + k4). Those calculated are 2.9 and 2.6％ at the energies of 500 and 900 kJ mol−1, respectively.

Figure 1.Simplified potential energy diagram for the isomerization of AN+• to 2-, 3-, and 4-MP+• and some dissociations, derived from the G3//B3LYP calculations. The energies are presented in kJ mol−1. Dashed lines denote pathways occurring through more than one step. See Scheme 1 for the notation of transition states.

In order to isomerize further to MP ions, 1H-AZ+• should surmount a relatively high barrier (E = 386 kJ mol−1) to form its 2H isomer (8c). 1H-AZ+• can undergo the following four reactions:

The corresponding rate constants, k5 – k8, were calculated on the basis of the potential energy surface in Figure 1. For reaction 5, the first isomerization step (E = 304 kJ mol−1) was taken as the rate-limiting step. The path degeneracies of 4, 1, 2, and 4 were used in the calculations for k5 – k8, respec-tively. We could not locate a transition state for reaction 6, which means that the reaction occurs though a loose transition state. Therefore, we assumed the frequencies of the transition state, so that the activation entropy at 1000 K (ΔS‡1000K) became 24 J mol−1 K−1, because most of the ΔS‡1000K values range from 13 to 45 J mol−1 K−1 for the one-step reactions occurring by a direct bond cleavage through a loose transition state.22 The RRKM rate constants thus calculated are shown in Figure 3. The portion of the isomerization to 2H-AZ+• among the reactions of 1H-AZ+• is estimated from k8/(k5 + k6 + k7 + k8). Those calculated are 0.1 and 5.2％ at the energies of 500 and 900 kJ mol−1, respec-tively. Most of the formed 1H-AZ+• ions undergo dissocia-tions, rather than isomerizations. Then, the portion of the IC+• ions isomerizing to 2H-AZ+• is estimated from {k3/(k2 + k3 + k4)} × {k8 /(k5 + k6 + k7 + k8)}, which is 0.001 and 0.1％ at the energies of 500 and 900 kJ mol−1, respectively. This shows that AN+• hardly isomerizes to the MP ions before dissociation, even though we assume that all of the AN cations isomerize initially to IC+•.

Figure 2.Energy dependences of the RRKM rate constants for the reactions of IC+•.

Figure 3.Energy dependences of the RRKM rate constants for the reactions of 1H-AZ+•.

Then, do the MP ions isomerize to AN+• before dissocia-tion? These isomerizations include the reaction 2H-AZ+• → 1H-AZ+• → IC+• → AN+•. The portion of 1H-AZ+• ions isomerizing to AN+• is estimated from {k7/(k5+ k6 + k7 + k8)} × {k4 /(k2 + k3 + k4)}, which is 0.3 and 1.1 ％ at the energies of 500 and 900 kJ mol−1, respectively. The portion of MP ions isomerizing to AN+• would be less than thus estimated values considering the other dissociation channels, such as the loss of H and HCN that occur without isomerization to 1H-AZ+•. The reported relative abundances of the loss of C2H2, which occurs through 1H-AZ+•, in the metastable ion dissociations of MP ions are around 30％.5 At higher energies, the abundance would be less than 30％, because the direct dissociations to lose H• or CH3• would become more abundant as the energy increases. Considering such competitive dis-sociations, the MP ions would also hardly isomerize to AN+• before dissociation.

To summarize, the potential energy surface for the iso-merization of AN+• to the MP ions was obtained with the G3//B3LYP method. The rate constants for some important reactions of IC+• and 1H-AZ+• were calculated using the RRKM formula. This kinetic analysis leads to the conclu-sion that AN+• and each MP ion hardly isomerize to each other before dissociation, which is different from the dis-sociations of neutral AN and MP.