ARTICLE pubs.acs.org/JPCA
Formation of C4H4•þ from the Pyridine Radical Cation: A Theoretical Mechanistic and Kinetic Study Min Kyoung Yim and Joong Chul Choe* Department of Chemistry, Dongguk University-Seoul, Seoul 100-715, Korea
bS Supporting Information ABSTRACT: The potential energy surface (PES) for the formation of C4H4•þ from the pyridine radical cation by loss of HCN was determined from quantum chemical calculations using the G3//B3LYP method. The complete reaction pathways for the formation of the low-energy C4H4•þ isomers, radical cations of methylenecyclopropene (MCP•þ), vinylacteylene (VA•þ), cyclobutadiene, and butatriene were obtained. Based on the PESs, a RiceRamsperger KasselMarcus model calculation was performed to investigate the dissociation kinetics. The calculated dissociation rate constants agreed with the previous experimental data. It was predicted that a mixture of MCP•þ and VA•þ was formed by loss of HCN. The formation of MCP•þ was more favored near the dissociation threshold and at high energies, whereas the formation of VA•þ was more favored at the low energies corresponding to the ion lifetime of microseconds.
1. INTRODUCTION The dissociation of the pyridine radical cation (C5H5N•þ, 1) to form C4H4•þ and HCN has been extensively studied by several experimental and theoretical techniques.112 C5 H5 N•þ f C4 H4 •þ þ HCN
ð1Þ
The dissociation rate constants were measured with a photoelectron-photoion coincidence (PEPICO) method.1,2 The kinetic energy releases in the dissociation were measured with tandem mass spectrometry37 and analyzed by the maximum entropy method.57 The ionization cross sections were measured using Fourier transform mass spectrometry.8 Attempts have been made to identify the structure of the C4H4•þ fragment.911 It is now generally accepted that the C4H4•þ ions formed in reaction 1 are a mixture of the methylenecyclopropene (MCP) and vinylacteylene (VA) radical cations (Scheme 1). The mechanistic pathway for reaction 1 has not been reported. It was mentioned in a recent study7 that the complete dissociation mechanism from 1 could not be obtained by ab initio calculations. For the neutral pyridine, the theoretical potential energy surface (PES) for the formation of MCP, VA, cyclobutadiene (CB), and butatriene (BT) by the loss of HCN was reported recently.13 On the other hand, the mechanistic pathways for the formation of C4H4•þ from the benzene radical cation, which is isoelectronic with 1, were studied by van der Hart14 using ab initio calculations at the HF/ 6-31G(d,p) level. The reported pathways include the formation of four low-energy isomeric C4H4•þ ions such as MCP•þ, VA•þ, CB•þ, and BT•þ by the loss of C2H2. The result showed the lowest energy pathway was the formation of MCP•þ, which was the most stable C4H4•þ isomer. According to the experimental study using ion r 2011 American Chemical Society
cyclotron resonance mass spectrometry,11 MCP•þ was mainly formed at the dissociation threshold of the benzene radical cation and the population of VA•þ increased at a higher internal energy. Unfortunately, however, the energy dependence of the relative abundances of MCP•þ and VA•þ in the dissociation of 1 was not measured experimentally. In this work, the PES for reaction 1 was theoretically constructed using the density functional theory (DFT)15,16 and Gaussian-3 (G3) theory17 methods. The complete pathways for the formation of the four low-energy C4H4•þ isomers (Scheme 1) by loss of HCN were obtained. The RiceRamspergerKasselMarcus (RRKM)18 model calculation was carried out on the basis of the obtained PES to gain insight into the dissociation kinetics.
2. COMPUTATIONAL METHODS The molecular orbital calculations were performed with the Gaussian 09 suite of programs.19 The geometries of the stationary points were optimized at the unrestricted B3LYP20,21 level of the DFT using the 6-31þG(d) basis set. The transition state (TS) geometries that connected the stationary points were examined and checked by calculating the intrinsic reaction coordinates at the same level. The geometries for important TSs were optimized at the B3LYP/6-311þG(3df, 2p) level for the purpose of comparison. For better accuracy of the energies, G3 theory calculations using the B3LYP density functional method (G3//B3LYP)17 were performed. In G3//B3LYP calculations, the geometries are obtained at the B3LYP/6-31G(d) Received: October 21, 2010 Revised: March 4, 2011 Published: March 23, 2011 3087
dx.doi.org/10.1021/jp110074r | J. Phys. Chem. A 2011, 115, 3087–3094
The Journal of Physical Chemistry A
ARTICLE
calculations were scaled down by a factor of 0.963628 and were used for the calculations of k and ΔS. The entropy of activation (ΔS‡) was used in the RRKM calculations for two dissociation steps, which will be described later, occurring without reverse barriers. The TSs of such dissociation steps can be varied with internal energy according to the variational transition state theory (VTST).18 Instead of the rigorous VTST formalism, the conventional RRKM method was used to model the loose TSs with the aid of ΔS‡. According to the data compiled by Lifshitz29 and subsequent work,3035 most of the ΔS‡ values ranged from 13 to 35 J mol1 K1 at 1000 K for the one-step reactions occurring by a direct bond cleavage via loose TSs. In such a bond cleavage reaction, the larger the bond distance of the TS is, the larger the ΔS‡ value becomes. Therefore, it was assumed that the variation of the TSs of the dissociation steps with the cleaving bond distance was in the range corresponding to the above ΔS‡1000K range. The TS structures were optimized with reasonable cleaving bond distances so that the ΔS‡1000K values calculated from the frequencies were in the above range.
Scheme 1
level, and the zero point vibrational energies are obtained at the same level and scaled by 0.96. All the other steps remain the same as the G3 method22 with the exception of the values of the higher-level correction parameters. For selected species, enthalpies of formation were calculated using the G3//B3LYP, Gaussian-4 (G4) theory,23 and CBS-APNO method24 to evaluate the accuracy of the G3//B3LYP calculations. The RRKM expression was used to calculate the rate constants for individual unimolecular reaction steps that were involved in the selected reaction pathways:18 kðEÞ ¼
σN ‡ ðE E0 Þ hFðEÞ
ð2Þ
In this equation, E is the reactant internal energy, E0 is the critical energy of the reaction, N‡ is the sum of the TS states, F is the density of the reactant states, σ is the reaction path degeneracy, and h is Planck’s constant. N‡ and F were evaluated through a direct count of the states using the BeyerSwinehart algorithm.25 The external rotational modes were treated to be adiabatic. To compare the calculated total dissociation rate constant with the PEPICO data obtained at 298 K, the thermal energy, kBT/2 where kB is Boltzmann’s constant and T is the temperature, was used for each adiabatic rotational energy of 1. The adiabatic rotational energies for the TSs and intermediates were calculated by comparing the calculated rotational constants with those of 1. The relative entropy (ΔS) of species β with respect to species R was calculated with the following formula:18,26 ΔS ¼ kB ln
Q β Uβ UR þ QR T
ð3Þ
where Q’s are the total partition functions and U’s are the thermodynamic internal energies at T. When R and β are the reactant and TS, respectively, for a reaction, ΔS becomes the entropy of activation (ΔS‡),26,27 which characterizes the “looseness” of the TS. For ΔS of an interesting species β, an intermediate, or TS, with respect to 1, Q’s and U’s were calculated from the vibrational frequencies of 1 and β because the external rotation was treated to be adiabatic in the calculation of k. The vibrational frequencies obtained from the B3LYP/6-31þG(d)
3. RESULTS AND DISCUSSION Thermochemistry. Several experimental studies were carried out to characterize C4H4•þ isomers3638 and quantum chemical calculations were performed to obtain the PESs for C4H439,40 and C4H4•þ 41,42 isomers. It is well-known that the four C4H4•þ isomers in Scheme 1 are much more stable than the other isomers.14,41,42 Therefore, only these four C4H4•þ isomers were chosen as candidates for the product ions in reaction 1. The total energies of 1 and the C4H4•þ isomers calculated at the G3// B3LYP level are listed in Table 1 together with those of their corresponding neutral molecules. For the C4H4•þ isomers, the stability order was MCP•þ > BT•þ > CB•þ > VA•þ. The energies of BT•þ, CB•þ, and VA•þ were higher than MCP•þ by 27, 36, and 39 kJ mol1, respectively. The method to calculate the enthalpy of formation (ΔfH) from the total energy (after conversion to enthalpy) is well established.43,44 Additional required data were the calculated enthalpies and experimental ΔfH’s of C, H, and/or N. For the ΔfH’s of the radical cations, the calculated adiabatic ionization energies were added to ΔfH’s of the corresponding neutral molecules. The ΔfH values calculated at the G3//B3LYP level for the neutrals and cations agreed with the available experimental values45,46 within (6 kJ mol1. For comparison purposes, the G4 and CBS-APNO calculations, which are more expensive methods, were carried out. Comparing to the experimental data, the performance of the G3//B3LYP calculations were similar with those of two higher level calculations (Table 1). Dissociation Pathways. Formation of MCP•þ. The formation of MCP•þ is initiated by a 1,2 shift of the γ-hydrogen atom to form 2 (Figure 1). The ring is opened by a direct cleavage of the bond between the R- and β- carbons of 2 to form 3. Subsequently, a cistrans isomerization occurs to form 4. The R-C of 4 approaches the γ-C to form a three-membered ring isomer 5. 5 dissociates to MCP•þ þ HCN via an ionmolecule complex, MCP•þ 3 3 3 HCN (6). This was the lowest energy pathway to form MCP•þ (channel I-a). Alternatively, another three-membered ring isomer 7 can be formed by one step from 2 by a direct CN bond cleavage. 7 dissociates to MCP•þ þ HCN via another ionmolecule complex 8 (channel I-b). The occurrence of channel I-b is less probable because the highest barrier 3088
dx.doi.org/10.1021/jp110074r |J. Phys. Chem. A 2011, 115, 3087–3094
The Journal of Physical Chemistry A
ARTICLE
Table 1. Total Energy at 0 K, Etot, Enthalpy of Formation at 298 K, ΔfH298, and Ionization Energy, IE ΔfH298, kJmol1 (IE, eV) exptla
species
point group
G3//B3LYP Etot, hartrees
pyridine•þ
C2v
247.756708
1039
1033
1031
MCP•þ
C2v
154.280217
1177
1173
1174
VA•þ
Cs
154.265232
1217
1217
1214
BT•þ
D2
154.269728
1206
1207
1202
CB•þ
D2h
154.266388
1212
1208
1208
CB•þ-rhb
C2v
154.265795
1214
1208
1208
pyridine MCP
C2v C2v
248.098261 154.579811
142 (9.29) 390 (8.15)
141 (9.24) 389 (8.13)
135 (9.28) 389 (8.13)
140.2 ( 0.5 (9.26 ( 0.01) 295 (9.58 ( 0.02)
G3//B3LYP
G4
CBS-APNO 1034 ( 2 1219
1215 ( 19
VA
Cs
154.618640
289 (9.62)
290 (9.61)
291 (9.57)
BT
D2h
154.606596
321 (9.17)
323 (9.16)
322 (9.12)
CB
D2h
154.563141
433 (8.08)
431 (8.06)
434 (8.03)
428 ( 16 c (8.16 ( 0.03)
HCN
C¥
93.378245
129
129
134
135.14 ( 8.4
From ref 45 except for ΔfH298 of CB. For ΔfH298’s of the radical cations, IE’s in parentheses were added to ΔfH298’s of the corresponding neutrals. b Rhombic CB•þ. c From ref 46. a
Figure 1. Potential energy diagram for the dissociation of 1 to MCP•þ þ HCN, which was derived from the G3//B3LYP calculations. The energies in italics are presented in kJ mol1.
(TS2_7, the TS between 2 and 7) in channel I-b was 27 kJ mol1 higher than that (TS4_5) in channel I-a. Formation of VA•þ. By consecutive 1,2 shifts of the γ-H of 1 to an R-C, 9 is formed (Figure 2). The ring is opened by a direct CC bond cleavage of 9 to form 10. Then, VA•þ is formed through an ionmolecule complex 11 (channe1 II). The final dissociation step was the highest barrier in this channel, which was just 6 kJ mol1 higher than that in channel I-a. The competition between the two channels is energetically possible. Several other pathways to form VA•þ þ HCN from 1 were found, which are not presented here, but their contributions to
the formation of VA•þ are negligible because the highest barriers (>320 kJ mol1 relative to 1) in the pathways were much higher and tighter than that in channel II. Formation of BT•þ. After a 1,2 shift of a β-H to the γ-C of 1, a ring contraction occurs to form a five-membered isomer 13 with a planar structure (Figure 3). The ring of 13 is opened through the 1,2 shift of the R-H to the β-C followed by a direct CC bond cleavage to form 15. A skeletal rearrangement of 15 to 17 occurs through a four-membered ring isomer 16 with a planar structure. 17 dissociates to BT•þ þ HCN via an ionmolecule complex 18 (channel III). The highest barrier (TS14_15) in 3089
dx.doi.org/10.1021/jp110074r |J. Phys. Chem. A 2011, 115, 3087–3094
The Journal of Physical Chemistry A
ARTICLE
Figure 2. Potential energy diagram for the dissociation of 1 to VA•þ þ HCN, which was derived from the G3//B3LYP calculations. The energies in italics are presented in kJ mol1.
Figure 3. Potential energy diagram for the dissociation of 1 to BT•þ þ HCN, which was derived from the G3//B3LYP calculations. The energies in italics are presented in kJ mol1.
channel III was much higher than those in channels I-a and II. Alternatively, 13 can form 18 through three steps. After the 1,2 shift of the β-H to the R-C, the CRN bond is cleaved to form an opened intermediate. After a rearrangement, 18 is formed. However, this pathway is less favored than channel III because its overall critical energy, 372 kJ mol1, is higher than that (353 kJ
mol1) in channel III. BT•þ can be formed via 2. As the β-H of the left side of 2 shown in Figure 1 shifts to the R-C, the CRCβ bond of the right side is cleaved to form an opened intermediate that eventually dissociates to BT•þ þ HCN. However, the energy of the TS for the first step was too high (450 kJ mol1) for this pathway to compete with the others. 3090
dx.doi.org/10.1021/jp110074r |J. Phys. Chem. A 2011, 115, 3087–3094
The Journal of Physical Chemistry A Formation of CB•þ. The isomerization to a Dewar pyridine radical cation 19 is the initial step in the formation of CB•þ (Figure 4). Through a direct CN bond cleavage of 19, a fourmembered ring isomer 20 is formed. 20 dissociates to CB•þ þ HCN via an ionmolecule complex 21 (channel IV). The highest barrier (TS20_21) in channel IV was much higher than those in channels I-a and II.
Figure 4. Potential energy diagram for the dissociation of 1 to CB•þ þ HCN, which was derived from the G3//B3LYP calculations. The energies in italics are presented in kJ mol1.
ARTICLE
Dissociation kinetics. The obtained PESs indicate that channels
I-a and II are energetically competitive in reaction 1, and contributions of the other channels are negligible. An RRKM model calculation was carried out to predict the rate constant for reaction 1 and the branching ratio for the two competitive channels. The total dissociation rate constant, ktot, was calculated on the basis of the PES shown in Figure 5, which included channels I-a and II and the isomerization to an R-distonic isomer 22, occurring through an 1,2 shift of an R-H of 1 to the nitrogen atom. The isomerization to 22 played the role of the kinetic trap because 22 was more stable than 1. ktot was diminished by a factor of 2 by the inclusion of 22. Several reaction pathways starting from 22 to form HCN and VA•þ or the other C4H4•þ isomers were obtained, but their contributions to the total dissociation rate were negligible because their overall critical energies (>445 kJ mol1) were much higher than those in channels I-a and II. To calculate ktot, the rate equations for the minima in Figure 5 were set up, which consisted of the individual rate constants for the forward and reverse isomerization and dissociation steps. The MATLAB program was used to numerically solve the coupled differential equations.47,48 The solution provided the time dependence of the concentrations of 1, the intermediates, MCP•þ, and VA•þ at a specific ion internal energy. ktot was obtained by fitting an exponential law to the sum of the time dependences of the concentrations of 1 and all the intermediates. The relative abundances of MCP•þ and VA•þ were obtained from the time dependences of their concentrations. This procedure was repeated for a range of the internal energy values. The individual rate constants for the reaction steps in Figure 5 were calculated using the RRKM formalism of eq 2. The critical energies and vibrational frequencies obtained from the G3// B3LYP and B3LYP/6-31þG(d) calculations, respectively, were used for the RRKM calculations. To check the reliability of the B3LYP/6-31þG(d) calculation for the TS vibrational frequencies, the B3LYP/6-311þG(3df,2p) calculation was carried out for all the TSs used for the RRKM calculations. The frequencies calculated and scaled at two levels were very similar for identical
Figure 5. Potential energy diagram for the isomerization and dissociation of 1 used for the RRKM rate constant calculation, which was derived from the G3//B3LYP calculations. The energies in italics are presented in kJ mol1. The entropies at 1000 K in the parentheses are presented in J mol1 K1. 3091
dx.doi.org/10.1021/jp110074r |J. Phys. Chem. A 2011, 115, 3087–3094
The Journal of Physical Chemistry A
Figure 6. Energy dependences of the RRKM rate constant for the reactions 1 f 2, 2 f 1, 2 f 3, 2 f 9, 4 f 5, and 10 f VA•þ þ HCN. The upper and lower curves for 10 f VA•þ þ HCN correspond to the results calculated by assuming ΔS‡1000K of 34 and 13 J mol1 K1, respectively.
TSs, which are listed in Tables S3 and S4 in the Supporting Information. 11 was ignored in the rate calculations and excluded in the PES in Figure 5 because its potential well was very shallow, as shown in Figure 2. The energy dependences of the RRKM rate constants for the important reaction steps are shown in Figure 6. The final dissociation steps (6 f MCP•þ þ HCN and 10 f VA•þ þ HCN) have no reverse barriers, which was confirmed by scanning the PESs. The activation entropy (ΔS‡) was used in the calculations for these steps as described above. The variation of ΔS‡1000K for 6 f MCP•þ þ HCN did not affect ktot at all, while the variation for 10 f VA•þ þ HCN affected ktot, but only at low internal energies, which will be described later. To choose the vibrational frequencies of the TS for 10 f VA•þ þ HCN reasonably, the corresponding PES was scanned by increasing the distance (RCN) of the departing CN bond taken as the reaction coordinate. The starting point was the intermediate 11 (RCN = 2.36 Å) located between 10 (RCN = 1.48 Å) and the products. At the optimized structure with RCN of 2.50 Å, the calculated ΔS‡1000K with respect to 10 was 13 J mol1 K1, which is the lower limit of the empirical ΔS‡1000K range mentioned above for a loose TS. Because 10 should pass along 11 (RCN = 2.36 Å) for the dissociation, it is reasonable to assume the structure optimized with RCN = 2.50 Å as the TS with the shortest RCN. At the optimized structure with RCN of 3.15 Å, ΔS‡1000K was 34 J mol1 K1, which is very close to the upper limit of the empirical ΔS‡1000K range. Namely, it was assumed that RCN varied in the range 2.503.15 Å. Then, the rate constants calculated with the two TSs (Figure 6) become approxmately the lower and upper limits of its variation. The energy dependence of the total dissociation rate constant, ktot(E), thus obtained is shown in Figure 7 together with the experimental PEPICO data reported by Eland et al.1 and Rosenstock et al.2 The variation of ΔS‡1000K for 10 f VA•þ þ HCN affected ktot at internal energies below 380 kJ mol1. The variation of ktot upon ΔS‡1000K for 10 f VA•þ þ HCN in the range 1334 J mol1 K1, which reflects the uncertainty of the present model calculation, is shown shaded in Figure 7. The calculated ktot(E) agrees with the PEPICO data considering the uncertainty (about (10 kJ mol1) of energy estimation of the PEPICO method.1,2 Figure 8 shows the calculated relative abundances of MCP•þ and VA•þ as a function of the internal
ARTICLE
Figure 7. Theoretical and experimental energy dependence of the rate constant, ktot(E), for the formation of C4H4•þ from 1 by loss of HCN. The vibrational and rotational thermal energies at 298 K were added to the original PEPICO data by Eland et al.1 and by Rosenstock et al.2 The shaded region of the theoretical curve reflects the uncertainty of the present calculation. The upper and lower curves for this work correspond to the results calculated by assuming ΔS‡1000K for 10 f VA•þ þ HCN of 34 and 13 J mol1 K1, respectively.
Figure 8. Theoretical relative abundances of MCP•þ and VA•þ formed from 1 by loss of HCN. The shaded region reflects the uncertainty of the present calculation. The upper curve for VA•þ and the lower curve for MCP•þ correspond to the results calculated by assuming ΔS‡1000K for 10 f VA•þ þ HCN of 34 J mol1 K1. The other two curves correspond to the results calculated by assuming the ΔS‡1000K of 13 J mol1 K1.
energy. MCP•þ was dominant near the dissociation threshold and at high energies, whereas VA•þ was more abundant at the low energies near 320 kJ mol1, which is in contrast to the experimental observation in the formation of the two C4H4•þ isomers from the benzene radical cation.11 It is possible that RCN of the TS for 10 f VA•þ þ HCN is larger than the assumed largest value, 3.15 Å, and hence ΔS‡1000K is larger than 34 J mol1 K1. ktot(E) and the product relative abundance were calculated by assuming that this dissociation step occurred via an extremely loose TS characterized by ΔS‡1000K = 70 J mol1 K1.49 The resultant ktot’s at higher than 350 kJ mol1 were the same as those of the upper curve in Figure 7. At lower than 350 kJ mol1, The resultant ktot’s were larger than those of the upper curve by only a factor of 3 on the average. The resultant relative abundance curves were very similar to those calculated by assuming ΔS‡1000K of 34 J mol1 3092
dx.doi.org/10.1021/jp110074r |J. Phys. Chem. A 2011, 115, 3087–3094
The Journal of Physical Chemistry A K1. The abundances of VA•þ between 300 and 350 kJ mol1 were larger than those of the upper curve in Figure 8 by only a factor of 1.04 on the average. This shows that assuming an extremely loose TS for 10 f VA•þ þ HCN hardly affected the quantitative results of the kinetic analysis. It was assumed that only channels I-a and II contributed to ktot in the present analysis, on the basis of the obtained PESs. To check the validity of this assumption, ktot(E) was obtained with additional inclusion of channel I-b of which its highest barrier (318 kJ mol1) was the lowest among the other ignored dissociation channels. The inclusion did not affect ktot(E), which confirms that channels I-a and II are the only dominant channels in reaction 1. The highest barriers in channels I-a and II, 291 and 297 kJ mol1, respectively, were similar, considering the accuracy of the present energy calculation ((6 kJ mol1). This suggests that the entropy factor can be important in the dissociation kinetics. To consider the entropy factor, the relative entropies at 1000 K (ΔS1000K) of the intermediates and TSs with respect to 1 were calculated using eq 3 and are presented in Figure 5. 2 is the first common intermediate in the formation of MCP•þ and VA•þ. The rate constant for 2 f 3 was much larger than those for 2 f 1 and 2 f 9, as shown in Figure 6. This indicates that once 2 is formed, the interconversion 2 h 3 h 4 occurs rapidly before further isomerization to each of 1, 5, and 9. Then, we can treat 24 as one potential well kinetically. The branching ratio of MCP•þ to VA•þ is determined by the further reactions occurring from the interconvertible intermediates, 24. Under this approximation, the isomerization 4 f 5 is the rate-limiting step for the formation of MCP•þ from 2 because the followed steps occur much more rapidly. Therefore, the uncertainty in the calculation of the rate constant for the final dissociation step, 6 f MCP•þ þ HCN, did not affect ktot as mentioned above. On the other hand, the variation of ΔS‡1000K for 10 f VA•þ þ HCN affected both ktot and the product branching ratio at low internal energies, as shown in Figures 7 and 8. This is because the final dissociation step, 10 f VA•þ þ HCN, limited the rate of formation of VA•þ from 2 at low energies. It should be noted that the barrier of the dissociation step was much higher than the other barriers, TS2_9 and TS9_10. Generally, the highest barrier limits the rate at low internal energies, near the reaction threshold, when a reaction occurs through several consecutive steps. Then, the branching ratio of MCP•þ to VA•þ is determined mainly by TS4_5 and TS10_VA•þ. Because their energies are similar, the entropy factor is important in the determination of the rates. The looser a TS is, the faster the reaction rate when energies of TSs are similar. The ΔS1000K values of TS4_5 and TS10_VA•þ were 43 and 7091 J mol1 K1, respectively. The latter was obtained by adding ΔS1000K of 10 (57 J mol1 K1) to ΔS‡1000K (13 34 J mol1 K1) in the reasonable range for a loose TS. Therefore, the formation of VA•þ was more favored than the formation of MCP•þ at low energies even though the overall critical energy of the former were higher than that of the latter. However, as the energy increases the rate can be limited by the tightest TS even though its energy is lower than others. In channel II, TS2_9 was such a case. ΔS1000K of TS2_9 (12 J mol1 K1) was much smaller than that of TS4_5. Then, the slope of k(E) for channel I-a would be steeper than that for channel II, and hence the relative abundance of MCP•þ would increase as the energy increases. This explains properly the energy dependence of the branching ratio shown in Figure 8.
ARTICLE
The PES shown in Figure 5 indicates that only MCP•þ is formed below 297 kJ mol1 without considering the estimated accuracy ((6 kJ mol1) of the present energy calculation. However, the rates were very slow near the reaction threshold. For example, the rate constant calculated at 296 kJ mol1 was about 0.2 s1. Therefore, the only formation of MCP•þ is hardly detectable in a usual mass spectrometer. At 300 kJ mol1, the relative abundance of VA•þ (Figure 8) was considerable (923%) even though the available energy for surmounting TS10_VA•þ (3 kJ mol1) was smaller than that (9 kJ mol1) for TS4_5. This is because the formation of VA•þ is entropically favored over the formation of MCP•þ at low energies. However, the relative abundance of VA•þ decreased with the internal energy at higher than about 320 kJ mol1, where the role of TS2_9, tighter than TS4_5, became kinetically more important in the formation of VA•þ. At the energy corresponding to the rate constant of 105 s1, typical for metastable ion dissociations50 occurring in usual mass spectrometers, the calculated branching ratio [VA•þ]/[ MCP•þ] was about 3. To summarize the competition between the formation of MCP•þ and VA•þ, their branching ratio was determined by the reaction steps after isomerization of 1 to the common intermediate 2. The rate-limiting step in the pathway from 2 to MCP•þ þ HCN was the isomerization 4 f 5 in regard to the whole internal energies investigated. In contrast, the rate-limiting step in the pathway to VA•þ þ HCN from 2 was the dissociation step at low energies but switched to the isomerization 2 f 9 at high energies. Near the dissociation threshold, the formation of MCP•þ was dominant. At somewhat higher energies, the formation of VA•þ was more favored because TS10_VA•þ was much looser than TS4_5, whereas at much higher energies, the formation of MCP•þ was more favored because TS4_5 was much looser than TS2_9.
4. CONCLUSIONS The reaction pathways for the formation of the low-energy C4H4•þ isomers, MCP•þ, VA•þ, CB•þ, and BT•þ, from 1 by the loss of HCN were obtained by the G3//B3LYP calculations. The formation of VA•þ was as important as the formation of MCP•þ in the HCN loss, even though VA•þ was thermodynamically the least stable among the four C4H4•þ isomers. The contributions of the formation of CB•þ and BT•þ to the HCN loss were negligible. The energy dependence of the rate constant for the HCN loss obtained by the RRKM model calculation agreed with the experimental PEPICO data. MCP•þ was dominant in the dissociation near the threshold because the highest energy barrier in the dissociation pathway to MCP•þ was somewhat lower than that to VA•þ. The entropy factor was important in the determination of the branching ratio. The formation of VA•þ was more favored at the low energies corresponding to the ion lifetime of microseconds, whereas the formation of MCP•þ was more favored at higher energies. ’ ASSOCIATED CONTENT
bS
Supporting Information. Reaction path degeneracies, vibrational frequencies, and rotational constants used in RRKM calculations, rate constants, and Cartesian coordinates of all the optimized structures. This material is available free of charge via the Internet at http://pubs.acs.org.
3093
dx.doi.org/10.1021/jp110074r |J. Phys. Chem. A 2011, 115, 3087–3094
The Journal of Physical Chemistry A
’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected] Tel: þ82-2-2260-8914, Fax: þ82-2-2268-8204.
’ ACKNOWLEDGMENT This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science, and Technology (2010-0008287). ’ REFERENCES (1) Eland, J. H. D.; Berkowitz, H. Int. J. Mass Spectrom. Ion Phys. 1978, 28, 297. (2) Rosenstock, H. M.; Stockbauer, R.; Parr, A. C. Int. J. Mass Spectrom. Ion Phys. 1981, 38, 323. (3) Burgers, P. C.; Holmes, J. L. Int. J. Mass Spectrom. Ion Processes 1984, 58, 15. (4) Arakawa, R.; Yoshikawa, Y. Bull. Chem. Soc. Jpn. 1987, 60, 49. (5) Urbain, P.; Leyh, B.; Remacle, F.; Lorquet, J. C. Int. J. Mass Spectrom. 1999, 185187, 155. (6) Gridelet, E.; Locht, R.; Lorquet, A. J.; Lorquet, J. C.; Leyh, B. Int. J. Mass Spectrom. 2003, 228, 389. (7) Gridelet, E.; Locht, R.; Lorquet, A. J.; Lorquet, J. C.; Leyh, B. J. Phys. Chem. A 2008, 112, 10086. (8) Jiao, C. Q.; DeJoseph, J. C. A.; Lee, R.; Garscadden, A. Int. J. Mass Spectrom. 2006, 257, 34. (9) Lifshitz, C. J. Phys. Chem. 1982, 86, 606. (10) Lifshitz, C.; Gibson, D.; Levsen, K.; Dotan, I. Int. J. Mass Spectrom. Ion Phys. 1981, 40, 157. (11) Ausloos, P. J. Am. Chem. Soc. 1981, 103, 3931. (12) Jobst, K. J.; De Winter, J.; Flammang, R.; Terlouw, J. K.; Gerbaux, P. Int. J. Mass Spectrom. 2009, 286, 83. (13) Lin, M. F.; Dyakov, Y. A.; Tseng, C. M.; Mebel, A. M.; Lin, S. H.; Lee, Y. T.; Ni, C. K. J. Chem. Phys. 2005, 123, 054309. (14) van der Hart, W. J. Int. J. Mass Spectrom. 1998, 176, 23. (15) Hohenberg, P.; Kohn, W. Phys. Rev. 1964, 136, B864. (16) Kohn, W. Phys. Rev. 1965, 140, A1133. (17) Baboul, A. G.; Curtiss, L. A.; Redfern, P. C. J. Chem. Phys. 1999, 110, 7650. (18) Baer, T.; Hase, W. L. Unimolecular Reaction Dynamics: Theory and Experiments; Oxford University Press: New York, 1996. (19) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A.; H. Nakatsuji, M. C., Li, X.; Hratchian, H. P.; Izmaylov, A. F.; Bloino, J.; Zheng, G.; Sonnenberg, J. L.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Vreven, T.; Montgomery, J. A., Jr.; Peralta, J. E.; Ogliaro, F.; Bearpark, M.; Heyd, J. J.; Brothers, E.; Kudin, K. N.; Staroverov, V. N.; Kobayashi, R.; Normand, J.; Raghavachari, K.; Rendell, A.; Burant, J. C.; Iyengar, S. S.; Tomasi, J.; Cossi, M.; Rega, N.; Millam, J. M.; Klene, M.; Knox, J. E.; Cross, J. B.; Bakken, V.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Martin, R. L.; Morokuma, K.; Zakrzewski, V. G.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Dapprich, € Farkas, Foresman, J. B.; Ortiz, J. V.; Cioslowski, J.; , S.; Daniels, A. D.; O. Fox, D. J. Gaussian 09, revision A.02; Gaussian Inc.: Wallingford, CT, 2009. (20) Becke, A. D. J. Chem. Phys. 1993, 98, 5648. (21) Lee, C.; Yang, W.; Parr, R. G. Phys. Rev. B 1988, 37, 785. (22) Curtiss, L. A.; Raghavachari, K.; Redfern, P. C.; Rassolov, V.; Pople, J. A. J. Chem. Phys. 1998, 109, 7764. (23) Curtiss, L. A.; Redfern, P. C.; Raghavachari, K. J. Chem. Phys. 2007, 126, 084108.
ARTICLE
(24) Ochterski, J. W.; Petersson, G. A.; Montgomery, J. A. J. Chem. Phys. 1996, 104, 2598. (25) Beyer, T.; Swinehart, D. R. ACM Commun. 1973, 16, 379. (26) Baer, T.; Mayer, P. M. J. Am. Soc. Mass Spectrom. 1997, 8, 103. (27) Rosenstock, H. M.; Stockbauer, R.; Parr, A. C. J. Chem. Phys. 1979, 71, 3708. (28) Merrick, J. P.; Moran, D.; Radom, L. J. Phys. Chem. A 2007, 111, 11683. (29) Lifshitz, C. Adv. Mass Spectrom. 1989, 11, 713. (30) Yim, Y. H.; Kim, M. S. J. Phys. Chem. 1993, 97, 12122. (31) Cho, Y. S.; Kim, M. S.; Choe, J. C. Int. J. Mass Spectrom. Ion Processes 1995, 145, 187. (32) Oh, S. T.; Choe, J. C.; Kim, M. S. J. Phys. Chem. 1996, 100, 13367. (33) Hwang, W. G.; Kim, M. S.; Choe, J. C. J. Phys. Chem. 1996, 100, 9227. (34) Hwang, W. G.; Moon, J. H.; Choe, J. C.; Kim, M. S. J. Phys. Chem. A 1998, 102, 7512. (35) Lim, S. H.; Choe, J. C.; Kim, M. S. J. Phys. Chem. A 1998, 102, 7375. (36) Zhang, M. Y.; Wesdemiotis, C.; Marchetti, M.; Danis, P. O.; Ray, J. C., Jr; Carpenter, B. K.; McLafferty, F. W. J. Am. Chem. Soc. 1989, 111, 8341. (37) Zhang, M. Y.; Carpenter, B. K.; McLafferty, F. W. J. Am. Chem. Soc. 1991, 113, 9499. (38) Shay, B. J.; Eberlin, M. N.; Cooks, R. G. J. Am. Soc. Mass Spectrom. 1992, 3, 518. (39) Cremer, D.; Kraka, E.; Joo, H.; Stearns, J. A.; Zwier, T. S. Phys. Chem. Chem. Phys. 2006, 8, 5304. (40) Mebel, A. M.; Kislov, V. V.; Kaiser, R. I. J. Chem .Phys. 2006, 125, 133113. (41) Hrouda, V.; Roeselova, M.; Bally, T. J. Phys. Chem. A 1997, 101, 3925. (42) Koster, G.; van der Hart, W. J. Int. J. Mass Spectrom. Ion Processes 1997, 163, 169. (43) Jensen, F. Introduction to Computational Chemistry; John Wiley & Sons: Chichester, U.K., 1999. (44) Saeys, M.; Reyniers, M. F.; Marin, G. B.; Van Speybroeck, V.; Waroquier, M. J. Phys. Chem. A 2003, 107, 9147. (45) NIST Chemistry WebBook; NIST Standard Reference Database Number 69; NIST: Gaithersburg, MD, 2010. (46) Fattahi, A.; Lis, L.; Tian, Z.; Kass, S. R. Angew. Chem., Int. Ed. 2006, 45, 4984. (47) Kim, S. Y.; Choe, J. C. Int. J. Mass Spectrom. 2010, 294, 40. (48) Kim, S. Y.; Choe, J. C. Int. J. Mass Spectrom. 2010, 295, 65. (49) At the optimized structures with RCN > 3.15 Å, more than one imaginary frequencies were obtained. So, to assume a set of frequencies of the TS corresponding to ΔS‡1000K = 70 J mol1 K1, the lowest six frequencies of the optimized structure with RCN = 3.15 Å were multiplied by a constant because the other higher frequencies were nearly invarient with RCN near 3.15 Å. (50) Cooks, R. G.; Beynon, J. H.; Caprioli, R. M.; Lester, G. R. Metastable Ions; Elsevier: Amsterdam, 1973.
3094
dx.doi.org/10.1021/jp110074r |J. Phys. Chem. A 2011, 115, 3087–3094
