Post-Transition State Dynamics in Gas Phase Reactivity: Importance of

Article pubs.acs.org/JCTC

Post-Transition State Dynamics in Gas Phase Reactivity: Importance of Bifurcations and Rotational Activation Ana Martín-Sómer,*,†,‡,§ Manuel Yáñez,† William L. Hase,∥ Marie-Pierre Gaigeot,‡,§,⊥ and Riccardo Spezia*,‡,§ †

Departamento de Química, Facultad de Ciencias, Módulo 13, Universidad Autónoma de Madrid, Campus de Excelencia UAM-CSIC, Cantoblanco, E-28049 Madrid, Spain ‡ Université d’Evry Val d’Essonne, UMR 8587 LAMBE, Boulevard F. Mitterrand, 91025 Evry Cedex, France § CNRS, Laboratoire Analyse et Modélisation pour la Biologie et l’Environnement, UMR 8587, F-91025 Evry Cedex, France ∥ Department of Chemistry and Biochemistry, Texas Tech University, Lubbock, Texas 79409-1061, United States ⊥ Institut Universitaire de France (IUF), 103 Blvd. St. Michel, 75005 Paris, France S Supporting Information *

ABSTRACT: Beyond the established use of thermodynamic vs kinetic control to explain chemical reaction selectivity, the concept of bif urcations on a potential energy surface (PES) is proving to be of pivotal importance with regard to selectivity. In this article, we studied by means of post-transition state (TS) direct dynamics simulations the effect that vibrational and rotational excitation at the TS may have on selectivity on a bifurcating PES. With this aim, we studied the post-TS unimolecular reactivity of the [Ca(formamide)]2+ ion, for which Coulomb explosion and neutral loss reactions compete. The PES exhibits different kinds of nonintrinsic reaction coordinate (IRC) dynamics, among them PES bifurcations, which direct the trajectories to multiple reaction paths after passing the TS. Direct dynamics simulations were used to distinguish between the bifurcation non-IRC dynamics and non-IRC dynamics arising from atomistic motions directing the trajectories away from the IRC. Overall, we corroborated the idea that kinetic selectivity often does not reduce to a simple choice between paths with different barrier heights and instead dynamical behavior after passing the TS may be crucial. Importantly, rotational excitation may play a pivotal role on the reaction selectivity favoring nonthermodynamic products.

1. INTRODUCTION What controls selectivity in a chemical reaction? Many efforts have been devoted to unraveling this question. Often it is assumed that the product ratio is determined by the products’ relative free energies (thermodynamic control) or, in the case that products are not allowed to fully equilibrate, by the activation barriers the reactants have to overcome along their pathways to form products (kinetic control). However, over the past few years, it has become apparent that there may be other features of the potential energy surface (PES) that influence selectivity in a chemical reaction. Other factors different from kinetics and thermodynamics may come into play concerning selectivity control, namely, dynamical factors resulting from nuclear motions and momenta of the atoms. Such factors are important for the dynamics of reactions that do not follow the intrinsic reaction coordinate (IRC), giving rise to what is called non-IRC dynamics.1−7 An interesting example of non-IRC dynamics arises for a PES that bifurcates on the downhill pathway toward products, after crossing the transition state (TS) (Scheme 1). The direct consequence is that one single TS may lead to two different products, commonly known as a PES bifurcation.8,9 When such a feature appears on the PES, the selectivity is controlled af ter © 2016 American Chemical Society

Scheme 1. Schematic Representation of Post-Transition State Bifurcation

the TS is crossed and not before as usually assumed for kinetic control. Evidence of the presence of bifurcations is becoming more extensive in a growing number of well-known chemical reactions. Some examples are Diels−Alder reactions,10 Received: December 1, 2015 Published: January 28, 2016 974

DOI: 10.1021/acs.jctc.5b01135 J. Chem. Theory Comput. 2016, 12, 974−982

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Journal of Chemical Theory and Computation sigmatropic rearrangements,11 enzyme catalysis,12 and transition metal-catalyzed reactions.13,14 Disagreements between experimental and computed reaction rates, product distributions, or temperature dependencies can often be explained by the presence of bifurcations on the underlying PES. A bifurcation is related to the presence of a valley−ridge inflection (VRI) point15 (mathematically, this is a point on the PES where one eigenvalue of the Hessian becomes zero and the gradient is orthogonal to the associated eigenvector). Therefore, methods to locate VRI points have been proposed as procedures to locate bifurcations. Some of them, based on topological analyses of the PES, are following the reaction path Hamiltonian,16 gradient extremals,17 Newton trajectories,18 and Gauss−Newton method.19 However, they require computing the Hessian at several points on the PES and are computationally intensive and prohibitive for large molecules. It is worth noting that the IRC fails to describe any branching of the PES,17 as is shown below. Chemical dynamics simulations starting from the TS provide detailed information concerning post-transition dynamics of chemical reactions20 and are often used to study reactions exhibiting post-TS bifurcations.10,21−26 Dynamics simulations may address several open fundamental questions concerning a bifurcating PES, i.e., what are the factors that control selectivity on a bifurcating PES and how can a bifurcation be predicted. Previous simulations (refs 8 and 9, and references therein) have considered these questions. Information concerning the factors that control selectivity on a bifurcating PES may be obtained by investigating the post-TS dynamics for different internal energy distributions at the TS. There are only a few studies of the effect rotational energy may play on post-TS reactivity.27,28 This prompted us to undertake a post-TS study for the PES of the [Ca(formamide)]2+ unimolecular reaction29 using “on the fly” quasiclassical post-TS trajectory calculations.20 In this system, Coulomb explosions, in which the doubly charged [Ca(formamide)]2+ ion splits into two singly charged ions, compete with neutral loss processes, in which a lighter doubly charged fragment is formed.29 This study has two aims: to provide evidence that competing processes may originate from the same TS of the PES and to show that although in most cases the product distribution is similar regardless of where the excitation energy is originally located (rotation or vibration) in the TS in some cases rotational energy may play a crucial role on the overall selectivity explaining the clear preference for one process with respect to the other.

energy (ZPE) of the TS. Then, a second set (b) for which the vibrational degrees of freedom of the TS were excited (EVIB), and a third set (c) for which the energy was used to excite external rotation (EROT). A schematic image is shown in Figure 1.

Figure 1. Scheme showing the different possibilities to locate the excitation energy in the molecular degrees of freedom at the beginning of the trajectory: (a) no excess energy, (b) vibrational degrees of freedom, and (c) external rotation.

With option (b), vibrational excitation, two different energies were used. For one, 35 kcal mol−1 was added in excess of the ZPE to each of the five TSs. For the other, 120 kcal mol−1 was added relative to the [Ca(formamide)]2+ potential energy minimum with ZPE. Thus, for this case, the initial TS energy depended on the TS considered. For option (c), rotational excitations of 35 and 64 kcal mol−1 were added to the TSs. These excitation energies were chosen according to results of energy transfer obtained from previous dynamics simulations of [Ca(formamide)]2+ CID.39 A total of 50 trajectories were computed for each set of trajectories; thus, a total of 250 trajectories were computed for each of the five TSs considered. The average compute time per trajectory is about 24 h on a single Intel Xeon processor. The vibrational and reaction coordinate energy at a TS, in excess of the ZPE, was added with microcanonical quasiclassical normal mode sampling.40 With this sampling, the phase for each vibrational mode is selected at random, while the reaction coordinate energy is added to its momenta. When rotational excitation is considered, 1/3 of the total rotational energy (EROT) is added about each rotational axis. A 0.2 fs step size was used for numerical integration of Hamilton’s equations of motion with a velocity Verlet integration algorithm, resulting in good energy conservation (within 0.1%). Trajectories were terminated after 2 ps or when the separation between reaction products exceeded 7 Å. At this separation there are no fragment interactions.

2. COMPUTATIONAL DETAILS Ab initio direct dynamics trajectory calculations30−32 at the G96LYP/6-31G(d)33,34 level of theory were performed to study the post-TS dynamics of [Ca(formamide)]2+ unimolecular decomposition. The level of theory used was benchmarked for this system in a previous work.35 The general chemical dynamics program VENUS,36,37 interfaced with the electronic structure theory software package Gaussian0938 (to compute the potential, gradients, and Hessians), was used for the simulations. The direct dynamics trajectories were initiated at five different TSs on the [Ca(formamide)]2+ PES. For each of them, we ran a set of trajectories (a) for which the initial structure has no excess energy (i.e., EMIN). In this case, the energy of the system corresponds to the potential energy difference between the reactants and the TS, plus the zero point

3. SIMULATION APPROACH A PES for [Ca(formamide)]2+ unimolecular dissociation was previously proposed based on collision induced dissociation (CID) experiments.29 This PES and RRKM theory were then used to describe the unimolecular dissociation assuming statistical kinetics.35 To obtain a deeper understanding of the unimolecular dissociation, chemical dynamics simulations of the CID process were performed, providing insight into the nonstatistical fragmentation pathways.39 In these simulations, a fraction of the activated ions did not react during the simulation time, although they have sufficient energy to reach different TSs. For the current simulations, we have assumed that a 975


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Figure 2. Different TSs that can be reached from the global minimum, min1, and final product structures obtained according to the PES proposed in ref 29. Products in red correspond to Coulomb explosions and in green neutral loss. Numbers show the activation barriers and product energies relative to min1, including ZPE, in kcal mol−1.

Figure 3. Potential energy curve explored by trajectories initiated at TS_1 (energies with respect to min1, including ZPE, in kcal mol−1).

pathways starting from the TSs that lead to the different products. Of the five TSs considered, four are directly connected to the global minimum as shown in Figure 2. The products obtained, according to the PES found from electronic structure calculations,29 are shown as well. On the basis of the IRC calculations, TS_1 is first connected with intermediates that dissociate to both the neutral loss D products and Coulomb explosion products A. TS_2 dissociates directly to Coulomb explosion products G. TS_3 connects with intermediates and

microcanonical equilibration is attained for these activated ions, and therefore, the internal energy of the ion has been uniformly redistributed within its internal degrees of freedom by the time the TS is reached. With this assumption, the trajectories are initiated at the TSs with selective excitation of vibrational or rotational modes, as described above. Thus, the lengthy computations required to simulate IVR and ensuing unimolecular dissociation for [Ca(formamide)]2+ are avoided, and the simulations focus on the post-TS dynamics and downhill 976


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Journal of Chemical Theory and Computation then dissociates to the neutral loss products B. TS_4 is first connected to intermediates and then dissociates to NH3 loss products via two pathways. TS_5 is not directly connected to the global minimum but is connected to TS_1 via intermediates. Its IRC connects with A Coulomb explosion products.

4. RESULTS In the following, product distributions obtained from the postTS dynamics are presented for the different vibrational and rotational excitations at TSs 1−5. Multiple products are obtained from a single TS, a result of interesting and important non-IRC dynamics. A. TS_1 Excitation. The PES explored by the trajectories starting at TS_1 is shown in Figure 3. Comparison with the PES previously proposed by Eizaguirre et al.29 (Figure S1, Supporting Information) shows the trajectories follow non-IRC dynamics since they follow paths different from the IRC proposed to form products. Starting from TS_1, two different products A (Coulomb explosion forming [CaOH]+ + [HCNH]+) and D (neutral loss of HNC yielding [Ca(H2O)]2+) are obtained. This is shown in Figure 4, where

Figure 4. Trajectories initiated at TS_1 ending in int3, products A and D, or going back to min1. Figure 5. Product distribution for trajectories starting from TS_1 with different initial rotational (a) and vibrational (b) excitation energy. Error bars are not shown in panels (a) and (b) for the sake of clarity, but they are similar to those in panel (c). (c) Comparison of product distribution for rotational and vibrational excitation of post-TS_1 dynamics.

the O−H2 distance is plotted against O−C distance for some prototypical trajectories. Whenever a product is formed, the O−C bond breaks, and the O−C distance increases. Depending on which fragment the hydrogen H2 is attached to, product A or D is formed. When the H2 proton attaches to the oxygen, D is formed, i.e., the O−H2 distance slightly shortens with respect to its value at the TS structure, remaining about 1 Å. When the O−H2 distance increases, the [CaOH]+ fragment moves from H2−CNH, and the H2 proton remains attached to the carbon. Figure 4 shows how some of the trajectories starting at TS_1 ended up in product D, while others yield the Coulomb explosion products A. In addition, some of the trajectories return to the initial reactant, min1, or fall into the int3 potential well and get trapped. Product distributions for trajectories with an increasing amount of excitation energy in both external rotation and vibration, with respect to the TS’ ZPE, are shown in Figure 5a and b. The same general trends are observed in both cases. As the energy increases, the product distributions change. The number of trajectories going back to min1 decrease, while those ending up in the A Coulomb explosion increase. For the intermediate energy of E = 35 kcal mol−1, few trajectories

follow the path ending in D. However, the main differences are found at high excitation energies. The Ca2+ product notably increases for high rotational energies, for which no intermediates are observed. With increasing vibrational energy, D formation is favored together with formation of other intermediates. To evaluate the influence of exciting different degrees of freedom on selectivity, we compared the results obtained when 35 kcal mol−1 is used to either excite external rotation or vibration (Figure 5c). Taking into account statistical uncertainties, it can be seen that there are no significant differences between the two sets of trajectories. Thus, we conclude that for TS_1, rotational energy is not the decisive factor for the dynamics selecting one path over the other but rather the total energy available is important. A higher energy favors the thermodynamic product A, corresponding to Coulomb explosion. 977


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Figure 6. (a) PES explored by trajectories started at TS_5 with 35 kcal mol−1 in external rotation. Black triangles mark stationary points along the path. Violet, blue, and green lines show trajectories going to min1, A, and D, respectively. (b) Comparison of product distributions for rotational and vibrational excitation of post-TS_5 dynamics.

trajectories go to A and more go to D. The number of trajectories that get trapped in the int8 potential well is practically independent of the nature of the excitation. However, for the highest energy, trajectories pass through int3 and do not remain there. In Figure S5 of the Supporting Information, product distributions are shown for increasing the initial rotational or vibrational excitation. Figure 6b compares the product distribution for EROT and EVIB = 35 kcal mol−1. Although there is more A and more D with rotational excitation, with uncertainties considered for this energy, there are no significant differences between the product distributions for EROT and EVIB. Detailed analyses of the trajectories show that the mechanisms to reach the products depend on the nature of the initial excitation. Without excitation, product A is not formed. With vibrational excitation, A is formed after passing through some of the intermediates (i.e., int3, int8, int9, ...). However, with rotational excitation, A is formed directly without passing through the intermediates. As more rotational energy is given to TS_5, A is more selectively obtained. The D product is always formed after passing int9 and/or 8. As mentioned above, the fact that two product channels (or more) are reached from a single TS may be related to the presence of a bifurcation on the PES. However, this effect may also arise from non-IRC dynamics. A way of checking whether this is the case is to start some trajectories at the TS with an initial energy below its ZPE. The (classical) excess energy in

A careful inspection of the post-TS trajectories showed that the region where the branching into the two products takes place is close to TS_5. Hence, we run trajectories starting from this TS in order to perform the same analysis from this point and clarify if the observed product branching is indeed due to a bifurcation in the PES. B. TS_5 Excitation. The same analyses were performed as above for trajectories initiated at TS_5, i.e., five sets of trajectories were computed with different excitation energies of 0, 35, and 75 kcal/mol. Figure 6a shows the potential energy explored by trajectories starting from TS_5 with 35 kcal/mol excitation in external rotation. The violet, blue, and green lines show trajectories going to min1, A, and D, respectively. Again, the dOH2 and dOC distances are used to distinguish products A and D. Figures S2−S4 of the Supporting Information show the PES explored by trajectories initiated at TS_5 with different excitation energies. As above, different products are obtained by trajectories initiated at the same TS, although the product distribution slightly depends on the nature of the excitation. Without excitation energy at TS_5, products are not formed during the simulation time. Instead, trajectories remain in different energy wells on the PES. The amount of product A increases with increasing rotational activation excitation (as could be anticipated based on the geometry of this TS), i.e. when TS_5 is excited with 35 and 75 kcal mol−1 in the external rotation, 68% and 96% of trajectories yield A, respectively. When instead vibrational excitation is increased, fewer 978


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Journal of Chemical Theory and Computation this case is 1 kcal/mol. If these unphysical trajectories still yield two different product channels, it supports the hypothesis of a bifurcation. Figure 7 shows the PES obtained from five such trajectories.

the bifurcation hypothesis is discarded. In Figure 6a, we see that trajectories yielding A are high in potential energy (about 80 kcal mol−1, orange dots). In contrast, the trajectories going to D pass through some intermediate minima (purple dots). When the vibrational modes are excited (Figure S4), some of the trajectories yielding A also explore local minima of the PES. Thus, we conclude that non-IRC behavior specially appears for trajectories leading to A products when TS_5 is rotationally excited, and these dynamics do not arise from a bifurcation on the PES. C. TS_2 Excitation. With TS_2 excitation, we once more observe that different product channels are followed after the TS is crossed, as shown in Figure 8a. A test with energy below the TS ZPE, as above, shows there is no bifurcation (i.e., there is only one route followed after crossing the TS; Figure S6a). When the TS is excited, the path leading to G is opened (Figure S6b−d). However, increasing the excitation energy does not seem to have any significant influence on the product distribution (Figure S7, Supporting Information), except for a slight increase in the G Coulomb explosion pathway with increasing rotational energy. Figure 8b shows the comparison between product distributions obtained when the same amount of energy is placed into either EROT or EVIB. For this TS, these

Figure 7. PES explored by trajectories started at TS_5 with energy below its ZPE (classical excitation energy of 1 kcal mol−1). Black triangles mark stationary points along the path.

From Figure 7, we observe that such unphysical trajectories evolve systematically to product D or go back to min1. Hence,

Figure 8. (a) Potential energy surface explored by trajectories started at TS_2 (energies, including ZPE, are given in kcal mol−1). Solid lines correspond to the IRC path, while dashed lines are for the alternative pathway found with post-TS trajectories. (b) Comparison of product distributions for rotational and vibrational excitation of post-TS_2 dynamics. 979


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can be expected that rotational energy favors product G formation. Nevertheless, the effects are more dramatic than expected. When the trajectories are initiated with low EROT = 0.4 kcal mol−1, we observe four product pathways. However, when rotational energy is added to TS_3, the product distribution completely changes and only product G is formed. In contrast, when the initial excitation is only vibration, the selectivity is lost and other products besides G are formed (Figure S15, Supporting Information). Hence, there is a clear difference on the product ratio depending upon the initial energy (Figure 9c). Rotational energy clearly favors one path over the others. Trajectories initiated from TS_3 with energy below the ZPE strongly suggest the presence of a bifurcation since both products G and B are obtained (Figure 10). Therefore, in this

two excitation patterns do not give any significant difference for the product branching ratio. D. TS_3 Excitation. When an IRC calculation is performed, TS_3 links directly with min1 and the Coulomb explosion products G, [Ca(NH2)]+ + [OCH]+ (see comments and Figures S8−S14, Supporting Information). However, after analyzing the post-TS trajectories for TS_3, we found that two different products are formed, i.e. Coulomb explosion forming G products and neutral loss of CO yielding product B [Ca(NH3)]2+ (Figure 9 and schematic PES, Figure 8a). In this case the representative distances are C−N, which indicates product formation when the bond is broken, and C−H2, which determines which of the two products is formed. Particularly important are changes in the product distributions for trajectories initiated at TS_3 when increasing rotational energy. On the basis of the geometry of this TS, it

Figure 10. PES corresponding to trajectories starting in TS_3 with energy below the ZPE (classical excitation energy of 1 kcal mol−1). Black triangles mark stationary points along the path.

case, there is a bifurcation, and the rotational energy controls the selectivity in the bifurcation region, illustrating its importance for the product selectivity. It is interesting to note that the nonthermodynamic product is the one preferably formed with increasing rotational energy. We would like to stress that when an IRC (intrinsic reaction coordinate) calculation is performed from TS_3, only one product, G, is obtained. The same applies for TS_2; IRC calculations only lead to product B. E. TS_4 Excitation. Contrary to all the cases explained above, trajectories initiated at TS_4 follow IRC dynamics independent of the nature of the initial excitation. From TS_4, the molecule evolves to an intermediate in which the O, C, and Ca atoms form a cycle and NH3 is attached to the carbon. From this local minima, two product channels are accessible leading to products E (OC−Ca2+) and F (CO−Ca2+), depending on how the cycle breaks (Figure S16, Supporting Information).

4. CONCLUSIONS We have shown that kinetic selectivity does not reduce to a simple choice between reaction paths based on their barrier heights but often depends crucially on the post-TS dynamics after passing the TS. Rotational excitation may have an important role in determining the reaction pathway. Our study strongly suggests the pivotal role of explicitly taking into account dynamics after passing the transition state to appropriately account for all the products since subtle dynamical effects such as bifurcations and rotational excitation may play crucial roles in determining the product branching

Figure 9. (a) Trajectories initiated at TS_3 and ending in products G and B or going back to min1. (b) PES explored by trajectories started at TS_3 with no excitation energy. Black triangles mark stationary points along the path. Violet, blue, and green lines show trajectories going to min1, G, and B, respectively. (c) Comparison of product distributions for rotational and vibrational excitation of post-TS_3 dynamics. 980


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Table 1. Fragments Obtained from CID Chemical Dynamics (CD-CID),39 RRKM,35 Post-TS Dynamics (This Work), and Experiments.29 product

m/z

CD-CID

RRKM

post-TS

experiments

Ca2+ Ca(OH)+ + HCNH+ [Ca(NH3)]2+ [Ca(H2O)]2+ [Ca(CO)]2+ HCO+ + (CaNH2)+

19.98 56.97 and 28.03 28.50 28.99 33.98 29.09 and 55.98

√ − √ − − √

√ − √ − − √

√ √ √ √ √ √

√ √ √ √ √ √

(2) Mann, D. J.; Hase, W. L. Ab initio direct dynamics study of cyclopropyl radical ring-opening. J. Am. Chem. Soc. 2002, 124, 3208− 3209. (3) Sun, L. P.; Song, K. Y.; Hase, W. L. A SN2 reaction that avoids its deep potential energy minimum. Science 2002, 296, 875−878. (4) Ammal, S. C.; Yamataka, H.; Aida, M.; Dupuis, M. DynamicsDriven Reaction Pathway in an Intramolecular Rearrangement. Science 2003, 299, 1555−1557. (5) Pomerantz, A. E.; Camden, J. P.; Chiou, A. S.; Ausfelder, F.; Chawla, N.; Hase, W. L.; Zare, R. N. Reaction Products with Internal Energy beyond the Kinematic Limit Result from Trajectories Far from the Minimum Energy Path: An Example from H + HBr → H2 + Br. J. Am. Chem. Soc. 2005, 127, 16368−16369. (6) Vayner, G.; Addepalli, S. V.; Song, K.; Hase, W. L. Post-transition state dynamics for propene ozonolysis: Intramolecular and unimolecular dynamics of molozonide. J. Chem. Phys. 2006, 125, 014317. (7) Lopez, J. G.; Vayner, G.; Lourderaj, U.; Addepalli, S. V.; Kato, S.; Dejong, W. A.; Windus, T. L.; Hase, W. L. A direct dynamics trajectory study of F−+ CH3OOH reactive collisions reveals a major Non-IRC reaction path. J. Am. Chem. Soc. 2007, 129, 9976−9985. (8) Ess, D. H.; Wheeler, S. E.; Iafe, R. G.; Xu, L.; Ç elebi-Ö lçüm, N.; Houk, K. N. Bifurcations on Potential Energy Surfaces of Organic Reactions. Angew. Chem., Int. Ed. 2008, 47, 7592−7601. (9) Rehbein, J.; Carpenter, B. K. Do we fully understand what controls chemical selectivity? Phys. Chem. Chem. Phys. 2011, 13, 20906−20922. (10) Thomas, J. B.; Waas, J. R.; Harmata, M.; Singleton, D. A. Control Elements in Dynamically Determined Selectivity on a Bifurcating Surface. J. Am. Chem. Soc. 2008, 130, 14544−14555. (11) Hrovat, D. A.; Duncan, J. A.; Borden, W. T. Ab Initio and DFT Calculations on the Cope Rearrangement of 1,2,6-Heptatriene. J. Am. Chem. Soc. 1999, 121, 169−175. (12) Hornsby, C. E.; Paton, R. S. Natural product biosynthesis: It’s all downhill from here. Nat. Chem. 2014, 6, 88−89. (13) Garayalde, D.; Gómez-Bengoa, E.; Huang, X.; Goeke, A.; Nevado, C. Mechanistic Insights in Gold-Stabilized Nonclassical Carbocations: Gold-Catalyzed Rearrangement of 3-Cyclopropyl Propargylic Acetates. J. Am. Chem. Soc. 2010, 132, 4720−4730. (14) Hansen, J. H.; Gregg, T. M.; Ovalles, S. R.; Lian, Y.; Autschbach, J.; Davies, H. M. L. On the Mechanism and Selectivity of the Combined C-H Activation/Cope Rearrangement. J. Am. Chem. Soc. 2011, 133, 5076−5085. (15) Taketsugu, T.; Tajima, N.; Hirao, K. Approaches to bifurcating reaction path. J. Chem. Phys. 1996, 105, 1933−1939. (16) González, J.; Giménez, X.; Bofill, J. M. A reaction path Hamiltonian defined on a Newton path. J. Chem. Phys. 2002, 116, 8713−8722. (17) Quapp, W.; Hirsch, M.; Heidrich, D. An approach to reaction path branching using valley ridge inflection points of potential-energy surfaces. Theor. Chem. Acc. 2004, 112, 40−51. (18) Quapp, W.; Schmidt, B. An empirical, variational method of approach to unsymmetric valley-ridge inflection points. Theor. Chem. Acc. 2011, 128, 47−61. (19) Schmidt, B.; Quapp, W. Search of manifolds of nonsymmetric Valley-Ridge inflection points on the potential energy surface of HCN. Theor. Chem. Acc. 2013, 132, 1−9.

ratio. A conventional computational study of only determining stationary points on the PES cannot predict “alternative” pathways, while dynamics provide a straightforward and global way for revealing the existence of post-TS bifurcations and dynamics on the PES. Methods based on topological analyses of the PES16−19 may not be necessary. The dynamical approach used here, together with short time dynamics and statistical kinetics for longer time dynamics previously reported,35,39 offers a complete picture of gas phase unimolecular fragmentation of the [Ca(formamide)]2+ complex, as shown in Table 1. We believe that this procedure may help clarifying disagreements between experimental and computational results in different fields such as organic chemistry, catalysis, and enzymatic chemistry.13,14,26,41−46

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jctc.5b01135. Computational details as well as some figures helping the discussion presented in the main text. (PDF)

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected] (A.M.-S.). *E-mail: [email protected] (R.S.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work has been partially supported by the Ministerio de Economiá y Competitividad (Project No. CTQ2012-35513C02), by the STSM COST Action CM1204, and by the Project FOTOCARBON-CM S2013/MIT-2841 of the Comunidad Autónoma de Madrid and by the ANR project DynBioReact (ANR Grant ANR-14-CE06-0029-01). A.M.-S. acknowledges a FPI contract from the Ministerio de Economiá y Competitividad of Spain. Support from the Robert A. Welch Foundation under Grant D-0005 is also greatly appreciated. Computational resources were provided by support from HPC resources from GENCI-France (Grant 2012-2014[072484] and 2015[x2015082484]). Computational time at Centro de ́ (CCC) of the Universidad Autónoma Computación Cientifica de Madrid is also acknowledged.

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REFERENCES

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