An automated transition state search using classical trajectories initialized at multiple minima.

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Cite this: DOI: 10.1039/x0xx00000x

Automated transition state search using classical trajectories initialized at multiple minima Emilio Martínez-Núñez*a

Received 00th January 2012, Accepted 00th January 2012 DOI: 10.1039/x0xx00000x www.rsc.org/

Very recently, we proposed an automated method for finding transition states of chemical reactions using dynamics simulations; the method has been termed Transition State Search using Chemical Dynamics Simulations (TSSCDS) (E. Martínez-Núñez, J. Comput. Chem., 2015, 36, 222-234). In the present work, an improved automated search procedure is developed, which consists of iteratively running different ensembles of trajectories initialized at different minima. The iterative TSSCDS method is applied to the complex C3H4O system, obtaining a total of 66 different minima and 276 transition states. With the obtained transition states and paths, statistical RRKM calculations and Kinetic Monte Carlo simulations are carried out to study the fragmentation dynamics of propenal, which is the global minimum of the system. The kinetic simulations provide a (three-body dissociation)/(CO elimination) ratio of 1.49 for an excitation energy of 148 kcal/mol, which agrees well with the corresponding value obtained in the photolysis of propenal at 193 nm (1.1), suggesting that at least these two channels: three-body dissociation (to give H2 + CO + C2H2) and CO elimination occur on the ground electronic state.

Introduction Transition state theory (TST)1-4 is a powerful tool to predict chemical reaction rates. Therefore, transition states, which correspond to first-order saddle points on the potential energy surface (PES), are of fundamental importance in chemistry. Finding transition states (TS) of a molecular system is not a trivial task, and several methods have been developed in the literature. The so-called single-ended methods5-11 require a guess TS structure, while double-ended methods need an initial knowledge of reactants and products.12-21 Besides, there is nowadays a wealth of automated methods that only need a reactant structure from which the TSs can be automatically found.22-48 Among the automated procedures, our lab has recently developed the so-called Transition State Search using Chemical Dynamics Simulations (TSSCDS) method.48 TSSCDS has two major components: high-energy chemical dynamics (or classical trajectory) simulations, and a very efficient geometry-based algorithm to identify bond breaking/formation (BBF) processes called BBFS (S for search). Several methods proposed in the literature49-68 share in common with TSSCDS the use of accelerated dynamics. However, the novelty of our method is the direct search of TS structures, using BBFS, from the simulation snapshots. So far, TSSCDS has been successfully applied to the following systems: formaldehyde, formic acid, and vinyl cyanide.48, 69 The importance of using automated methods like TSSCDS can be exemplified with the finding of a completely new HCN elimination route for vinyl cyanide, which proved to be very competitive with the traditional 3-center and 4-center channels.69

This journal is © The Royal Society of Chemistry 2013

The chemical dynamics simulations, which are an essential part of the method, have been initialized at a single minimum (typically the global one) in all test cases.48 However, complex systems may have several isomers (or minima), and some may present deep potential wells. The presence of these very stable minima may result in trapping of the short-time trajectories, hindering the exploration of the PES. In the present work, an iterative TSSCDS procedure will be proposed, where multiple ensembles of trajectories are initialized at different minima. More specifically, a guess minimum energy structure is provided to initialize an initial ensemble of trajectories and to run the whole machinery of TSSCDS. From the initial list of transition states thus obtained, intrinsic reaction coordinates (IRC) calculations70 are performed, which, eventually, will provide us with an enlarged list of isomers. Then, the TSSCDS procedure can be repeated with the trajectories initialized at the new minima. This second iteration can, again, lead to new minima and transition states, and the whole process can be repeated in a third iteration, and so on and so forth until the minima and TS lists stop growing. The iterative TSSCDS procedure proposed in this work will be employed to study the fragmentation pathways of the C3H4O molecular system. The dissociation mechanisms of propenal (CH2CHCHO), which is the global minimum of the system, have been studied by Fang on the S0, S1, and T1 PESs using multiconfigurational electronic structure methods.71 More recently, Lee and co-workers72 found 6 different minima and 15 transition states in the ground electronic state of C3H4O, using B3LYP/6-311G(d,p) optimizations. Lee’s theoretical work also includes kinetics calculations, which point out the importance of the

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triple (or three-body) dissociation channel to give H2 + CO + C2H2. The three-body dissociation was thoroughly studied by Lee in a separate experimental study,73 as well as by Suits and co-workers.74


The discrepancies found between the product branching ratios calculated theoretically at 148 kcal/mol72 with those obtained in the photolysis of propenal at 193 nm,73, 75 led Lee and co-workers to suggest that the three major channels (found experimentally): C3H3O + H, C2H3 + HCO and the C2H4 + CO occur on an excited potential energy surface. To compare with Lee’s theoretical branching ratios,72 as well as with the corresponding ratios obtained in the 193 nm photolysis of propenal, the reaction paths, obtained in the present study with the iterative TSSCDS method, are employed to simulate the fragmentation dynamics.

Methodology TSSCDS calculations. The automated TSSCDS method has been presented elsewhere,48 and here only a brief summary is provided. It combines high-energy chemical dynamics (or trajectory) simulations (CDS) with the efficient BBFS algorithm that searches for good guess transition states structures. TSSCDS employs two levels of theory: a low level (LL) is used for the CDS step, as well as for an initial optimization of the TSs. Then, the structures are re-optimized at a high level (HL) of theory. As LL, one may typically employ a semiempirical method, and then, to refine the calculations, a HL (DFT or ab initio) is selected. The BBFS algorithm that picks guess TS structures from the CDS snapshots plays a key role in the method. It selects the structure(s) where one or several bonds break or form along the trajectory, and it also determines which atoms are involved in the chemical process.48 More specifically, for each jk pair of atoms and step i along the trajectory, a normalized distance δjki can be defined as δjki = djki/djki,ref, where djki and djki,ref are the jk distance and some reference value, respectively. The algorithm considers that a reaction takes place when the following condition is fulfilled:48 (1)

Where the subscripts n and o run over the list of neighbors (atoms bonded to j) and outer atoms (non-bonded) of j, respectively. The superscript indicates that the inequality has to be held for at least a time window ∆t, which is another parameter of the algorithm. Once BFFS is performed, the procedure carries on optimizing the structure(s) selected by BFFS. The optimization is partial, with the atoms involved in the chemical reaction kept frozen. The effect of this step is a relaxation of the normal modes perpendicular to the reaction coordinate, which leads to a structure of lower energy and, most likely, closer to the TS we are looking for. Finally, the partially optimized structure is subjected to transition state optimization using the Eigenvector Following (EF) algorithm, which is implemented in the electronic structure programs interfaced with TSSCDS. In our previous work, the TS structures were screened to remove duplicates using their vibrational frequencies and energies as the

2 | J. Name., 2012, 00, 1-3

only criteria. In the present work, an additional postprocessing tool is employed to improve screening efficiency. In particular, we use the so-called social permutation invariant (SPRINT) coordinates,76 as well as other features of the adjacency and Laplacian matrices from spectral graph theory.77 An interesting property of these topological coordinates is their invariance with respect to permutation of like atoms. On the other hand, the number of zero eigenvalues of the Laplacian (or Kirchhoff) matrix is also employed as a criterion to discard structures involving separate fragments (the reader is referred to the Supporting Information (SI) for more details). All the above tasks are automated thanks to a collection of scripts and fortran programs. Currently, TSSCDS is interfaced with MOPAC201278 and GAUSSIAN0979 to run the LL and HL calculations, respectively. In the present work, TSSCDS has been employed, although in a slightly improved version (vide infra), to find TSs for the C3H4O system, and Table 1 collects the input parameters. Like in previous work, a time window ∆t and simulation time tCDS of 20 and 500 fs, respectively, are selected.48 The latest Stewart’s PM7 semiempirical method80 is employed for the dynamics. The geometries of the TSs obtained with PM7 are then refined using B3LYP/6-311G(d,p) optimizations, and their energies evaluated with single point CCSD(T)/6-311+G(3df/2p) calculations. These levels of theory correspond to those employed by Lee and co-workers in their theoretical study72 to make a direct comparison. Table 1: Input parameters of the TSSCDS method employed in this work to find the transition states of the C3H4O system. 20 ∆t (fs)a LL method PM7 CCSD(T)/6-311+G(3df/2p)// HL method B3LYP/6-311G(d,p) ECDS (kcal/mol)b 300 and 400 tCDS (fs)c 500 jk djkref(Å) CH 1.24 HH 0.84 i,ref djk OH 1.24 CC 1.63 CO 1.63 a Time window. bEnergy of the chemical dynamics simulations. c Simulation time. dReference distances vector. See the text and also ref. 48. Iterative TSSCDS. Previously, TSSCDS was applied to formaldehyde, formic acid (FA) and vinyl cyanide (VC), finding 7, 12 and 83 TSs, respectively.48, 69 In all cases, the chemical dynamics simulations were initialized at a single minimum. Besides testing TSSCDS in a new molecular system, the major goal of the present work is to show how to improve its efficacy by running ensembles of trajectories initialized at the different minima. Figure 1 shows the flow chart of the improved TSSCDS procedure. In the first iteration, the input minimum energy structure is used to initialize M ensembles of trajectories, each of them with a different excitation energy ECDS. Then, from the list of TSs obtained initially (first iteration), subsequent IRC calculations can lead to the finding of additional minima. If a number of N new minima is found, a new TSSCDS iteration can start, which would eventually consist of running M = N ensembles of trajectories starting at the N minima (M



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ARTICLE DOI: 10.1039/C5CP02175H

Kinetic calculations. The branching ratios of the different elimination pathways from the global minimum of C3H4O (propenal) are computed using a combination of both Rice-Ramsperger-KasselMarcus (RRKM) theory 81 and Kinetic Monte Carlo (KMC)82, 83 calculations.

Generate input MIN Stop i=1

N=1

NO New MIN?

YES, N


i=i+1

MIN list

TCCDS (ith iteration): M ensembles of trajectories starting at the N new minima, or using different ECDS

Update TS list

TS list

According to RRKM theory, the microcanonical ki(E) rate coefficients for an elementary step i can be calculated as: ݇௜ ሺ‫ܧ‬ሻ = ߪ௜

YES Update MIN list

explore regions far apart from the initial phase space point, and multiple-minima initialization provides a simple and useful way to achieve better efficacy.

IRC calculations

New TSs? NO

Stop Figure 1. Flow chart of the iterative TSSCDS procedure. N is the number of additional minima obtained in each iteration i. MIN and TS stand for minimum(or minima) and transition state, respectively. In the present study, the above iterative TSSCDS procedure has been carried out for the C3H4O system using only 2 iterations. In the first iteration, two ensembles (M = 2) are employed with the excitation energies ECDS of 300 and 400 kcal/mol (see Table 1). The initial minimum energy structure employed to initialize the two ensembles corresponds to MIN1a in Figure 2 (s-trans-propenal). This first iteration leads to N = 52 additional minima. However, in the second iteration, “only” M = 11 ensembles of trajectories are employed, initialized at the lowest energy isomers of the list: MIN1b, MIN2, MIN3, MIN4a, MIN4b, MIN5a, MIN5b, MIN6, MIN7, MIN8, and MIN9, respectively (see Figure 2 and also the SI for details of those structures). As will be seen later, this second iteration significantly increased the total number of structures in the TS list. As mentioned above, although the CDS are carried out at very high energies, the short time dynamics (500 fs) is not able to efficiently


ௐ೔೅ೄ ሺாሻ ௛ఘ೔ ሺாሻ

(2)

where σi is the reaction path degeneracy, WiTS(E) is the sum of states at the TS, ρi(E) is the density of states at the reactant, and E is the excitation (vibrational) energy of the system. In the present study, two different excitation energies are employed: 148 and 182 kcal/mol, which correspond, respectively to the typical laser wavelengths of 193 and 157 nm. The sums and densities of states were evaluated by direct count of the harmonic vibrational states using the Beyer-Swinehart algorithm.81 To simplify the number of processes involved in the kinetic study, only those channels with barrier heights lower than 150 kcal/mol are considered. An additional approach was to assume that all conformers of a given minimum form a microcanonical ensemble and are, therefore, in equilibrium84 (see the SI for further details on how the density of states is calculated). Despite the above two approximations, the total number of elementary processes considered in the kinetic study was 297. Namely, 210 isomerizations, 37 H2 eliminations, 19 CH2O eliminations, 15 H2O eliminations, 12 CO eliminations and 4 threebody dissociations leading to H2 + CO + C2H2. We included here the barrierless process MIN2 → CO + CH3CH, and the rate coefficients are taken from Lee’s work,72 which were calculated using variational RRKM theory. The computed RRKM rate coefficients were subsequently employed in a KMC simulation82, 83 to follow the transient behavior of the various molecular species that participate in the fragmentation of propenal at 148 and 182 kcal/mol. More details of the KMC simulations are given in the SI.

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can also be greater than N if one uses different excitation energies). The process stops when either no more transition states or minima are found in a given iteration.




MIN1a Cs 0.0

MIN9

MIN2 Cs 0.45


Cs

MIN17a Cs

66.35

89.05

20.35

MIN11a Cs

MIN4a

MIN5a

Cs

C1

25.69

MIN19a MIN20 Cs C1

MIN26 C1

89.87

92.44

MIN21a C1

72.81

MIN27 Cs

29.05

57.25

MIN18a C1

70.16

Cs

49.50

54.99

MIN28 C1

95.15

MIN7

Cs

MIN14 Cs

43.98

67.88

28.67

MIN6

MIN12a MIN13 Cs C1

42.70

MIN25 CS

Cs

MIN10

C1 41.87

MIN3

30.21

MIN15 Cs 61.30

MIN22a MIN23a CS C1

MIN8 Cs 30.97

MIN16a C1 64.83

MIN24 C1

72.99

75.23

76.92

83.63

MIN29

MIN30

MIN31a C1

MIN32a C1

126.77

140.63

Cs

95.55

C1

120.81

Figure 2. Different minima found in this study for the C3H4O system. The structures, arranged in ascending order of their relative energy, are optimized at the B3LYP/6-311G(d,p) level of theory. The numbers are relative energies in kcal/mol calculated at the CCSD(T)/6311+G(3df,2p)//B3LYP/6-311G(d,p) level of theory with the zero-point energy correction obtained from B3LYP/6-311G(d,p) frequency calculations. For those minima with multiple conformational isomers, only the lowest energy one is depicted (the different conformational isomers are labeled with small letters). The geometries and relative energies of the 66 minima can be found in the Supporting Information.

Results and discussion TSSCDS results. Figure 2 shows the minimum energy structures found in this study for the C3H4O system (conformational isomers are not depicted). They were obtained after performing IRC calculations in the forward and reverse directions, at the B3LYP/6311G(d,p) level of theory, from each of the transition states obtained automatically with TSSCDS. Using two iterations of the improved TSSCDS method, a total of 66 minima were found (53 in the first iteration). The full list of the Cartesian coordinates and relative energies of the 66 minima are collected in the SI. By contrast, in a previous theoretical study, Lee and co-workers72 only found six minima using the same levels of theory of the present study. The six minima correspond to those labeled as MIN1a, MIN1b, MIN2, MIN4a, MIN9 and MIN23a in the present study. The use of TSSCDS entails an order of magnitude increase in the number

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of minima, compared with the previous theoretical study. Furthermore, as will be shown below, several structures that are significantly populated in the course of the fragmentation of propenal at 148 and 182 kcal/mol are not reported in Lee’s paper.72 This highlights the importance of using an automated method like ours to find transition states and minima of complex systems. As mentioned above, one important finding of the present work is that the efficacy of TSSCDS can be improved by running different ensembles of trajectories started at the different minima. This can be more easily visualized in Figure 3, where the number of optimized TS structures is plotted as a function of the number of trajectories. The plot displays a stair-like shape, with each step corresponding to the different trajectory ensembles started at the different minima and/or using a different energy. As in previous work, Hase’s normal mode sampling85 is employed to prepare the initial ensembles of trajectories.



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300 MIN9

MIN5b MIN6 MIN4b MIN2

150

MIN5a

30

MIN4a MIN3

MIN1a Etraj = 400

100 MIN1a Etraj = 300

25

MIN1b

2nd TSSCDS iteration M = 11

0 0

5000

10000

15000

20000

25000

Number of trajectories Figure 3. Number of transition state structures found in this study as a function of the number of trajectories employed in two iterations of the improved TSSCDS method. M is the number of ensembles of trajectories employed in each iteration. Only the TSs optimized at the HL are depicted in the figure. An initial ensemble of trajectories was initiated at the global minimum (s-trans-propenal or MIN1a) using an energy of 300 kcal/mol. This set of simulations provided a total of 81 TS structures. A second ensemble of trajectories was also initialized at s-trans-propenal using a vibrational energy of 400 kcal/mol; this second TSSCDS step led to 47 additional structures. These two ensembles of trajectories constitute the first iteration of the new TSSCDS procedure. As mentioned above, IRC calculations lead to a total of 53 minima after this first iteration. The second iteration consists of 11 different trajectory simulations started at the next 11 lowest energy isomers found in the first iteration (MIN1b-9). In general, each of these subsequent 11 TSSCDS steps provides little increments in the total number of TS structures, compared to the first two. Overall, the total number of cumulative TSs achieved with the 13 (2+11) different trajectory simulations was 81, 128, 136, 144, 148, 179, 188, 211, 218, 240, 256, 264, and 276, respectively. Obviously, further TSSCDS iterations and/or ensembles of trajectories at the second iteration could be performed, leading, very likely, to new TS structures. However, this was not done here since the main goal of the paper is to present an improvement of the methodology rather than obtaining the full list of TS structures. Additionally, the most relevant structures, in terms of the kinetics at the excitation energies of this study, were already found in the first TSSCDS iteration. The above iterative TSSCDS procedure gives rise to 276 transition states. The distribution of their relative energies with respect to strans-propenal is depicted in Figure 4. The average relative energy of the distribution is 105.3 kcal/mol, and it peaks at approximately the same value. The distribution is relatively symmetric with respect to the average value and the number of TSs found in the ranges 0-50, 50-100, 100-150 and 150-200 kcal/mol are 8, 121, 124, and 23, respectively. The lowest energy TS structure found in this study has a relative energy of 1.4 kcal/mol and it corresponds to the torsional barrier that


Number of TSs

Number of TSs

200

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MIN8 MIN7

1st TSSCDS iteration M=2

250

separates equivalent conformational isomers of MIN2. The highest energy TS has an energy of 182.3 kcal/mol and it connects MIN10 with the H2 + HCO + CCH triple dissociation channel. The complete list of the TSs, with their geometries, relative energies and IRC information is gathered in the SI.

20 15 10 5 0 0

50

100

150

200

Energy (kcal/mol) Figure 4. Relative energy distribution of the different transition state structures found in this study at the HL with TSSCDS. The IRC calculations performed in this work indicate that the transition states found with TSSCDS can connect: two isomers of the C3H4O system, a minimum with a dissociation channel, or two different dissociation channels. The latter type may appear odd since the trajectory simulations are unimolecular, i.e., the TSs are supposed to connect at least with one minimum. However, it has been shown48 that high-energy trajectory simulations display, relatively often, non-IRC behavior.86 Non-IRC means that the (highenergy) trajectories do not necessarily follow the paths calculated in an IRC calculation. By way of example, when TSSCDS was applied to formic acid, the new (non-IRC) pathway for the water-gas shift reaction (WGSR) CO + H2O ↔ CO2 + H2 was found.48 Another possible explanation for the finding of a number of transition states connecting two dissociation channels can be the fact that the TSSCDS and/or EF algorithms can fail, leading to a deviation from the original target structure. This also explains why it is possible to find transition states connecting conformational isomers with TSSCDS, even though they do not involve bond breaking/formation. As it has been shown previously, deviations from the original target do not happen very often and TSSCDS is very efficient (the failure rate was below 5% for the systems studied previously).48 However, since the number of trajectories is quite high, even small failure rates can lead to the unintentional finding of some “extra” transition states. More specifically, the TSs and the corresponding paths obtained from IRC calculations found in this study can be grouped in the following categories: 1.

Bim/trim channel: A + B (+C) ↔ D + E (+F), where two or three reactants are connected with two or three products. Most transition states are involved in bimolecular reactions, and a few in trimolecular reactions (see below).

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ARTICLE CO channel: MINx → CO + C2H4, where either ethylene or CH3CH can be obtained. MINx is any of the 66 minima. CH2O channel: MINx → CH2O + C2H2, where either acetylene or vinylidene can be obtained. Also, formaldehyde or the higher energy isomers s-cis- and strans-HOCH can be formed. H2 channel: MINx → H2 + C3H2O, with C3H2O displaying different isomers. H2O channel: MINx → H2O + C3H2, with C3H2 displaying different isomers. Iso channel: MINx ↔ MINy. Isomerization reaction between minima x and y. Triple channel: MINx → H2 + CO + C2H2, where either acetylene or vinylidene can be obtained. Also the higher energy triple dissociation channels leading to H2 + HCO + CCH are included here.

3.

4. 5.


6. 7.

The distribution of the TSs among channels 1-7 is 25, 11, 20, 48, 16, 150 and 6, respectively. The previous theoretical work provided only 15 transition states, of which 0, 3, 2, 2, 2, 5, and 1 correspond to channels 1-7, respectively. The use of the automated TSSCDS method provides a ∼20-fold increase in the number of optimized TS structures. Quite clearly, relying on chemical intuition can lead to a serious loss of important structures. The structures of all the TSs are gathered in the SI. Also, the 12 lowest energy TSs of each type are depicted graphically in Figures 1-7S of the SI.

theory with the zero-point energy correction obtained from B3LYP/6-311G(d,p) frequency calculations. Dashed lines indicate some of the bonds that are being broken/formed. The transition state TS1-3_triple leads to acetylene, whereas TS4_triple leads to the other isomer of C2H2: vinylidene. The much higher-energy TS5_triple and TS6_triple lead, by contrast, to H2 + HCO + CCH. IRC calculations indicate that transition states TS1-6_triple lead to MIN1a, MIN17d, MIN12e, MIN12b, MIN12f, and MIN10, respectively. As shown below, TS1_triple contributes almost exclusively (∼99%) to the H2 + CO + C2H2 triple dissociation channels at 148 kcal/mol. At the higher excitation energy of 182 kcal/mol, the contribution of the other TSs doubles, accounting for ∼2% of the triple dissociations.

TS1_CO

C1 C1

Cs 56.70

76.27

TS4_CO In the following paragraphs some interesting features of these TSs are discussed, paying special attention to the triple, CO and iso TSs, as they are the most relevant ones when studying the fragmentation of the molecule at 148 and 182 kcal/mol.

TS2_triple

Cs

CS

84.16

TS4_triple

TS3_triple

C1

87.55

87.60

TS7_CO

TS5_triple

104.53

TS8_CO

TS9_CO

140.77

140.92

C1

C1 124.12

96.96

TS6_CO C1

CS

96.36

76.88

TS5_CO

C1

The triple dissociation channel leading to H2 + CO + C2H2 is the most abundant one (at the excitation energies of the present study) according to the previous theoretical work72 and also to our results (vide infra). Six triple TSs are found in this study and they are depicted in Figure 5. The lowest-energy structure TS1_triple coincides with that found in the previous theoretical study.72

TS1_triple

TS3_CO

TS2_CO

TS10_CO C1

TS11_CO C1

TS6_triple C1

CS 124.28

144.88

C1 176.14

182.28

Figure 5. Different TS structures leading to CO + H2 + C2H2 (triple channel) found in this study with the TSSCDS method. The structures, arranged in ascending order of their relative energy, are optimized at the B3LYP/6-311G(d,p) level of theory. The numbers are relative energies (with respect to MIN1a) in kcal/mol calculated at the CCSD(T)/6-311+G(3df,2p)//B3LYP/6-311G(d,p) level of

6 | J. Name., 2012, 00, 1-3

145.03

Figure 6. Different TS structures leading to CO + C2H4 found in this study with the TSSCDS method. The structures, arranged in ascending order of their relative energy, are optimized at the B3LYP/6-311G(d,p) level of theory. The numbers are relative energies (with respect to MIN1a) in kcal/mol calculated at the CCSD(T)/6-311+G(3df,2p)//B3LYP/6-311G(d,p) level of theory with the zero-point energy correction obtained from B3LYP/6311G(d,p) frequency calculations. Dashed lines indicate some of the bonds that are being broken/formed.



2.



Journal Name The CO channel is the second most abundant one at the excitation energies of this study (vide infra), and the TSs are collected in Figure 6. These eleven transition states connect, respectively, MIN3, MIN13, MIN2, MIN1a, MIN1b, MIN12e, MIN17e, MIN21a, MIN31d, MIN32c, MIN17d with the CO + C2H2 asymptote. All TS structures give rise to acetylene, except TS2_CO and TS7_CO that produce the higher energy CH3CH isomer.


As seen below, transition states TS3-5_CO are the most important ones when studying the fragmentation dynamics of propenal at 148 and 182 kcal/mol. Of those structures, only TS4_CO has been reported before by Lee and co-workers.72 In the previous theoretical study,72 two structures resembling TS3_CO and TS5_CO are reported, but their energies differ substantially from those computed here.72 In particular, TS3_CO (that connects MIN2 with CO + ethylene) has an energy of 76.88 kcal/mol, while the corresponding structure found previously had an energy of 88.44 kcal/mol (structure called TS3-P3 in Lee’s paper).72 Additionally, TS5_CO has an energy of 87.6 kcal/mol, and it is similar to transition state TS2-P3 of the previous theoretical study, but the energy of TS2-P3 is 83.54 kcal/mol.72 The remaining structures (TS1-2_CO and TS6-11_CO) have not been reported before. As many as 25 transition states are associated to bimolecular/trimolecular reactions (bim/trim TSs using our nomenclature). In particular, 21(4) structures correspond to bimolecular (trimolecular) processes. As can be seen in the SI, some of these structures connect the products of the H2 channels with those of the CO, CH2O, H2O and triple channels. Also, some TSs are found for the CO + C2H4 ↔ CH2O + C2H2 set of reactions, with C2H4, CH2O and C2H2 presenting different isomers. The remaining TSs connect the products of a given elimination channel with themselves; in these cases there is either isomerization of one the reactants, or hydrogen scrambling between reactants. Twenty transition states of the list lead to formaldehyde or to a higher energy isomer of the molecule (called CH2O TSs here). Only two of such transition states (TS3_CH2O and TS6_CH2O) have been reported before by Lee and co-workers.72 As seen below, TS3_CH2O and TS4_CH2O give rise to formaldehyde with a branching greater than 1%, and are, therefore, the most important ones when studying the kinetics of fragmentation. IRC calculations show that some of these CH2O TS structures lead to the higher energy isomers of formaldehyde: cis and trans-HOCH, like transition states TS9-11_CH2O (see Table 3S of the SI). The H2 elimination channel is connected to any of the 66 minima via 48 transition state structures (called H2 TSs). Despite an important number of H2 TSs are found here, this channel is only the fourth most important in terms of the product branching ratio. Moreover, no H2 eliminations are found in the photolysis of propenal at 193 nm.75 Of all the H2 TSs found in this study, the kinetically relevant are TS2_H2, TS5_H2, TS6_H2 and TS8_H2, as seen below. However, only TS5_H2 have been reported before in Lee’s work.72 Sixteen H2O TSs are optimized in the present work, of which only structures TS1_H2O and TS2_H2O have been also found by Lee and co-workers.72 Water elimination is a negligible channel (the least


ARTICLE DOI: 10.1039/C5CP02175H abundant) in the unimolecular decomposition of propenal at the excitation energies of this study. The lowest energy TS structures correspond to isomerizations between two minima (iso channels), and 150 iso TSs are optimized in the present study. Besides the TS structure that Lee and coworkers found connecting the lowest energy minima MIN1 and MIN2 (TS26_iso in our study; see the SI), we found another one connecting the same minima, being ∼3 kcal/mol more stable. The new structure, labeled as TS22_iso has a relative energy of 70.65 kcal/mol and its optimized structure is depicted in Figure 7 showing some relevant distances. As will be shown below, the finding of this TS explains, to some extent, the differences found between our computed product branching ratios and those obtained by Lee and co-workers.72

2.13

1.29

1.33

Figure 7. Transition state TS22_iso, connecting MIN1 with MIN2, optimized in this work (the distances, in Å, of the bonds that are being formed o broken are shown). Its relative energy (with respect to MIN1a) is 70.65 kcal/mol. Kinetic results and comparison with experiment. The fragmentation dynamics of the C3H4O system has been studied using excitation energies of 148 and 182 kcal/mol, which correspond, respectively to the typical laser wavelengths of 193 and 157 nm. The photofragments obtained upon photolysis at 193 nm include radical and molecular channels.75 The major channels correspond to dissociations to give H and HCO, and the CO elimination and the C2H2 + CO + H2 triple channel have equivalent branching ratios. By contrast, Lee and co-workers found in a separate theoretical study72 that the prevailing channel is the triple dissociation, which led them to suggest that the H, HCO and CO channels occur primarily in the excited state. The present KMC simulations are initialized at the global minimum of the C3H4O system (MIN1) and, although only the molecular channels are included, a comparison can be made with the theoretical and experimental results obtained by Lee and coworkers.72, 75 Figure 8 shows the population of the minima and products, as a function of time, obtained in our simulation when an ensemble of molecules is initialized at MIN1 with 148 kcal/mol of excitation energy. As indicated above, the kinetic study does not take into account conformational dynamics, as they are assumed to be much faster than the other reaction mechanisms (see the SI). As seen in the figure, besides the global minimum (not depicted for clarity), other isomers of propenal: MIN2, MIN4, MIN5, MIN7 and MIN12 play an important role in the fragmentation dynamics at 148 kcal/mol. The structures of MIN5, MIN7 and MIN12 are missing in Lee’s theoretical work.72

J. Name., 2012, 00, 1-3 | 7


Page 7 of 10




Triple dissociation via TS1_triple is, by far, the most abundant product channel found in this study, followed by MIN2 → CO + CH3CH dissociation, CO elimination via TS4_CO, CH2O elimination via TS3_CH2O, and CO elimination via TS5_CO. Then, H2 eliminations via TS2_H2 and TS5_H2, CH2O elimination via TS4_CH2O, and CO elimination via TS3_CO follow in importance.

relative population of MIN4, MIN5, MIN7 and MIN12 rises at the higher excitation energy. In a similar fashion, more decomposition channels contribute significantly to the fragmentation of the molecule. Thus, at 182 kcal/mol, the H2O elimination channel via TS1_H2O, as well as the H2 elimination channels via TS6_H2 and TS8_H2 have a branching ratio greater than 1%. Minima

The other channels are obtained with branching ratios lower than 1%.

MIN2 MIN4 MIN5 MIN7 MIN12

TS4_CO

10

TS3_CO TS4_CH2O

0

200

400

Time (ps)

Figure 8. Population of the most abundant species involved in the fragmentation dynamics of propenal at 148 kcal/mol (the exponential decay of MIN1 has been removed for clarity). The populations of minima and products (in logarithmic scale) are shown on the left and right panels, respectively. Products are indicated by the corresponding transition state. Like in the previous theoretical study,72 the triple dissociation channel dominates over the other, but the CO elimination is substantially more important in the present work. Table 2 shows that the (triple dissociation)/(CO elimination) ratio is 6.82 in Lee’s theoretical work,72 vs a value of 1.49 found in the present study. The result obtained here is surprisingly close to the experimental value of 1.1, obtained in the 193 nm photolysis of propenal.75 As indicated above, many minima and TS structures are missing in Lee’s paper.72 One of the most important structures not considered in the previous theoretical study is the isomerization transition state TS22_iso (connecting the two lowest energy minima). By way of example, when this structure is not considered in our KMC simulation, the triple/CO ratio becomes 2.04. The remaining differences between both theoretical kinetic results can be explained by the much larger scale kinetic study presented here. The water, formaldehyde and molecular hydrogen elimination channels are of minor importance, in agreement with experiment.75 However, quite surprisingly, the H2 elimination channel has not been detected in the photolysis of propenal at 193 nm,75 while in the present study the H2/CO branching ratio is not negligible (about 0.19). Additional KMC simulations were also carried out at the higher excitation energy of 182 kcal/mol. The population of minima and products of an ensemble of propenal molecules excited at this energy is shown in Figure 9 as a function of time. At this excitation energy the decomposition of propenal takes place approximately one order of magnitude faster than at the lower energy. As expected, the

8 | J. Name., 2012, 00, 1-3

TS4_CO 10 TS3_CH2O MIN2 → CO + CH3CH TS5_CO TS2_H2 TS4_CH2O TS3_CO TS1_H2O 1

0

25

50

Time (ps)

TS5_H2

1

400

MIN2 MIN4 MIN5 MIN7 MIN12

TS3_CH2O TS5_CO TS2_H2

Time (ps)

Population

MIN2 → CO + CH3CH

Population


TS1_triple

200

TS1_triple

Products

Minima

0

Products

TS5_H2 TS8_H2 TS6_H2

0

25

50

Time (ps)

Figure 9. Population of the most abundant species involved in the fragmentation dynamics of propenal at 182 kcal/mol (the exponential decay of MIN1 has been removed for clarity). The populations of minima and products (in logarithmic scale) are shown on the left and right panels, respectively. Products are indicated by the corresponding transition state. Table 2 shows that the (triple dissociation)/(CO elimination) ratio increases with the excitation energy: from 1.49 to 2.32. Also, as mentioned above, the branching ratio of the water, formaldehyde and H2 elimination channels becomes higher. Differences between the present KMC simulations, based on 297 elementary processes, and the previous kinetic results are still substantial at the higher excitation energy. The relatively good agreement obtained between the KMC simulations at 148 kcal/mol and the experimental photolysis results at 193 nm indicate that, most likely, at least the triple dissociation and the CO elimination channels take place on the ground electronic state. However, our simulations assume that internal conversion is a fully statistical process, which might not be the case. At any rate, the results presented here point out the importance of using automated procedures to find minimum energy and transition state structures of a molecular system. Chemical intuition, though very important, is not enough to ensure an exhaustive sampling of the potential energy surface of a complex system. TSSCDS is designed to find transition states (either “tight” or “loose”). However, it does not find barrierless pathways, like the MIN2 → CO + CH3CH process employed above in the kinetic study. In future work, it would be desirable to incorporate an automated search of these pathways as well, which could be done following these steps: 1.

Set an upper value for the dissociation energy, as well as the excitation energy or temperature to be employed in the kinetics.



ARTICLE

Page 9 of 10


Journal Name


3.

For each mimimum found with TSSCDS, perform potential energy surface scans using an appropriate level of electronic structure theory. Use the results of step 2 to calculate, using variational TST or RRKM theory,81 the variational transition states of the molecule, at the temperature or energy defined in step 1.

Finally, in this study, and also in the original paper where the method is proposed,48 the applications are restricted to photodissociation dynamics. However, current work in our group includes the use of TSSCDS to study: organic reactions, combustion processes, and collision-induced dissociation (CID) of ions. Table 2: Relative product abundances (with respect to the CO channel) obtained in this study at 148 and 182 kcal/mol in comparison with previous experimental and theoretical results. E = 148 kcal/mol

E = 182 kcal/mol

Channel

Ref 72

This work

Exp75

Ref 72

This work

H2O

0.01

0.03

0.07

0.10

0.08

CH2O

0.65

0.20

0.07

1.12

0.43

H2

0.09

0.19

0.00

0.17

0.42

CO

1.00

1.00

1.00

1.00

1.00

Triple

6.82

1.49

1.10

9.09

2.32

Conclusions The main conclusions of this paper are summarized as follows: 4. An improved iterative TSSCDS method is presented in the present work. The new development consists of performing different sets of trajectory simulations initialized at multiple minima or using different excitation energies. 5. The new strategy was tested in the C3H4O system, with the chemical dynamics simulations starting from the twelve lowest energy minima, and using two excitation energies. 6. The iterative TSSCDS procedure leads to a total of 66 minima and 276 transition states for the C3H4O system. Previous theoretical work on the same system only reported 6 minima and 15 transition states. 7. The transition states can be categorized as: Bimolecular/trimolecular, CO elimination, CH2O elimination, H2 elimination, H2O elimination, isomerization, or triple dissociation. 8. The kinetic simulations performed at 148 kcal/mol provide branching ratios for the molecular channels that agree with those obtained in the photolysis of propenal at 193 nm. This suggests that at least the triple dissociation and CO elimination channel may take place on the ground electronic state. 9. The methodology presented in the present paper is implemented in a set of scripts and it runs very efficiently in parallel machines. The results obtained


here point out the importance of using an automated method to find transition states of complex molecular systems.

Acknowledgements The author thanks “Centro de Supercomputación de Galicia (CESGA)” for the use of their facilities.

Notes and references a

Departamento de Química Física and Centro Singular de Investigación en Química Biológica y Materiales Moleculares (CIQUS), Campus Vida, Universidade de Santiago de Compostela, 15782, Santiago de Compostela, Spain Electronic Supplementary Information (ESI) available: Details of the TSSCDS procedure. Energies and optimized geometries of all stationary points of the C3H4O system found by TSSCDS. Details of the KMC simulations. See DOI: 10.1039/b000000x/

1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14.

15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31.

H. Eyring, J. Chem. Phys., 1935, 3, 107. E. Wigner, Trans. Faraday Soc., 1938, 34, 29. J. C. Keck, Adv. Chem. Phys., 1967, 13, 85. P. Pechukas, Dynamics of Molecular Collisions, Plenum, New York, 1976. H. N. Schlegel, J. Comput. Chem., 1982, 3, 214. C. J. Cerjan and W. H. Miller, J. Chem. Phys., 1981, 75, 2800. J. Baker, J. Comput. Chem., 1986, 7, 385. P. Csaszar and P. Pulay, J. Mol. Struct., 1984, 114, 31. G. Henkelman and H. Jonsson, J. Chem. Phys., 1999, 111, 7010. A. Heyden, A. T. Bell and F. J. Keil, J. Chem. Phys., 2005, 123, 224101. J. Kastner and P. Sherwood, J. Chem. Phys., 2008, 128, 014106. F. Jensen, Introduction to Computational Chemistry, 2nd ed., Wiley, Chichester, England, 2006. E. Weinan and E. Vanden-Eijnden, Annu. Rev. Phys. Chem., 2010, 61, 391. H. Jonsson, G. Mills and K. W. Jacobsen, in Classical and Quantum Dynamics in Condensed Phase Simulations, eds. B. J. Berne, G. Ciccoti and D. F. Coker, River Edge, NJ, 1998. G. Henkelman, B. P. Uberuaga and H. Jonsson, J. Chem. Phys., 2000, 113, 9901. G. Henkelman and H. Jonsson, J. Chem. Phys., 2000, 113, 9978. E. Winan, W. Ren and E. Vanden-Eijnden, Phys. Rev. B, 2002, 66, 052301. E. Weinan, W. Ren and E. Vanden-Eijnden, J. Chem. Phys., 2007, 126, 164103. B. Peters, A. Heyden, A. T. Bell and A. Chakraborty, J. Chem. Phys., 2004, 120, 7877. H. Chaffey-Millar, A. Nikodem, A. V. Matveev, S. Kruger and N. Rosch, J. Chem. Theory Comput., 2012, 8, 777. A. Behn, P. M. Zimmerman, A. T. Bell and M. Head-Gordon, J. Chem. Theory Comput., 2011, 7, 4019. J. Pancir, Collect. Czech. Chem. Commun., 1975, 40, 1112. M. V. Basilevsky and A. G. Shamov, Chem. Phys., 1981, 60, 347. M. V. Basilevsky, Chem. Phys., 1982, 67, 337. D. J. Rowe and A. Ryman, J. Math. Phys., 1982, 23, 732. D. K. Hoffman, R. S. Nord and K. Ruedenberg, Theor. Chim. Acta, 1986, 69, 265. P. Jorgensen, H. J. A. Jensen and T. Helgaker, Theor. Chim. Acta, 1988, 73, 55. W. Quapp, Theor. Chim. Acta, 1989, 75, 447. H. B. Schlegel, Theor. Chim. Acta, 1992, 83, 15. J. Q. Sun and K. Ruedenberg, J. Chem. Phys., 1993, 98, 9707. K. Bondensgard and F. Jensen, J. Chem. Phys., 1996, 104, 8025.

J. Name., 2012, 00, 1-3 | 9


2.



33. 34. 35. 36. 37.


38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. 50. 51. 52. 53. 54. 55.

56. 57. 58. 59. 60. 61. 62. 63. 64. 65. 66. 67. 68. 69. 70. 71. 72. 73. 74. 75.

Journal Name DOI: 10.1039/C5CP02175H W. Quapp, M. Hirsch, O. Imig and D. Heidrich, J. Comput. Chem., 1998, 19, 1087. W. Quapp, M. Hirsch and D. Heidrich, Theor. Chem. Acc., 1998, 100, 285. J. M. Bofill and J. M. Anglada, Theor. Chem. Acc., 2001, 105, 463. R. Crehuet, J. M. Bofill and J. M. Anglada, Theor. Chem. Acc., 2002, 107, 130. M. Hirsch and W. Quapp, J. Comput. Chem., 2002, 23, 887. M. Dallos, H. Lischka, E. Ventura Do Monte, M. Hirsch and W. Quapp, J. Comput. Chem., 2002, 23, 576. M. Hirsch and W. Quapp, J. Mol. Struct. (Theochem), 2004, 683, 1!3. K. Ohno and S. Maeda, Chem. Phys. Lett., 2004, 384, 277. S. Maeda and K. Ohno, J. Phys. Chem. A, 2005, 109, 5742. K. Ohno and S. Maeda, J. Phys. Chem. A, 2006, 110, 8933. K. Ohno and S. Maeda, Phys. Scr., 2008, 78, 058122. X. Yang, S. Maeda and K. Ohno, J. Phys. Chem. A, 2007, 111, 5099. X. Yang, S. Maeda and K. Ohno, Chem. Phys. Lett., 2006, 418, 208. X. Yang, S. Maeda and K. Ohno, J. Phys. Chem. A, 2005, 109, 7319. Y. Watanabe, S. Maeda and K. Ohno, Chem. Phys. Lett., 2007, 447, 21. S. Maeda and K. Ohno, Chem. Phys. Lett., 2008, 460, 55. E. Martínez-Núñez, J. Comput. Chem., 2015, 36, 222. M. R. Sorensen and A. F. Voter, J. Chem. Phys., 2000, 112, 9599. Y. Shim, N. B. Callahan and J. G. Amar, J. Chem. Phys., 2013, 138, 094101. D. R. Glowacki, E. Paci and D. V. Shalashilin, J. Phys. Chem. B, 2009, 113, 16603. D. R. Glowacki, E. Paci and D. V. Shalashilin, J. Chem. Theory Comput., 2011, 7, 1244. D. V. Shalashilin, G. S. Beddard, E. Paci and D. R. Glowacki, J. Chem. Phys., 2012, 137, 165102. E. Martinez-Nunez and D. V. Shalashilin, Journal of Chemical Theory and Computation, 2006, 2, 912. J. Booth, S. Vazquez, E. Martínez-Núñez, A. Marks, J. Rodgers, D. R. Glowacki and D. V. Shalashilin, Phil. Trans. R. Soc. A, 2014, 372, 20130384. R. Elber, Biophys. J., 2007, 92, L85. A. K. Faradjian and R. Elber, J. Chem. Phys., 2004, 120, 10880. K. Kuczera, G. S. Jas and R. Elber, J. Phys. Chem. A, 2009, 113, 7461. L. Maragliano, E. Vanden-Eijnden and B. Roux, J. Chem. Theory Comput., 2009, 5, 2589. E. Vanden-Eijnden, M. Venturoli, G. Ciccoti and R. Elber, J. Chem. Phys., 2008, 129, 174102. A. M. A. West, R. Elber and D. Shalloway, J. Chem. Phys., 2007, 126, 145104. E. Vanden-Eijnden and M. Venturoli, J. Chem. Phys., 2009, 130, 194101. A. F. Voter, Phys. Rev. Lett., 1997, 78, 3908. A. F. Voter, J. Chem. Phys., 1997, 106, 4465. G. M. Torrie and J. P. Valleau, J. Chem. Phys., 1977, 66, 1402. G. M. Torrie and J. P. Valleau, J. Comput. Chem., 1977, 23, 187. J. Kastner, Wiley Interdiscip. Rev. Comput. Mol. Sci., 2011, 1, 932. D. Frenkel and B. Smit, Understanding Molecular Simulations, Academic Press, London, UK, 2002. S. A. Vazquez and E. Martinez-Nunez, Phys. Chem. Chem. Phys., 2015, 17, 6948. K. Fukui, Acc. Chem. Res., 1981, 14, 363. W.-H. Fang, J. Am. Chem. Soc., 1999, 121, 8376. C.-H. Chin and S.-H. Lee, J. Chem. Phys., 2011, 134, 044309. S.-H. Lee, C.-H. Chin and C. Chaudhuri, ChemPhysChem, 2011, 12, 753. A. Dey, R. Fernando and A. G. Suits, J. Chem. Phys., 2014, 140, 154301. C. Chaudhuri and S.-H. Lee, Phys. Chem. Chem. Phys., 2011, 13, 7312.

10 | J. Name., 2012, 00, 1-3

76. 77. 78.

79.

80. 81.

82. 83. 84. 85. 86.

F. Pietrucci and W. Andreoni, Phys. Rev. Lett., 2011, 107, 085504. B. Bollobas, Modern Graph Theory, Springer-Verlag, Berlin, 1998. J. J. P. Stewart, MOPAC2012, Stewart Computational Chemistry. , Colorado Springs, CO, USA. Available at: http://OpenMOPAC.net. M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, G. Scalmani, V. Barone, B. Mennucci and G. A. Petersson, et. al. Gaussian 09 (2009) Gaussian Inc., Wallingford CT. J. J. P. Stewart, J. Mol. Model., 2013, 19, 1. G. Smith and R. G. Gilbert, Theory of unimolecular and recombination reactions, Blackwell Scientific Publications, Oxford, 1990. A. B. Bortz, M. H. Kalos and J. L. Lebowitz, J. Comput. Phys., 1975, 17, 10. D. T. Gillespie, J. Comput. Phys., 1976, 22, 403. G. H. Peslherbe and W. L. Hase, J. Chem. Phys., 1994, 101, 8535. W. L. Hase, D. G. Buckowski and K. N. Swamy, J. Phys. Chem., 1983, 87, 2754. U. Lourderaj and W. L. Hase, J. Phys. Chem. A, 2009, 113, 2236.



ARTICLE 32.


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Transition-state theory predicts clogging at the microscale.

Attention in visual search: multiple search classes.

Dissociation of 1,1,1-trifluoroethane is an intrinsic RRKM process: classical trajectories and successful master equation modeling.

Development of an Automated Medical Diagnosis System for Classifying Thyroid Tumor Cells using Multiple Classifier Fusion.

Initialized decadal prediction for transition to positive phase of the Interdecadal Pacific Oscillation.

Affinity purification of tissue plasminogen activator using transition-state analogues.

An intuitive graphical webserver for multiple-choice protein sequence search.

Control of plasmon emission and dynamics at the transition from classical to quantum coupling.

Another Look at the Mechanisms of Hydride Transfer Enzymes with Quantum and Classical Transition Path Sampling.

Creating an automated trigger for sepsis clinical decision support at emergency department triage using machine learning.

An inhibitory gate for state transition in cortex.

Potential energy landscapes for the 2D XY model: minima, transition states, and pathways.

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Using ToxCast™ Data to Reconstruct Dynamic Cell State Trajectories and Estimate Toxicological Points of Departure.

Automated identification of depsipeptide natural products by an informatic search algorithm.

MG-Digger: An Automated Pipeline to Search for Giant Virus-Related Sequences in Metagenomes.

Simulating quantum state engineering in spontaneous parametric down-conversion using classical light.

Lumen Segmentation in Intravascular Optical Coherence Tomography Using Backscattering Tracked and Initialized Random Walks.