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Theor Chem Acc (2016) 135:16 DOI 10.1007/s00214-015-1792-6

REGULAR ARTICLE

Accessing the free energy profile of a ring closure in a prolinecatalyzed reaction using a reactive force field

Pierre O. Hubin1 Denis Jacquemin2,3 Laurence Leherte1 Daniel P. Vercauteren1

Received: 13 October 2015 / Accepted: 10 December 2015 Springer-Verlag Berlin Heidelberg 2015

1 Introduction

Organic reaction mechanisms are nowadays commonly investigated by means of quantum mechanics (QM) calcu-lations. In particular, density functional theory (DFT) has been successfully applied to rationalize a large number of organic reactions [14]. However, QM methods can hardly be routinely applied to systems containing several hundreds of atoms, and various strategies were proposed to over-come this problem. For instance, QM/MM that consists in treating one part of the system with a high-accuracy QM method while the rest is described with a computation-ally cheaper molecular mechanics (MM) scheme [5, 6], allows to treat large systems [7, 8]. Nevertheless, achieving a relevant sampling often remains a challenge because the number of states of the system that can be modeled is often limited by the computational cost of the high-accuracy method.

On the other hand, force fields (FF) allow to study the dynamics of systems containing tens of thousands of atoms on microsecond timescales, but their application is gener-ally limited for reactivity and reaction mechanism issues. Indeed, most FFs cannot describe the breakings and forma-tions of chemical bonds as they impose a fixed atomic con-nectivity. A solution, which finds its origins in the 1980s in the empirical valence bond (EVB) method [9], is to couple two FFs, one describing accurately the reactant state and the other the product state. Besides EVB, other strategies that rely on a similar FF coupling idea were proposed more recently, for instance the adiabatic reactive FF approach [10]. Another strategy consists in designing a FF that can intrinsically handle the breakings and formations of chemi-cal bonds. The ReaxFF reactive FF belongs to this category [11]. Bond orders between each atomic pairs are computed as a function of the interatomic distances to determine the

Abstract The free energy profile of a ring closure involv-ing a carboxylate and an iminium functional group in a proline-derived compound is determined by applying the adaptive biasing force scheme along molecular dynamics simulations. As the reaction considered implies the for-mation of a covalent bond, the system is modeled with a reactive force field (FF), namely ReaxFF. The impact of the surrounding water molecules on the reaction mecha-nism is investigated in detail using three FF models for the water molecules. In particular, a hybrid reactive/non-reactive FF is used to assess explicit solvent effects while avoiding solutesolvent reactions. Combined with existing experimental observations, our results provide an explana-tion for the role of water molecules in the proline-catalyzed aldol reaction, which is one of the hallmark reactions in organocatalysis.

Keywords ReaxFF Molecular dynamics Free energy calculations Organocatalysis Proline catalysis

Electronic supplementary material The online version of this article (doi:10.1007/s00214-015-1792-6) contains supplementary material, which is available to authorized users.

* Pierre O. Hubin pierre.hubin@unamur.be

1 Laboratoire de Physico-Chimie Informatique (PCI), Unit de Chimie Physique Thorique et Structurale, Universit de Namur, 61 rue de Bruxelles, 5000 Namur, Belgium

2 Laboratoire CEISAM - UMR CNRS 6230, Universit de Nantes, 2 rue de la Houssinire, BP92208, 44322 Nantes Cedex 3, France

3 Institut Universitaire de France, 103 Boulevard St Michel, 75005 Paris Cedex 5, France

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connectivity at every step of the calculation [11]. Due to its specific formalism, ReaxFF can be used in combination with molecular dynamics (MD) simulations to achieve a proper sampling of a system containing thousands of atoms wherein chemical reactions occur. One can already find numerous literature examples where ReaxFF was used to study the spontaneous alteration of different compounds in various conditions, e.g., the oxidation of hydrocarbons [12], the stability of particular species, such as siloxane polymers [13], metalorganic frameworks [14], or the reactivity of explosive compounds [15]. In several cases, significant energy barriers must be overcome to form the product state. Therefore, simulations going far beyond the nanosecond timescale should be required to observe those transitions. Early approaches to overcome large energy bar-riers while using ReaxFF notably relied on the addition of constraints on several geometrical variables of the system to force a transition toward a given structure [1618]. We notably relied on this strategy in a previous study to inves-tigate the isomerization between the iminium and enamine species, step (d) represented in Fig. 1 [18]. The major prob-lem of the former strategy is to quantify the energy differ-ences between the states visited during the constrained MD simulation. Alternatively, the nudged elastic band (NEB) approach [19] was also applied in the ReaxFF framework to identify the minimum energy path (MEP) connecting a reactant and a product state. It was, for example, selected to study the hydrolysis of penicillin and cefotaxime [20]. The latter NEB approach is efficient to locate the MEP connect-ing two well-defined structures, but it mainly consists in an optimization procedure that is not necessarily adequate to

achieve a proper sampling for large systems. A variety of methods are available to efficiently overcome energy bar-riers during MD simulations allowing a proper sampling of the states relevant for the system under study [2126].

In the present work, we mainly rely on the adaptive biasing force (ABF) scheme and combine it with ReaxFF. ABF has notably been used to investigate conformational changes in peptides [27]. The general idea is to record the force undertaken by a chosen reaction coordinate (RC), i.e., the system force, and apply a biasing force to compensate it so to achieve a proper sampling along the RC. As long as the simulation goes on, the estimation of the system force in the different regions of the RC is improved and the bias-ing force accordingly updated. At the end of the simulation, the free energy profile is obtained by integrating the sys-tem force [23, 28]. To the best of our knowledge, ABF has not been applied previously to model a chemical reaction, in the sense of the formation of a chemical bond in a sys-tem modeled with a reactive FF; the present article aims to tackle this goal. Nevertheless, we underline that there have been a few attempts to combine a free energy method with ReaxFF. For instance, umbrella sampling, steered MD, and metadynamics have been used conjointly to model the breaking mechanism of a disulfide bond [29]. Likewise, in a study focusing on radical recombination reactions taking place in lithium ion battery, free energy differences were computed on the basis of steered MD simulations [30].

The case study that has been chosen here is a key step of a proline-catalyzed aldol reaction. Proline-catalyzed aldol reactions belong to the broader field of asymmetric organo-catalysis, a branch of organic synthetic chemistry which

Fig. 1 Representation of the mechanism of the proline-cat-alyzed aldol reaction following the enamine (in black) and oxa-zolidinone (in gray) pathways N

COOH

H (a) (b)

(d)(e)

(c)

O

NH+ COO-

OH

N+ COO-

N COOH

O

H2O

N+ COO-

HON COOHHO

OH

H2O

(f)

HO O

NO

O

N COO-

basebase

H+-H+

O

NO

OO-N

O

OOH

H2O

H+

(g)

(h) (i)

(j)

(k)(l)

II IIII-zwitterion

IV

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rapidly developed during the last 15 years [31]. It consists in using relatively small chiral organic molecules to achieve asymmetric synthesis. The proline-catalyzed aldol reaction is one of the seminal examples of such chemistry [32]. The mechanism of this reaction has been extensively investi-gated in the literature from both experimental [3338] and theoretical [33, 3942] points of view. It was essentially shown that depending on the reaction conditions, especially the presence or absence of a basic agent in the reaction mixture, two mechanistic pathways must be considered, the neutral enamine one (depicted in black in Fig. 1) and the oxazolidinone one (in gray in Fig. 1). Interestingly, it was also shown experimentally that using water as an additive has a positive impact on the reaction, increasing both the yield and the enantioselectivity of the reaction [34, 36]. On the basis of experimental results, it was proposed that water could partly prevent the formation of the oxazolidinone species (I) [34]. This intermediate was indeed character-ized as a dead-end in the context of the enamine pathway [43]. However, to the best of our knowledge, the impact of water on the stability of I remains to be investigated and rationalized with theoretical tools. Here, we therefore mainly focus on this specific step of the reaction using the aforementioned theoretical approach. Particularly, water molecules will be modeled using both the reactive FF and the all-atom version of OPLS [44] (OPLS-AA) to deter-mine which kind of solutesolvent interactions impacts the free energy profile of the reaction. Besides avoiding solutesolvent reactions, the use of a non-reactive FF to describe the surrounding molecules provides a valuable speedup of the simulations, as ReaxFF remains more computationally demanding than traditional non-reactive FFs. Our results provide a pertinent explanation for the role of water mol-ecules in the mechanism of the considered reaction. The influence of the selection of various FF schemes used to model the water molecules is discussed as well.

2 Computational methods

All simulations were performed with the LAMMPS pro-gram [45] in which the ReaxFF FF is implemented [46]. We relied on a version of the ReaxFF potential specifi-cally trained for the molecules of interest. The training set used to obtain the FF parameters has already been described elsewhere [18]. It consists in DFT results at the M062-2X/6-31+G(d,p) [47] level of theory which stands as a reliable reference for the considered reaction [18, 48]. Three independent MD runs were performed for each simulation. As required by the ABF algorithm [28], simulations were performed in the NVT ensemble, a NosHoover thermostat [49] being used to control the temperature. A time step of 0.2 fs was chosen to ensure the

energy conservation in the studied systems. The version of the Colvar module implemented in LAMMPS was used to apply the ABF scheme [5052]. The statistical errors on the computed free energy differences were determined with Eq. (1), following a procedure described in the litera-ture [28]:

The RC being divided into a number of bins of equal width , Eq. (1) provides the statistical error on the free energy computed between the bins a and b; i is the auto-correlation time of the system force applied on the RC; ni is the number of samples in bin i; t is the time step of the simulation; and F2 i is the variance of the system force applied on the RC. In a previous work, the same value of the autocorrelation time was used in all bins as only small variations in different regions of the RC were found [28]. In our case, non-negligible variations were observed. The statistical errors were thus computed on the basis of both the lowest and highest autocorrelation times, and we pro-vide both values in our results.

To investigate the effects of explicit water molecules, the reactive solute species was put in a cubic box containing 104 water molecules (15 15 15 ). To justify the choice of a relatively small box size, the same simulation was performed in a box containing 900 water molecules (30 30 30 ); it showed no influence on the com-puted free energy profile. To accelerate the sampling, a multiple replica approach [53] was used for simulations in the water box. Three different potentials were considered to model the water molecules. The first one is the ReaxFF potential with the set of parameters described above. The second is a modified version of this potential to disable the formation of bonds between oxygen atoms of water and carbon atoms of the solute. Finally, as described in the Introduction, water molecules were also modeled using a non-reacting FF. The OPLS-AA FF implemented in LAMMPS was selected for this task. In this latter case, sol-utesolute interactions were completely defined with ReaxFF, solventsolvent interactions with OPLS-AA (bonding and non-bonding terms), and solutesolvent inter-actions with the non-bonding terms of the OPLS-AA FF. Charges on the solute were computed using the QEq scheme [54], as usual for ReaxFF, while TIP3-P charges were used for the non-reactive water molecules. It is worth mentioning that the building of such hybrid FF requires the attribution of OPLS-AA atomic types to the atoms consti-tuting the solute in order to compute the Lennard-Jones (LJ) term of the OPLS-AA potential. A discussion of the chosen LJ parameters is available in the Electronic

(1)Err(Aab) =

ib

i=ia

i

nit

F2

i

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Supplementary Material1 (ESM). A cutoff of 10 was applied for the LJ term, while a long-range solver [55] was used for the Coulombic term. More details about each sim-ulation are available in the ESM.

3 Results and discussion

3.1 Iminiumoxazolidinone conversion in vacuum

Let us first consider the reaction in vacuum. The free energy profiles for the iminiumoxazolidinone conversion are pre-sented in Fig. 2a. The selected RC (x-axis) corresponds to the distance between the C-17 carbon and the O-15 oxy-gen atoms forming the new bond, as shown in the inset of Fig. 2. The sampling was performed in the range 1.43.8 with 48 bins of 0.05 width. Values describing the rela-tive stability of both intermediates (A), as well as free energy barriers (A), are reported in Table 1. We note that the values are consistent for the three independent runs. As expected, oxazolidinone (I) is more stable than its iminium

1 Electronic Supplementary Material (ESM) available: more techni-cal details about the simulations, an analysis of the influence of the set of LJ parameters on the free energy profiles. The evolution of two dihedral angles with time highlighting various conformations encoun-tered during the simulations. Details about the procedure used to locate the MEP connecting two minima in the free energy 2d-grids. An analysis of QEq and QM charge distributions.

(II) counterpart, an outcome in agreement with previous DFT calculations [48]. Quantitatively, the relative stabil-ity of both intermediates, 21.1 kcal/mol at 300 K, is well captured by the ReaxFF potential, the QM method of refer-ence predicting a difference of 21.7 kcal/mol in favor of I at 298 K. The free energy barrier, 33.8 kcal/mol at 300 K, is, however, overestimated by the FF, the QM value being 24.2 kcal/mol [48]. One part of this discrepancy can be attributed to the parameterization of ReaxFF used here. It was indeed designed to reproduce QM tendencies for vari-ous reaction steps of the mechanisms presented in Fig. 1 [18]. Both intermediates considered here were included in the training set but not the corresponding transition state (TS) [18]. In addition, the QM value is related to only one conformation of each species, while several conformations contribute to the values computed via the MD simulation. Two conformations of the pyrrolidine cycle of proline are, for example, observed. Various conformations of the ethyl group can be distinguished as well. A short analysis of conformations observed during the simulations based on dihedral angle values is available in the ESM. Finally, one should also bear in mind the ideal gas approximation and the harmonic vibrational frequencies that are applied to compute free energies at the QM level.

Increasing the kinetic energy of the system by perform-ing the simulation at a higher temperature slightly favors II over the other species. The variation is, however, rela-tively small, with less than 2 kcal/mol in A. This could be

Fig. 2 Free energy profiles of the iminiumoxazolidinone (III) con-version at different temperatures (a). Evolution of the RC in the range 1.43.0 throughout the ABF MD simulation (b). Inset three-dimen-

sional representation of the iminium intermediate with atom number-ing; the green arrow highlights the chosen RC

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attributed to a gain of entropy associated with the breaking of the CO bond. As seen by comparing the trajectories at 100 and 400 K in Fig. 2b, the temperature has also a clear influence on the dynamics of the simulation. As expected with the ABF scheme, after a variable time the simulations reach a diffusive state where the whole range of the RC is sampled as if there was no more energy barrier. More than 500 ps are needed to reach this state at 100 K, while about 100 ps are sufficient at 400 K.

3.2 Iminiumoxazolidinone conversion in water

In order to mimic experimental conditions, we now con-sider a system containing the reactive solute species in a box of 104 water molecules. We point out that, experi-mentally, proline-catalyzed aldol reactions are commonly performed in DMSO with water as co-solvent. Water can also be used without any organic solvent, provided that the substrates are soluble in this medium. The stereose-lectivity is, however, lost in these conditions due to the interaction between water molecules and the solutes pre-venting the formation of a crucial hydrogen bond between the enamine and the aldehyde during the CC bond for-mation (step (d) in Fig. 1) [56]. Nevertheless, the system described here is appropriate for studying the impact of water on the iminiumoxazolidinone conversion. As described in the Introduction, three different ways of describing the water molecules were considered: (1) the ReaxFF FF, (2) a modified version of this potential disa-bling the formation of chemical bonds between the oxy-gen of water and carbon atoms of the solute (ReaxFF), and (3) a combination of ReaxFF with a non-reacting FF (HybridFF). Interestingly, as shown in Fig. 3a, the free energy profile obtained with a full ReaxFF description is clearly different from those obtained with the other models. Comparing the RC trajectories in Fig. 3b, it is seen that the simulation performed with the full ReaxFF

potential never reaches a state where the whole range of the RC is freely sampled, as it is the case for the two other models. The large deviation in the A values obtained between run 2 (3.3 kcal/mol) and the two others (8.0 and 9.0 kcal/mol) is also indicative of some pitfalls in the simulations (Table 2). This issue is related to the binding of one water molecule to the solute (III). The oxygen of the water molecule indeed remains in the vicinity of the carbon atom of the iminium group, the distance between the two atoms staying in the 1.701.85 range. In some cases, the water molecule also forms a hydrogen bond with one oxygen atom of the carboxylate, as highlighted in the inset of Fig. 3. The occurrence of these persistent species has a tremendous impact on the ABF scheme as it obviously hampers the sampling along the chosen RC preventing the formation of I. To avoid the formation of such structures, we relied on the modified version of ReaxFF (ReaxFF) and on the HybridFF. As seen in Fig. 3a, both models provide similar free energy profiles. The HybridFF offers a ca. 30-fold speedup compared to its ReaxFF counterpart, the surrounding water molecules being modeled at a low computational cost. Comparing the free energy profiles with the vacuum one, we note that the water molecules have only a small impact on the com-puted quantities (Table 2). Charge values borne by several key atoms, i.e., the two oxygen atoms of the carboxylate group, the carbon of the iminium group, and the nitrogen atom, are collected in Table 3. The charges obtained with the hybrid model are very close to the ones calculated in vacuum. This is due to the fixed charges attributed to the atoms of the water molecules in the HybridFF, the QEq charge equilibration being only performed for atoms of the solute species. In contrast, a polarization is observed with the ReaxFF potential as all the atoms of the systems are included in the charge equilibration procedure.

So far, we have considered the binding of one water molecule with the solute as a parasitic event while

Table 1 Free energy differences between the iminium (II) and oxazolidinone (I) intermediates (A) and free energy barriers (A) computed from the ABF MD simulations at different temperatures

The oxazolidinone species is taken as reference (set to 0.0 kcal/mol). The A values are the differences between the oxazolidinone reference and the TS (highest energy point along the RC)

Run 1 Run 2 Run 3

A (kcal/mol)

T = 100 K 22.1 0.0(4)0.1 22.2 0.0(4)0.1 22.0 0.0(4)0.1 T = 200 K 21.7 0.10.2 21.6 0.10.2 22.2 0.10.2 T = 300 K 21.1 0.10.2 21.1 0.10.2 21.2 0.10.2 T = 400 K 20.7 0.10.2 20.6 0.10.2 20.7 0.10.2A (kcal/mol)

T = 100 K 33.8 0.0(2)0.0(5) 34.3 0.0(2)0.0(5) 34.2 0.0(2)0.0(5) T = 200 K 33.9 0.0(4)0.1 33.9 0.0(4)0.1 34.1 0.0(4)0.1 T = 300 K 33.8 0.0(4)0.1 33.9 0.0(4)0.1 33.7 0.0(5)0.1 T = 400 K 33.8 0.0(5)0.1 33.8 0.0(5)0.1 33.9 0.0(5)0.1

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attempting to model the breaking and formation of the CO bond in the solute. However, such binding with water spontaneously occurs when the selected model enables reactions between the solvent and the solute. In the next paragraph, we focus on the competing processes, namely the formation of the oxazolidinone and the binding of one water molecule.

3.3 Formation of the oxazolidinone versus binding of a water molecule to the iminium

We again consider the solute reactive species solvated in a box of 104 water molecules. The ReaxFF potential is used

Fig. 3 Free energy profiles of the iminiumoxazolidinone (III) con-version for different solvation models at 300 K (a). Evolution of the RC in the range 1.43.0 throughout the ABF MD simulation (b).

Inset three-dimensional representation of the solute interacting with one water molecule (III); the other water molecules were removed from the picture for clarity

Table 2 Free energy differences between I and II (A) and free energy barriers (A) computed from the ABF MD simulations for different solvation models at 300 K

The A values are the differences between the oxazolidinone refer-ence and the TS (highest energy point along the RC)

Run 1 Run 2 Run 3

A (kcal/mol)

ReaxFF 8.0 0.10.2 3.3 0.20.4 9.0 0.10.3 ReaxFF 23.0 0.10.2 22.9 0.10.2 23.1 0.10.2 HybridFF 21.2 0.10.2 21.2 0.10.2 21.2 0.10.2 Vacuum 21.1 0.10.2 21.1 0.10.2 21.2 0.10.2A (kcal/mol)

ReaxFF 28.9 0.0(2)0.1 25.2 0.0(5)0.1

30.6 0.0(2)0.0(5)

ReaxFF 34.0 0.0(2)0.0(5)

34.0 0.0(2)0.1

34.0 0.0(2)0.1

HybridFF 33.4 0.0(5)0.1 33.4 0.0(4)0.1

33.4 0.0(5)0.1

Vacuum 33.8 0.0(4)0.1 33.9 0.0(4)0.1

33.7 0.0(5)0.1

Table 3 Partial atomic charges (e) of four selected atoms for differ-ent water models

The values are obtained by averaging the QEq charges extracted from the ABF MD simulations (standard deviations of 0.012, 0.023, and 0.012 for the first, second, and third models, respectively). The RC values are used to discriminate between the three states (I below 1.8 , TS from 1.8 to 2.4 , and II over 2.4 )

O-15 O-16 C-17 N-19

ReaxFF (vacuum)

II 0.439 0.440 0.018 0.152 TS 0.442 0.443 0.055 0.179 I 0.450 0.448 0.153 0.212

ReaxFF (H2O) II 0.524 0.532 0.023 0.224 TS 0.512 0.532 0.083 0.242 I 0.509 0.527 0.178 0.267

HybridFF (H2O)

II 0.432 0.437 0.018 0.150 TS 0.440 0.441 0.054 0.178 I 0.449 0.447 0.149 0.213

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to describe not only the solute but also one water molecule, while the other solvent molecules are modeled with the HybridFF. As above, we select the first RC (RC-1) as the distance between one oxygen atom of the carboxylate group (O-15) and the carbon of the iminium group (C-17), but we now introduce a second RC, namely the distance between the oxygen atom of the reactive water molecule and C-17 (RC-2) to perform a bi-dimensional ABF MD simulation. For RC-2, the system force is measured on the oxygen atom only. The free energy landscape is built following a previ-ously described procedure [51]. We underline that forming both bonds simultaneously would lead to either the forma-tion of a pentavalent carbon, or the decomposition of the solute due to the breaking of the bond between C-17 and one of its substituents. To avoid such situation, the simula-tion is partitioned into two windows. In the first, we sample RC-1 from 1.5 to 1.9 and RC-2 from 1.8 to 3.8 , while in the second, the sampling is performed from 1.8 to 3.8 for RC-1 and from 1.5 to 3.8 for RC-2. The free energy landscape resulting from the ABF simulation is displayed in Fig. 4. Three energy minima are identified: the most sta-ble structure corresponds to the oxazolidinone intermediate (I), the water-bonded entity (III) is slightly higher in energy (1.6 kcal/mol), and there is a broad region above 20 kcal/mol for large RC-1 and RC-2 values that corresponds to the iminium intermediate (II). The MEP connecting those three minima is represented by solid lines in Fig. 4. These paths were searched satisfying two constraints, i.e., avoid-ing bins of high energy and reducing the length of the path. More details about the procedure used to locate the MEP are available in ESM. From the MEP, energy barriers can be computed between the different minima; key values are listed in Table 4. Due to the much larger conformational space to sample, the statistical errors are larger for this bi-dimensional scenario than they were in the one-dimensional cases. Indeed, as seen in Eq. (1), the error is proportional to the root of the number of structures belonging to each bin included in the path. Each RC is sampled in the range 1.53.8 with 0.05 bins, taking into account that 36 bins were not sampled to avoid simultaneous low values of RC-1 and 2, and it makes a total number of 2080 bins, contrasting with the 48 bins needed in the one-dimensional ABF simu-lations. In addition, as the paths considered expand into two dimensions, there are generally more elements in the sum of Eq. (1). For each run, the results are collected on a total simulation time of 38 ns.

Focusing on the III transition, the obtained results are very similar to those of the one-dimensional case with dif-ferences of 0.6 and 0.8 kcal/mol for A and A, respec-tively. As stated above, the interaction of one water mol-ecule with the solute yields another energy minimum (III) which is slightly higher in free energy (1.6 kcal/mol) than I. Interestingly, the free energy barrier required to pass from

II to III is significantly smaller (21.719.0 = 2.7 kcal/mol) than the one corresponding to the formation of I from II (34.220.6 = 13.6 kcal/mol). In addition, once I is formed, it appears that the free energy barrier associated with its opening by a water molecule (29.4 kcal/mol) is slightly smaller than the one directly leading back to II (34.2 kcal/mol). To support these ReaxFF results, DFT calculations were performed to estimate the relative stability of the three intermediates at the QM level. The structures and the cor-responding free energy values are displayed in Fig. 5. As

Fig. 4 Representation of the free energy landscape for the ring clo-sure step in a box containing 104 water molecules among which one is described with ReaxFF. RC-1 corresponds to the O-15C-17 dis-tance and RC-2 to the distance between the oxygen of the reactive water molecule and C-17. The MEP located for each transition is rep-resented with solid lines: III in yellow, IIII in black, and IIIII in green. The shadowed area was intentionally not sampled to avoid the formation of a pentavalent carbon or the decomposition of the solute moiety. Inset isolines representation of the free energy landscape

Table 4 Free energy differences (A) between intermediates I, II, and III and corresponding free energy barriers (A)

A values are computed as the difference between the most stable of the two intermediates and the highest free energy point along the MEP (TS)

Run 1 Run 2 Run 3

A (kcal/mol)

III 20.6 0.92.1 20.1 0.82.0 19.8 0.51.3 IIII 1.6 0.92.1 1.8 0.71.8 2.0 0.81.8 IIIII 19.0 0.30.7 18.3 0.41.0 17.9 0.20.5A (kcal/mol)

III 34.2 0.71.8 34.0 0.10.4 32.8 0.20.4 IIII 29.4 0.30.8 31.1 0.30.8 28.3 0.30.7 IIIII 21.7 0.20.6 21.2 0.10.4 20.7 0.20.4

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stated previously, one should be careful when comparing free energy differences obtained from the ABF MD simu-lations and DFT values. Nevertheless, QM results predict the same order of relative stability for the three species, II and III being 13.1 and 3.6 kcal/mol, respectively, above I. One notices the increased stability of species II at the DFT level compared to ReaxFF predictions. This difference is mainly attributed to the large negative charge on the car-boxylate stabilized by the presence of the water molecule. The QEq procedure, used in conjunction with ReaxFF to compute atomic charges, indeed underestimates the charge difference on the oxygen atoms of iminium and oxazoli-dinone. Further discussions are available in ESM. We also point out a major structural difference in III, where one proton of the water molecule has clearly been transferred to the carboxylate group. The CO distance of 1.45 is also shorter than the one of the corresponding minima in the MD simulations, ca. 1.80 . Actually, such structures were also observed during the MD simulations. However, the formation of this species hampers the reversibility of the reactions observed during the ABF simulations. The OH distances of the water molecule were indeed not selected as RC; consequently, the proton transfer to the carboxylate is not expected to be reversible which causes a major issue for the ABF simulation as the water molecule is not recov-ered. For this reason, a constraint was added to the OH bond of the reactive water molecule to prevent the proton transfers. To allow a fair comparison between DFT and ReaxFF results, we performed a separate ABF simulation in which the proton transfer between O-15 and the oxygen atom of the water molecule was investigated constraining the C-17O(water) distance to values inferior to 1.55 . The minimum of the free energy profile is obtained for a distance of 1.05 between O-15 and the proton which cor-responds to the DFT optimized structure of III. It is worth mentioning that this structure is actually the neutral form of the zwitterion which appears in the reaction mechanism in Fig. 1. To relate these results to the experimental obser-vations, as stated in the Introduction, it was proposed that the proline-catalyzed aldol reaction can benefit from addi-tion of water as it inhibits the formation of the oxazolidi-none intermediate. The experimentally proposed rationale

behind this outcome was that following the Le Chteliers principle, water increases the amount of catalyst (proline) as it reduces the concentration of spectator intermediates, especially the oxazolidinone [36]. On the other hand, the authors also pointed out that following the same princi-ple, water reduces the concentration of reactive species II and IV [36]. The net balance of these effects depends on the substrates. Our results corroborate these assumptions. Indeed, the interaction of one water molecule with the sol-ute yields an intermediate (III) which can enter again in the enamine catalytic cycle presented in Fig. 1. From a ther-modynamic point of view, this intermediate has a stability comparable to the oxazolidinone species. Kinetically, large energy barriers are still observed explaining why the oxa-zolidinone intermediate is commonly observed in the reac-tion mixture [35]. Nevertheless, our results suggest that water could ease the opening of the oxazolidinone cycle as the barrier for the IIII transition is 4.8 kcal/mol lower than the III one.

4 Conclusions

We combined a reactive FF, ReaxFF, and a free energy method, namely the ABF, to model a ring closure in a proline-catalyzed aldol reaction. The ABF scheme ena-bles the crossing of the energy barrier for the bond break-ing (and formation) in the considered step of the reaction allowing the determination of a free energy profile for the ring closure. With the inclusion of water in the model, we have shown how a concurrent reaction could prevent the observation of the expected phenomenon, a major pitfall in simulations based on a reactive FF. Two approaches were proposed to circumvent this problem. The first con-sists in turning off several terms in the ReaxFF potential, and the second implies the combination of ReaxFF with the all-atom version of the OPLS FF. Bi-dimensional ABF simulations were also performed to tackle a more sophisticated mechanistic aspect. In particular, we showed how one water molecule could interfere in the considered ring closure step of the reaction. On a mechanistic point of view, we simulated the interaction of water with two

Fig. 5 Three-dimensional structures of intermediates I, II, and III optimized at the DFT level and their computed rela-tive stabilities

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intermediates, namely the iminium and the oxazolidinone species. It turns out that water has an impact on both of them so to produce an intermediate which appears in a previous step of the enamine pathway. According to this mechanism, the addition of water in the reaction mix-ture increases the yield of proline-catalyzed aldol reac-tion as it converts the oxazolidinone spectator intermedi-ate in a species which is part of the catalytic cycle. Due to the limitations of this ReaxFF parameterization, DFT calculations were performed to corroborate the conclu-sions drawn from the simulations. With the current set of parameters, ReaxFF overestimates the free energy barrier of the considered ring closure. It also provides an inac-curate description of the difference in charge distributions between the iminium and the oxazolidinone intermedi-ates. For this reason, we plan to perform a new param-eterization of ReaxFF based on a more complete training set in order to reach an accurate description for key steps of the mechanism of proline-catalyzed reactions. In paral-lel, the investigation of the energy profile of other steps of this mechanism using free energy methods is currently under study.

Acknowledgments PH thanks the Fund for Scientific Research (FRS-FNRS) for his PhD Fellowship. PH, LL, and DPV also thank the Interuniversity Attraction Poles Programmes no 7/05: Functional supramolecular systems initiated by the Belgian Science Policy Office for partial financial support. This research used resources of the Plateforme Technologique de Calcul Intensif (PTCI) (http://www.ptci.unamur.be) located at the University of Namur, Belgium, which is supported by the F.R.S.-FNRS (convention 2.4.617.07.F). The PTCI is a member of the Consortium des quipements de Cal-cul Intensif (CECI). DJ indebted to the ERC StG program (Grant: Marches278845) for financial support.

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Accessing the free energy profile ofa ring closure ina proline-catalyzed reaction using a reactive force fieldAbstract 1 Introduction2 Computational methods3 Results anddiscussion3.1 Iminiumoxazolidinone conversion invacuum3.2 Iminiumoxazolidinone conversion inwater3.3 Formation ofthe oxazolidinone versusbinding ofa water molecule tothe iminium

4 ConclusionsAcknowledgments References