Borohydride Ion Pair: Dynamics of

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A: Kinetics, Dynamics, Photochemistry, and Excited States

Structurally Flexible Oxocarbenium/Borohydride Ion Pair: Dynamics of Hydride Transfer on the Background of Conformational Roaming Mojgan Heshmat, and Timofei Privalov J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.8b02151 • Publication Date (Web): 29 May 2018 Downloaded from http://pubs.acs.org on May 29, 2018

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The Journal of Physical Chemistry

Structurally Flexible Oxocarbenium/Borohydride Ion Pair: Dynamics of Hydride Transfer on the Background of Conformational Roaming

Mojgan Heshmat and Timofei Privalov* Department of Organic Chemistry, Stockholm University, Stockholm, 10691, Sweden E-mail: [email protected]

ABSTRACT

We apply Born-Oppenheimer molecular dynamics to the practically significant [dioxane-H(+)acetone][(C6F5)3B-H(-)]

and

[Et2O-H(+)-OCPr2][(C6F5)3B-H(-)]

ion

pair

intermediates.

Dynamics of hydride transfer in cation/anion ion pair takes place on the background of largeamplitude configurational changes. Geometry of oxocarbenium/borohydride ion pairs is flexible – meaning, we uncover significant actual structural disorder at a finite temperature. Therefore, despite that the starting structure can be fairly close to the configurational area of the hydride transfer transition state (TS) and despite a low potential energy barrier (circa 1.5 kcal/mol, according to the literature), already at T ≈ 325 K the system can remain ignorant of the TS-region and move round and about (“roam”) in the configurational space for a period of time in the range between 10 ps to 100 ps. This indicates structural flexibility of oxocarbenium/borohydride ion pair on apparently a flat potential energy “landscape” of cation/anion interaction and this has not been taken into consideration by the free energy estimations in static considerations made thus far. The difference between the dynamics-based representation of the system versus the static representation amounts to the difference between quasi-bimolecular versus unimolecular descriptions of the hydride transfer step.

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1. INTRODUCTION One of significant chemical reactions is hydrogenation of substrates with the unsaturated O=C bonds (ketones and aldehydes).1,

2, 3

Catalysis of this chemical transformation with the

transition-metal complexes has distinguished track-record; however, a desirable alternative is a metal-free process. Recently, it had been demonstrated that one can carry out hydrogenation of carbonyl compounds with H2 in ether solutions using catalytic amount of a Lewis acid (LA) – i.e., reaction 1 in Scheme 1 with B(C6F5)3 or its analogs as LA and 1,4-dioxane, THF or diethyl ether (Et2O) as ether donor-solvents with moderate Lewis basic character.4, 5, 6, 7, 8, 9, 10, 11

The field of the frustrated Lewis pairs (FLP) chemistry is expanding and there is vast

contemporary literature on the subject. For reaction 1, different mechanisms were proposed and are currently discussed.

12, 4, 5, 13, 10, 14, 15

In short, the difference between the proposed

mechanisms is whether reaction 1 involves a borohydride or a boroalkoxide intermediate.

Scheme 1. Hydrogenation of carbonyl compounds with H2 in ether with catalytic amount of B(C6F5)3 or its analogs (borane LA). 4, 5

For the computational elucidation of a probable reaction pathway involving one or the other form of borohydride intermediate,

10, 13, 12

the methodological basis had been the static

(the minimum energy path) approach using the geometry-optimized intermediates and TSs with the free energy estimations provided by thermochemical calculations with ideal gas rigid rotor harmonic oscillator approximation applied to the optimized geometries.16 Dynamicsbased insight with the account of actual molecular motion at finite (non-zero) temperature is insufficient at present – hence this article. Nowadays, computational chemistry is an essential part of chemistry, material and biology sciences. However, currently predominant static computational approach to chemical reaction mechanisms has limitations – i.e., the minimum energy path that supposedly connects the preordained static intermediate(s) and transition state (TS) geometries can be informative but it is actually far off from realities of chemical reaction and molecular interaction taking place at finite temperature. An alternative to the static approach is the ab initio molecular dynamics (AIMD).17,18,19,20 AIMD is computationally expensive method and it requires advanced computer architectures permitting parallel calculations. Thanks to development of 2 ACS Paragon Plus Environment

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GPU-computing and its relative affordability,21 computational approach based on efficient Born-Oppenheimer molecular dynamics (BOMD) has risen to certain prominence.22, 23, 24, 25 For reaction 1, one of proposed mechanisms involves heterolytic splitting of H2 (activation) by borane LA and ether followed by the part described in Scheme 2.4, 5, 13 Prior to oxocarbenium ion pair with borohydride as the anion – i.e., an intermediate of the type [etherH(+)-substrate][LA-H(-)] where substrate is a ketone or an aldehyde – that mechanism makes use of boron as LA-center and O-atom of ether or ketone/aldehyde as LB-center for the heterolytic cleavage of H2. In the interest of space and given that details can be found in the literature, let us just say that an important mechanistic element is the proposed transformation of [ether-H(+)-substrate][(C6F5)3B-H(-)] to the alcohol product complex via the hydride-transfer transition state (TS). In the latter, Scheme 2, the boron-bound hydride is thought to execute facile nucleophilic attack on electrophilic carbonyl carbon, C(carb.), of the protonated substrate with hydrogen bond to ether solvent molecule. It had been reported that the hydridetransfer TS corresponds to a rather low barrier – i.e., circa 1.5 kcal/mol and 5.5 kcal/mol for the potential and free energies, respectively – with respect to the energy of the geometryoptimized [ether-H(+)-substrate][LA-H(-)] intermediate (e.g. structures shown in Figure 1).10, 13

Scheme 2. A part of the proposed mechanism for reaction 1 – the transformation of [ether-H(+)substrate][LA-H(-)] to the alcohol product complex via the low-barrier hydride-transfer TS.4,5,10,13

The oxocarbenium ion pair intermediate with borohydride as anion, [ether-H(+)substrate][LA-H(-)], relates to Jutzi’s acid [(Et2O)2H(+)][(C6F5)4B(-)] 26 and its derivative of the type [ether-H(+)-ketone][(C6F5)4B(-)] obtained and characterized by Stephan’s group.5 Specific structural characteristic of an anion of the type [(EWG)3B-H(-)] is that it has only three boronbound groups and the direction defined by B→H “vector” that is perpendicular to the “equatorial” plane encompassing the trio of the boron-bound C-atoms; here EWG abbreviates electron withdrawing group. With regard to the hydride-transfer step in [ether-H(+)substrate][LA-H(-)], currently it is unknown whether the cation could be thought of as



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localized in a specific manner with respect to [LA-H(-)] or the cation actually could have freedom of movement with respect to [LA-H(-)]. If the latter is the case – and we will show that this is indeed the case – description of [ether-H(+)-substrate][LA-H(-)] with one optimized structure is a limited approach to this system. We would like to mention, albeit very briefly, that the extensively studied phenomenon of the roaming chemical reaction mechanisms

27, 28, 29, 30, 31, 32

– e.g., formaldehyde

unimolecular decomposition (dissociation) – has a bearing on the results presented herein. The common fundamental aspect is the mechanistic influence of a flat portion of the potential energy surface (PES) which is accessible to the system on its way to the product(s) – hence, trapping of the system on the flat PES instead of “supposedly direct” passage to the TS-area. And, please note that entropic terms have been used by Chesnavich.29 Regarding various important aspects and details of the roaming chemical reaction mechanisms, the literature is rather extensive and herein we are content with giving only a few relevant references. The matter with fairly a broad relevance, touched by us in this article in a qualitative manner, is the account for entropy of an intermediate in the computational descriptions of a chemical transformation. The most commonly used approach involves ideal gas rigid rotor harmonic oscillator approximation applied to an optimized geometry.16 This can give informative estimation as long as the used optimized structure is actually representative of the configurational space of the intermediate in question. Qualitatively speaking, entropy is the measure of structural disorder in a molecular system. The fundamental difficulty arises when the selected optimized structure does not represent its actual configurational “neighborhood” especially if different configurations belong to a flat potential energy “landscape”. For [etherH(+)-substrate][LA-H(-)], the viewpoint based on the ad hoc selected optimized cation/anion structure10,13 introduces into calculations (i) the notion of immobility (structural localization) of [ether-H(+)-substrate] cation with respect to [LA-H(-)] anion, and (ii) preordained transition to the area of configurational space where hydride transfer could take place without considering alternatives to such a minimum energy path originating from an ad hoc local configuration. Our results will cast a shadow of doubt on this viewpoint by showing actual behavior of the system in BOMD simulations at finite temperature. Herein we focus on a step that is reported to have fairly low potential energy barrier.10,13 Typically, chemical transformation is regarded as a rare event in the dynamics simulations due to the associated barrier. But given our system of interest, this assessment appears to be limited because it does not take into account configurational space of the intermediate preceding the preordained TS of chemical transformation. Qualitatively speaking, the 4 ACS Paragon Plus Environment

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fundamental difference between the static and dynamics-based description would arise from the treatment of the configurational space of the structurally feeble intermediate. With this article, we shed new light on the reaction-path segment outlined in Scheme 2 with help of Born-Oppenheimer molecular dynamics (BOMD). Since BOMD simulations are computationally expensive, we do not attempt to address the whole path for reaction 1 as described in the literature using static approach but we focus specifically on hydride transfer because it is important element of the overall mechanism proposed for reaction 1. We will demonstrate surprising flexibility of the geometry of oxocarbenium/borohydride ion pair intermediate [ether-H(+)-substrate][(C6F5)3B-H(-)] – a characteristic that can make static considerations limited with regard to account for actual entropy of this intermediate. The bulk of herein reported BOMD simulations focuses on [dioxane-H(+)-acetone][(C6F5)3B-H(-)] system; modelling of [Et2O-H(+)-OCPr2][(C6F5)3B-H(-)] system produced similar results. In order to be able to carry out rather long-duration BOMD simulations reported herein, the anion/cation system is in gas phase without any additional solvent molecules in the molecular model. The BOMD simulation in gas phase is a sound approach herein because the central reason for our findings is the weak ion pairing governed by the sum of the long-range and non-covalent interactions between the cationic [ether-H(+)-acetone] and the anionic [BCFH(-)] fragments. Given conclusions derived for similar systems in a number of our previous articles, it is clear that explicit solvation is not going to fundamentally alter the weak ion pairing especially since solvent is already a part of the cationic fragment including the proton, i.e. [ether-H(+)-acetone]. Solvent might have a role to play but the explicit solute-solvent interactions are expected to be additive to already quite complex “web” of non-covalent interactions that we deal with already. Furthermore, the solvation shells are by no means static – thus, our results should give fairly adequate description of the said ion pairs in solvent although presence of solvent might affect timescales of interconversion between conformers. Last but not least, please note that herein used non-constrained BOMD trajectory propagation of cation/anion system has an important advantage in comparison to the metadynamics sampling techniques

17,19

- meaning, that no actual foreknowledge of the so-called

sampling order parameters is required. Still, due to unavoidable computational limitations and necessity to reach out to 100 ps long trajectory propagation, the present article reports more qualitative rather than fully quantitative insight into the matter under investigation; undoubtedly so, meta-dynamics approaches could be useful for the next stage of a more quantitative exploration which could involve the free energy mapping plus explicit solvation.



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METHODS All herein reported Born-Oppenheimer molecular dynamics (BOMD) simulations and geometry-optimizations of initial geometries were carried out using commercially available package TeraChem (v. 1.9)23,24,25 at the level of the dispersion-corrected density functional theory, DFT-D3,

33, 34

using BLYP functional and the double-zeta basis set 6-31g** with

added polarization functions on all atoms. According to our experience, this is sufficiently accurate and fast approach for long-duration BOMD simulations of relatively large systems. For systems we consider herein, simulations done with BLYP are fully in accord to those done with more widely used B3LYP functional. The benefit of using BLYP is computational speed. For a batch of 10 trajectories, our own state-of-the-art GPU-computing nodes allow circa 5 ps trajectory propagation per day (24 hours) for system of circa 100 atoms. This makes 25 ps range fairly attainable. However, herein in this article we encountered the need for trajectory accumulation in 100 ps range (and above) and this was a computational challenge. For overlay of BOMD snapshots and RMSD calculations mentioned in this article, structures are always put in maximal coincidence (via translation and rotation using VMD’s RMSD Trajectory Tool with “align” function). VMD is the molecular visualization program which we typically use for visualization and analysis of BOMD trajectories. VMD was developed by the Theoretical and Computational Biophysics Group in the Beckman Institute for Advanced Science and Technology at the University of Illinois at Urbana-Champaign.35,36 The root mean squared deviation (RMSD) is calculated as follows: ( , )=

∑ [ ( )

( )]

(Eq. 1)

( ) is the position-vector of atom i at time t along trajectory and the sum includes either all N atoms or a select group of particular interest; the reference structure corresponds to time t0. All stationary structure (non-BOMD) calculations were carried out using the commercially available package Gaussian 37 with B3LYP density functional, fairly large splitvalence triple-zeta basis set 6-311g** with polarization functions on all atoms and the dispersion correction developed by Grimme’s group.33,34 For thermochemical calculations, i.e. entropy estimations, we used ideal gas rigid rotor harmonic oscillator approximation.


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2. RESULTS AND DISCUSSION 2.1. Dynamics of [ether-H(+)-ketone][LA-H(-)] system and hydride transfer Using GPU-accelerated BOMD and state-of-the-art hardware, as a first step we relatively quickly calculated 20 trajectories with 25 ps duration at nearly room temperature (T ≈ 325 K with the standard deviation σT ≈ 35 K) starting from the fully optimized structure of [dioxane-H(+)-acetone][(C6F5)3B-H(-)] ion pair (Figure 1A) and with standard sampling of the initial velocities of all atoms from the Maxwell-Boltzmann distribution at given temperature. A)

B)

Figure 1. Optimized structures of [dioxane-H(+)-acetone][(C6F5)3B-H(-)] (A) and [Et2O-H(+)OCPr2][(C6F5)3B-H(-)] (B) oxocarbenium/borohydride ion par intermediates. All distances are in Å.

Our starting geometries (Figure 1A with dioxane plus acetone and Figure 1B with Et2O plus OCPr2) are in accord with [ether-H(+)-ketone][LA-H(-)] geometries in the literature.10,13 The case of [Et2O-H(+)-OCPr2][(C6F5)3B-H(-)] will be discussed in the very end of this section. For [dioxane-H(+)-acetone][(C6F5)3B-H(-)] ion pair, the hydride transfer took place in circa 50% of 25 ps long trajectories. If the geometry of the ion pair complex is suitable and sufficient vibrational energy is present in B-H…C(carb.) mode of motion, transformation to alcohol via hydride transfer is nearly a vertical (fast) transition to C(carb.)-H ≈ 1.1Å (Figure 2); BOMD-snapshots illustrating the hydride transfer yielding alcohol are shown in Figure 3. In Figure 3A the hydride transfer is just about to start and in Figure 3B it is already under way; the C(carb.)…B distances are 3.12 Å and 3.11 Å, respectively. For facile hydride transfer, C(carb.)…B distance must be sufficiently short and orientation of [dioxane-H(+)acetone] with respect to [(C6F5)3B-H(-)] is subject to requirements imposed by the Bürgi– Dunitz and Flippin–Lodge angles for nucleophilic attack on C(carb.) of a ketone. In short, those are: (i) the H(-)CO angle is between 110o and 90o degrees, and (ii) the plane drawn through H(-) and C=O is circa perpendicular to the plane of the carbonyl itself (i.e. the plane in 7 ACS Paragon Plus Environment


which the ketone’s CCC=O atoms reside). In terms of all essential geometrical parameters the BOMD-described hydride transfer area (Figure 3) is in accord with the TSs reported by others.

5.7 C(carb.) ...hydride (Å)

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4.7 3.7 2.7 1.7 0.7 0

5

10

15

20

25

time (ps)

Figure 2. Conformational dynamics and the reactive event, hydride transfer yielding product alcohol, in [dioxane-H(+)-acetone][(C6F5)3B-H(-)] system simulated at T ≈325 K according to a set of 25 long BOMD trajectories – herein we show C(carb.)…hydride distances in Å and time in ps. A)

B)

Figure 3. Hydride transfer step in representative BOMD snapshots for the ion pair [dioxane-H(+)acetone][(C6F5)3B-H(-)] at T ≈ 325 K. In A) the hydride transfer is about to start and in B) it is already under way; the C(carb.)…B distances are 3.12 Å and 3.11 Å, respectively. All distances are in Å.

In the first batch of twenty 25 ps long trajectories we have noticed that (i) geometrical parameters of [dioxane-H(+)-acetone][(C6F5)3B-H(-)] system varies a lot and C(carb.)…hydride distance can reach circa 6 Å because cation reaches the far side of [(C6F5)3B-H(-)] (Figure 4) even in a relatively short-duration reactive trajectory; and (ii) there is significant variation of the time period from the start of a simulation till the instance of hydride transfer (Figure 2). In illustration having side-on position of [dioxane-H(+)-acetone] with respect to [(C6F5)3B-H(-)] 8 ACS Paragon Plus Environment

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(Figure 4), we show a plane drawn through boron-bound carbons (CCC-plane for short). Due to side-on position of [dioxane-H(+)-acetone], C(carb.) is actually below CCC-plane and the BHC(carb.) angle is about 50o. In the initial structure and configurations suitable for hydride transfer, the whole of [dioxane-H(+)-acetone] including C(carb.) is above the CCC-plane and BHC(carb.) angle is typically in the range between 115o and 175o.

Figure 4. Representative BOMD-snapshot of [dioxane-H(+)-acetone][(C6F5)3B-H(-)] with the [etherH(+)-substrate] cation at the side of [BCF-H(-)] near fluorophenyls. All distances are in Å.

Since circa 50% of trajectories ended their 25 long propagation remaining in the configurational space of [dioxane-H(+)-acetone][(C6F5)3B-H(-)] ion pair without hydride transfer, the next logical step for us was that all trajectories which remained in the configurational space of [dioxane-H(+)-acetone][(C6F5)3B-H(-)] without reactive events for full 25 ps were propagated further on into 50 ps and 100 ps ranges. For some of those longer trajectories we have eventually observed the hydride transfer step but even after 100 ps propagation there were some trajectories which still remained in the configurational space of [dioxane-H(+)-acetone][(C6F5)3B-H(-)] intermediate without the reactive event (i.e., hydride transfer). In total, ion pair was simulated for circa 1 ns at fairly moderate T ≈ 325 K. Yet, simulations revealed unexpected scope of possible configurational changes and it is apparent to us that seemingly straightforward transition to hydride transfer configuration “gets lost” in the pool of other possible configurational motions. That points out the difference between considering and calculating only preordained transitions between stationary points – i.e., the static approach – versus simulating actual dynamics with inherently multitude of motions that the system can have. For [Et2O-H(+)-OCPr2][(C6F5)3B-H(-)], we followed same approach. While 25 ps range is fairly attainable for relatively fast sampling due to our state-of-the-art GPU-nodes, with the systems size in the range of 100 atoms reaching out into 100 ps had been a considerable computational effort even with taking full advantage of GPU-computing. 9 ACS Paragon Plus Environment

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C(carb.)...Hydride distance (Å)


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5.7 4.7 3.7 2.7 1.7 0.7 0

10

20

30

40

50

60

70

time (ps)

Figure 5. Time-evolution of C(carb.)…hydride distances in [dioxane-H(+)-acetone][(C6F5)3B-H(-)] system at T ≈325 K; we compare three representative BOMD-trajectories with different durations. The period of time from the start of a simulation till hydride transfer (ΔtR) is in 10ps to 100ps range.

In the interest of clarity, let us now focus on three representative reactive trajectories of considerably different durations and try to comprehend the message emanating from timeevolution of C(carb.)…hydride distance in [dioxane-H(+)-acetone][(C6F5)3B-H(-)] system (Figure 5). Data in Figure 5 indicates that (i) the period of time from the start of a simulation till hydride transfer (ΔtR) can vary in 10ps to 100ps range, and (ii) geometry of the oxocarbenium/borohydride ion pair does not appear to be localized to a specific minimum. That was a surprise for us because our initial geometries (Figure 1) are fairly close to geometries of hydride transfer TSs reported in the literature and also because the reported barrier is fairly low as we have already mentioned above (ΔE# ≈ 1.5 kcal/mol).10,13 Yet, our BOMD simulations apparently show that [ether-H(+)-substrate][(C6F5)3B-H(-)] system can spend considerable time in configurational space till the instance of hydride transfer step arrives. Let us remind that even after 100 ps propagation we still had BOMD trajectories which remained in the configurational space of [dioxane-H(+)-acetone][(C6F5)3B-H(-)] intermediate without hydride transfer as the reactive event. Therefore, we suspect that this behavior can extend well above 100 ps range but statistically meaningful exploration of such long time interval is beyond our computational capabilities at present. But one must conclude that regions of configuration space sampled by the dynamics at T ≈ 325 K can be far apart. Using BOMD trajectories with relatively short, medium and long periods of time elapsed from start till hydride transfer yields product alcohol (Figure 5), we produced overlays of every 10th BOMD snapshot from dynamics of [dioxane-H(+)-acetone][(C6F5)3B10 ACS Paragon Plus Environment

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H(-)] computed with 1 fs time step. This is shown in Figure 6; all contributing snapshots were put into maximal coincidence (via translation and rotation) and we look at the system from the above with respect to the direction of B→H “vector”. For clarity of presentation of cation and anion, atoms are colored according to their masses: dark blue for F-atoms, light blue for Oatoms, white for C-atoms and red for H-atoms. Specifically, Figures 6 A-C show three snapshot-overlays for trajectories with the longest, medium and the shortest periods of “roaming” behavior prior to the reaction-event (red, blue and green in Figure 5, respectively). A)

B)



C)

Figure 6. Overlays of every 10th BOMD snapshot from dynamics of [dioxane-H(+)-acetone][(C6F5)3BH(-)] prior to hydride transfer as the reaction-event; 1 fs time step, T ≈ 325 K with σT ≈ 35 K. Specifically, A), B) and C) correspond to the longest, medium and the shortest periods of dynamics prior to the hydride transfer reaction-event (see Figure 5 above). For clarity of presentation in A) - C), atoms are colored according to their masses: dark blue for F-atoms, light blue for O-atoms, white for C-atoms and red for H-atoms. BOMD-snapshots were put into maximal coincidence (via translation and rotation) and we look at the system from the above with respect to the direction of B→H “vector”.

Since the lightest H-atoms (red in Figure 6) belong exclusively to [dioxane-H(+)acetone], overlays of BOMD-snapshots clearly reveal the scope of actual amplitude of motion of [dioxane-H(+)-acetone] with respect to [BCF-H(-)]. Apparently, there is indeed (very) large flexibility in the configurational space of herein considered cation/ion system. The range of visited configurations includes those with oxocarbenium cation at a far side of [BCF-H(-)] near ends of fluorophenyls and with C(carb.)…hydride distance about 6 Å (Figure 4). This is generally the case for a representative short trajectory with ΔtR ≈ 10 ps (Figure 6A), a representative trajectory with 10 ps < ΔtR < 100 ps (Figure 6B) and the relatively long with ΔtR ≈ 100 ps follows the suite as well (Figure 6C). Given all the results presented thus far in this article, we sincerely doubt that anyone would disagree with a conclusion that a single optimized structure (e.g. Figure 1A) does not really represent the configurational space of this cation/ion system. Large-amplitude configurational change involving C(carb.)…hydride distance variation in the range from 3 Å to 6 Å has circa 10 ps time-scale (Figures 2 and 5). The fact that it takes place in BOMD simulations at fairly moderate T ≈ 325 K indicates long-range flatness of the potential energy surface (PES) for interactions of cationic and anionic parts of the ion pair [dioxane-H(+)-acetone][(C6F5)3B-H(-)]. This is in accord with the notion of weak cation/anion 12 ACS Paragon Plus Environment

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pairing for related species composed of oxonium cation [ether-H(+)-ether] and a borate as an anion (e.g., Jutzi’s or Bookhart’s acids).38 To avoid possible misunderstanding, please note that the notion of weak cation/anion pairing does not refer to actual binding energy of cation/anion but it means that cation’s positioning is not geometrically restricted with respect to the anion. In other words, weak ion pairing means that a relatively light cation retains considerable freedom of motion with respect to the pairing but relatively heavier anion. While comparing snapshot-overlays in Figure 6, the point is that even the trajectory that reacted relatively quickly – green in Figure 5 – still shows the amplitude of relative cation/anion motion of the same kind as other trajectories in which considerably longer time elapsed prior to hydride transfer yielding the product alcohol complex. Complementary to Figure 6A and Figure 6C illustrating trajectories with relatively long and short durations of evolution in configurational space prior to hydride transfer (red and green in Figure 5), in Figure 7 we show histograms of C(carb.)…hydride distances. With C(carb.)…hydride distance as a simple but relevant geometrical characteristic, one can see that in both cases the range of configurational change appears to be quite similar. For the histogram in Figure 7A, the mean value is 3.89 Å and the standard deviation is 0.88Å; for the histogram in Figure 7B, the mean value is 3.88 Å and the standard deviation is 0.61Å. A)

B)

Figure 7. Histograms of C(carb.)…hydride distances on the basis of the long- and short-duration trajectories of [dioxane-H(+)-acetone][(C6F5)3B-H(-)] at T ≈ 325 K (red and green in Figure 5 corresponding to Figure 6A and Figure 6C, respectively). In A) the mean value is 3.89 Å and the standard deviation is 0.88Å, in B) the mean value is 3.88 Å and the standard deviation is 0.61Å.

To give a clearer perspective on the occurring configurational change with respect to the starting structure (Figure 1A) and structures in which hydride transfer took place in BOMD simulations at T ≈ 325 K (Figure 3), in Figure 8 we show traces of all reactive trajectories projected on the plane described by B…C(carb.) and C(carb.)…hydride distances. As mentioned earlier, the starting geometry and geometries suitable for hydride transfer are fairly 13 ACS Paragon Plus Environment


close; the RMSD difference is circa 0.5 Å. However, trajectories show that a direct passage into the reaction-suitable configuration competes with significant configurational change. The later takes place even in trajectories that reacted relatively fast and this involves configurations with C(carb.)…B and C(carb.)…hydride distances about 6 Å because [dioxaneH(+)-acetone] reaches out to a far side with respect to fluorophenyls of [BCF-H(-)]. Such configurations with [dioxane-H(+)-acetone] side-on to [BCF-H(-)] are (very) different from the initial structure – RMSD difference is about 1.5 Å – but they are present in nearly every reactive trajectory (Figures 2 and 5 and Figure 6 as well). Qualitatively speaking, the difference between trajectories that reacted relatively quickly versus those that took relatively a longer time to react is related to the number of “visits” to side-on configurations (Figure 4). 6.5 C(carb.)...Hydride distance (Å)

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5.5 4.5 3.5 2.5 1.5 0.5 2.5

3

3.5

4

4.5

C(carb.)...B

5

5.5

6

distance (Å)

Figure 8. Reactive BOMD trajectories on the plane of B…C(carb.) and C(carb.)…hydride distances. The marker in black corresponds to the initial structure (Figure 1A). The marker in red corresponds to structures in which hydride transfer took place in BOMD simulations at T ≈ 325 K (Figure 3).

Last but not least, let us mention without going into details that [Et2O-H(+)OCPr2][(C6F5)3B-H(-)] system behaved similarly to [dioxane-H(+)-acetone][(C6F5)3B-H(-)] in all BOMD simulations that we have carried out at T ≈ 325 K starting from the initial structure shown in Figure 1B. For [Et2O-H(+)-OCPr2][(C6F5)3B-H(-)] system, in Supporting Information (SI) we show BOMD snapshots of hydride transfer step (Figure S1), representative BOMD snapshot with oxocarbenium cation at a side of [BCF-H(-)] near fluorophenyls (Figure S2) and an overlay of every 10th BOMD snapshot from circa 60 ps long phase of dynamics from the start till hydride transfer step (Figure S3). All the data is in accord to what we herein present for the case of [dioxane-H(+)-acetone][(C6F5)3B-H(-)]. 2.2. Entropy of [ether-H(+)-ketone][LA-H(-)] – qualitative considerations. 14 ACS Paragon Plus Environment

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Please note that all three BOMD trajectories in Figure 5 describe the very same system and eventually show the same chemical transformation – hydride transfer to the activated C(carb.) – but the lengths of trajectories from the start till reactive event are vastly different. According to basic principles, one might think that a low-barrier transformation with the reported ΔE# ≈ 1.5 kcal/mol 10,13 should correspond to consistently short reactive trajectories. However, this might not be the case for an intermediate with a large configurational space generating entropic stabilization. Our data appears to indicate presence of configurational entropic stabilization in [ether-H(+)-ketone][LA-H(-)] system, albeit at qualitative level. In static computational approach to reaction paths, the free energy estimation is provided by thermochemical calculations with ideal gas rigid rotor harmonic oscillator approximation applied to stationary geometries – e.g., a structure shown in Figure 1A could be thought to straightforwardly connect with the configurational region where hydride transfer can take place (Figure 3). Thus, static approach portrays hydride transfer as unimolecular step leaving actual cation/anion relative motion completely aside of the picture but focusing only on energetics of the preordained transition between the stationary structures instead. However, all the data presented above shows that trajectories of our system visit far out regions in the configurational space – meaning, [ether-H(+)-ketone] is by no means static with respect to [LA-H(-)] and it partially retains three-dimensional freedom of movement. Due to relative motion present at finite temperature, collisions between different parts of [ether-H(+)ketone] and [LA-H(-)] take place. Furthermore, orientation of ether with respect to ketone, in [ether-H(+)-ketone], is not static either but is reminiscent of a fairly weakly restricted rotamer with several rotational modes; relative rotations of ether with respect to ketone in [ether-H(+)ketone] have circa 2 ps timescale and it had been fairly common in all of trajectories we computed. All of that is in accord with the notion of weak – i.e., non-restrictive – cation/anion pairing and this effectively means that hydride transfer step has quasi-bimolecular character. Since we show that [ether-H(+)-ketone][LA-H(-)] system is not static and has significant amount of structural disorder at finite temperature, its entropy should be larger than that estimated by static approach. Due to computational power limitations, our trajectories do not amount to provide quantitative level estimation of “true” entropy of [ether-H(+)-ketone][LAH(-)] system at finite temperature with account of relative cation/anion motion. However, one can estimate the room for entropy lowering. For stationary structures of [dioxane-H(+)acetone][(C6F5)3B-H(-)] and [Et2O-H(+)-OCPr2][(C6F5)3B-H(-)], Figure 1, the entropy is 255 cal/mol/K and 274 cal/mol/K, respectively. However, for isolated cations and an anion the entropies are as follows: 113 cal/mol/K for [dioxane-H(+)-acetone], 151 cal/mol/K for [Et2O15 ACS Paragon Plus Environment


H(+)-OCPr2] and 195 cal/mol/K for [(C6F5)3B-H(-)]. This means that at T ≈ 300 K there is circa 15 kcal/mol and 21 kcal/mol loss in the free energy, G = H – TS, due to entropy-term for [dioxane-H(+)-acetone][(C6F5)3B-H(-)] and [Et2O-H(+)-OCPr2][(C6F5)3B-H(-)], respectively. These are estimations done in static approach using optimized structures and ideal gas rigid rotor harmonic oscillator approximation. Expanded configurational space, according to our BOMD data, means that some of this “lost” entropy can be recovered and this should lower free energy of [ether-H(+)-ketone][LA-H(-)] system below of that given by static approach. In other words, entropy of [ether-H(+)-ketone][LA-H(-)] system relates to the degree of its structural disorder that cation/anion interactions permits at finite temperature. Our BOMD data indeed indicates structural disorder and simple estimations show that there is considerable volume of entropy that can be recovered by [ether-H(+)-ketone][LA-H(-)] system. For facile hydride transfer, cation/anion arrangement must meet several geometrical restrictions – i.e., sufficiently short C(carb.)…B distance and orientation of [dioxane-H(+)acetone] with respect to [(C6F5)3B-H(-)] is subject to requirements imposed by the Bürgi– Dunitz and Flippin–Lodge angles for nucleophilic attack on C(carb.) of a ketone. That effectively determines suitable cation/anion relative arrangement with little room for alterations. That’s why BOMD-based representation of the configurations suitable for hydride transfer (Figure 3) is not much different from previously reported hydride transfer TSs.10,13 Thus, the entropy of hydride transfer suitable configurations appears to be certain even within static approach – meaning, configurational space of structures suitable for hydride transfer is limited. But since structural disorder allows for entropic stabilization of the ion pair intermediate, the free energy barrier for hydride transfer should be more than what is predicted by static approach. The culprit is a broad configurational space of weakly paired [dioxane-H(+)-acetone] [(C6F5)3B-H(-)] ion pair intermediate. This had not been recognized previously. The notion that three-dimensional flexibility of molecular pairing is connected with entropic gain has been productively used by Kim and Rhee for consideration of Frustrated Lewis pair formation.39 And, entropic stabilization is known to be important with regard to entropic contributions to free energy by main- and side-chains degrees of freedom in proteins;40 and, entropic stabilization of crystals has been observed as well.41 3. CONCLUSIONS In conclusion, we have applied Born-Oppenheimer molecular dynamics to practically relevant [dioxane-H(+)-acetone][(C6F5)3B-H(-)] and [Et2O-H(+)-OCPr2][(C6F5)3B-H(-)] ion pair 16 ACS Paragon Plus Environment

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intermediates in order to shed light on dynamics of hydride transfer that can yield product alcohol (Scheme 2) in reaction 1 (Scheme 1). This is an important part of the reaction-path which has been proposed for hydrogenation of carbonyl compounds with H2 in an ether solution using catalytic amount of borane Lewis acid (reaction 1 defined in Scheme 1). All BOMD data considered, each of the two systems was simulated for circa 1 ns in total. With that, we have found that geometry of oxocarbenium/borohydride ion pairs is much more flexible (structurally disordered) than previously though (i.e., static consideration made by others). Despite that the starting structure can be fairly close to the area of configurational space where previously reported hydride transfer TS resides and despite low potential energy barrier (circa 1.5 kcal/mol, according to the literature), we now show that at finite temperature (T ≈ 325 K) the system can remain ignorant of the said TS-region and “roam” in a vast configurational space for a period of time in the range between 10 ps and 100 ps. We have qualitative indications that this behavior can extend well above 100 ps range but meaningful exploration of such a long time interval is beyond our computational capabilities at present. Given the apparently necessary duration of trajectory propagation (10 ps to 100 ps) we had to disregard possible effects of explicit solvent in herein reported BOMD simulations. A comment about expected role of explicit solvent is given in the Introduction. However, our results give enough substance, albeit qualitatively, to a concern about actual magnitude of entropic stabilization of the oxocarbenium/borohydride ion pair intermediate which, according to basic principles, can arise from vast and accessible configurational space. This can significantly raise the free energy barrier of hydride transfer step, according to qualitative estimations. Also, the fundamental difference between herein given representation of the system and the static approach is quasi-bimolecular versus unimolecular description of hydride transfer. Since herein uncovered configurational space and corresponding structural disorder – i.e., surprising flexibility of oxocarbenium/borohydride ion pair geometries on apparently flat potential energy “landscape” – has not been taken into account by the free energy estimations in static considerations made thus far, this article could be instrumental for further development of the field via better mechanistic understanding. Acknowledgements We thank Carl Tryggers Foundation for Scientific Research (CTS 15:396 and CTS KF16:20) for the financial support. Part of calculations reported in this article had been carried out using resources provided by computer-center HPC2N via the project SNIC 2017/1-338.



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TOC Graphics:

TOC Entry: For [ether-H(+)-ketone][(C6F5)3B-H(-)] ion pairs, we show that an optimized structure is not representative of its vast configurational “neighborhood” and “roaming” in configurational space with flexibility of binding motifs indicate a flat potential energy “landscape” of cation/anion interaction.

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Borohydride Ion Pair: Dynamics of

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