cooperative effects

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Cite this: Phys. Chem. Chem. Phys., 2015, 17, 7443

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An alternative interpretation of the ultracold methylhydroxycarbene rearrangement mechanism: cooperative effects Sara F. de A. Morais, Kleber C. Mundim and Davı´ A. C. Ferreira* Recent studies have reported surprising results related to the rearrangement of carbenes under ultracold conditions, making use of sophisticated models of quantum tunnelling to explain the observed phenomena. Here, we demonstrate that a methylhydroxycarbene (H3C–C–OH) rearrangement is possible by making changes in molecularity (i.e., through cooperative effects), owing to intermolecular hydrogen bond/H-transfer. The model used for accomplishing these changes in molecularity suggests the occurrence of two chemical species during the rearrangement and preferential formation of acetaldehyde. We propose an alternative interpretation for the methylhydroxycarbene rearrangement, as well as for a bimolecular isomerization

Received 13th December 2014, Accepted 11th February 2015

mechanism for acetaldehyde formation with an activation barrier, Ea, of +0.25 kcal mol1, relative to 1a 0

DOI: 10.1039/c4cp05842a

Schreiner et al. We also note that the mechanism for obtaining vinyl alcohol leads to the simultaneous

(8.06 kcal mol1 relative to 1a); this barrier is lower than that required by H-tunnelling as proposed by formation of acetaldehyde through an Ea of +13.53 kcal mol1, relative to 1a (+0.93 kcal mol1 relative

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to 1b), again confirming the predominant presence of acetaldehyde.

Introduction Recent advances in the control of chemical analysis techniques for molecular systems under ultracold conditions are increasingly making it possible to investigate the reactivity of the intermediates such as carbenes1–3—species whose half-life is generally very short. At the same time, these techniques signal the possibility of measuring the contribution from a phenomenon such as tunnelling in ultralow-temperature chemical processes.4–7 On the other hand, in structural chemistry, little has been done to elucidate the real effects of the ultracooling of the intermediates and other molecular systems,8–10 generating gaps in current knowledge on how reduction in the temperature really affects chemical reactivity. Several decades ago, it was believed that ultracooling had a negative effect on the kinetics of a given reaction. However, recent studies have shown that the chemical kinetics can be redirected as a function of the temperature.5,6,11 During many chemical processes, an increase in the temperature increases the number of molecular collisions but, statistically speaking, with a nonideal orientation, which limits overlapping and the formation of chemical bonds. However, the basis for chemical kinetics suggests that the increase in the number of

Laborato´rio de Modelagem de Sistemas Complexos, Universidade de Brası´lia, ´rio Darcy Ribeiro, Instituto de Quı´mica (IQ-UnB), Campus Universita P.O. Box 04478, CEP: 70904-970, Asa Norte - Brası´lia-DF, Brazil. E-mail: [email protected]/[email protected]

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collisions should increase the probability of generating products, resulting in an increase in the reaction rate. There is another factor with much greater importance within the tenets of chemical kinetics, the transition-state theory.12–14 This holds that one of the main conditions for a reaction to occur is the establishment of a transition-state geometry, which is the outcome of the reagent molecules moving closer in orientation, with the energy being enough to lead to the transfer of groups. Using this approach, one can infer that the chemical reactivity of a given system can be controlled partially. In other words, a fundamental criterion for chemical reactivity continues to be molecular.14 When chemical species are dispersed in a given solvent, they tend to move closer to or farther apart, depending on the nature of the solvent in question. When the interaction between the dispersed and the dispersant is high, the dispersed species will not be present in the form of dimers, trimers, or other types of clusters; however, if the interaction is weak, there is an extremely high probability for the almost immediate formation agglomerates.15 Thus, the isolation of chemical species in ultracold matrices can lead to the formation of molecular aggregates in cavities, favouring and intensifying intermolecular interactions.4,15 Recent studies15 on the generation of agglomerates owing to the formation of hydrogen bonds have shown that species dispersed in liquid helium tend to agglomerate (preferably as trimers) by means of hydrogen bonds, so that the total isolation of the molecules in this medium is possible only when another

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Scheme 1 General representation of the rearrangement of methylhydroxycarbene to 3 and 5 through a unimolecular or bimolecular mechanism (i.e., through a cooperative effect).

much stronger interaction is established. In this same study, it was observed that heating the system under analysis did not cause molecular expansion but instead led to greater agglomeration, further corroborating the idea that molecular systems can establish relatively strong intermolecular interactions even under adverse conditions. It is evident that the total isolation of chemical systems is not possible, as exemplified by the reactions that occur in the outer atmosphere16,17 or in space18,19—until recently considered regions with an almost absolute vacuum. Another study on the deposition of retinoic acid on gold surfaces showed that an organizational preference for the formation of trimers, tetramers, pentamers, or hexamers depends on the number of layers or the deposition facet.20 On the basis of these results as well as on the possibility of the existence of changes in the corresponding reaction’s molecularity,21 we carried out calculations on the electronic structure for the rearrangement of methylhydroxycarbene and the predominant formation of acetaldehyde in a cryogenic matrix by means of dimer formation, in order to seek an alternative explanation. The rearrangement process is illustrated in Scheme 1; it should be noted that we did not take into account the quantum tunnelling effect.22,23

Methods All initial geometrical optimizations and vibrational frequency calculations for all the molecular species (carbenes, transition states, and products) on the ground-state singlet surface were made using the Complete Basis Set (CBS-4M)24,25 model chemistry. For all the transition-state geometries, we employed the Berny algorithm and took as the real transition state just one imaginary vibrational mode. To accurately compute the thermodynamic properties, we used the CBS-4M zero point correction [CBS-4(0 K)] for all the representative stationary points on the reaction coordinate path. Rigorous electronic structural

7444 | Phys. Chem. Chem. Phys., 2015, 17, 7443--7448

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computations were performed using the correlation-consistent aug-cc-pVDZ26,27 basis sets of atomic orbital and all-electron (AE) single-reference coupled-cluster theories, incorporating all single and double excitations (AE-CCSD)28–31 and the perturbative inclusion of the connected triple excitations [AE-CCSD(T)].32 The coupled-cluster method was used to determine the dicentric bond index and in population analysis (NBO).33–37 The molecular dynamics of the carbene symmetrical dimer were performed, using the Born–Oppenheimer molecular dynamics (BOMD)38,39 at the frozen core (FC) MP2/6-31G40–45 level with 100 steps and 77.8 fs. A molecular dynamics analysis is essential for determining the van der Waals complex,46,47 as it eliminates ambiguous interpretations such as the negative activation energy.46 The first thirteen steps in the dynamics were taken and recalculated at the same level, in order to obtain the wave function for the BCP (The Quantum Theory of Atoms in Molecules or QTAIM)48,49 analysis and to generate an alternative reaction coordinate involving symmetric proton transfer during the rearrangement of the carbenes. All the calculations were performed using the Gaussian 09,50 AIMAll,51 and AIM-UC52 quantum chemistry packages.

Results and discussion To obtain a general reaction coordinate for the isomerization of carbenes, we performed CBS calculations in which the precision level was comparable to that of recent studies on the same intermediate. According to these CBS calculations, if we consider the possibility of an intramolecular rearrangement of methylhydroxycarbene, the same may give rise to acetaldehyde, via a barrier of the order of +26.36 kcal mol1, or to vinyl alcohol, via a barrier of the order of +21.44 kcal mol1. These energy barriers are of the same order of magnitude as are the barriers reported by Schreiner6 and co-workers using coupledcluster methods. However, the probability of molecular isolation of polar systems is low, owing to the possibility of occurrence of intermolecular interactions,53 so that the most probable arrangement at low temperatures would at least be in the dimer form.4,15,54,55 Taking this information as a basis and allowing for the formation of agglomerates at low temperatures, we performed calculations for symmetric and asymmetric dimerized systems for methylhydroxycarbene. The results showed a surprising inversion of the kinetic tendency imposed by the classical model—the generation of carbene dimers by the establishment of hydrogen bonding leads to a symmetric intermolecular proton transfer, favouring the formation of an aldehyde via a negatively activated barrier46,56 (i.e., the apparent activation barrier), as described in the reaction coordinate below (Fig. 1). NBO analyses were performed via AE-CCSD(T)/aug-cc-pVDZ// CBS-4M. In these, we observed a greater electronic dislocation for the orbitals of the O–H C fragments involved in the nonclassical hydrogen bonds of the symmetric carbene dimer (step 1: nC - sO–H* = 48.06 kcal mol1); (step 2TS: nO - sC–H* = 256.34 kcal mol1), when compared to its monomeric form (step 1: nC - sO–H* = 0.53 kcal mol1); (step 2TS: nO - sC–H* = 89.36 kcal mol1).


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Table 1 Analysis of Wiberg dicentric indices for the carbene-to-aldehyde isomerization by a unimolecular or bimolecular rearrangement

BOND

1

2TS

3

MONOMER O–H C–O C–H

0.7161 1.1356 0.0083

0.2461 1.5181 0.4489

0.0518 1.8042 0.9258

DIMER O–H C–O C–H

0.5446 1.2558 0.1435

0.3632 1.3790 0.3869

— 1.7591 0.9255

Fig. 1 Coordinate reaction path obtained through stationary point calculations (using a CBS model) for the rearrangement of methylhydroxycarbene to 3 or 5 through a cooperative effect. Note that evolution of 1a 0 to 3 is kinetically and thermodynamically favoured, according to experimental observations.

The main argument for the formation of dimers is that this phenomenon can result in the instantaneous stabilization of carbene-type intermediates. Thus, upon the formation of dimers, the proton transfer at low temperatures would be immediate, as a function of the energy associated with the vibrational stretching mode of O–H, making it more or less accessible, as well as a function of the degree of symmetry of the complex formed. As is expected for transition states, the vibrational stretching mode of O–H for the symmetrical dimer (oi = 1192.93i cm1) is more accessible in terms of energy compared to the mode related to the C–O–H angular deformation of the monomeric carbene during the formation of an aldehyde (oi = 2610.08i cm1) or the formation of an enol (oi = 1708.67i cm1). Another important fact is that the dimerized carbene system already presents a vibrational mode that can reveal intermolecular interactions; however, these occur at wavenumbers lower than 400 cm1 (o = 159.89–255.66 cm1), while the mode related to the classic rearrangement for the formation of an aldehyde occurs only at o = 1453.61 cm1. The high values of the dislocation energies are strong evidence of the preference carbenes show for forming dimers in the stage that precedes the establishment of the transition state. Analyses of the Wiberg indices corroborate the results of the NBO analysis of the stabilization of systems owing to the formation of symmetric dimers, as can be seen in Table 1. As described in the reaction coordinate in Fig. 1, the preferential form of the symmetric dimer 1a would lead to the majority formation of 3 via the transition state 2, which can be kinetically interpreted as being apparently negative, if the formation of the van der Waals type complex47,57 (1a 0 ) is not considered. For this alternative approach, the identification of complex 1a 0 was possible only using BOMD. Thus, the activation energy ceases to be negative, allowing the molecular evolution of 1a to 3 via an activation barrier of the order of +0.25 kcal mol1, as seen in Fig. 2. Another important point regarding the dimer formation approach is that proton transfer would happen in terms of


Fig. 2 Initial stages of the molecular dynamics and the Laplacian of the density evolution for proton transfer during methylhydroxycarbene rearrangement. These dynamics correspond to the interval of 0–20.8 fs. Here, we observed a van der Waals complex (1a 0 ) a few instants before the transition state (2TS), conducting to 3 0 , across the very short activation barrier.

QTAIM by means of the bond path (BP); this further reinforces the model of proton transfer in methylhydroxycarbene through the formation of dimers. An analysis of the evolution of the electronic structure of the symmetric dimer of carbene that considered the first 13 steps of molecular dynamics showed the dynamics of critical points that is compatible with the changes expected for systems linked by hydrogen bonds. As can be seen in Fig. 3, throughout the

Fig. 3 QTAIM parameter (in a.u.) for the labelled points for the molecular structures along the reaction path. Note that rx is the electron density at point x, and r2rx is the Laplacian density at point x.


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reaction, there is a gradual reduction in ra, indicating a break in the O–H bond, until the step when rb increases along with rc, indicating the formation of a C–H bond and strengthening of the C–O bond. Another sign of the gradual evolution of the system from 1 (1a) to 13 (30 ) can be seen in the Laplacians of the density at points a (which goes from 1.4029 to 0.1687, that is, from a covalent bond to a hydrogen bond) and b (which goes from 0.0946 to 1.2308, that is, from a hydrogen bond to a covalent bond). In an attempt to corroborate at a theoretical level the predominance of cooperative effects on the rearrangement of methylhydroxycarbene, we determined the parameter d,58 which is a measure of the quantum tunnelling effect. The parameter d 58 is defined through a nonextensive thermodynamic formalism,59 which takes into account the possibility of tunnelling for this rearrangement. It is important to point out that the nonextensive thermodynamics is a possible generalization of the standard Boltzmann–Gibbs formalism. The parameter d was determined using eqn (1): 1 hcoi 2 d ¼ NA (1) 3 2E0 where d is the deformation parameter, h is Planck’s constant, c is the speed of light, oi is the imaginary vibrational mode of TS, NA is the Avogadro constant, and E0 is the monomer activation barrier. Thus, for a unimolecular rearrangement, we have d = 0.0067, a relatively small factor to indicate the tunnelling phenomenon. The approach used for the tunnelling itself contains the embedded entropy, since d = (1 q). According to Tsallis’ nonextensive entropy formalism, the entropy of a interacting system is ð1 qÞ Sq ðA; BÞ ¼ SA þ SB þ SA SB , where Sq(A,B) is the entropic kB state of the interacting system, SA and SB are the entropic states of noninteracting systems, kB is the Boltzmann constant, and q is the parameter of nonextensiveness. We would like to point out that the contribution of vibrational entropy to methylhydroxycarbene dimerization is DSvib = +12.92 cal mol1 K1; very common in the case of cooperative effects, when the real entropic gain occurs through an increase in the vibrational entropy.60 By using the parameter d in eqn (2), we determined that the corrected activation energy for tunnelling is Ea = +2.91 kcal mol1, 1 1 1 (2) ¼ d Ea E0 RT These results show that the quantum tunnelling effect does not occur under these conditions, since the activation energy barrier associated with the dimer rearrangement occurs at 0.25 kcal mol1. We also determined the possibility of a unimolecular rearrangement using the Tsallis-like probability distribution function, which is displayed in Fig. 4. As can be seen, the probability P(T) of a unimolecular rearrangement occurring at low temperatures is remote, probably owing to the high energy required for the angular deformation of the C–O–H group to occur. It can be seen from Fig. 4 that the phenomena with high activation barriers are unlikely to occur, so that the possibility of the rearrangement occurring is statistically (and physicochemically) more acceptable by dimerization.


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Fig. 4 Tsallis-like probability distribution function corresponding to several temperature states for dimeric (blue), tunnelling (red), and monomeric (black) rearrangements.

Conclusions Finally, on the basis of experiments and observations carried out recently by various research groups, including ours, we suggest that the vibrational modes in the region corresponding to wavenumbers lower than 400 cm1 should be revisited, as suggested by Liu et al.,10 as this will yield new information on the collective effects on various chemical processes. We would also like to mention that, depending on the magnitude of the interactions between the molecules in a given reaction,53,61,62 considerable changes may occur in the order and molecularity of the reaction, leading to interpretations that cannot be mechanistically justified a priori. Studies on cooperative phenomena are being performed by our group, and the initial data already indicate that the sub-Arrhenius behaviour63,64 is due to the occurrence of the same chemical transformation with different molecularities, such as rearrangements similar to those described in previous studies.5,7

Acknowledgements This work was supported by the CAPES and PNPD Institucional (post-doctoral fellowship to D.A.C.F. and doctoral fellowship to S.F.A.M.) and the CNPq (fellowship to K.C.M.). Computational resources were provided by the Instituto de Quı´mica at the Universidade de Brası´lia, which is supported by FINEP, and by ´rio de Modelagem de Sistemas Complexos (LMSC), the Laborato which is supported by CAPES and CNPq.

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