Mapping the Kinetic and Thermodynamic Landscape of Formaldehyde

Nov 5, 2013 - Our study provides a baseline free energy map for further study of ... Our protocol was based on several points of agreement with experi...
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Mapping the Kinetic and Thermodynamic Landscape of Formaldehyde Oligomerization under Neutral Conditions Jeremy Kua,*,†,‡ Joseph E. Avila,† Christopher G. Lee,† and William D. Smith§ †

Department of Chemistry and Biochemistry, University of San Diego, 5998 Alcala Park, San Diego, California 92110, United States Yale-NUS College, 6 College Avenue East #B1-01, Singapore 138614 § Christian High School, 2100 Greenfield Drive, El Cajon, California 92019, United States ‡

S Supporting Information *

ABSTRACT: Density functional theory calculations, including Poisson− Boltzmann implicit solvent and free energy corrections, are applied to study the thermodynamic and kinetic free energy landscape of formaldehyde oligomerization up to the C4 species in aqueous solution at pH 7. Oligomerization via C−O bond formation leads to linear polyoxymethylene (POM) species, which are the most kinetically accessible oligomers and are marginally thermodynamically favored over their oxane ring counterparts. On the other hand, C−C bond formation via aldol reactions leads to sugars that are thermodynamically much more stable in free energy than POM species; however, the barrier to dimerization is very high. Once this initial barrier is traversed, subsequent addition of monomers to generate trimers and tetramers is kinetically more feasible. In the aldol reaction, enolization of the oligomers provides the lowest energy pathway to larger oligomers. Our study provides a baseline free energy map for further study of oligomerization reactions under catalytic conditions, and we discuss how this will lead to a better understanding of complex reaction mixtures with multiple intermediates and products.

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INTRODUCTION Much of the chemistry that takes place outside the controlled reactions in a laboratory setting involves complex reaction mixtures. The lithosphere, hydrosphere, and atmosphere of our planet contain a multitude of molecular species. Coupled with myriad chemical reactions that take place, this makes the study of these systems very challenging. In fact, a single molecular species that self-oligomerizes in solution may lead to a very complex mixture depending on the reaction conditions. Our goal in the present study is to provide a preliminary baseline free energy map for such a system, leading to a better understanding of complex reaction mixtures with multiple intermediates and products. The starting molecular species we chose was the simple molecule formaldehyde, CH2O. The oligomerization of concentrated solutions of formaldehyde is well-known although the reaction energetics of individual steps is difficult to determine experimentally because of the cascade of reactions that take place. Since the first preparation of formaldehyde by Butlerov,1 there have been extensive studies of formaldehyde and its oligomers culminating in a compilation of formaldehyde chemistry by Walker in the mid-20th century.2 The potential promise of synthetic food production through formaldehye oligomerization via the formose reaction was extensively studied and the experimental results documented by Mizuno and Weiss in 1974;3 the reaction mechanism had been proposed earlier by Breslow in 1959.4 The physical and chemical behavior of formaldehyde (and its oligomers) in solution has also been extensively probed because of its synthetic use as both building block and reactive intermediate in industrial chemistry.2,5−10 In addition, form© 2013 American Chemical Society

aldehyde oligomerization is of interest in origin-of-life chemistry as a pathway to prebiotic sugar synthesis.11 In dilute aqueous solution, formaldehyde exists predominantly as methylene glycol. Oligomers and polymers are formed as the concentration of formaldehyde in solution increases, and this reaction is catalyzed under acidic or basic conditions.2 Under neutral or acidic conditions, acetal/ hemiacetal oligomers and oxane rings are observed3 and methanol is often added to aqueous formaldehyde solutions to prevent oligomerization and oxidation.6 Under alkaline conditions, the formose reaction takes place, forming a wide variety of C4−C7 sugars; however, aldol condensation reactions also compete with the Cannizzaro reaction under these conditions, further widening the product distribution.3 Computational chemistry is useful in studying complex systems with large and varied product distributions because we can tease out and identify the energetic contributions of the many different species present in a reaction mixture. We had previously utilized a relatively fast protocol to map the thermodynamic and kinetic energy landscape for the preliminary steps of both glyoxal12 and methylglyoxal13 oligomerization in solution. Both these α-aldehydes are involved in the formation of atmospheric secondary organic aerosol. Our protocol was based on several points of agreement with experimental observations of the species, but there were few quantitative numbers with which to compare the relative accuracy of our computational results. To refine our protocol, Received: October 3, 2013 Revised: November 5, 2013 Published: November 5, 2013 12658

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Table 1. Energies of Oligomers and Intermediates

a

Eelec (au)

Esolv (kcal/mol)

H2O 1a 1ha 2a 2e 2o 2ha 2p 3a 3e 3k 3o 3ha 3hk 3p 4a 4e 4f 4k 4o 4ha 4hk 4p

−76.44744 −114.53629 −191.00777 −229.11010 −229.09642 −229.06626 −305.57126 −305.56752 −343.67598 −343.66179 −343.67676 −343.66164 −420.14286 −420.14643 −420.12608 −458.24059 −458.23063 −458.23756 −458.24596 −458.21850 −534.70921 −534.70902 −534.68505

−8.11 −2.66 −9.23 −7.47 −6.84 −5.85 −15.37 −10.25 −10.78 −10.58 −13.34 −7.26 −15.45 −14.03 −12.40 −14.99 −13.70 −17.41 −14.38 −10.94 −18.05 −17.83 −14.03

4a3 4f2 4f3 4f4

−458.23947 −458.23620 −458.23958 −458.24045

−14.42 −17.65 −17.14 −16.57

CH3OH HCO2H HCO2CH3

−115.75737 −189.81948 −229.13005

−5.48 −6.90 −2.76

Hcorr (kcal/mol)

Gcorr (kcal/mol)

−0.5TScorr (kcal/mol)

G298 (kcal/mol)

ΔGr (kcal/mol)

−6.72 −7.79 −9.28 −10.08 −10.37 −9.20 −11.32 −11.03 −11.78 −12.08 −12.51 −10.29 −12.81 −12.66 −12.98 −13.50 −13.67 −13.17 −15.19 −11.83 −14.51 −14.30 −14.93

−47970.59 −71864.06 −119838.78 −143744.75 −143735.37 −143713.97 −191714.69 −191706.39 −215618.34 −215609.23 −215622.43 −215602.88 −263588.41 −263589.32 −263574.65 −287492.28 −287484.44 −287491.71 −287496.68 −287471.30 −335461.84 −335461.64 −335442.62

0.0 −4.1 −16.6 −7.3 +14.1 −16.0 −7.7 −26.2 −17.0 −30.2 −10.7 −25.6 −26.6 −11.9 −36.0 −28.2 −35.5 −40.4 −15.1 −35.0 −34.8 −15.8

−13.56 −13.17 −12.87 −12.78

−287491.19 −287491.09 −287492.32 −287492.01

−35.0 −34.9 −36.1 −35.8

−8.48 −8.84 −9.69

−72618.08 −119105.47 −143752.12

15.74 2.30 19.01 3.44 38.94 20.38 41.58 21.43 41.54 21.80 42.35 23.96 60.90 38.26 61.44 39.38 64.19 40.64 64.50 40.34 63.88 38.87 65.64 45.07 83.52 57.91 83.28 57.97 83.88 57.92 86.57 59.58 87.04 59.71 87.34 61.00 86.62 56.25 87.98 64.32 105.89 76.86 105.53 76.93 106.34 76.49 Relevant Additional Diastereomersa 86.46 59.34 87.34 61.01 87.42 61.69 87.62 62.07 Side Products 34.74 17.79 23.82 6.14 41.63 22.26

4a = D-threose, 4a3 = D-erythrose, 4f = D-β-threofuranose, 4f2 = D-α-threofuranose, 4f3 = D-β-erythrofuranose, 4f4 = D-α-erythrofuranose.

landscape for formaldehyde oligomerization. Previous studies15−22 typically (1) concentrated on isolated reactions of interest, (2) were for gas-phase conditions, and/or (3) were performed semiempirically. This paper is organized as follows. After detailing the computational and experimental methods used, we examine the calculated thermodynamic and kinetic energy landscape using our protocol. Comparisons are made to experimental results where applicable. Not surprisingly, we find that under dilute aqueous conditions at pH 7 and 25 °C, methylene glycol (hydrated formaldehyde) is the predominant species. We find that POM species are the most kinetically accessible oligomers and are marginally thermodynamically favored over their oxane ring counterparts. On the other hand, aldol products (sugars) are thermodynamically much more stable but have a very high initial barrier to form the dimer glycolaldehyde because there is no kinetically accessible enol intermediate. The products from potentially competing Cannizzaro and Tishchenko reactions are favorable thermodynamically but are kinetically less accessible, the latter having enormously high barriers. In the conclusion, we briefly discuss the next steps in utilizing the baseline energy map for further study under catalytic conditions, and how this will lead to a better understanding of complex reaction in different chemical environments.

we recently studied the oligomerization of aqueous glycolaldehyde, the dimer of formaldehyde, and made a detailed comparison of our computational results with NMR measurements.14 Our method was successful in predicting the equilibrium concentrations of the dominant species in solution (monomers and dimers). In addition we were able to predict the concentrations of trimers in solution, 2 orders of magnitude lower than the monomers. We also did relatively well in estimating some rate constants and activation barriers. There are, however, several potential issues stemming from the approximations and assumptions made in our protocol. These are covered briefly in the Computational Methods section and discussed more extensively in our previous study.14 In the present study, we apply our computational protocol to map the energy landscape of formaldehyde oligomerization in aqueous solution up to the tetramer. This allows us to compare the energetics of the two main oligomerization pathways: (1) C−O bond formation leading to linear polyoxymethylene (POM) species and cyclic oxanes and (2) C−C bond formation leading to sugars. As a baseline for future studies, we have chosen noncatalytic conditions at pH 7 and a temperature of 25 °C. These were also the conditions used in our previous studies on the self-oligomerization of aldehydes.12−14 We are not the first to use computational methods to study some of the reactions in the present system; however, to our knowledge we are the first to systematically provide a broad map of the energy 12659

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Table 2. Transition State Energies Eelec (a.u.)

Esolv (kcal/mol)

1a⇔1ha

−343.90414

−16.45

1ha⇔2p 2p⇔3p 3p⇔4p 3p⇔3o 4p⇔4o 4p⇔3o 1a⇔3o

−458.46638 −573.02664 −687.59005 −649.45212 −764.00568 −764.00891 −343.59346

−17.24 −16.89 −15.33 −28.49 −29.22 −30.31 −9.73

1a⇔2a 2a⇔2ha 2a⇔2e 2e⇔3a 3a⇔3ha 3a⇔3e 3e⇔3k 3k⇔3hk 3e⇔4k 4k⇔4hk 4k⇔4e 4e⇔4a 4a⇔4ha 4a⇔4f 4a⇔4f2 4a3⇔4f3 4a3⇔4f4

−381.92683 −458.47242 −458.45804 −496.55744 −573.00409 −573.02960 −573.02094 −573.03994 −611.12541 −687.61549 −687.59352 −687.58433 −687.60552 −611.13850 −611.13582 −611.14260 −611.14903

−17.39 −20.74 −18.75 −12.81 −24.27 −19.61 −24.34 −23.11 −18.86 −22.01 −23.11 −24.22 −27.48 −24.25 −24.21 −21.27 −20.38

Cannizzaro Tischencko

−305.51325 −458.36297

−9.77 −23.94

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Hcorr (kcal/mol)

Gcorr (kcal/mol)

−0.5TScorr (kcal/mol)

67.39 43.29 −12.05 C−O Bond Formation Oligomerization Pathway 90.61 61.33 −14.64 112.98 82.09 −15.45 136.34 103.46 −16.44 132.36 95.83 −18.27 153.59 113.77 −19.91 154.80 114.06 −20.37 61.60 38.58 −11.51 C−C Bond Formation Oligomerization Pathway 69.62 42.64 −13.49 90.07 62.15 −13.96 84.33 55.99 −14.17 94.16 65.23 −14.47 112.76 81.53 −15.62 112.87 81.17 −15.85 110.14 76.99 −16.58 112.37 81.37 −15.50 115.82 84.12 −15.85 135.36 102.31 −16.53 134.46 98.05 −18.21 132.69 96.56 −18.07 135.32 100.64 −17.34 116.54 85.06 −15.74 116.09 84.55 −15.77 116.28 85.32 −15.48 116.98 86.22 −15.38 Side Reactions 55.00 32.70 −11.15 88.24 56.98 −15.63

COMPUTATIONAL METHODS Our computational methods use the same protocol as several of our previous studies discussed in the Introduction. All calculations were carried out using Jaguar 6.023 at the B3LYP24−27 level of density functional theory (DFT) with a 6-311G** basis set. To maximize the probability of finding the global minimum, we performed calculations on various conformers of each structure with different internal hydrogen bond networks. The Poisson−Boltzmann (PB) continuum approximation28,29 was used to describe the effect of water as a solvent with a dielectric constant of 80.4 and a probe radius of 1.40 Å. The forces on the quantum mechanical solute atoms due to the solvent can be calculated in the presence of the solvent. However, as in previous work, the solvation energy was calculated at the optimized gas-phase geometry because in most cases there is practically no change between the gas-phase and implicit solvent optimized geometries. The electronic energy of the optimized gas-phase structures and the solvation energy are designated Eelec and Esolv, respectively in Table 1. It is important to note that even though the solvation energy contribution is to some extent a free-energy correction, it certainly does not account for all of the free energy. A comparison of our chosen level of theory, basis set, and implicit solvent scheme, with other methods can be found in our previous work.13,14 The analytical Hessian was calculated for each optimized structure, and the gas-phase energy corrected for zero-point vibrations. Negative eigenvalues in transition state calculations were not included in the zero-point energy (ZPE). The temperature-dependent enthalpy correction term is straightfor-

G298 (kcal/mol)

ΔGr (kcal/mol)

−215764.26

+11.6

−287633.32 −359499.07 −431364.79 −407451.84 −479316.44 −479318.81 −215567.83

+6.6 +4.9 +3.2 +22.7 +22.1 +19.8 +24.3

−239624.01 −287640.47 −287635.41 −311527.68 −359515.28 −359504.17 −359506.92 −359514.30 −383405.95 −431388.50 −431378.39 −431375.36 −431388.56 −383418.73 −383417.48 −383418.32 −383420.66

+45.3 −0.6 +4.5 +5.7 −11.3 −0.2 −3.0 −10.4 −8.5 −20.5 −10.4 −7.4 −20.6 −21.3 −20.1 −20.9 −22.3

−191678.42 −287578.49

+20.29 +61.40

ward to calculate from statistical mechanics where we assume that translational and rotational corrections are a constant times kT, that low frequency vibrational modes will generally cancel out when enthalpy differences are calculated, and that the vibrational frequencies do not change appreciably in solution. The vibrational scaling factor of 0.967 for B3LYP//6-311G** was not applied in this case because when relative energies are calculated, the difference to the enthalpy correction becomes negligible within the computational error. The combined ZPE and enthalpy corrections to 298 K are designated Hcorr and the corresponding gas-phase free energy correction to 298 K is designated Gcorr in Table 1. The corresponding free-energy corrections in solution are much less reliable.30−32 Changes in free energy terms for translation and rotation are poorly defined in solution, particularly as the size of the molecule increases. Additional corrections to the free energy for concentration differentials among species (to obtain the chemical potential) can be significant, especially if the solubility varies among the different species in solution. Furthermore, because the reactions being studied are in solution, the free energy being accounted for comes from two different sources: thermal corrections and implicit solvent. Neither of these parameters is easily separable, nor do they constitute all the required parts of the free energy under our approximations of the system. To estimate the free energy, we followed the method of Lau and Deubel33 who assigned the solvation entropy of each species as half of its gas-phase entropy. Wertz34 and Abraham35 had previously suggested that upon dissolving in water, 12660

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molecules lose a constant fraction (∼0.5) of their entropy. In Table 1, this is designated −0.5TScorr and is calculated by 0.5(Gcorr − Hcorr). Recent computational studies in other unrelated systems have come to the same conclusion.36,37 The free energy of each species, designated G298 in Table 1, is the sum of Eelec, Esolv, Hcorr, and −0.5TS. Although we calculated multiple conformers, only the most stable conformer (both stable minima and transition states) for each unique molecular species is reported in our free energy map. ΔG values are calculated from the difference in G298 between the reactants and products and therefore include the zero-point energy, enthalpic, and entropic corrections to 298 K for a reaction in aqueous solution. In Table 1, the rightmost column (ΔGr) is the relative free energy of each species with respect to formaldehyde and water as the reference states. With this choice of reference states, formaldehyde is assigned ΔGr = 0.0 and water molecules are added where necessary to ensure the reactions are stoichiometrically balanced. This allows us to quickly and easily visualize a map of the energy landscape, for the myriad reactions that can take place. Although water is a reactant in hydration reactions, concentration corrections are not included in this landscape, the advantages and disadvantages of which are discussed in our previous work.14 The ΔGr values are also provided in the energy landscape figures for easy reference. For transition state calculations, additional water molecules were explicitly added to the system to find the lowest energy barrier for proton transfers. We tried different numbers of water molecules to find the optimum structure that gives the lowest barrier. All calculated transition states have one large negative eigenvalue corresponding to the reaction coordinate involving bond breaking/forming and accompanying proton transfer. The corresponding energy components of the transition states are listed in Table 2. In our previous study examining the equilibrium distribution of glycolaldehyde and its oligomers in solution,14 we found that this protocol for calculating free energies provided good agreement with NMR experimental results. The activation barriers compared to experiment are reasonable, but the agreement is not as close. Given the impetus for a relatively fast protocol, we have not included basis set superposition error corrections as part of the process. In the Results and Discussion section, we will make similar comparisons where experimental values are available.

Figure 1. Formation of POM oligomers and oxane rings (ΔGr in kcal/ mol).

as described in the Computational Methods section, ΔGr(1ha) = −4.1 kcal/mol. Because three water molecules are involved in the optimal transition state, the reaction barrier is G298(1a⇔ 1ha) − [G298(1a) + 3G298(H2O)] = +11.6 kcal/mol, and similarly ΔGr(1a⇔1ha) = +11.6 kcal/mol. In the second reaction forming dimethoxymethane, the reaction is 1ha + 1a → 2p. The change in free energy is G298(2p) − [G298(1ha) + G298(1a)] = −3.6 kcal/mol, but relative to the reference state, ΔGr(2p) = −7.7 kcal/mol. The reaction barrier for this second step is G298(1ha⇔2p) − [G298(1ha) + 2G298(H2O)] = +10.7 kcal/mol, but relative to the reference state, ΔGr(1ha⇔2p) = +6.6 kcal/mol. These first two steps are illustrated in the energy diagram in Figure 2. When the phrase “calculated barrier” is used in the paper, we will be referring to the reaction barrier just for that step, i.e., +10.7 kcal/mol in this example. When we refer to the relative energy of the transition state with respective to formaldehyde so that we can see this value in light to the entire landscape, we will explicitly state “ΔGr”.

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RESULTS AND DISCUSSION Labeling Scheme, Reference State, and Formaldehyde Hydration. In Table 1, each species is labeled according to the number of carbons in the molecule followed by letters designating the functional group or structural arrangement (a = aldehyde, e = enol, f = furanose, h = hydrate, k = ketone, o = oxane ring, p = POM oligomer). The transition states in Table 2 are labeled with a ⇔ symbol flanked by the reactant on the left and product on the right. Water molecules that balance the reaction and formaldehyde molecules that are added to a growing oligomer are not reflected in the label. There are two reactions in the top row of Figure 1: (i) the hydration of formaldehyde and (ii) the subsequent addition of a second formaldehyde molecule to form dimethoxymethane (2p), the smallest POM oligomer. For the hydration of formaldehyde, the reaction free energy change is G298(1ha) − [G298(1a) + G298(H2O)] = −4.1 kcal/mol. Because formaldehyde is the reference state and assigned ΔGr = 0.0 kcal/mol

Figure 2. Transition states of formaldehyde hydration and dimerization via C−O bond formation. 12661

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Figure 3. Oxane formation transition states from POM tetramer.

ours, in the 13−23 kcal/mol range.39−42 One recent study of the dehydration barrier of methylene glycol underestimates the barrier compared to the experimental values.43 POM Oligomers and Oxanes via C−O Bond Formation. Figure 1 summarizes the free energy landscape for POM oligomer and oxane formation up to the tetramer. The POM dimer 2p is formed by the reaction of formaldehyde and methylene glycol. As shown in Figure 2, this reaction has a low barrier eight-center transition state, similar to formaldehyde hydration. Nucleophilic attack by an OH group of methylene glycol on the carbonyl of formaldehyde is accompanied by proton transfer via two assisting water molecules. Although this reaction is thermodynamically favorable if formaldehyde is one of the reactants, in dilute solution, almost all formaldehyde molecules are hydrated as methylene glycol. Two molecules of 1ha have ΔGr = −8.2 kcal/mol, which is lower in free energy than 2p (ΔGr = −7.7 kcal/mol). The formation of POM trimer (3p) and tetramer (4p) proceed in the same fashion with subsequent additions of formaldehyde. The reactions are thermodynamically favored with increasing size of POM (ΔGr(3p) = −11.9 kcal/mol; ΔGr(4p) = −15.8 kcal/mol) compared to the reference state of formaldehyde. Our preliminary calculations, which are a work in progress, suggest that ΔGr continues to decrease in the C5 to C6 POMs, albeit in smaller increments. Thus we expect the formation of progressively larger POMs as the concentration of formaldehyde increases in solution, but predominantly monomeric 1ha in dilute solution, in good agreement with experiment.2 POMs can cyclize into their respective oxanes with loss of a water molecule. From Figure 1 we see that the oxanes are slightly less thermodynamically favorable than their corresponding POMs (ΔGr(3o) = −10.7 kcal/mol; ΔGr(4o) = −15.1 kcal/mol). Work in progress indicates this trend continues for the C5 and C6 oxanes. Thus we expect not to find significant amounts of cyclic oxane unless water is actively removed from the system. The barrier to cyclization is higher because an SN2 reaction is required, and the present calculation requires a string of water molecules to assist in the proton transfer. Interestingly, the barrier to forming trioxane is ∼3 kcal/mol lower when starting from the POM tetramer as indicated in Figure 1. The two lowest energy transition states for cyclization starting from the POM tetramer and forming the tetraoxane and the trioxane are shown in Figure 3. Note that in Table 1, the strained four-membered ring oxane (2o) is rather

The optimum transition state for formaldehyde hydration is an 8-center transition state with two catalytic water molecules (in addition to the one reactant water molecule) facilitating proton transfer, as shown in Figure 2. The energy barriers for the corresponding 4-, 6-, and 10-center transition states, involving zero, one, and three catalytic water molecules, respectively, are all higher. This is similar to what we found in our glycolaldehyde study and is discussed in more detail in that work.14 Earlier extensive computational work by Wolfe et al. at the MP2//6-31G* level studying the different transition states of formaldehyde hydration also concluded that the 8center transition state is indeed the most favorable.38 In the transition state, the newly forming C−O bond distance is 1.69 Å, the CO has lengthened to 1.29 Å, and the O−H bonds being made and broken are between 1.13 and 1.29 Å; i.e., these bonds are approximately 20−30% longer than the equilibrium bond lengths, as expected in the transition state. The hydration and dehydration reactions were extensively studied experimentally by Winkelman et al.7,8 Their measured equilibrium constant for formaldehyde hydration in the temperature range 293−333 K and pH range 5−7 is given by K = exp(3769/T − 5.494). At 298 K, this yields K = 1279, and therefore ΔG = −4.2 kcal/mol.8 Our computed value of −4.1 kcal/mol is very close to the experimental value, similar to what we find in our previous work.13,14 Their measured Arrheniuslike activation energy barrier for the dehydration reaction of methylene glycol (i.e., the reverse of the formaldehyde hydration reaction) is 55.8 kJ/mol or 13.3 kcal/mol;7 therefore, the experimental hydration reaction of formaldehyde has a barrier of −4.1 + 13.3 = 9.1 kcal/mol. Our present computed value of the relative transition state free energy is 11.6 or 2.5 kcal/mol higher. There are several factors that may contribute to this difference. First, the assumptions in our method may inherently result in a small overestimation of the barriers as suggested in our previous analysis of glycolaldehyde.14 There is also a difference between the measured Arrhenius-like Ea and ΔG‡ although the two values should be close if ΔH‡ provides the dominant energetic contribution (which is usually the case for making and breaking covalent bonds in the transition state). The mildly acidic pH in the experiment could also contribute to a slight lowering of the barrier compared to neutral conditions. We are not the first to calculate the hydration barrier. There have been several theoretical and computation estimations of the barrier at neutral pH that also include assisting water molecules in the transition state, most of them higher than 12662

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Figure 4. Formation of sugars via aldol reactions (ΔGr in kcal/mol).

unfavorable (ΔGr(2o) = +14.1 kcal/mol) and will not be observed. Forming the oxanes directly from formaldehyde is more difficult. For example, the direct trimerization of formaldehyde to form the trioxane has ΔGr(1a⇔3o) = +24.3 kcal/mol, i.e., ∼3 kcal/mol higher than the other cyclization transition states. This mechanism could be operational in neat formaldehyde; however, in aqueous solution, because the majority of monomers are in hydrated form, it is unlikely that three nonhydrated monomers will collide in the right orientation with sufficient energy to form trioxane. Sugars via C−C Bond Formation. Figure 4 summarizes the free energy landscape for sugar formation up to the tetramer. Molecules with the same number of carbon atoms are grouped in the same row; molecules sharing the same functional group are grouped in the same column. From left to right, the columns are hydrated aldehyde, aldehyde, enol, ketone, and hydrated ketone. The C4 furanose (4f) is in its own area at the bottom of Figure 4. We chose double-headed arrows to represent isomerization/tautomerization reactions; singleheaded arrows are used for hydration and oligomerization reactions. The dimerization of two formaldehyde molecules to form glycolaldehyde (2a) has the highest barrier in the entire landscape with ΔGr(1a⇔2a) = +45.3 kcal/mol. An aldol reaction via an enol intermediate is not possible in this case. The lowest energy transition state for dimerization, shown in Figure 5, has two assisting water molecules. The newly forming C−C bond is 2.06 Å; the breaking C−H bond has stretched substantially at 1.47 Å. Although this transition state leads to the OH trans to the carbonyl, subsequent free rotation around the C−C bond results in the more stable cis structure of glycolaldehyde. Once glycolaldehyde is formed, it can add a water to form the hydrate 2ha. Our extensive study of glycolaldehyde, its oligomers, and corresponding hydrated species in solution comparing computational and NMR data provides detailed information on this group of molecules14 but is not the focus of the present work. Because glycolaldehyde is significantly more

Figure 5. Transition state for glycolaldehyde formation (1a⇔2a).

stable (ΔGr(2a) = −16.6 kcal/mol) than formaldehyde or methylene glycol, and the reverse barrier is huge; this first dimerization reaction is essentially irreversible. The enolization of glycolaldehyde is key to forming trioses. The enol is 9.3 kcal/mol higher in free energy than the aldehyde and the barrier to enolization is 21.1 kcal/mol starting from the aldehyde. The lowest free energy transition state for enolization (2a⇔2e) shown in Figure 6 has three assisting

Figure 6. Transition state for glycolaldehyde enolization (2a⇔2e).

water molecules leading to the cis enol. Addition of formaldehyde to the cis enol to form glyceraldehyde (3a) is thermodynamically favorable and the barrier for this aldol reaction is much lower with ΔGr(2a⇔3e) = +5.7 kcal/mol compared to the dimerization barrier with ΔGr(1a⇔2a) = +45.3 kcal/mol. This is in agreement with experimental 12663

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discusses the relative merits of the concentration corrections and their role when an energy landscape of a complex reaction mixture is presented.14 Not surprisingly, 3hk is less stable than 3k by a larger amount; i.e., the ketone is less favorably hydrated compared to its aldehyde counterpart. To form the C4 sugars, the key intermediate once again is the enol. The aldol addition of formaldehyde to 3e leads to the C4 ketone 4k. Once again, this follows the mechanism laid out by Breslow for the formose reaction.4 The lowest energy transition state for this reaction is shown in Figure 8. The forming C−C

observations that a long induction period is required in the formose reaction starting from monomeric formaldehyde, and that once glycolaldehyde is formed, the reaction becomes autocatalytic and the monomer is quickly consumed.4 The addition of a small amount of glycolaldehyde can act as an initiator to bypass this induction period. The transition state is rather symmetric, as shown in Figure 7, with the formaldehyde

Figure 7. Transition state for glyceraldehyde formation from C2 enol and formaldehyde (2e⇔3a).

carbon equidistant to the enol CC bond. Because the barrier to aldol addition is slightly higher (by 1.2 kcal/mol) than the tautomerization of enol back to aldehyde, triose formation will only be favorable if the concentration of formaldehyde is sufficiently high. Attempts to add formaldehyde directly to glycolaldehyde without going through the enol resulted in transition states with prohibitively high barriers (typically over 50 kcal/mol), confirming that aldol addition is indeed the preferred mechanism for this reaction. Attempting to directly form the C3 ketone (dihydroxyacetone, 3k) from the addition of formaldehyde to the C2 enol also resulted in barriers that were significantly higher compared to forming glyceraldehyde, 3a. This result is in line with Breslow’s proposed mechanism for the initial steps in the formose reaction.4 Although the formose reaction takes place at higher pH experimentally, our calculations suggest that the mechanisms are similar (albeit with higher barriers) under neutral conditions with no added catalysts. The thermodynamically favored C3 ketone forms as a result of isomerization from the aldehyde via the C3 enol. 3k is calculated to be 4.0 kcal/mol more stable than 3a. Although there are relatively recent studies of the isomerization reaction using NMR and FTIR spectroscopy,44,45 they do not report the experimental equilibrium constant, although it is clear that the ketone is thermodynamically more stable than the aldehyde with a “marked thermodynamic driving force”.44 The C3 enol 3e is 9.2 kcal/mol higher in energy than 3a, i.e., very similar to the difference (9.3 kcal/mol) between the C2 enol and glycolaldehyde. The calculated barrier from 3a to 3e is 26.0 kcal/mol; this is somewhat higher than the 21.1 kcal/mol from 2a to 2e. It may indicate that we have not found the lowest energy transition state yet, but in any case, this indicates that the isomerization of aldehyde to ketone might be relatively sluggish at room temperature and pH 7 in the absence of a catalyst. Water can be added to both 3a and 3k to form their respective hydrates 3ha and 3hk. The calculated aldehyde hydration barrier of 14.9 kcal/mol is significantly lower than the ketone hydration barrier of 19.8 kcal/mol. In the present free energy map without taking relative concentrations into account, 3ha is 0.6 kcal/mol higher in energy than 3a, similar to the difference between 2ha and 2a; our extensive study of the latter

Figure 8. Transition state for C4 ketone formation from C3 enol and formaldehyde (3e⇔4k).

bond is relatively short at 1.81 Å and the enol CC has lengthened to 1.42 Å. The calculated barrier from 3e to 4k is 8.5 kcal/mol, i.e., lower than the 12.4 kcal/mol from 2e to 3a. The transition state leading from 3e to 4a had a much higher barrier, as did any transition states starting from 3a or 3k rather than 3e, suggesting that these are not viable routes. In the present map, 4k is the thermodynamic sink considering formaldehyde and its oligomers in aqueous solution up to the tetramer. The trend, though, suggests that pentoses and hexoses will be lower in free energy than the tetroses. At present, we are calculating the free energies of larger species to confirm if indeed this is the case. Hydrating 4k to form 4hk is uphill as expected. Isomerization of 4k to form the aldehyde 4a can be accessed via the enol 4e. The difference in free energy between 4a and 4k is 4.4 kcal/mol, very similar to the difference between 3a and 3k. The enol 4e is 7.8 kcal/mol higher in energy than 4a, close to the differences seen in the dimer and trimer. For the open chain aldehydes, threose is calculated to be more stable than erythrose by 1.0 kcal/mol. For the furanose rings, the β-erythrofuranose is calculated to be the most stable although the other three species are within ∼1 kcal/mol. These values could well be within the computational error given the approximations in our method. The structures and relative energies for the D-stereoisomers of these tetroses are summarized in Figure 9. The transition state 4a ⇔ 4f, shown in Figure 10, is typical of the nucleophilic addition

Figure 9. D-Tetrose isomers (ΔGr in kcal/mol). 12664

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Figure 10. Ring closure transition state.

Figure 11. Cannizzaro and Tishchenko reaction transition states.

reactions seen in aldehyde hydration and POM formation above. The calculated barriers for ring closure are in the 14−15 kcal/mol range, suggesting that the ring-opening/closing reaction is relatively fast at room temperature. Our calculated barriers are similar to those calculated by Alkorta and Popelier (in the 15−20 kcal/mol range) at the G3MP2B3 level in PCM solvent.46 Experimental estimates of the barrier by NMR are in the 14−24 kcal/mol range.47,48 Compared to the POM oligomers with C−O link backbones, the sugars synthesized via C−C bond formation are significantly more stable in free energy under neutral conditions in the absence of a catalyst. The barriers to forming larger oligomers, however, are much higher for the sugars, typically in the range 8−12 kcal/mol from the enol tautomer, which is in itself typically 9−13 kcal/mol higher in energy than the aldehyde or ketone. Thus the overall barrier starting from the aldehyde or ketone is in the 17−25 kcal/mol range. The enolization barriers are also in the same range. In contrast, the barrier to adding formaldehyde to successive POMs is in the 11−15 kcal/mol range, and therefore the POMs are kinetically more accessible than the sugars. The dimerization barrier to form glycolaldehyde is particularly restrictive at 45 kcal/mol because enolization is not an option. Cannizzaro and Tishchenko Side Reactions. It is wellknown that under basic conditions formaldehyde can disproportionate into methanol and formic acid, and this Cannizzaro reaction mechanism has been studied extensively.49 More recently, it has been shown that this reaction can take place in hot water (225 °C) under neutral conditions; acidifying the mixture leads to more complex products such as glycolic acid.50 Our calculations show that the disproportionation reaction is favorable under neutral conditions at 25 °C with ΔG = −20.7 kcal/mol for the reaction CH2O + CH2(OH)2 → CH3OH + HCOOH. The lowest energy transition state is six-center and does not require a catalytic water molecule, as shown in Figure 11. The calculated barrier is +20.3 kcal/mol; adding water molecules to assist in H transfer increases the barrier in this case. Given that this barrier is higher than the POM dimerization barrier of +10.7 kcal/mol, we expect that POM formation will predominate over Cannizzaro reactions under neutral conditions at lower temperatures. The fact that Cannizzaro side products can be formed, however, increases the complexity of the mixture as alcohols and carboxylic acids can further react with the POM oligomers or sugars in solution. We are currently mapping the energy landscape of these products but they are beyond the scope of the present study. One other side product that can potentially be generated by dimerization of formaldehyde is methylformate (2CH2O →

HCOOCH3). Although this reaction is thermodynamically favorable with ΔG = −24.0 kcal/mol, the barrier is very high. The lowest energy barrier we have found so far is +61.4 kcal/ mol and has a ten-center transition state, as shown in Figure 11. Although the Tishchenko reaction is used for the crosscoupling of aldehydes in organic synthesis, the reactions require specialized catalysts and are not run in aqueous solvent.51,52 Our calculations suggest that, in the absence of suitable catalysts, this reaction will not be a contributing factor to the complex mixture.

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CONCLUSION Our goal in this study was to map a baseline free energy landscape for the self-oligomerization of formaldehyde in aqueous solution at pH 7. In the present work, we restricted the reactions to hydration, tautomerization, isomerization, and in the case of oligomerization only the addition of formaldehyde molecules to intermediate species. Our calculations, up to the tetramer, reveal some trends in these reactions, e.g., enolization of the aldehyde is ∼8−9 kcal/mol uphill in free energy with barriers in the 21−25 kcal/mol range, or the formation of successive POM oligomers decreases the free energy by ∼4 kcal/mol and their corresponding oxanes are ∼1 kcal/mol higher in free energy. Our current and future work includes confirming if such trends hold for C5 and C6 species, thereby extending the map of the energy landscape. The present work at pH 7 only involves neutral molecules with catalytic water molecules in the transition state. We are extending this work to study the same reactions at low and high pH conditions where acid and base catalysis mechanisms are significantly operational. Preliminary work suggests that the thermodynamic landscape changes only slightly whereas the kinetic landscape changes more dramatically. These observations are not in themselves surprising, however; given that we have provided the baseline calculations at pH 7, we may be able to extrapolate the energy landscape under different conditions. As to the present study at pH 7, we find that the most thermodynamically favored species are the sugars involving new C−C bond formation via aldol addition. Dimerization to form glycolaldehyde has a very high barrier, but once this C2 species is formed, enolization allows access to the larger oligomers via much lower barriers. Glyceraldehyde is the first C3 product formed; however, among the C4 species the ketone is formed first. Because forming glycolaldehyde has such a high barrier, it is more likely that collision of two monomers will result in disproportionation to methanol and formic acid. The most likely first dimerization products, however, under the reaction conditions studied, are the POM oligomers. Although not as thermodynamically favored as disproportionation or sugar 12665

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Formaldehyde Polymer Formation in Water, Deuterium Oxide, and Methanol. Ind. Eng. Chem. Res. 1995, 34, 440−450. (7) Winkelman, J. G. M.; Ottens, M.; Beenackers, A. A. C. M. The kinetics of the dehydration of methylene glycol. Chem. Eng. Sci. 2000, 55, 2065−2071. (8) Winkelman, J. G. M.; Voorwinde, O. K.; Ottens, M.; Beenackers, A. A. C. M.; Janssen, L. P. B. M. Kinetics and chemical equilibrium of the hydration of formaldehyde. Chem. Eng. Sci. 2002, 57, 4067−4076. (9) Ott, M.; Fischer, H. H.; Maiwald, M.; Albert, K.; Hasse, H. Kinetics of oligomerization reactions in formaldehyde solutions: NMR experiments up to 373 K and thermodynamically consistent model. Chem. Eng. Process. 2005, 44, 653−660. (10) Maiwald, M.; Grutzner, T.; Strofer, E.; Hasse, H. Quantitative NMR spectroscopy of complex technical mixtures using a virtual reference: chemical equilibria and reaction kinetics of formaldehydewater-1,3,5-trioxane. Anal. Bioanal. Chem. 2006, 385, 910−917. (11) Cleaves, H. J. The prebiotic geochemistry of formaldehyde. Precambrian Res. 2008, 164, 111−118. (12) Kua, J.; Hanley, S. W.; De Haan, D. O. Thermodynamics and Kinetics of Glyoxal Dimer Formation: A Computational Study. J. Phys. Chem. A 2008, 112, 66−72. (13) Krizner, H. E.; De Haan, D. O.; Kua, J. Thermodynamics and Kinetics of Methylglyoxal Dimer Formation: A Computational Study. J. Phys. Chem. A 2009, 113, 6994−7001. (14) Kua, J.; Galloway, M. M.; Millage, K. D.; Avila, J. E.; De Haan, D. O. Glycolaldehyde Monomer and Oligomer Equilibria in Aqueous Solution: Comparing Computational Chemistry and NMR Data. J. Phys. Chem. A 2013, 117, 2997−3008. (15) Azofra, L. M.; Alkorta, I.; Elguero, J.; Popelier, P. L. A. Conformational study of the open-chain and furanose structures of Derythrose and D-threose. Carbohydr. Res. 2012, 358, 96−105. (16) Simakov, A.; Sekiguchi, O.; Bunkan, A. J. C.; Uggerud, E. Energetics and Mechanisms for the Unimolecular Dissociation of Protonated Trioses and Relationship to Proton-Mediated Formaldehyde Polymerization to Carbohydrates in Interstellar Environments. J. Am. Chem. Soc. 2011, 133, 20816−20822. (17) Jalili, S.; Aghdastinat, H. Study of hydrogen bonding in dihydroxyacetone and glyceraldehyde using computational methods. J. Mol. Struct. (THEOCHEM) 2008, 857, 7−12. (18) Jalbout, A. F.; Abrell, L.; Adamowicz, L.; Polt, R.; Apponi, A. J.; Ziurys, L. M. Sugar synthesis from a gas-phase formose reaction. Astrobiology 2007, 7, 433−442. (19) Jalbout, A. F.; Contreras-Torres, F. F.; de Leon, A. Formation of simple organic molecules in the interstellar medium. Int. J. Quantum Chem. 2008, 108, 598−606. (20) Jalbout, A. F.; Pavanello, M.; Adamowicz, L. The water mediated ring closing in the formose reaction. Int. J. Quantum Chem. 2007, 107, 2024−2031. (21) Tajima, H.; I., H.; Masato, M. I. A Computational Study on the Mechanism of the Formose Reaction Catalyzed by the Thiazolium Salt. J. Comput. Chem. Jpn. 2003, 2, 127−134. (22) Balashov, A. L.; Krasnov, V. L.; Danov, S. M.; Chernov, A. Y.; Sulimov, A. V. Formation of cyclic oligomers in concentrated aqueous solutions of formaldehyde. J. Struct. Chem. 2001, 42, 398−403. (23) Jaguar. Jaguar v6.0; Schrodinger, LLC: Portland, OR, 2005. (24) Vosko, S. H.; Wilk, L.; Nusair, M. Accurate spin-dependent electron liquid correlation energies for local spin density calculations: a critical analysis. Can. J. Phys. 1980, 58, 1200−1211. (25) Becke, A. D. Density-functional exchange-energy approximation with correct asymptotic behavior. Phys. Rev. A 1988, 38, 3098−3100. (26) Lee, C.; Yang, W.; Parr, R. G. Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density. Phys. Rev. B 1988, 37, 785−789. (27) Becke, A. D. Density-functional thermochemistry. III. The role of exact exchange. J. Chem. Phys. 1993, 98, 5648−5652. (28) Tannor, D. J.; Marten, B.; Murphy, R.; Friesner, R. A.; Sitkoff, D.; Nicholls, A.; Honig, B.; Ringnalda, M.; Goddard, W. A., III. Accurate First Principles Calculation of Molecular Charge Distributions and Solvation Energies from Ab Initio Quantum Mechanics and

formation, the calculated barriers are significantly lower at 14− 16 kcal/mol. Cyclization to oxanes is less likely unless the system is significantly dehydrated. A significant advantage of using the same computational protocol as our previous work is that we have the added benefit of directly comparing the free energies of related species across different studies. For example, the energy landscape of our previous extensive work on the dimers and trimers of glycolaldehyde can be directly compared to the present work on the same scale (the energy values for the monomers in both studies are identical).14 As a second intersecting example, our previous study of the oligomerization energy landscape of methylglyoxal (C3H4O2), the dehydrated product of the C3 sugars, uses the same protocol.13 In this way, we are building up a larger free energy landscape connecting intersecting chemistry with different applications. Given that our study provides a baseline free energy map for the self-oligomerization of formaldehyde, further studies examining different conditions and catalysts will lead to a better understanding of complex reaction mixtures with multiple intermediates and products in changing chemical environments. Our computational protocol is useful in studying complex systems with sizable product distributions because we can tease out and identify the energetic contributions of the many different species in a reaction mixture. Identifying trends for these preliminary oligomerization steps will allow us to parametrize a coarse-grain method to capture longer time scales and more complex mixtures as the system evolves.

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ASSOCIATED CONTENT

* Supporting Information S

Supporting Information includes XYZ coordinates of the most stable structures and transition states listed in Tables 1 and 2. This information is available free of charge via the Internet at http://pubs.acs.org

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AUTHOR INFORMATION

Corresponding Author

*J. Kua: e-mail, [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This research was supported by a Camille and Henry Dreyfus Teacher-Scholar award (J.K.), an American Chemical Society Summer Research Fellowship for High School Teachers (W.D.S.), and a research grant from the Singapore Ministry of Education (J.K.)

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REFERENCES

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