Solvation Induction of Free Energy Barriers of Decarboxylation Reactions in Aqueous Solution from Dual-Level QM/MM Simulations

Abstract

Carbon dioxide capture, corresponding to the recombination process of decarboxylation reactions of organic acids, is typically barrierless in the gas phase and has a relatively low barrier in aprotic solvents. However, these processes often encounter significant solvent-reorganization-induced barriers in aqueous solution if the decarboxylation product is not immediately protonated. Both the intrinsic stereoelectronic effects and solute–solvent interactions play critical roles in determining the overall decarboxylation equilibrium and free energy barrier. An understanding of the interplay of these factors is important for designing novel materials applied to greenhouse gas capture and storage as well as for unraveling the catalytic mechanisms of a range of carboxy lyases in biological CO₂ production. A range of decarboxylation reactions of organic acids with rates spanning nearly 30 orders of magnitude have been examined through dual-level combined quantum mechanical and molecular mechanical simulations to help elucidate the origin of solvation-induced free energy barriers for decarboxylation and the reverse carboxylation reactions in water.

1. Introduction

The carboxylate group is among the most versatile functional groups in organic chemistry and key intermediates in degradation of organic compounds.¹⁻⁷ Decarboxylation reactions are involved in a variety of biological transformations, including the biosynthesis of alcohols, terminal olefins, and nucleobases.^1,8−10 The reverse process corresponds to carbon dioxide capture and storage for mitigation of this greenhouse gas in the environment, which has also attracted considerable recent interest in the development of novel materials.¹¹⁻¹³ In nature, metabolic decarboxylation and CO₂ fixation in photosynthesis take place on a scale of billions of tons per year.¹ Consequently, decarboxylation reactions have attracted sustained interest,^{2,5,6,14−17} but these reactions are inherently slow unless an activating mechanism is present.^{14,15,18−21} An illustrative example is the decarboxylation of N-methylorotate in water, a model reaction for the last step of pyrimidine nucleotide biosynthesis by orotidine 5′-monophosphate decarboxylase, having an extrapolated half-life of 78 million years for the spontaneous process. Remarkably, the rate is accelerated by 17 orders of magnitude without the aid of a covalent bond intermediate or a metal cofactor in the active site of the enzyme.²²⁻²⁴ Thus, studies aimed at an understanding of the underlying principles that govern the intrinsic reactivity toward decarboxylation of organic acids in aqueous solution are of considerable interest.

Solvent effects play an important role in decarboxylation reactions of organic acids.^19,25−30 An early example is the large solvent effects on the decarboxylation of 3-carboxybenzisoxazole observed by Kemp and Paul, exhibiting a rate variation of over 8 orders of magnitude in going from water into an organic solvent (hexamethyl phosphoramide).³¹⁻³⁵ In the case of orotate derivatives, Lewis and Wolfenden found a modest rate enhancement of about 1000-fold from aqueous solution into polar aprotic solvents such as dimethylformamide and acetone,²⁶ consistent with computational predictions of a small solvent-induced barrier of about 3–5 kcal/mol in water relative to that in the gas phase.^34,36,37 The effects of solvation strongly depend on the extent of anion delocalization of the dissociation product, as does the rate of spontaneous decarboxylation itself.^{14,15,18,20,21} Indeed, direct decarboxylation of simple organic acids in the gas phase typically does not have a barrier separating the decomposition product. Thus, in the gas phase, the reverse process, CO₂ capture, is spontaneous or has a low barrier in aprotic solvents.^2,38 Experiments have revealed that decarboxylation and CO₂ recombination are reversible in aprotic solvents such as dimethylformamide or dimethylsufoxide and that protonation of the decomposition product can compete with CO₂ capture in the presence of water.^2,3,39−44 Both substituent and solvation effects are critical and have been illustrated by the decarboxylation of N-heterocyclic carboxylate compounds, which are stable both in water and in anhydrous organic solvents but can rapidly decompose, followed by irreversible protonation in an aqueous and organic solvent mixture.³⁸

In the present study, we have selected a set of organic acids whose rates of decarboxylation span nearly 30 orders of magnitude in water to carry out molecular dynamics simulations employing a dual-level combined quantum mechanical and molecular mechanical (QM/MM) potential. Our aim is to understand the interplay of the intrinsic stereoelectronic effects that determine the free energy of CO₂ decomposition from the corresponding carboxylate ion and solute–solvent interactions that induce solvation barriers in the reverse process, CO₂ capture, in aqueous solution. We focus on direct decarboxylation processes without involvement of covalent bond catalysts,^20,45,46 proton-transfer-coupled decarboxylation,^17,47 and nucleophilic assistance to the carboxyl group.^39,48 Analysis of the interaction energy components provides further insights into the origin of the solvation effects.⁴⁹ In what follows, we first present a summary of the dual-level QM/MM approach and validation of the method to achieve high accuracy that balances computational efficiency in condensed-phase simulations. Then results on free energy reaction profiles and the trends of differential solvation effects in the reactant state and at the transition state are described along with detailed energy decomposition analysis and solute–solvent distributions. Finally, we summarize the main findings of this study.

2. Methods

Potentials of mean force (PMFs) have been determined for a set of decarboxylation reactions of carboxylates in water through umbrella-sampling free energy simulations using a dual-level combined quantum mechanical and molecular mechanical (QM/MM) potential energy function.⁵⁰⁻⁵³ This series of reactions were selected to span a large range of reaction rates, covering major functional group substitutions. Moreover, the general trends of these compounds illustrate the capability of a dual-level approach to achieve high accuracy that balances computational efficiency.^{25,29,34,54−59} To this end, we have developed a procedure in which (1) an efficient QM/MM method is used to model solute–solvent interactions and (2) a high-level quantum chemical method is employed to achieve the required accuracy.⁶⁰⁻⁶⁴ For completeness, here we briefly summarize the computational procedure for separating computational levels in combined QM/MM calculations.

2.1. Dual-Level QM/MM

The standard effective Hamiltonian of a combined QM/MM potential is given by

1

where H_X is the Hamiltonian for the solute molecule in solution, H_Xs describes the interaction between a QM-represented solute molecule and all solvent molecules, and V_ss denotes the potential energy function for the solvent system.⁵²Equation 1 is typically used directly in combined QM/MM calculations, but its efficiency is limited by the cost and unfavorable scaling of high-level QM methods. In fact, it is more convenient to adopt an alternative, equivalent representation by separating the electronic energy for the solute (the first term of eq 1) into a constant reference-value (E_X^o) in the gas phase and a net solute–solvent interaction energy.^62,64,65

2

where the second term, ΔH_Xs^tr = (H_X + H_Xs) – E_X, formally defines the energy of the transfer for solute X from the gas phase into solution, and E_X^o can be the global energy minimum at a fixed geometry as the reference state (the zero of relative energies) or could be a variable as a function of the reaction coordinate along a minimum-energy path. In the first case, the energy variation is included in ΔH_Xs, whereas in the second choice, the transfer term corresponds purely to the solute–solvent interaction energy. In the present study, we used the second approach, i.e., E_X^o(R_C), where R_C is the reaction coordinate, the C–C distance of the dissociating carboxylate group.

Nothing has changed so far, but eq 2 provides a convenient way of separating a QM/MM potential into a high-level (HL) description of the intrinsic properties of the “QM” molecule in the gas phase (E_X^o), and a lower-scaling (LS) method (ΔH_Xs). In a dual-level QM/MM potential, we make the approximation that a high-level quantum chemical model can be used to describe the intrinsic reactivity of the solute molecule itself, whereas solute–solvent polarization interactions⁶⁶ can be described by a computationally efficient quantum chemical technique such as a semiempirical method or density functional theory. Then the total energy of the dual-level QM/MM potential is given by

3

In eq 3, the superscripts emphasize the relative levels of theory used to determine the corresponding energies. The second term is the transfer energy, computed using a different (LS) QM method from the first term (HL):

4

where Ψ_X is the polarized wave function of the solute molecule in solution and ΔH_Xs^tr,LS is the transfer interaction Hamiltonian.

Dual-level approaches have been applied to many systems,^{25,34,50,54−59} and a most successful method is that developed by the Moliner and Tunon groups for enzymatic reactions.^64,67,68Equations 3 and 4 emphasize that a dual-level QM/MM approach differs from a single-level QM/MM calculation in the (relative) energy difference between the HL and LS methods used for the solute molecule in the gas phase. Condensed-phase simulations are carried out using an LS-QM/MM approach in which the most critical quantity is the solute–solvent interaction term.

2.2. Validation of QM/MM Interactions

Combined QM/MM models are empirical potential energy functions due to a multiscale representation of a condensed-phase system by partitioning it into a “QM” region that includes electronic degrees of freedom and a classical environment that is modeled by a ball-and-stick model. To quantify short-range exchange repulsion and long-range dispersion interactions between the two regions, it is unavoidable to introduce empirical terms by separating the total interaction energy (transfer term) into electronic and empirical van der Waals (vdW) contributions:

5

Here and below, we have omitted the superscript LS for convenience. The Lennard-Jones potential is often used to approximate the vdW contribution:

6

where q and m denote atoms in the QM and MM regions, respectively, and standard combining rules are used on the basis of atomic parameters such that ε_qm = (ε_qε_m)^1/2 and σ_qm = (σ_q + σ_m)/2. The van der Waals parameters for atoms in the MM region (σ_m and ε_m) are taken directly from the force field. In the present study, the three-point-charge TIP3P model for water is adopted. The parameters for the QM atoms are new and different for each specific QM/MM combination, which must be optimized to accurately describe solute–solvent interactions,^51,69 but this step has often been neglected.

In this work, a set of 34 bimolecular complexes between organic acids and a water molecule at different geometries have been optimized using Kohn–Sham density functional theory (DFT) with the Minnesota functional M06-2X and the aug-cc-pVTZ basis set.⁷⁰ The results are used as a consistent target for modeling the relative interaction energies due to steric and substituent effects on hydrogen-bonding complexes. Then the Lennard-Jones parameters for atoms represented by the LS semiempirical method, the Austin Model 1 (AM1),⁷¹ were optimized in QM/MM calculations to best reproduce the full DFT binding energies. Starting from the Lennard-Jones parameters obtained previously⁵¹ and those for new atom types generated by the CHARMM general force field for small molecules, we found that a single set of parameters for most elements is sufficient, consistent with early studies of similar complexes (to account for the difference in geometric versus arithmetic combining rules used in CHARMM, the NBFIX option was used to determine each atom pair).⁵¹ In closing this section, we emphasize that the quality of the optimized LS-QM/MM model is not dictated by the level of the QM model used in a QM/MM combination since it needs to be empirically optimized whatever QM method is used. The present validation provides results for hydrogen-bonding interaction energies as good as full DFT calculations at the M06-2X/aug-cc-pVTZ level, albeit at a fraction of its computational costs.

2.3. Energy Decomposition Analysis of Solvent Polarization

In addition to its ability to model chemical reactions in condensed phases, an important reason to use combined QM/MM potentials is to gain an understanding of intermolecular interactions in solution, which cannot be conveniently or feasibly obtained using a force field.⁵¹ We have developed an interaction energy decomposition scheme to divide the total electrostatic component of the ΔE_Xs^tr term (eq 5) into permanent electrostatic (or vertical) interaction and polarization terms:^51,62,72

7

where the vertical interaction term E_Xs^o is the energy of transfer for the solute, obtained by keeping its wave function and charge density strictly the same as in the gas phase at the same molecular geometry:

8

Equation 8 is equivalent to the first-order perturbation energy obtained by treating the solute–solvent interaction Hamiltonian as an external perturbation to the gas-phase wave function.^51,62 The remaining energy contributions all involve changes in the solute wave function due to intermolecular interactions and are collectively called polarization energy.

9

The polarization term (eq 9) includes a net gain in interaction energy () and a work penalty needed to distort the solute wave function () to create charge (polarization).⁵¹ The total dual-level energy can be written in terms of energy components as follows:

10

It is important to define the molecular geometries used to determine the high-level energy since the structures generated from the LS-QM/MM simulations cannot be directly employed. One could employ the average structure over the dynamic trajectories such as the free energy reaction path used by Yang and co-workers⁷³ or generated by modern machine-learning techniques. Here we decided to use the energies determined at the geometries optimized using the HL and LS methods, respectively, and match their difference at the same reaction coordinate value. This automatically takes into account the geometry difference in different electronic structure methods and the energy diffrence is expressed as ΔE_X^o,DL(R_C) = E_X(R_C^HL) – E_X(R_C^LS), where R_C and R_C^LS denote molecular geometries obtained using the method indicated by the superscript with the same reaction coordinate value R_C. Therefore, ΔE_X(R_C) is a high-level correction to the LS potential energy surface used in the molecular dynamics simulation. If ΔW^LS(R_C) is the potential of mean force determined using the LS-QM/MM method, the dual-level potential of mean force is given by

11

3. Computational Details

The minimum-energy path for each decarboxylation reaction in the gas phase was determined using Kohn–Sham DFT with the M06-2X/aug-cc-pVTZ combination.⁷⁰ The reaction coordinate for this simple bond cleavage process can be conveniently represented by the bond distance between the carbon atom of CO₂ and that of the substrate (R_C(X–CO₂)). The optimal geometries were scanned at a step of 0.05 Å in the region of R_C = 1.4 to 3.2 Å and a step of 0.1 Å in the interval of R_C = 3.2 to 5.0 Å. M06-2X/aug-cc-pVTZ and AM1 were used to obtain E_X^o,HL(R_C) and E_X^o,LS(R_C), respectively, along the reaction path to yield the dual-level energy difference ΔE_X^o,DL in eq 11. In addition, a set of 34 hydrogen-bonding complexes involving all 11 carboxylate ions (Figure S2) were optimized also using M06-2X/aug-cc-pVTZ to yield a consistent data set; many of the carboxylate ions have been studied in the past.^51,69,74,75 In the bimolecular calculations,^{51,69,74,76,77} the geometries of the anions were fixed at their optimized geometries, and the TIP3P water model was used for water as in the simulation; thus, only the geometrical parameters for the hydrogen-bonding interactions were optimized.

Molecular dynamics simulations were performed to determine the free energy profiles or the potentials of mean force along the C–C distance of the carboxyl group and the carbanion site of the product of decarboxylation. For each of the 11 reactions, we employed a dual-level QM/MM potential^52,62 to yield results at the quality of density functional theory with the M06-2X/aug-cc-pVTZ functional for the reactive species,⁷⁰ supplemented by solvation effects determined using an optimized low-scaling QM/MM potential combining AM1⁷¹ and TIP3P⁷⁸ for treating solute–solvent interactions. All of the simulations were executed in the isothermal–isobaric ensemble at 25 °C and 1 atm at an integration step of 1 fs. Each system contained one carboxylate that was solvated in a cubic box containing 4720 to 6485 water molecules (Table S1). Periodic boundary conditions were used along with the particle mesh Ewald method to treat long-range electrostatic interactions in the QM/MM potential with a real-space distance of 12 Å.⁷⁹ The latter was also used to switch off the van der Waals potential. Potassium ions were added to keep charge neutrality. For each PMF, the calculation was divided into 20 separate simulations to span the reaction coordinate for a cumulative simulation time of 1 ns.^80,81

All of the high-level electronic structure calculations were performed with the Gaussian 16 package,⁸² and molecular dynamics simulations were carried out using CHARMM.⁸⁰

4. Results and Discussion

4.1. Dual-Level Energy Correction to the Decarboxylation Reactions

To validate the performance of the M06-2X density functional as an adequate high-level method for the decarboxylation reactions considered in this study (Table S1), we computed the enthalpies of reaction for the reactions of four representative cases (Table 1), and the energy curve for the decarboxylation reactions of acetate ion and benzoate ion is presented in Figure 1. The results are compared with those obtained from coupled cluster calculations at the CCSD(T)/aug-cc-pVTZ//M06-2X/aug-cc-pVTZ level of theory, in which single-point energy calculations were done using CCSD(T) at the geometry optimized with M06-2X. CCSD(T) is considered to be the gold standard in electronic structure methods, whereas M06-2X has been shown to yield good results for anionic species of hydrocarbons.⁸³⁻⁸⁶ The relatively large basis set used in the present work is sufficient for the decarboxylation reactions.

Table 1. Experimental and Calculated Enthalpies of Reaction for Decarboxylation Reactions in the Gas Phase (The aug-cc-pVTZ Basis Set Was Used in All of the Calcualtions).

	ΔHr (kcal/mol)
RCO2–	exptla,b	CCSD(T)	M06-2X	AM1
CH3CO2–	59.6 (59.6 ± 3.1)	60.5	62.7	89.1
PhCO2–	57.9 (58.0 ± 3.3)	57.1	58.9	61.8
NCCH2CO2–	37.7 (37.5 ± 7.6)	34.6	32.3	42.1
CF3CO2–	40.7 (40.3 ± 4.3)	38.4	41.8	26.8

^aValues without parentheses were determined using experimental heats of formation of neutral molecules and proton affinities of anions (obtained from https://webbook.nist.gov/chemistry).

^bValues in parentheses were calculated as ΔH_r = ΔH_f(R^–) + ΔH_f(CO₂) – ΔH_f(RCO₂^–) using ΔH_f(CO₂) = −94.05 kcal/mol.

Figure 1.

Computed reaction energy profiles for the decarboxylation reactions of acetate ion and benzoate ion in the gas phase along the reaction coordinate (RC), defined as the length of the dissociating bond, using coupled cluster CCSD(T) and the M06-2X density functional, both with the aug-cc-pVTZ basis set, and the semiempirical AM1 method.

Qualitatively, there is no recombination barrier separating the reaction products in the gas phase (Figure 1). For other decarboxylation reactions, this trend is generally followed, with only shallow local minima in a few cases where the barriers are below the dissociation limit (see below). At short distances of product separation, the accord between the M06-2X and CCSD(T) results is good, whereas small deviations are seen beyond a C–CO₂ separation of about 2.6–2.7 Å. At the dissociation limit, the M06-2X DFT calculations yield an enthalpy of reaction of 62.7 kcal/mol relative to acetate ion (Table 1), which may be compared with a value of 60.5 kcal/mol from CCSD(T) calculations and 59.6 kcal/mol from experiments on the basis of gas-phase heats of formation of neutral molecules and proton affinities of anions (https://webbook.nist.gov/chemistry). For the decomposition of benzoate ion to phenyl anion and carbon dioxide, the M06-2X and CCSD(T) results are within 1.0 and 0.8 kcal/mol of the experimental data, respectively, suggesting that the performance of M06-2X/aug-cc-pVTZ is adequate for these simple decarboxylation reactions. Table 1 lists the computed enthalpies of decarboxylation for other cases along with experimental data (the data listed in Table S3 further show the reliability of M06-2X/aug-cc-pVTZ).

Although the energy profiles for CO₂ recombination from the low-scaling AM1 calculations follow the trends of the M06-2X results (Figure 1), having an average deviation of 0.04 Å in bond length (Figure S1), the energetic results are dependent on the system investigated. Thus, direct use of the semiempirical model could result in large uncertainties in certain cases, whereas the performance of AM1 is reasonable for other decarboxylation reactions such as that of N-methylorotate. On the basis of the reaction profiles in Figure 1, the errors in the LS theory can be corrected by its energy difference from the HL data along the reaction coordinate. The differential potential between the HL (M06-2X) and LS (AM1) methods, along with the solvation free energy from the QM/MM simulation, was used to construct the dual-level PMF (eq 11), shown in Figure S3. The smooth variations of the HL – LS energy correction along the entire reaction coordinate suggest that such a dual-level approach is reasonable.

4.2. Bimolecular Complexes for Description of QM/MM Interactions

The performance of the present LS-QM/MM potential for the decarboxylation reactions was assessed by comparison with full DFT M06-2X/aug-cc-pVTZ results in Figure 2 for a set of 34 bimolecular complexes between an anion and one water molecule (structure and energy details are given in Table S2 and Figure S2). For each carboxylate ion, the most stable complex corresponds to the bifurcated form, which is typically not frequently sampled in fluid simulations because of statistical fluctuations and competition from structural packing.⁸⁷ In principle, to achieve good agreement between the full DFT results and the LS-AM1/TIP3P interaction energies, the Lennard-Jones parameters for each element in the QM fragment can be optimized.^51,69,74 Here we found that the original set of parameters reported in 1992 were adequate in the present study (Table S4).⁵¹ Overall, Figure 2 shows that the results from the full QM M06-2X optimizations are in good accord with data obtained using the LS-QM/MM method, with a root-mean-square deviation of 0.78 kcal/mol for an energy range over 25 kcal/mol.⁸⁸

Figure 2.

Comparison of computed bimolecular interaction energies from the full treatment by density functional theory using M06-2X/aug-cc-pVTZ (QM) and the combined quantum mechanical and molecular mechanical (QM/MM) potential for the 34 complexes whose structures are given in Figure S2. In the combined QM/MM calculations, the organic acid is represented by the AM1 method and water by the TIP3P model. The QM/MM interaction energy is given by E_Xs^tr – E_X – E_s^TIP3P, and the QM interaction energy is defined as E_Xs – E_X^HL – E_s.

4.3. Potentials of Mean Force and Free Energies of Decarboxylation Reactions

The computed PMFs for four of the decarboxylation reactions, including benzoate, N-methylorotate, cyanoacetate, and malonate dianion, in water along with the energy profiles from M06-2X/aug-cc-pVTZ calculations in the gas phase and solvation free energies are displayed in Figure 3 (results for all of the other systems are given in Figure S3). Several observations can be made from the computed free energy profiles.

Figure 3.

Computed potentials of mean force for benzoate, N-methylorotate, cyanoacetate, and malonate ions. The high-level potential energy curve E_X^o,HL(R_C) was determined using M06-2X/aug-cc-pVTZ, and the hydration free energy represents the difference of the PMFs obtained from umbrella sampling simulations using the AM1-TIP3P potential, ΔG_hyd(R_C) = ΔW^LS(R_C) – E_X^o,LS(R_C). The dual-level PMF is given by ΔG_DL(R_C) = ΔG_hyd(R_C) + E_X^o,HS(R_C), equivalent to eq 11.

First, in each of the 11 decarboxylation reactions examined in this work, a substantial solvent-induced barrier is observed for the recombination process of CO₂ capture to form the corresponding carboxylate ion. The computed free energy barriers range from less than 5 kcal/mol for N-methylorotate to as high as 23 kcal/mol for malonate dianion. In contrast, the reaction energy profiles in the gas phase monotonically increase as the CO₂ group is removed from the carboxylate substrate, except in two cases, nitroacetate ion and 2-oxoimidazolidine-1-carboxylate ion (Figure S3), in which shallow minima are located along the recombination path. Therefore, solvent effects play a major role in modulating the free energy barriers for CO₂ capture reactions in water.

Second, if we use the reactant carboxylate ion as a reference, we find that the resulting product carbanions from the decarboxylation reaction are relatively stabilized by aqueous solvation with lower solvation free energies. An exception occurs in the only formally non-carbanion product, 2-oxoimidazolidone anion (an amide anion), which has a smaller solvation free energy than the initial 2-oxoimidazolidine-1-carboxylate ion. The stronger solvation stabilization for the carbanion species is reasonable since the anionic charges are typically more localized than the resonance delocalization of a carboxylate group. Moreover, the product anions, which possess more localized charge distribution such as sp³-hybridized carbanions, can be better solvated than those delocalized product anions, as indicated by the hydration free energies shown in Table 2.

Table 2. Calculated and Experimental Free Energy Barriers (ΔG^⧧) and Free Energies of Reaction (ΔG°)^a.

rxnb	k (s–1)	ref	ΔGexp⧧	ΔGcalc⧧	ΔGexp°c	ΔGcalc°	ΔGhyd⧧	ΔGhyd°
1	<4 × 10–32	(82)	60.3	62.4	54.4	49.8	21.9	–13.5
2	1.36 × 10–28	(82)	55.4	57.3	49.7	51.1	22.5	–7.8
3	3.0 × 10–16	(26)	38.6	33.7	32.6	30.1	13.3	–6.5
4	4.77 × 10–13	(83), 84	34.2	25.1	29.1	15.1	6.8	–27.1
	2.08 × 10–13		(34.7)
5	3.0 × 10–12	(86)	33.2	36.0	20.1	27.8	19.0	–5.9
6	6.7 × 10–11	(85)	31.3	33.9	29.3	7.3	7.3	–56.8
7	1.5 × 10–9	(19)	29.4	32.7	21.3	23.5	19.4	–2.4
8	9.0 × 10–9	(84), (86)	28.4	25.3	13.5	13.1	13.5	–9.3
	4.8 × 10–10		(30.1)
9	3.0 × 10–7	(19)	26.3	31.9	10.8	18.9	18.2	–7.9
10	6.1 × 10–5	(87)	23.2	27.3	14.6	20.0	17.2	1.4
11	2.5 × 10–3	(88)	21.0	22.9	3.1	5.8	13.3	–14.1

^aValues are in kcal/mol. Error bars were estimated on the basis of separate averages over blocks of 500 ps during the simulation, and they are approximately ±0.5 kcal/mol for ΔG_calc^⧧ and ±1.5 kcal/mol for ΔG_calc.

^bCarboxylate ions: (1) acetate anion; (2) benzoate anion; (3) N-methylorotate anion; (4) trifluoroacetate anion; (5) cyanoacetate anion; (6) malonate dianion; (7) malonate monoanion; (8) trichloroacetate anion; (9) acetoacetate anion; (10) oxoimidazolidine-1-carboxylate ion; (11) nitroacetate anion.

^cValues were taken from ref (21), except that for oxoimidazolidine-1-carboxylate ion, which was taken from ref (29), and those for N-methylorotate and nitroacetate, which were computed using experimental pK_a values and computational free energy differences for the corresponding conjugate acids (Table S5).

Finally, in the recombination process, solute–solvent interactions induce strong desolvation that must take place as CO₂ approaches the formal carbanion (or carbene) site. In all of the systems, the greatest loss in free energy of hydration occurs at the location of the transition state along the recombination path. At these solute geometries, there is a cavity between the carbanion carbon and carbon dioxide, whereas direct interactions with the solvent are not feasible and chemical bonding has not gained sufficient energy, resulting in an overall barrier in the aqueous solution in the recombination reaction. Therefore, the free energy barriers associated with the reverse, recombination processes of decarboxylation are entirely due to solvent reorganization. Inspection of Figure 3 reveals that solvation effects produce very different features in the reaction profiles between the solution-phase and gas-phase processes. Whereas there is a continuous decrease in energy in the gas-phase reaction profile from M06-2X optimizations, significant (>10 kcal/mol) free energy barriers are present in essentially all cases in aqueous solution. Interestingly, N-methylorotate, which has been widely used as a model for the uncatalyzed process corresponding to the enzymatic reaction by 5′-orotidine monophosphate decarboxylase (OMPDC), an enzyme among the most profiled in nature,^22,23,37,89 has the smallest recombination barrier in water (about 3.5 kcal/mol).

Table 2 summarizes the computed activation free energies for the decarboxylation processes relative to the carboxylate anions, free energies of reaction, and hydration free energies for all of these reactions from the PMFs, and Figure 4 depicts the correlation between the computed and experimental free energy barriers.^{19,26,90−96} Overall, the dual-level estimates of the free energy barriers are in accord with the experimental values, with a correlation coefficient of 0.883, spanning a range of 29 orders of magnitude in reaction rate or a difference of about 39 kcal/mol in barrier height. An exception is trifluoroacetate ion, whose free energy barrier from the experimental rate constant is 34.2 kcal/mol^91,92 whereas the dual-level simulations yielded a free energy of activation of 25.1 kcal/mol. Without including this datum, the correlation between experiment and computation would have been 0.942. Experimentally, the enthalpy of reaction is 40.3 ± 4.3 kcal/mol in the gas phase from heats of formation, which is not unusual in comparison with a value of 41.8 kcal/mol from M06-2X optimizations. Thus, the large difference could have originated from oversolvation of trifluoromethyl anion or uncertainties in the experiments. Trichloroacetate decomposition has been extensively investigated.^{21,25,47,91,92,94} The present study yielded a recombination barrier of ca. 12 kcal/mol (corresponding to a decarboxylation barrier of 25 kcal/mol), in exact agreement with a recent ab initio molecular dynamics simulation employing PBE and a hybrid Gaussian and plane-wave basis set along with dispersion corrections^21,25 and in accord with experiments (27–28 kcal/mol).^92,97 It should be noted that in all cases there will be a spontaneous proton transfer to neutralize the anionic species after decarboxylation in water because these carbanions are highly basic species, but we have prevented this process from taking place in the present computation by treating all of the solvent molecules with a force field.

Figure 4.

Comparison between calculated and experimental free energies of activation.

4.4. Linear Free Energy Relationship and Interaction Energy Components

The computed and experimental free energies of activation for the decarboxylation of carboxylate species examined in this work fall closely on a linear Bell–Evans–Polanyi free energy relationship on the basis of the Gibbs energies of reaction (Figure 5). It is interesting to note that the experimental and theoretical correlations have a parallel trend with slopes of 0.76 and 0.78, respectively, along with regression coefficients (R²) of 0.924 and 0.835. In physical organic chemistry, the slope of the Bell–Evans–Polanyi relationship has an interpretation in terms of the position of the transition state. A direct consequence is that as the solvent polarity decreases, the slope should approach unity with a zero intercept, in accordance with the observation that there is no barrier above the dissociation limit in all decarboxylation reactions examined in this study. This correlation is also consistent with the findings by Wolfenden and co-workers on decarboxylation reactions, which can be described by a Brønsted plot against the pK_a values of the acid of the decarboxylation products, reflecting significant charge development on the product fragment. Both linear free energy relationships report relative anion stability in aqueous solution.

Figure 5.

Bell–Evans–Polanyi relationship for the experimental (red) and computational (green) free energies of activation for decarboxylation reactions plotted against the Gibbs energies of reaction. The regressions are shown as dashed lines with slopes of 0.76 and 0.78 for the experimental data and computational results, respectively, along with intercepts of 15.5 and 16.8 kcal/mol, respectively.

To gain further insights into the origin of the differential hydration effects at the transition state and in the product state, additional simulations of these species were carried out to yield the interaction energy components in solvation. A total of 100 000 configurations from the dynamic trajectories were used in each case, and the results are listed in Table S6. The differences in total solute–solvent interaction energy at the transition state relative to the carboxylate reactant state, which have been determined for interaction energy terms due to the permanent (gas-phase) charge distribution and electronic polarization, are displayed in Figure 6. Clearly, the dominant factor in differential solvation for the transition state is due to the intrinsic charge distribution of the reacting species in the gas phase, the E_X^o term, as a result of the redistribution of the anionic charge from the carboxylate group to form the product anions (most of the reactions yield carbanions). There are notable differences in polarization at the transition state and in the reactant state, but they are relatively small, contributing about 10% to the total energy for these ionic solute molecules. This is consistent with findings on anionic solvation from QM/MM simulations.

Figure 6.

Difference in interaction energies with the solvent between the transition state and reactant state for each of the reactions summarized in Table 2. Energy components are obtained from QM/MM decomposition analysis in eq 10: ΔE_Xs^elec, ΔE_Xs, ΔE_Xs^pol, ΔE_Xs, and ΔE_Xs^dist.

4.5. Radial Distribution Functions

The radial distribution functions (RDFs) from the present QM/MM simulations for several selected carboxylate reactants are displayed in Figures 7–10. The distribution g_xy(r) gives the probability of finding a solvent atom y at a distance r away from a solute atom x relative to the bulk distribution of the solvent. Peaks and valleys are typically associated with solvation shells, whose integration from the reference center (atom x) gives the number of solvent molecules within the given solvation layer:

13

where ρ₀ = N/⟨V⟩ is the average number density, in which N is the number of solvent atoms and ⟨V⟩ is the average volume of the simulation box. The error range in the computed RDFs can be estimated as half of the bin size (0.02–0.03 Å) in data collection.

Figure 7.

Computed radial distribution functions between the carboxylate oxygen (O) of acetate ion and the hydrogen (HW) and oxygen (OW) atoms of water, respectively, in the reactant state (RS, black), at the transition state (TS, red), and in the product state (PS, blue). The corresponding snapshot structures are shown at the right.

Figure 10.

Radial distribution functions of the N1 nitrogen (N1), C2 carbonyl oxygen (O2), and N3 hydrogen (H3) of 2-imidazolidinone anion with solvent atoms in the reactant state (RS, black), at the transition state (TS, red), and in the product state (PS, blue). The corresponding snapshot structures are shown at the right.

We begin with the prototypical case of acetate ion decarboxylation in water (Figure 7), in which the carboxylate oxygen (averaged over both carboxylate oxygen atoms) and water RDFs are shown. The striking first peaks both from the O–H and O–O RDFs are clear indications of hydrogen-bonding interactions for the reactant state, whose maxima are found at 1.86 and 2.83 Å, respectively, similar to those from a previous study.^87,98 As the reaction takes place, the hydrogen-bonding peaks gradually disappear, leaving only minor structural features at the transition state, suggesting that the hydrogen-bond strength is significantly weakened when the transition state is reached. Integration of the first peak of the O–HW distribution to its minimum at 2.4 Å yields coordination numbers of 6.4 H per carboxylate oxygen atom for the reactant, 1.0 at the TS, and 0.4 for the product (CO₂). Clearly, hydrogen-bonding interactions with the carboxylate group are diminished as the reaction proceeds, and there are a minimal number of specific coordinating interactions remaining in the product state for carbon dioxide in water. There are weak peaks near 3.2 and 4.7 Å in the g_OH and g_OO RDFs, respectively, in the reactant state, reflecting hydrogen-bond donation to the second oxygen of the carboxylate group from water molecules. These features for the carboxylate group of acetate ion are the same in all other cases. Thus, we will focus on the variations of substituent groups below.

The RDFs of the carbonyl oxygen at C3 of acetoacetate ion (CH₃COCH₂CO₂^–) are given in Figure 8. The carbonyl group is a good hydrogen-bond acceptor with strong first peaks at 1.85 and 2.76 Å in the O3–HW and O3–OW RDFs, respectively. In the reactant state, we obtained an integration number of 2.2 hydrogen bonds in the first solvation layer. The carboxylate group prefers a conformation perpendicular to the carbonyl plane at C3 to enhance hydrogen-bonding interactions of both functional groups (Figure 8). Interestingly, the peak height increases sharply as the reaction reaches the transition state and finally the product state. Consequently, the computed average coordination numbers N_x are 2.3 for the TS and 4.8 for the product. We attribute this progression to electronic effects, as an enolate ion is developed as the decarboxylation reaction takes place. It is interesting to notice that by the transition state the charge delocalization is nearly complete, as reflected by the computed coordination number to the carbonyl oxygen, which is close to the final value of the enolate anion. Snapshots of structures depicting the nearest neighbors of water molecules to the carbonyl group mirror the trends shown in the RDFs. This general feature is observed in other cases involving carbanion delocalization with an electron-withdrawing group at the β-carbon, including NC–CH₂–CO₂^–, COOH–CH₂–CO₂^–, O₂N–CH₂–CO₂^–, and ^–O₂C–CH₂–CO₂^– (Figure S3).

Figure 8.

Radial distribution functions between the carbonyl oxygen (O3) of acetoacetate ion and the hydrogen (HW) and oxygen (OW) atoms of water, respectively, in the reactant state (RS, black), at the transition state (TS, red) and in the product state (PS, blue). The corresponding snapshot structures are shown at the right.

The two cyclic carboxylate systems, N-methylorotate (NMO) zwitterion and 2-imidazolidinone anion, are of particular interest and have biological significance. The former has been used as a model system for the uncatalyzed process in water to compare with the extraordinary catalytic power of orotidine 5′-monophosphate decarboxylase (OMPDC), which accelerates the unimolecular decarboxylation by 16 orders of magnitude.^22,23 The RDFs of C6 and the oxygen atom of the C4 carbonyl group with water are shown in Figure 9. As the product is formed, the formal C6 carbanion is fully hydrated, exhibiting a sharp first peak in the C6–HW RDF, whose integration to the first minimum at 2.50 Å yields 3.6 water molecules in the first solvation layer. In water, it is expected that the C6 carbanion is immediately protonated by the solvent since the pK_a of this site has been determined to be about 30–35.^99,100 The quick development of the hydrogen-bonding peak on the C4 carbonyl group at the transition state of the decarboxylation reaction of NMO is in marked contrast to the slower rise of the peak height at C6. Although a formally anionic charge is developed as CO₂ departs from the substrate, carbon is not an effective hydrogen-bond acceptor, and there is significant charge delocalization through the β-framework of the pyrimidine ring. The development of the O4–HW RDFs in Figure 9 clearly reflect the significance of such a cooperative effect of β-charge migration and countereffects of β-delocalization in the decarboxylation reaction of NMO, leading to net stabilization of the carbonyl group and an overall minimal effect on the solvent-induced recombination barrier (Figure 4).

Figure 9.

Radial distribution functions between the carbonyl oxygen (O4) and C6 of N-methylorotate zwitterion and the hydrogen atom of water (HW) in the reactant state (RS, black), at the transition state (TS, red), and in the product state (PS, blue). The corresponding snapshot structures are shown at the right.

The decarboxylation of 2-imidazolidinone anion in water shows similar trends as that of NMO (Figure 10) in the formally charge-localized N1 anion and the neighboring C2 carbonyl group. The relatively slow rise of the hydrogen-bonding peak in the N1–HW RDFs is analogues to that of C6 in NMO (Figure 10), whereas the quick appearance of the hydrogen-bonding peak in the O2–HW distribution at the transition state can be attributed to charge delocalization through β-conjugation. It is interesting to note that the hydrogen-bond-donating effect from the N3 hydrogen is hardly affected throughout the reaction. In fact, there is no clear hydrogen-bond-donating peak in the H3–OW RDFs since the overall charge of the reacting system is negative, disfavoring hydrogen-bond donation by the entire molecule.

5. Conclusions

Decarboxylation reactions of organic acids in aqueous solution are exceedingly slow, typically requiring activation functional groups and high reaction temperatures.⁹⁶ The reverse processes, CO₂ recombination or carboxylation reaction, are typically not competitive with protonation by the protic solvent water, rendering the process essentially irreversible.⁴⁸ However, under certain conditions, such as for substrates with electron-withdrawing groups at the β-carbon position to enhance the carbon acidity, exchange with isotope-labeled carbon dioxide has been observed,⁹⁶ and this process can be the main reaction pathway in aprotic solvents.^2,3,38,41,49 There is little direct information on the thermodynamic stability accompanying decarboxylation and carboxylation reactions in water from experiments and on the origin of free energy barriers in aqueous solution. In this study, we examined the free energy reaction profiles for a range of decarboxylation reactions and thus the reverse CO₂ capture processes in water using a dual-level combined quantum mechanical and molecular mechanical simulation approach. We found that differential solvation effects between the carboxylate ions in the ground state and species along the carbon–carbon bond-breaking pathway create large free energy barriers that separate the organic carboxylate ions and the transient carbanion intermediates. Since there is typically no barrier dividing these species in the gas phase, the free energy barriers in water for CO₂ capture are entirely due to solvation effects. Analyses of the computational results and experimental data revealed that the reaction rate constants are linearly correlated with the Gibbs energies of reaction in a Bell–Evans–Polanyi relationship. This mirrors a similar Brønsted relationship of the pK_a values of the corresponding acids of the carbanions from decarboxylation reactions. The origin of the different solvation effects is further shown by interaction energy decomposition analysis and examination of the solvent structural changes in terms of radial distribution functions as the reaction proceeds from the reactant state to the transition and product states.

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/jacsau.0c00110.

• Summary of computational details, reaction schemes, structures and geometries of bimolecular complexes, and computed solvation free energies for all reactions (PDF)

The authors declare no competing financial interest.