Rigorous pKa Estimation of Amine Species Using Density-Functional

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Rigorous pKa Estimation of Amine Species Using DensityFunctional Tight-Binding-Based Metadynamics Simulations Aditya Wibawa Sakti, Yoshifumi Nishimura, and Hiromi Nakai J. Chem. Theory Comput., Just Accepted Manuscript • DOI: 10.1021/acs.jctc.7b00855 • Publication Date (Web): 05 Dec 2017 Downloaded from http://pubs.acs.org on December 11, 2017

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Journal of Chemical Theory and Computation

Rigorous pKa Estimation of Amine Species Using Density-Functional Tight-Binding-Based Metadynamics Simulations

Aditya Wibawa Sakti,a Yoshifumi Nishimura,b and Hiromi Nakaia,b,c,d,*

a

Department of Chemistry and Biochemistry, School of Advanced Science and Engineering,

Waseda University, Tokyo 169-8555, Japan b

c

Research Institute for Science and Engineering, Waseda University, Tokyo 169-8555, Japan

Core Research for Evolutional Science and Technology (CREST), Japan Science and

Technology Agency (JST), Saitama 332-0012, Japan d

Elements Strategy Initiative for Catalysts and Batteries (ESICB), Kyoto University, Kyoto 615-

8520, Japan

1 Environment ACS Paragon Plus

Journal of Chemical Theory and Computation 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ABSTRACT Predicting pKa values for different types of amine species with high accuracy and efficiency is of critical importance for the design of high performance and economical solvents in carbon capture and storage with aqueous amine solutions. In this study, we demonstrate that density-functional tight-binding-based metadynamics simulations are a promising approach to calculate the free energy difference between the protonated and neutral states of amines in aqueous solution with inexpensive computational cost. The calculated pKa values were in satisfactory agreement with the experimental values, the mean absolute deviation being only 0.08 pKa units for 34 amines commonly used in CO2 scrubbing. Such superior reproducibility and correlation compared to estimations by static quantum mechanical calculations highlight the significant effect of dynamical proton transfer processes in explicit solvent molecules for the improvement of the estimation accuracy.


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1. INTRODUCTION In the present era, the increasing abundance of CO2 in the atmosphere is arguably leading to global warming.1 To reduce the CO2 levels emitted by fossil fuel combustion sources, consideration efforts have been devoted to the development of carbon capture and storage (CCS) systems.2–4 Aqueous amine solutions play a central role as advanced materials in CCS by chemical absorption.5,6 The pKa values of the conjugate acids of amines are considered to be an indicator of absorption efficiency.7,8 Experimental measurements have thus been performed for a wide range of amine species.8–11 On the theoretical side, quantitative evaluation of pKa values is still challenging. The routinely adopted procedure is a combination of thermodynamic cycles and free energy calculations of associated molecules in individual steps.12,13 Since the pioneering study by da Silva and Svendsen,14 a great deal of attention has been paid to the pKa calculation of amines, in which solvent effects are included implicitly and often explicitly.15–21 In these early theoretical studies, a mean absolute deviation (MAD) of 0.2–0.4 pKa units relative to the selected experimental values was considered an elaborated achievement. Unfortunately, static theoretical calculations are unable to process the various possible solvation patterns in deprotonation reactions. The delicate structural changes and proton transfer processes involved in acid dissociation reactions can be favorably described by full quantum mechanical molecular dynamics (MD) simulations. Density functional theory (DFT)-based MD simulations have provided not only mechanistic insight22–24 but also the ability to predict pKa values25–33 for typical acid–base reactions. Most of those investigations have adopted the metadynamics sampling technique34–36 to study such infrequent deprotonation events within accessible simulation times. The free energy difference between the protonated and deprotonated



species calculated from reconstructed free energy profiles in metadynamics has shown an error of approximately 0.2 pKa units relative to the experimentally determined values.26–29 The density-functional tight-binding (DFTB)37–39 method is a highly efficient approximation to the Kohn–Shan DFT, which uses atomic and diatomic parameters obtained from DFT calculations. Computational speeds 2–3 orders magnitude faster than that of conventional DFT implementation have been achieved.37,39 Furthermore, the DFTB method retains the robustness of the chemical reaction dynamics by virtue of the self-consistent determination of charge distributions.40 The authors’ group has implemented an efficient program of the DFTB-MD simulation,41 especially, by combining with the linear scaling divideand-conquer technique.42–45 The successes of describing several chemical phenomena in aqueous solutions46–48 have stimulated us to investigate whether the DFTB-based simulations can become an alternative for predicting pKa values of amines that enables fast screening for new compounds. In the present study, we have estimated the pKa values of amine species in solution using metadynamics simulations at the DFTB level. Although the combination of the DFTB method and the metadynamics technique has attracted recent interest for application in complex environments and yielded encouraging results,49–51 evaluation of DFTB accuracy for various types of amine species needs to be addressed for prediction purpose. To this end, the calculated pKa values are compared with available experimental data for 34 amine species. We also examine the effect of system size to the quality of theoretical predictions, which is hard to obtain from computationally more demanding DFT-based MD simulations. The paper is organized as follows. The computational details of the DFTB metadynamics simulations are provided in Section 2. Section 3 presents the accuracy and efficiency of the investigated approach. Finally, concluding remarks are described in Section 4.


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2. COMPUTATIONAL DETAILS Canonical ensemble simulations were performed for a cubic cell with three-dimensional periodic boundary conditions unless noted otherwise. In the initial condition, the system consisted of one protonated amine, one hydroxide ion, and 50 water molecules. For monoethanolamine (MEA), three larger simulation boxes containing 100, 200, and 500 water molecules were additionally prepared to investigate the system size dependence on the calculated pKa values. The density of each system was determined from classical MD simulations using the general CHARMM force field52 and NAMD package.53 This pre-equilibration procedure was performed for 3 ns with a time step of 1.0 fs under NVE, NVT, and NPT ensembles. The classically equilibrated structure was further equilibrated at the third-order DFTB (DFTB3)54 level with 3ob parameter set55 for 50 ps with a time step of 1.0 fs. The choice of DFTB model and parameter was based on the best estimation of pKa values for MEA at two different temperatures among several DFTB variants considered in preliminary simulations. During the DFTB equilibration, the temperature was controlled using an Andersen thermostat at 298.15 or 313.15 K. The structure and velocity of last equilibration step were adopted as initial conditions of the DFTB metadynamics simulations. In the production run, the time step was 0.5 fs. All DFTB calculations were performed using the DC-DFTB-K program.41 In order to observe the deprotonation reaction given by [Amine(H)]+ + H2O

Amine + H3O+,

(1)

the number of hydrogen atoms coordinated to the nitrogen atom of the amine species (nNH) was chosen as the collective variable (CV) for the DFTB metadynamics simulations. In accordance with previous successful free energy samplings,26–29,56 the rational form of nNH was adopted:



( )6 ∑ 1 − (rNH r0 )12 i =1 , NH

nNH =

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1 − rNHi r0

(2)

i

where rNH is the distance between the nitrogen and hydrogen atoms, r0 is the cut-off distance set i

to 1.6 Å, and the summation runs over the NH hydrogen atoms initially coordinated to the nitrogen atom. In the DFTB metadynamics simulations, the height and width of the Gaussian function to describe the bias potential were set to 1.31 kJ/mol and 0.1, respectively. Note that the CV is dimensionless. The Gaussian bias potential was deposited at time intervals of 0.04 ps. After reaching the convergence of free energy profile, the pKa value at temperature T was calculated using the following relationship: pKa =

∆G 2.303RT ,

(3)

where R is the universal gas constant and ∆G is the free energy difference between the two states in Eq. (1), directly calculated from the sampled free energy profile.


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3. RESULTS AND DISCUSSION 3.1. pKa Estimation of Aqueous MEA Solution First, we discuss the accuracy and efficiency of DFTB metadynamics simulations taking MEA, which is one of the most commonly used amines in CO2 capture process,5 as representative example. The time-course change of the CV during the deprotonation process of protonated MEA (MEA(P)) at 313.15 K is shown in Figure 1a. The nNH values of ~1.9 and ~2.8 correspond to MEA and MEA(P), respectively. A proton is shuttling between MEA(P) and an adjacent water molecule at 3.5–4.8 ps. The fluctuation at 5.2–5.9 ps is a manifestation of the instantaneous formation of a MEA(P)–water pair. The CV starts to be diffusive from ∼6.5 ps, at which the metadynamics sampling was stopped. In the diffusive region, the proton dissociated from MEA(P) migrates through the hydrogen bond network of water molecules, the so-called Grotthuss shuttling.57,58 The relatively short simulation time to complete the reaction in Eq. (1) is a consequence of the sufficient equilibration achieved before the production run.26–29 Figure 1b shows the time-course change of the free energy difference between the protonated and neutral states of MEA at 313.15 K. Sampling of the diffusive region hardly changes the free energy difference, demonstrating that the reconstructed free energy profile is well converged. Figure 1c shows the free energy profile for the deprotonation of MEA(P) at 313.15 K. Two minima are found at nNH = ~1.9 and ~2.8, representing the MEA and MEA(P) states, respectively. The calculated free energy difference is 54.19 kJ/mol, equivalent to a pKa value of 9.15. This estimation is in good agreement with the experimental value of 9.09.10 We also performed the DFTB metadynamics simulations of MEA at different conditions. One is to treat different unit cell sizes containing a larger number of water molecules. The time-



course changes of CV and calculated free energy profiles for 100, 200, and 500 water molecules are presented in Figures S1–S3 in the Supporting Information. The estimated pKa values of 100, 200, and 500 water molecules system are 9.19, 9.03, and 9.07, respectively. Considering the insensitivity of calculated pKa value with respect to the system size, 50 water molecules to solvate amine species seems to be sufficient for prediction purpose and was used throughout this study. The other is to calculate the pKa value at 298.15 K (for corresponding simulation results, see Figure S4 in the Supporting Information). The agreement of estimation (9.40) with experimental data (9.47)10 is again excellent, which indicates that the metadynamics sampling is able to capture the effect of slight change in temperature reasonably. The efficiency of the DFTB metadynamics simulation is remarkable. Calculation of a 60 ps long trajectory took less than an hour using an 8-core Intel Xeon E5-2637 v3 (3.50 GHz) workstation. The results demonstrate that the region shown in Figure 1 can be generated within minutes. In contrast, previous DFT-based metadynamics simulations of systems containing a similar number of solvent water molecules have been reported to require more expensive computational resources (i.e., an IBM Blue Gene cluster with 256 processors).26,29

3.2. pKa Estimation of Various Types of Amines The obtained results in Section 3.1 give us confidence to evaluate the performance of DFTB metadynamics simulations for amines being in common use in the CCS technology. Specifically, the number of target amines was extended to 34 in total, including seven primary (10), nine secondary (20), nine tertiary (30), four cyclic secondary (c-20), and five cyclic tertiary (c-30) species. A comparison of the calculated pKa values with the experimental results8–11 is shown in Table 1. The time-course changes of the CV and the simulated free energy profiles are given


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Figures S5–S37 in the Supporting Information, except for MEA at 313.15 K, already shown in Figure 1. In all cases, sampling of reactive region to fulfill the free energy profile with bias potential was continued no longer than 12 ps and protonated and neutral states were clearly distinguished from each other in the free energy profile. Overall consistency was observed between the estimated and experimental pKa values. Moreover, the obtained MAD was only 0.09 pKa units. The largest error was 0.21 pKa units (1.20 kJ/mol) for n-cyclohexylethanolamine. It should be noted that this specific group of amines does not present an obvious trend toward a certain range of pKa values. The averaged statistical error bar based on five MD trajectories for each amine is 0.26 pKa units, with the maximum deviation of 0.53 pKa units for 3-piperidino-1,2propanediol. More details of the estimated pKa values for individual metadynamics runs are given in Table S3 in the Supporting Information. The correlation of pKa values in Table 1 is graphically displayed in Figure 2. An excellent correlation coefficient of R2 = 0.990 was obtained for the 34 amines, with pKa values ranging from 6.6 to 11.1. For comparison with previous studies using static theoretical calculations, see Figures S38–S40 in the Supporting Information. The outperformance of the present approach strongly supports the need to account for the multiple arrangements of the solvent water molecules and the forward/backward proton shuttling processes in order to accurately determine pKa values.



4. CONCLUSION In conclusion, DFTB-based metadynamics simulations are able to estimate pKa values of amine species in aqueous solution with remarkable accuracy. The calculated MAD for 34 amines commonly used in CO2 capture was only 0.09 pKa units with respect to the experimental results, superior by a factor of 2–3 to common static theoretical calculations. The observed accuracy may be attributed to the inclusion of Grotthuss shuttling effects and the sampling of solvation shells around the reaction centers during the deprotonation process. In contrast, the single-point calculations at the DFTB3/3OB level underestimate the gas-phase acidities and proton affinities of amines, as shown in Table S1 in the Supporting Information. Incorporation of polarizable continuum model cannot improve the pKa values for single-point calculations, as shown in Table S2 in the Supporting Information. We also found that the pKa values obtained with DFTB metadynamics simulations are less sensitive with respect to the system size while temperature effect can be incorporated adequately. Although possible error sources exist, such as metadynamics sampling errors, DFTB model/parameter dependence, and the neglect quantum effects, those negative factors seem to be cancelled out in the resultant free energy difference results.26–29,59 The required computational demands are small with no deterioration of the prediction accuracy; hence, the present approach presents a great advantage over DFT- and/or wavefunction-based protocols in that prospective candidates for efficient chemical absorption of CO2 can be explored in a feasible manner. The accurate determination of acid dissociation constants for different groups of compounds may be feasible after careful inspection of the DFTB performance.


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ACKNOWLEDGMENT This study was supported in part by a Grant-in-Aid for Scientific Research (A) “KAKENHI Grant Number JP26248009” from the Japan Society for the Promotion of Science (JSPS), a Grand-in-Aid for Challenging and Exploratory Research “KAKENHI 15K13629” from the Ministry of Education, Culture, Sports, Science, and Technology (MEXT), Japan, and by MEXT as “Priority Issue on Post-K computer” (Development of new fundamental technologies for highefficiency energy creation, conversion/storage, and use). One of the authors (A.W.S.) acknowledges financial support from the Yoshida Scholarship Foundation (YSF). Some of the calculations were performed at the Research Center for Computational Science (RCCS), Okazaki, Japan.

ASSOCIATED CONTENT Supporting Information The Supporting Information is available free of charge on the ACS Publication website. Time-course changes of collective variable and free energy profile for deprotonation reaction of 34 amine species obtained from production run of DFTB metadynamics simulations and correlations between estimated pKa values obtained from previous static theoretical calculations and the experimental results.



AUTHOR INFORMATION Corresponding Author *Corresponding author: H. Nakai, Phone: +81-3-5286-3452, E-mail: [email protected]

Author Contributions The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript.

Notes The authors declare no competing financial interest.


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(50) Knaup, J. M.; Wehlau, M.; Frauenheim, T. Permutation-Invariant Collective Variable to Track and Drive Vacancy Dynamics in Simulations of Solids. Phys. Rev. B 2013, 88, 220101. (51) Cuny, J.; Korchagina, K.; Menakbi, C.; Mineva, T. Metadynamics Combined with Auxiliary Density Functional and Density Functional Tight-Binding Methods: Alanine Dipeptide as a Case Study. J. Mol. Model. 2017, 23, 72. (52) Vanommeslaeghe, K.; Hatcher, E.; Acharya, C.; Kundu, S.; Zhong, S.; Shim, J.; Darian, E.; Guvench, O.; Lopes, P.; Vorobyov, I.; Mackerell, A. D., Jr. CHARMM General Force Field: A Force Field for Drug-Like Molecules Compatible with the CHARMM All-Atom Additive Biological Force Fields. J. Comput. Chem. 2009, 31, 671–690. (53) Phillips, J. C.; Braun, R.; Wang, W.; Gumbart, J.; Tajkhorshid, E.; Villa, E.; Chipot, C.; Skeel, R. D.; Kalé, L; Schulten, K. Scalable Molecular Dynamics with NAMD. J. Comput. Chem. 2005, 26, 1781–1802. (54) Gaus, M.; Cui, Q.; Elstner, M. DFTB3: Extension of the Self-Consistent-Charge DensityFunctional Tight-Binding Method (SCC-DFTB). J. Chem. Theory Comput. 2011, 7, 931– 948. (55) Gaus, M.; Goez, A.; Elstner, M. Parametrization and Benchmark of DFTB3 for Organic Molecules. J. Chem. Theory Comput. 2013, 9, 338–354. (56) Iannuzzi, M.; Laio, A.; Parrinello, M. Efficient Exploration of Reactive Potential Energy Surfaces Using Car-Parrinello Molecular Dynamics. Phys. Rev. Lett. 2003, 90, 238302. (57) Agmon, N. The Grotthuss Mechanism. Chem. Phys. Lett. 1995, 244, 456–462. (58) Marx, D. Proton Transfer 200 Years after von Grotthuss: Insights from Ab Initio Simulations. ChemPhysChem 2006, 7, 1848–1870.



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TABLES Table 1. Comparison of the pKa values calculated from DFTB metadynamics simulations with the experimental results for 34 amine species in aqueous solution Entry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 MAD

Amine Monoethanolamine 2-Amino-2-methyl-1-propanol 2-(2-Aminoethoxy)ethanol 2-Amino-2-ethyl-1,3-propanediol 3-Amino-1-propanol Serinol(2-aminopropane-1,3-diol) Tris(hydroxymethyl)aminomethane Methylmonoethanolamine 2-(Ethylamino)ethanol 2-(tert-Butylamino)ethanol Diisopropanolamine n-Cyclohexylethanolamine Diethanolamine n-Cyclopentylethanolamine Tricine n-Cyclopropylethanolamine Methyldiethanolamine 2-(Diisopropylamino)ethanol Triethanolamine Tris[2-(2-methoxyethoxy)ethyl]amine Triethylamine 3-Dimethylamino-1-propanol Ethyldiethanolamine N,N-Dimethylisopropanolamine tert-Butyldiethanolamine Piperazine 2-Piperidinemethanol 2-Piperidineethanol 3-Piperidinemethanol 1-Piperidinepropanolamine 3-Piperidino-1,2-propanediol 3-Quinoclidinol 4,2-Hydroxyethylmorpholine 3-Morpholinopropylamine

Abbreviation MEA AMP 2-AEE AEPD MPA SAPD THMAM MMEA EAE TBAE DIPA n-CHEA DEA n-CPEA TRC n-CPREA MDEA 2-DIPA TEA TMEEA TREA 3-DMAP EDEA DMIPA t-BDEA PZ 2-PPM 2-PPE 3-PPM 1-PPP 3-PPPD 3-QCD 4,2-HEMO 3-MOPA

Typea 10 10 10 10 10 10 10 20 20 20 20 20 20 20 20 20 30 30 30 30 30 30 30 30 30 c-20 c-20 c-20 c-20 c-30 c-30 c-30 c-30 c-30


T /K 313.15 313.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 313.15 313.15 313.15 313.15 313.15 298.15 298.15 298.15 298.15 313.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15

pKa (Calc.) 9.14 9.16 9.49 8.78 9.86 8.58 8.16 9.94 10.00 9.76 8.80 9.89 8.80 10.25 8.00 8.50 8.43 9.27 7.41 6.67 10.30 9.30 8.66 9.45 8.92 9.30 10.47 11.08 10.98 9.32 8.79 10.22 6.82 9.89 0.09

pKa (Exptl.) 9.09b 9.23c 9.42c 8.82c 9.96c 8.55d 8.08d 9.85c 10.00d 9.70d 8.88d 10.10d 8.88d 10.10d 8.10d 8.40d 8.31b 9.11b 7.45c 6.69b 10.32c 9.27d 8.80e 9.47e 9.03e 9.38b 10.60d 10.90d 10.80d 9.43d 8.91d 10.10d 6.90e 9.95e


a

Primary, secondary, tertiary, cyclic secondary, and cyclic tertiary amines are denoted as 10, 20,

30, c-20, and c-30, respectively. bRef. 10. cRef. 11. dRef. 8. eRef. 9. FIGURE CAPTIONS Figure 1. Time-course changes of the (a) CV, nNH, and (b) free energy difference, and (c) the free energy profile as a function of the CV for the deprotonation of MEA(P) at 313.15 K.

Figure 2. Correlation between the calculated pKa values from DFTB metadynamics simulations and the experimental results8–11 for 34 amine species in aqueous solution.


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FIGURES

(a)

(b)

(c)

Figure 1. Time-course changes of the (a) CV, nNH, and (b) free energy difference, and (c) the free energy profile as a function of the CV for the deprotonation of MEA(P) at 313.15 K.



Figure 2. Correlation between the calculated pKa values from DFTB metadynamics simulations and the experimental results8–11 for 34 amine species in aqueous solution.


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TABLE OF CONTENTS GRAPHICS



Fig. 1a 85x59mm (300 x 300 DPI)

ACS Paragon Plus Environment

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Fig. 1b 85x59mm (300 x 300 DPI)



Fig. 1c 88x62mm (300 x 300 DPI)


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Fig. 2 635x635mm (72 x 72 DPI)



Table of contents 338x190mm (96 x 96 DPI)


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Rigorous pKa Estimation of Amine Species Using Density-Functional

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