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Postcombustion CO2 Capture Solvent Characterization Employing the Explicit Solvation Shell Model and Continuum Solvation Models Mayuri Gupta,*,† Eirik F. da Silva,‡,§ and Hallvard F. Svendsen† †

Department of Chemical Engineering, Norwegian University of Science and Technology, Trondheim 7491, Norway Department of Process Technology, SINTEF Materials and Chemistry, Trondheim 7034, Norway

‡

S Supporting Information *

ABSTRACT: A study on the explicit and implicit solvation models for calculation of solvation free energy of ions and pKa of amino acids presented recently [Gupta, M.; et al. J. Chem. Theory. Comput. 2013, 9, 5021−5031] is extended for the study of amines and alkanolamines. Solvation free energies and pKa’s of a data set of 25 amines and alkanolamines are calculated using the explicit solvation shell (ESS) model given by da Silva et al. [J. Phys. Chem. A 2009, 113, 6404] and continuum solvation models (polarized continuum solvation model (PCM), SM8T, and DivCon). An extensive overview involving the gas-phase basicity and proton affinity, calculated using density functional methods (B3LYP/6-311++G(d,p)) and composite methods (G3MP2B3, G3MP2, CBS-QB3, G4MP2) and compared with corresponding experimental results for amines and alkanolamines, is also included in the present work. This data set was selected based on the components’ potential as solvents for postcombustion CO2 capture (PCC) processes. Results of gaseous-phase thermochemistry and pKa obtained from different models employed in this work are analyzed against experimental results for obtaining error estimates involved in each theoretical model. The ESS model for the calculation of the solvation free energy of ions combined with composite methods for gaseous-phase thermochemistry is found to give reasonable accuracy for pKa calculations of amines and alkanolamines and thereby constitutes a method for validation of pKa for new potential PCC solvents.

1. INTRODUCTION Postcombustion CO2 capture (PCC) by reactive absorption is one of the most mature technologies available today for combating global warming.1 Amines and amino acids are commonly used solvents for CO2 capture in this technology.2 The pKa of the solvent is one of the most crucial properties, which has to be taken into consideration when evaluating the performance of a solvent.3−5 Depending upon the pKa of a solvent, the reaction equilibria, kinetics, absorption capacity, reaction rate, heat of absorption of CO2, and temperaturedependent properties of the system vary.6−8 As explained by Svendsen et al.,9 the energy required in a typical amine-based CO2 capture solvent is used to heat the solvent, to reverse the absorption process, and to dilute the recovered CO2, and the pKa of the solvent governs the extent and heat of reaction of bicarbonate formation (mainly in tertiary amines),10 which successively influences the rate of CO2 transport in the system. Versteeg et al.11 have found a linear relationship between the basicity of the solvent and the logarithm of the reaction rate constant of solvent molecules for their data set of molecules. Aronu et al.12 have demonstrated that the rate of CO2 absorption in the solvent increases with the increase in pKa of the solvent. Additionally, the temperature swing PCC process benefits from the solvent having a hightemperature-sensitive pKa, which helps in reversing the reaction equilibrium with low energy requirements.13−15 Also, to measure the influence of operating conditions © XXXX American Chemical Society

(pressure and temperature), the pKa of amines and alkanolamines is considered as an important variable.11,13,16 Reliable prediction of pKa by incorporating quantum chemical approaches is cheap and is of crucial importance to define the biological and chemical behavior of any molecule.17,18 pKa determination from computational chemistry requires gaseous-phase and solution-phase free-energy calculations. Reliable gaseous-phase basicities can be calculated using density functional theory (DFT) and advanced composite methods within similar or lower experimental error bars.19,20 Experimental error bars for the calculation of gaseous-phase basicity and proton affinity (PA) are around ±4−8 kJ/mol.19 On the other hand, determination of the acidity or basicity in a solution within reasonable accuracy is still difficult and demanding approaches are required to calculate these meticulously.21,22 Solvation models range from implicit23−30 to explicit solvent models;31,32 some molecules are studied employing quantum mechanical treatment33−35 of the system. Despite various efforts,35−38 capturing solvation effects in a system accurately is still challenging39 and contributes the largest error in the theoretical determination of pKa. To attend to this issue, various theoretical models such as supermolecule-style calculations, variants of dielectric conReceived: April 21, 2016 Revised: July 26, 2016

A

DOI: 10.1021/acs.jpcb.6b04049 J. Phys. Chem. B XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry B tinuum theory, and cluster−continuum approaches are employed. Calculation of solvation free energy using continuum solvation models for the ionic species involved in the calculation of pKa induces large errors. These models have neutral species in their training set and do not account for explicit solute−solvent interactions such as hydrogen bonding.40 Explicit solvation methods are considered to be more promising, as presented in our recent41 and present works. Tomasi et al.42 have outlined a comprehensive review of state-of-the-art computational solvation models. The considerable ongoing interest in the determination of theoretical dissociation constants has given rise to huge number of research publications in this area.43−50 The objective of the present study is twofold. First, the pKa’s of amines and alkanolamines are calculated by employing various gaseous-phase composite methods and DFT levels of theory along with various solvation models viz. the explicit solvation shell (ESS) model introduced by da Silva et al.51 and various continuum solvation models. This provides an opportunity to benchmark the outcome and compare the performance of various gaseous-phase and aqueous-phase methods of theory against experimental results. In other words, the present work exploits the theoretical limits of calculating pKa to obtain reasonable accuracy using various gaseous- and aqueous-phase computational chemistry calculations. Second, this study helps in the initial screening and determination of the potential of amine or alkanolamine molecules as PCC solvents which are not commercially available and thereby can save much time and resources in the development of the carbon capture and storage (CCS) industry. The calculated gaseous and aqueous thermochemistry data would also provide an opportunity to compare the thermochemistry data of these potential CCS solvents to those of new suggested solvents in the future. The present work comprises benchmarking of quantum electronic structure methods against experiments for calculation of PAs and gas-phase basicities (GBs), calculation of free energy of solvation of amines and their ionic counterparts, and calculation of amino group pKa at 298 K using various continuum and ESS models. The results from gaseousphase PA, GB, and pKa are compared against experimental results, where available.

Gaussian 03 in water. PCM model56 calculations are performed using DFT at the PCM/B3LYP/6-311++G(d,p)//SM8/B3LYP-6-311++G(d,p) level. Self-consistent reaction field (SCRF) and keyword read were added in the input file for invoking PCM calculations and adding different specifications of the solute cavity along with PCM-specific modifiers, respectively. The united atom for Hartree−Fock (UAHF) model was employed in the PCM to create the cavity using the RADII = UAHF and GEPOL algorithm of Nilsson et al.57 The united atom approach constructs the van der Waals surface using spheres that are based on nonhydrogen atoms. For the calculation of free energy of solvation ΔGsolv using the PCM, both electrostatic and nonelectrostatic (i.e., cavitation, repulsion, and dispersion) contributions are retained. Aqueous-phase SM8T calculations58 are performed using DFT at the SM8T/B3LYP/6311++G(d,p)//SM8/B3LYP-6-311++G(d,p) level in Gamessplus,59 using optimized geometries obtained earlier. The SM8T model is not parameterized for ionic molecules and has an unsigned mean error (UME) of 0.08 kcal/mol for Ncontaining compounds (i.e., neutral amines in the present work); however, it is expected to give good qualitative results for ions.58 The ESS model extracts solvation shell geometries from molecular simulations of the solute in the bulk solvent as given in da Silva et al.51 Quantum mechanical calculations are used to fully optimize cluster geometries, and cluster solvation free energies are calculated employing the Poisson− Boltzmann (PB)-based model in the DivCon code.2 The physical insights into the PB continuum solvation model have been given in the Supporting Information of da Silva et al.51 The PB model calculations were performed for the determination of the free energy of solvation as single-point calculations at the AM1 level on the optimized HF/631+G(d) clusters. The results of ΔGsolv for a single solute obtained using the DivCon model are also estimated for analyzing the results obtained using the ESS and DivCon models. All quantum mechanical calculations were carried out in Gaussian 03 software, and all simulations were carried out using Sander from the AMBER 12 suite.60 A detailed overview of molecular dynamics simulations and the PB model is given in the Supporting Information.

2. COMPUTATIONAL DETAILS The gas-phase geometries of amines and alkanolamines (Am) and their protonated counterparts (AmH+) have been fully optimized using the functional B3LYP and the 6-311+ +G(d,p) basis sets as compiled in Spartan 08 and Gaussian 03.52 (The optimized molecular geometries in Cartesian coordinates are given in the Supporting Information.) Frequency calculations were used to characterize the minimum-energy structure for all of the molecules. Gaussian-n theories (G3MP2B3, G3MP2, G4MP2, CBSQB3) and DFT at a B3LYP/6-311++G(d,p) level are used to calculate GB and PA. G3MP2B3, G3MP2, CBS-QB3, and DFT calculations are performed using Gaussian 03.52 G4MP2 thermochemical calculations were done in Gaussian 09.53 For the calculations of the polarized continuum solvation model (PCM) and SM8T, all molecules were optimized in the aqueous phase at HF and B3LYP54 levels using the 6311++G(d,p) basis set,55 employing solvent model SM8 in Spartan 08 in equilibrium calculations. Solvation free energies are obtained using PCM calculations and default settings in

3. METHODS AND THEORETICAL BACKGROUND 3.1. Gas-Phase Thermochemical Properties of Amines and Alkanolamines. The standard enthalpy and standard free energy of reaction given in eq 1 can be defined as the gas-phase thermochemical properties related to the basicity and acidity of an amine or alkanolamine molecule (M) at 298 K as follows61,62 MH+2 → MH + H+

PA(MH) = ΔH10 and GB(M)

= ΔG10

(1)

GB and PA for amines and alkanolamines are calculated from eqs 2 and 3 below, following the reaction in eq 1. GB = [ΔG 0(MH) − ΔG 0(MH+2 )] + ΔG 0(H+)

(2)

PA = [ΔH 0(MH) − ΔH 0(MH+2 )] + ΔH 0(H+)

(3)

Using an ideal gas expression, the enthalpy of a proton is calculated as B


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The Journal of Physical Chemistry B H(H+) = U + PV = 5 2 RT

(4)

where U is the internal energy, P is the pressure, V is the volume, and R and T are the universal gas constant and absolute temperature, respectively. Obeying the Sackur− Tetrode equation,63 the entropy of the proton is given as ⎛ e5/2k T ⎞ B ⎟ S(H+) = R ln⎜⎜ 3 ⎟ Λ p ⎝ ⎠

Figure 1. Thermodynamic cycle for computing solvation free energies with the ESS model.

(5)

Here, kB represents the Boltzmann constant, Λ is the thermal de Broglie wavelength [Λ = (h2/2πmkBT)1/2, where h is Plank’s constant, m denotes the mass of the proton], and T and p represent the temperature and pressure, respectively. The values of gas-phase free energy and enthalpy for a proton are ΔG0(H+) = −26.28 kJ/mol and ΔH0(H+) = 6.19 kJ/mol at 298 K, respectively, under standard-state conditions. 3.2. Thermodynamic Cycle for ESS Model Solvation Energy Calculation. Many cluster/continuum calculations employing various thermodynamic cycles for estimating solvation free energy of ions have been published in the literature.64−73 The ESS model overcomes the drawbacks of continuum solvation models to calculate the accurate free energy of solvation of ions by introducing a part of the solvent explicitly. The ESS model combines the continuum models with explicit solvent representation, unlike a conventional continuum model or classical simulation, and to some extent take account of all contributions to the solvation energy. Continuum solvation models account for long-range electrostatics, solute polarization, and cavitation energy contributions, whereas solute−solvent hydrogen bonding and entropy contributions are taken into consideration during the calculation of cluster formation energy. The results for the solvation energy from the DivCon model used in the present work correspond to those for the solvation free energy of a single solute from the DivCon model, which is further optimized with explicit water clusters in the ESS model. The DivCon model implements SCRF calculation combining the linear-scaling divide-and-conquer semiempirical algorithm with the PB equation. The free energy of solvation calculated by the DivCon model is the SCRF solvation energy for a single solute, and the ESS solvation free energy is obtained by taking an optimized single molecule of solute from DivCon and adding explicit water molecules to it for the best possible representation of solute−solvent interactions. The expected improvement of ESS solvation free energies over the DivCon results is easily understandable based on the inclusion of all of the solute−solvent interactions. The comprehensive description of the thermodynamic cycle used to calculate solvation free energies using cluster−continuum models has been explained earlier.41,51,74 Thus, the thermodynamic cycle used is only briefly outlined in the present work. In the present work, the solvation free energy of the solute, ΔG*solv(A), is calculated by the thermodynamic cycle shown in Figure 1. The gas-phase reaction between solute molecules, A, and clusters of water molecules (specified as(H2O)n) is depicted by the upper horizontal leg, given in eq 6, of the water cluster cycle (Figure 1).

The solvation free energies, ΔGsolv * (A), of the solute molecules, A, were computed according to eq 7, using the thermodynamic cycle shown in Figure 1, as * (A) = ΔGclust,g * (A(H 2O)n ) + ΔGsolv * (A(H 2O)n ) ΔGsolv * ((H 2O)n ) − ΔG 0 →* − ΔG* → l − ΔGsolv

This is the sum of the free energies of forming the gas-phase solute−water cluster (ΔG*clust,g(A(H2O)n)) with n explicit water molecules and the difference between the hydration free energies of the solute−water cluster (ΔGsolv * (A(H2O)n)) and the water cluster, ΔG*solv((H2O)n). The standard-state corrections adjust the gas-phase concentrations (ΔG0→* = RT ln(24.46)) from 1 mol/24.46 L to 1 M and the water cluster concentration from 1 M to 55.34/n M75,76 (ΔG*→1 = RT ln([H2O]/n)). The gas-phase standard-state correction (ΔG0→*) is 1.89 kcal/mol at room temperature. The above cycle was used to study the solvation of a large series of cations and anions with clusters containing five explicit water molecules.51 3.3. pKa Determination. The fundamental equation of thermodynamics relating dissociation constant pKa to the free energy of protonation in solution (ΔGaq * ) is pK a =

* ΔGaq RT ln(10)

(8)

where R is the universal gas constant and T is the temperature. The deprotonation reaction in the system can be shown as * ΔGaq,deprot(AH +)

AH+S ⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯→ A S + H+S

(9)

An error of 1 pKa unit is introduced in the calculation with a variation of 1.36 kcal/mol in the ΔGaq * value. The free energy of protonation in solution (ΔGaq * ) corresponds to the summation of the gaseous-phase and solvation free energies for the deprotonation reaction given in eq 9, using a thermodynamic cycle described in our previous work.45 Nproducts

* = ΔGgas * + ΔGsol

∑ i=1

Nreactants

* i− niΔGsolv,

∑ j=1

* j njΔGsolv, (10)

Here * indicates the standard state of 1 mol/L. Assuming ideal gas behavior, a correction corresponding to ΔnRT ln(R*T) must be added to the gas-phase reaction energy, which is denoted ΔGgas * . This is typically calculated for a standard state of 1 atm. Δn refers to the change in the number of species in the reaction and R and R* are the gas constants in units of J/mol K and L atm/mol K, respectively. Absolute pKa calculations in the present work are based on the thermodynamic cycle shown in Figure 2.

ΔGclust,g

A(g) + (H 2O)n (g) ⎯⎯⎯⎯⎯⎯⎯→ A(H 2O)n (g)

(7)

(6) C


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The Journal of Physical Chemistry B

by not compromising the reasonable solvation of relatively small amine molecules studied in the present work. Although there are many views on the issue of the number of solvent molecules to be added to exactly represent solute−solvent interactions, recent studies74 have shown that methods like adding solvent molecules until the calculated solvation energies converge could be more reliable than methods that are based on the size and polarization of ionic molecules. But these methods would be computationally expensive and would possibly not result in complete cancelation of errors within one studied data set of molecules. No convergence of free energy of solvation is observed in case of 2-aminoethanol (MEA) by increasing the number of explicit water molecules. From Figure S3, it can be suggested that the additional explicit water molecules are not involved at the important interaction site with the molecule, which would mean that additional water molecules would not help in lowering the energy of the molecule. The free energies of solvation obtained for the MEA cluster using 5, 6, and 7 explicit water molecules are given in Table S4, and they remain similar without having any visible trends on increasing the explicit water molecules in the solvation shell. Therefore, we believe that the molecules studied in this work are small and they can be reasonably solvated with five explicit water molecules.

Figure 2. Thermodynamic cycle employed for the calculation of pKa values.

The full method describing the calculation of free energy of protonation in solution as a summation of aqueous and gaseous solvation free energies is described in our previous study.45 3.4. Cluster Configurations. The ESS model comprises a cluster containing five explicit water molecules. The encouraging results obtained in the studies by da Silva et al.51 and Gupta et al.41 on a similar set of molecules motivated us to continue our present study with similar cluster configurations. The underlying motivation for having five explicit water molecules is the greater opportunity of cancelation of consistent errors in the calculation of ΔGsolv emerging from gaseous-phase free-energy, entropy, and continuum solvation free-energy calculations for different molecules and maintenance of optimum computational cost

4. RESULTS Table 1 lists the data set of 25 amines and alkanolamines examined in the current work, including the experimental pKa values. The choice of this data set was based on the possibility

Table 1. Amines and Alkanolamines Studied in This Work and Their Experimental pKa Data at 298 K exp pKab (298 K) a

no.

amine and alkanolamine

abbreviation

type

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.

2-aminoethanol 3-amino-1-propanol ethylenediamine propanamine 2-methyl-1-propanamine 2-amino-2-methylpropanol 2-amino-2-methyl-1,3-propanediol 2-amino-2-ethyl-1,3-propanediol 2-amino-1-propanol diethanolamine monomethylethanolamine morpholine piperazine piperidine 3-amino-1-methylaminopropane thiomorpholine 1-methylpiperazine 4-piperidinemethanol 4-piperidineethanol aminoethylpiperazine dimethylethylenediamine 2-methylpiperazine 1-ethylpiperazine ammonia diethylenetriamine

MEA 3-AP EDA PA 2-MPA AMP AMPD AEPD 2-AP DEA MMEA MOR PZ PIP MAPA TMOR 1-methylPZ 4-PIPM 4-PIPE AEP DMEDA 2-methylPZ 1-ethylPZ NH3 DETA

p p p p p p, sh p, sh p, sh p s s s, c s, c s, c s, p s, c c s, c s, c p, s, t, c s c c p p, s

9.50 10.0 9.9 10.6 10.5 9.7 8.8 8.8 9.4 9.0 9.8 8.33 9.83 (1), 5.55 (2) 11.10 9.89 8.7 9.14 10.56 10.62 9.48 (1), 8.45 (2) 10.03 9.57 9.20 9.24 9.94

a

In the type of amines studied, p, s, t, sh, and c stand for primary, secondary, tertiary, sterically hindered, and cyclic amines and alkanolamines, respectively. bPerrin 196592 and Perrin 1972.92 D


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The Journal of Physical Chemistry B Table 2. GBsa of the Data Set of Amines and Alkanolamines Studied in This Work at 298 Kb

a

amines and alkanolamines

G3MP2B3

G3MP2

G4MP2

CBS-QB3

DFT(B3LYP/6-311++G(d,p))

experimental


893 919 913 889 892 928 925 931 901 949 920 894 919 925 889 897 919 931 922 884 887 927 920 820 883

894 919 915 889 893 929 924 930 901 947 920 895 920 926 889 899 918 931 922 883 887 927 921 821 883

894 919 914 889 892 927 925 931 901 950 920 895 919 925 889 899 919 931 922 885 887 927 920 820 884

896 917 913 887 891 926 922 928 899 945 917 891 916 923 887 896 916 928 919 883 885 924 917 820 882

895 920 917 888 891 932 925 932 902 950 918 892 919 925 888 897 919 930 921 886 887 928 921 818 884

896.8c 917.3c, 912.5d 912.5c 883.9c 890.8c

920c, 920.48e 891.2c 914.7c 921c

819c

The GBs are calculated using eq 2. bAll values are in kJ/mol. cHunter et al.79 dBouchoux et al.80 eSunner et al.81

Table 3. Gas-Phase PAsa of the Data Set of Amines and Alkanolamines Studied in This Work at 298 Kb amines and alkanolamines

G3MP2B3

G3MP2

G4MP2

CBS-QB3

DFT(B3LYP/6-311++G(d,p))

experimental


926 951 947 919 923 961 956 962 931 976 951 919 951 957 920 930 950 962 953 914 917 958 951 855 913

927 951 948 920 924 962 955 962 932 976 951 920 951 958 920 931 948 963 953 914 918 959 952 855 913

925 951 948 920 924 961 956 963 932 977 951 921 951 957 921 931 950 963 953 915 918 959 951 854 914

931 949 947 918 922 961 953 959 930 972 948 923 948 955 918 928 947 960 951 913 916 956 948 854 912

926 951 951 920 922 967 959 962 930 978 949 922 949 957 920 928 951 962 951 915 917 959 954 853 912

930.3c 962.5c, 945.3d 951.6c, 941.8e, 951.4f 917.8c, 907.5f 924.8c

953c, 953.9g 924.3c 943.7c 954c

853.6c

a The gas-phase PAs are calculated using eq 3. bAll values are in kJ/mol. cHunter et al.79 dBouchoux et al.80 eHahn et al.82 fWang et al.83 gSunner et al.81

for these amines and alkanolamine molecules being energyefficient solvents for PCC processes.15

GBs and PAs of amine and alkanolamine molecules were calculated using different theoretical methods. Tables 2 and 3 E


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The Journal of Physical Chemistry B Table 4. Free Energy of Solvation of Amines and Alkanolamines Calculated by the ESS Modela amines and alkanolamines (neutral)

ΔGsolv (calcd)b

ΔEcluster * c

−TΔScluster * d

ΔGs(A(S)n)e

areaf


−3.4 0.0 −2.2 2.4 1.4 −4.4 −3.1 −3.3 −1.0 −1.7 0.0 −1.9 −3.0 0.3 −1.0 0.9 −2.2 −4.8 −4.0 −5.6 −1.2 −2.4 −0.9 −4.29 −5.5

−6.0 −6.4 −7.3 −6.3 −7.3 −13.3 −10.4 −9.1 −6.9 −6.0 −7.3 −5.5 −5.4 −8.9 −5.3 −2.1 −7.9 −8.5 −7.8 −5.9 −7.6 −5.3 −6.1 −13.1 −3.1

9.7 10.7 10.7 10.9 10.7 12.2 12.2 11.4 10.3 11.0 11.0 9.1 8.5 10.3 10.5 8.7 9.8 9.4 9.8 9.0 10.6 8.5 9.6 11.9 9.0

−19.48 −16.71 −17.91 −14.51 −14.34 −15.72 −17.29 −18.00 −16.74 −19.05 −15.93 −17.84 −18.43 −13.44 −18.63 −18.10 −16.50 −17.98 −18.32 −21.06 −16.62 −17.85 −16.79 −15.12 −23.75

215.52 225.70 212.94 220.46 239.05 233.35 234.76 255.48 223.81 246.71 223.18 233.07 239.06 237.24 255.70 242.70 249.49 266.00 288.30 287.24 251.33 253.43 266.08 232.15 272.64

All values are in kcal/mol. bCalculated free energy of solvation; all values shifted by −2.41 kcal/mol to remove systematic errors relative to experimental values as in the ESS model presented by da Silva et al.51 Estimated sampling standard deviation is 1 kcal/mol. cEnergy of formation of the cluster at the HF/6-31+G(d) level, converted from a standard state of 1 atm to 1 mol/L. Thermal corrections to the energy and zero-point energies not included. dTemperature (298 K) multiplied by the entropy of formation of the cluster at the HF/6-31+G(d) level. eFree energy of solvation of the cluster calculated with the PB continuum model. fArea of clusters calculated with the PB continuum model. a

with the ESS model, presented by da Silva et al.,51 are given in Tables 4 and 5, respectively. The ESS model is parameterized for ionic molecules. The cluster formation energies, entropies and cluster solvation energies for a set of 25 amines and alkanolamines and their corresponding protonated counterparts calculated in the present study are presented in Table 4 and 5, respectively. A PB continuum solvation model is used to calculate cluster solvation free energies, which are also given in Tables 4 and 5. All of the results were combined to get free energy of solvation of molecules as explained in the model presented by da Silva et al.51 In the present work, the cluster geometries of some molecules would not converge to a minimum-energy structure and had imaginary frequencies. These geometries resulted in a breakdown of such clusters and could have been initiated from poor initial geometries retrieved from molecular dynamics simulations as also observed by da Silva et al.51 in their work. Some vibration frequency calculations were also accompanied with imaginary frequencies. In pursuance of identifying and disregarding all unconverged geometries and accommodating results from stable cluster geometries, an energy cutoff of ±80 kcal/mol from the obtained minimumenergy structure was applied. Approximately 10−15 cluster geometries resulted in breakdown and could not converge to a stable structure from a set of 100 submitted cluster geometries for each molecule. The most stable cluster geometries obtained in the present work for neutral and

give GBs and PAs using G3MP2B3, G3MP2, G4MP2, CBSQB3, and DFT methods, respectively. We evaluated the performance of various composite and DFT methods from the results given in Tables 2 and 3 for gas-phase thermochemical properties. From Tables 2 and 3, it can be seen that all composite and DFT methods estimate GBs and PAs within experimental error bars. However, in the case of DEA, the errors encountered are relatively high. The detailed discussion on the results and errors in gas-phase thermochemical properties is given in Section 5 below. In this work, we have found that the errors obtained from the CBSQB3 method are lower in comparison to those in other methods. Pokon et al.77 have studied various gas-phase deprotonation reactions using the G3, CBS-QB3, and CBSAPNO methods and also concluded that CBS-QB3 is the best choice because of its high accuracy and relatively low computational cost amongst all three methods. Ruusuvuori et al.78 have also concluded in their recent work that the CBSQB3 method is reliable for studying nitrogen-containing bases similar to the amines and alkanolamines that we have in our present study. Therefore, as the CBS-QB3 results were more accurate and relatively cheaper, this method was employed in the pKa calculations in the present work. The optimized structures of gas-phase neutral and protonated amines and alkanolamines obtained in this work at the CBS-QB3 level of theory are given in the Supporting Information (Figures S1 and S2). The free energies of solvation of amines and alkanolamines and their corresponding protonated counterparts, calculated F


Article

The Journal of Physical Chemistry B Table 5. Free Energy of Solvation of Protonated Amines and Alkanolamines Calculated by the ESS Modela protonated amines and alkanolamines (cation)

ΔGsolv (calcd)b

ΔEcluster * c

−TΔScluster * d

ΔGs(A(S)n)e

areaf


−74.3 −62.0 −64.5 −66.4 −63.1 −60.2 −59.1 −57.4 −63.4 −55.7 −59.4 −61.9 −59.1 −56.3 −69.0 −62.2 −56.9 −57.9 −60.8 −71.5 −65.7 −55.3 −57.9 −76.3 −71.1

−36.9 −29.9 −29.1 −35.3 −34.2 −29.7 −26.7 −25.6 −31.1 −24.6 −29.9 −31.0 −25.4 −29.9 −34.0 −31.5 −28.3 −24.5 −26.3 −30.8 −34.5 −23.5 −29.7 −35.3 −28.1

9.0 8.9 7.8 9.6 10.5 9.8 9.5 9.2 9.4 10.2 10.5 9.6 7.7 10.1 9.3 9.3 10.1 9.1 9.0 8.1 10.4 8.2 9.8 8.8 9.0

−58.84 −53.41 −55.52 −53.12 −51.77 −52.70 −54.21 −53.23 −54.16 −53.62 −52.37 −52.81 −53.82 −48.77 −56.63 −52.39 −51.11 −54.83 −55.90 −61.11 −53.97 −52.38 −50.31 −62.18 −64.29

219.81 230.34 221.37 226.76 237.87 242.94 249.35 263.71 228.42 249.37 225.99 232.34 242.62 238.22 261.11 239.33 250.33 267.92 285.40 289.88 253.79 255.99 267.55 175.40 276.26

All values are in kcal/mol. bCalculated free energy of solvation; all values shifted by −2.41 kcal/mol to remove systematic errors relative to experimental values as in the ESS model presented by da Silva et al.51 Estimated sampling standard deviation is 1 kcal/mol. cEnergy of formation of the cluster at the HF/6-31+G(d) level, converted from a standard state of 1 atm to 1 mol/L. Thermal corrections to the energy and zero-point energies not included. dTemperature (298 K) multiplied by the entropy of formation of the cluster at the HF/6-31+G(d) level. eFree energy of solvation of the cluster calculated with the PB continuum model. fArea of clusters calculated with the PB continuum model. a

alkanolamines.61,79−83 The experimental sources from the literature for GBs and PAs of amines and alkanolamines are reported in Tables 2 and 3. The error bars in the GBs and PAs obtained in the present work, using different theoretical models, are plotted in Figure 5. It can be seen from Figure 5 that the differences between experimental and calculated gas-phase thermochemical properties using the B3LYP/6-311++G(d,p) level of theory and Gaussian-n theories are within ±5 kJ/mol. In the case of DEA, the differences are relatively large. DEA and protonated DEA molecules form cyclized lowest-energy conformers in the gas phase and involve hydrogen bonding, as shown in Figures S1 and S2, respectively, in the Supporting Information. The experimental values were determined by Sunner et al.81 using pulsed high ion source pressure mass spectrometry with binary mixtures. The probable reason for the difference between the theoretical and experimental results can be suggested as the possibility of formulation of proton-bridged dimers upon ionization, and the experimental methods do not consider entropy changes combined with cyclization during protonation. A second explanation could be the low volatility of DEA because of the presence of two −OH groups taking part in hydrogen bonding. Similar results were obtained by da Silva et al. in their study of basicity of alkanolamine molecules.84 They concluded that there are uncertainties in the experimental determination of the basicity of alkanolamine molecules because of alkanolamine dimer formation and their low volatility. Thus, the results presented for GBs and PAs of amine and alkanolamine molecules in this work give

protonated amines and alkanolamines, respectively, are shown in Figures 3 and 4. Tables 6 and 7 list the free energy of solvation of neutral and protonated amines and alkanolamines calculated with the ESS method, respectively. Free energies of solvation calculated from the continuum solvation shell models, that is, PCM, SM8T, and DivCon, are also presented in Tables 6 and 7 along with the results of ESS solvation free energies for the molecules studied in the present work. Results given in Tables 6 and 7 provide us with the possibility of a thorough comparison between the values of free energies of solvation obtained from different solvation models and from explicit and implicit solvation models. The results for the pKa determined employing the ESS model and the various implicit solvation models, that is, PCM, SM8T, and DivCon, are presented in Table 8. The respective experimental pKa values at 298 K are also tabulated in this table for estimating the accuracy of each model for the determination of the dissociation constants. For each model, the resulting UMEs in the calculated pKa values against the respective experimental pKa for all amine and alkanolamine molecules are also given in this table.

5. DISCUSSION The GBs and gas-phase PAs for amines and alkanolamines calculated in the present work using various composite and DFT methods are given in Tables 2 and 3 and are compared against experimental results. There exist some studies in the literature for gas-phase thermochemistry of amines and G


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Figure 3. continued

H


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Figure 3. (a), (b) Optimized most stable ESS clusters of protonated amines and alkanolamines obtained in this work. (Dotted lines show hydrogen bonds, and the bond length of hydrogen bonds is given in angstrom.)

(G3MP2, G3MP2B3, G4MP2, and CBS-QB3) and DFT in this work varied by ∼1% or less in terms of relative difference (5 kJ/mol), and different experimental results mostly have a deviation of approximately ∼2% relative to each other.85 In this view, the results for gas-phase thermochemistry presented in this work have errors which are in the range of

benchmark values from computational chemistry for these thermodynamic properties. The results obtained for GB and PA using the calculations based on CBS-QB3 theory have a discrepancy of ±3 kJ/mol relative to the experimental results for most of the molecules. The gas-phase thermochemical properties determined using different Gaussian-n theories I


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Figure 4. continued

J


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Figure 4. (a) (b) Optimized most stable ESS clusters of protonated amines and alkanolamines obtained in this work. (Dotted lines show hydrogen bonds, and the bond length of hydrogen bonds is given in angstrom.)

experimental uncertainties and are regarded as contingent in nature.

The results for free energies of solvation of amines and alkanolamines using the explicit and implicit solvation models K


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The Journal of Physical Chemistry B Table 6. Comparison of Free Energies of Solvation of Amines and Alkanolamines Calculated Using the ESS Model and Implicit Solvation Models (PCM, SM8T, and DivCon)a

Table 7. Comparison of Free Energies of Solvation of Protonated Amines and Alkanolamines Calculated Using the ESS Model and Implicit Solvation Models (PCM, SM8T, and DivCon)a

ΔGsolv (calcd) ESS model

ΔGsolv (calcd)

implicit solvation shell models

amine and alkanolamine (neutral)

ΔGsolv (calcd)b

PCM

SM8T

DivCon


−3.42 −4.01 −5.22 2.38 1.39 −4.43 −3.09 −3.34 −1.04 −5.75 0.04 −1.90 −3.00 0.34 −1.02 0.86 −2.25 −4.79 −3.98 −5.65 −1.19 −2.37 −0.91 −4.29 −5.49

−11.65 −9.28 −10.38 −4.14 −3.03 −6.64 −12.22 −10.46 −8.67 −13.43 −8.44 −12.67 −13.06 −6.17 −9.74 −9.37 −10.25 −11.69 −11.99 −13.82 −10.64 −11.29 −9.79 −4.09 −14.76

−9.144 −8.192 −7.823 −3.294 −2.564 −6.27 −10.011 −9.137 −7.051 −11.255 −6.672 −9.414 −10.061 −4.201 −7.239 −5.4 −8.296 −8.513 −8.599 −9.649 −7.57 −8.055 −7.626 −4.609 −10.483

−6.23 −4.36 −6.14 −2.09 −1.83 −7.28 −6.36 −7.35 −4.32 −5.83 −3.79 −4.01 −4.92 −1.27 −5.8 −3.6 −4.17 −5.26 −5.16 −7.5 −4.42 −4.78 −3.45 −3.11 −9.38

ESS model

a

All values are in kcal/mol. bCalculated free energy of solvation; all values shifted by −2.41 kcal/mol to remove systematic errors relative to experimental values as in the ESS model presented by da Silva et al.51 Estimated sampling standard deviation is 1 kcal/mol.

implicit solvation shell models

protonated amines and alkanolamines (cation)

ΔGsolv (calcd)b

PCM

SM8T

DivCon


−74.33 −62.02 −64.47 −66.40 −63.09 −60.22 −59.07 −57.35 −63.41 −55.69 −59.42 −61.90 −59.12 −56.28 −69.04 −62.21 −56.92 −57.91 −60.82 −71.46 −65.72 −55.28 −57.85 −85.40 −71.07

−76.70 −63.00 −65.81 −65.75 −62.69 −65.64 −61.40 −59.20 −64.67 −62.16 −63.16 −72.7 −71.42 −62.46 −70.62 −69.89 −69.59 −65.81 −68.72 −74.63 −68.39 −68.96 −67.4 −80.35 −75.35

−81.94 −65.99 −67.89 −73.79 −71.29 −66.26 −63.07 −61.69 −68.18 −59.74 −63.43 −70.21 −67.52 −63.35 −76.54 −68.52 −66.76 −65.67 −68.31 −69.66 −68.02 −65.15 −65.11 −92.30 −78.26

−77.66 −66.01 −68.2 −71.36 −69.32 −63.98 −62.64 −61.43 −67.47 −57.81 −61.92 −65.69 −63.44 −60.36 −73.91 −65.46 −62.35 −62.93 −64.8 −75.55 −72.39 −59.84 −61.43 −88.17 −77.24

a

All values are in kcal/mol. bCalculated free energy of solvation; all values shifted by −2.41 kcal/mol to remove systematic errors relative to experimental values as in the ESS model presented by da Silva et al.51 Estimated sampling standard deviation is 1 kcal/mol.

are presented in Tables 6 and 7. Examining the results, we can say that ESS solvation free energies for neutral amines and alkanolamine molecules are overestimated in comparison to those from continuum solvation models. This is also true for protonated amine and alkanolamine molecules, but the difference between the ESS and continuum solvation models for solvation free energy is relatively small. The ESS model has been developed to study accurately the solvation free energy of ionic molecules, so solvation free energies predicted by ESS for protonated amines and alkanolamines are considered to be more reliable compared to those by continuum solvation models. Absolute and relative errors in pKa values obtained from the explicit and implicit solvation models studied in the present work, for the data set of 25 amines and alkanolamines, are shown in Tables 9 and S5, respectively. The difference between the calculated pKa values and the corresponding experimental pKa values is referred to as absolute error, whereas relative error corresponds to the error given by primarily adding a signed mean error (SME) for each model to its calculated pKa value and later subtracting the calculated pKa value from the corresponding experimental pKa value. SME, UME, and RMSEs for the present data set of molecules are listed in Table 9. On comparison of errors

resulting from pKa determinations employing the ESS model and continuum solvation models (PCM, SM8T, and DivCon), the better accuracy observed in pKa calculations from the EES model over that from implicit models is clearly observed. The UME of 0.99 pKa units for ESS against 2.70, 1.65, and 1.05 pKa units for PCM, SM8T, and DivCon, respectively, reassures that the ESS model provides significantly better results for pKa calculations compared to the pKa calculations from implicit solvation models. Furthermore, as the ESS model has no parametrization for molecules in the present data set, the absolute RMSE of 1.26 pKa units obtained from the ESS pKa calculations becomes very encouraging. Based on the present study, the performance of the ESS model for the determination of solvation free energy of ions and dissociation constants is found to be satisfactory. The computational calculation of pKa is very demanding, and an error of 1.36 kcal/mol in the deprotonation reaction would introduce an error of 1 pKa unit.46,47 This error can be minimized on the basis of the choice of thermodynamic cycle and methods used for gas-phase and aqueous-phase calculations. The main error in pKa calculations comes from solvation free energies, as continuum models are parametrized to experimental free energy of solvation for ions, which have error bars of L


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Table 8. Comparison of pKa Calculated from the ESS Model and Implicit Solvation Shell Models with the Experimental pKa at 298 K pKa at 298 K

a

UME

amine and alkanolamines

expa

ESS

PCM

SM8T

DivCon

ESS

PCM

SM8T

DivCon

MEA 3-AP EDA PA 2-MPA AMP AMPD AEPD 2-AP DEA MMEA MOR PZ PIP MAPA TMOR 1-methylPZ 4-PIPM 4-PIPE AEP DMEDA 2-methylPZ 1-ethylPZ NH3 DETA average error

9.50 9.96 9.93 10.60 10.50 9.72 8.80 8.80 9.40 8.96 9.77 8.33 9.83 11.12 9.89 8.70 9.14 10.56 10.62 9.48 10.03 9.57 9.20 9.24 9.94

10.51 9.71 9.97 12.38 9.85 9.68 9.00 8.72 9.75 8.67 10.74 6.63 8.16 9.66 11.83 9.73 7.05 7.99 9.22 9.40 8.90 7.14 8.88 9.61 9.03

6.19 6.56 7.15 7.10 6.31 12.04 3.99 4.84 5.07 7.78 7.25 6.66 9.81 9.41 6.58 7.85 10.48 8.72 9.14 5.72 3.91 10.64 9.38 6.04 5.36

11.89 9.56 10.57 13.64 12.98 12.77 6.85 7.64 8.84 7.60 8.76 7.22 9.14 11.52 12.77 9.76 9.84 10.96 11.34 5.13 5.89 10.21 9.29 14.45 10.65

10.89 12.39 12.03 12.74 12.07 10.35 9.22 8.77 10.33 10.17 9.76 7.87 9.93 11.48 11.90 8.84 9.63 11.34 11.28 11.05 11.43 8.72 9.65 12.52 10.71

1.01 0.25 0.04 1.78 0.65 0.04 0.20 0.08 0.35 0.29 0.97 1.70 1.67 1.46 1.94 1.03 2.09 2.57 1.40 0.08 1.13 2.43 0.32 0.37 0.91 0.99

3.31 3.40 2.78 3.50 4.19 2.32 4.81 3.96 4.33 1.18 2.52 1.67 0.02 1.71 3.31 0.85 1.34 1.84 1.48 3.76 6.12 1.07 0.18 3.20 4.58 2.70

2.39 0.40 0.63 3.04 2.48 3.05 1.95 1.16 0.56 1.36 1.01 1.11 0.69 0.40 2.88 1.06 0.70 0.40 0.72 4.35 4.14 0.64 0.09 5.21 0.71 1.65

1.39 2.43 2.10 2.14 1.57 0.63 0.42 0.03 0.93 1.21 0.01 0.46 0.10 0.36 2.01 0.14 0.49 0.78 0.66 1.57 1.40 0.85 0.45 3.27 0.77 1.05

Experimental data from Perrin 196592 and Perrin 1972.92

approximately 2−5 kcal/mol.58 On the other hand, explicit solvation methods take specific solute−solvent interactions into consideration and do not include uncertainty due to experimental errors.86 Pliego et al.,69 in a similar work involving calculation of pKa using explicit and implicit solvation models, have obtained an RMSE of 2.2 pKa units with an explicit model compared to that of 7 pKa units using implicit solvation models. In other words, we can say that in the challenging realm of calculating computational pKa, the present results can be helpful in the initial screening of PCC solvents and in identifying promising PCC solvents, which are not yet available or are very expensive. In the literature, many references are found for a DFTbased explicit solvent approach for pKa calculation.87−90 The transferability to heterogeneous redox reactions at electrochemical interfaces is a main advantage of the DFT-based molecular dynamics (DFTMD) method. However, the huge computational cost of the DFTMD method imposes a serious drawback. Cluster−continuum or quantum mechanics/molecular mechanics methods are relatively cheaper for computations of pKa and redox free energies.88 DFTMD and cluster−continuum methods are comparable in terms of errors observed in the calculation of pKa. Mangold et al.87 in their DFTMD simulation study containing six amino acids report a UME of 2.1 pKa units with a maximum error of 4.0 pKa units. In DFTMD, approximations in DFT can be the main source of error in the results, and these calculations also have limitations of time scales and model system size. The explicit solvation model used in the present work gives very encouraging results for pKa’s of amines and

alkanolamines and provides the possibility of substantially cheaper calculations than DFTMD.

6. CONCLUSIONS The comprehensive study of the gas-phase thermochemical properties of the 25 molecules shows that the calculated gaseous-phase PA and basicity computational results are within experimental error bars and could serve as benchmark results for the molecules for which experimental results are not available or are difficult to obtain. The calculated GBs and PAs provide reliable thermochemical results for the molecules and could be employed for evaluating the consistency within various experimental sources reported in the NIST database.91 However, poor agreement between experimental and calculated GB and PA for DEA is observed, and in this case, the experimental results are suggested to be more uncertain than computational results. As experimental determination of solvation free energies is challenging, the results for solvation free energy for protonated amines and alkanolamines could help as guiding values for future advances in this demanding domain of computational chemistry. The better performance and lower RMSE for the ESS model compared to those of various implicit models for the calculation of pKa are reported in the present work. Hence, the explicit solvation model provides a potential approach for calculating solvation energies of ions and thermochemical properties with relatively high degree of accuracy. M


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Figure 5. Plots of GB differences (ΔGB = GBexp − GBcalcd) and gas-phase PA differences (ΔPA = PAexp − PAcalcd) of G3MP2B3, G3MP2, G4MP2, CBS-QB3, and DFT (B3LYP/6-311++G(d,p)) in kJ/mol for the amines and alkanolamines studied in this work.

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Table 9. Comparison of Absolute Errors for pKa from the ESS Model and Continuum Solvation Models (PCM, SM8T, and DivCon)a

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcb.6b04049. Constant terms utilized in calculations for the ESS model. Underlying data for Tables 4 and 5, energy of the solute and cluster in gas phase, thermal corrections to the energy and entropy of the solute and cluster. Optimized structures of gas-phase neutral and protonated amines and alkanolamines studied in the present work at the CBS-QB3 level of theory. Simulation

Absolute Errors errors

ESS

PCM

SM8T

DivCon

SME UME RMSE

0.38 0.99 1.26

2.30 2.70 3.10

−0.31 1.65 2.15

−0.94 1.05 1.33

ASSOCIATED CONTENT

S Supporting Information *

a

Different errors are abbreviated as SME (signed mean error), UME (unsigned mean error), and root-mean-square error (RMSE). N


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details. Comparison of relative errors for pKa from the ESS model and continuum solvation models (PCM, SM8T, and DivCon). All of the optimized xyz Cartesian coordinates in angstroms for the minima of neutral and protonated amines and alkanolamines used in the text. Quantitative details of the optimized structures of the first solvation shell from molecular simulations for a set of 100 initial geometries of MEA (PDF)

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +47 47616959. Fax: +47 73594080. Present Address §

Shell Technology, The Netherlands. E-mail: Eirik.daSilva@ shell.com. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The work is done under the SOLVit SP4 project, performed under the strategic Norwegian research program CLIMIT. The authors acknowledge the partners in SOLVit Phase 3, Aker Solutions, Gassnova, EnBW and the Research Council of Norway for their support.

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