Prediction of the p K a Values of Amines Using ab Initio Methods and

Comparison of Quantum Mechanical and Experimental Gas-Phase Basicities of Amines and Alcohols. Eirik F. da Silva. The Journal of Physical Chemistry A ...
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Ind. Eng. Chem. Res. 2003, 42, 4414-4421

RESEARCH NOTES Prediction of the pKa Values of Amines Using ab Initio Methods and Free-Energy Perturbations Eirik F. da Silva* and Hallvard F. Svendsen Department of Chemical Engineering, Norwegian University of Science and Technology, N-7491 Trondheim, Norway

A computational study has been performed on predicting the pKa values for amines and alkanolamines used in CO2 absorption processes. Gas-phase energies were calculated using common basis sets at Hartree-Fock (HF), MP2, and B3LYP levels. Free energies of solvation were calculated using continuum models and Monte Carlo free-energy perturbations. Results are compared with experimental pKa data. While the continuum methods could reproduce trends between similar molecules, they failed to predict the overall trends for series involving amines with different numbers of amine-group hydrogens and different numbers of intramolecular hydrogen bonds. Considerably better results were obtained using free-energy perturbations. On the basis of calculations of molecular vibrations, good estimates were also achieved for changes of pKa with temperature. Introduction As a measure for preventing global warming, there is a steadily increasing interest in methods for removing carbon dioxide from exhaust gases as well as natural gas and refinery gases. Traditionally, absorption with alkanolamines in mixtures with promoters has been used for this purpose. For high-pressure applications, N-methyldiethanolamine (MDEA)-based systems have been used successfully for many years. For exhaust gases, the most common amine has been ethanolamine (MEA). However, high energy demand for regeneration and high degradation rates makes this an undesirable amine to use for large fossil fuel power plants. During the last years, new systems such as the PSR1-31 and KS1-32 have been developed and promise improved performance compared to the conventional MEA. The interactions between amino compounds and CO2 have been studied extensively using both experimental and theoretical methods.3 For both CO2 reaction rate and absorption capacity, the pKa values of the conjugate acids of the alkanolamines applied are important variables.4 Reasonable prediction of pKa values would therefore be of great value when screening for new candidate compounds for exhaust gas CO2 removal. A lot of work has been done in computational chemistry on the prediction of pKa. While this is considered to be a difficult task, works have been published that show good results for some sets of compounds.5,6 The general applicability of these methods would, however, still seem to be uncertain. The intention of this work is to explore the application of these models to the kinds of molecules used for CO2 recovery. * To whom correspondence should be addressed. Tel.: +47 73594125. Fax: +47 73594080. E-mail: [email protected].

Several studies have been published on the basicity of methylamines.7-9 While these molecules are not directly relevant to the CO2 absorption process, they clearly represent a closely related modeling task. Inclusion of these molecules in this work allows a more general validation of the models being used. Methods The dissociation of the conjugate base of the amine can be written as

BH+ + H2O h B + H3O+

(1)

When the mole fraction based activity of water is assumed to be 1 and H3O+ is written as H+, the following equilibrium constant is obtained:

Ka ) aBaH+/aBH+

(2)

The definition of pKa is

pKa ) -log Ka

(3)

The free energy of protonation in an aqueous solution (∆Gps) is related to Ka by the following equation:

∆Gps ) -2.303RT log Ka

(4)

This gives us the relation between pKa and ∆Gps.

pKa )

1 ∆Gps 2.303RT

(5)

Model predictions for ∆Gps should therefore give a linear correlation with the pKa.

10.1021/ie020808n CCC: $25.00 © 2003 American Chemical Society Published on Web 08/23/2003

Ind. Eng. Chem. Res., Vol. 42, No. 19, 2003 4415

The general approach to calculating ∆Gps is to use a thermodynamic cycle such as8

The focus of this work is to reproduce trends in pKa. The energy of the proton (H+) itself is constant for all amines. It is therefore not relevant in this context and not included in the present calculations. On the basis of the thermodynamic cycle, ∆Gps can be divided into two contributions:

∆Gps ) ∆Gpg + ∆Gs

(6)

∆Gpg ) Gg(B) - Gg(BH+)

(7)

∆Gs ) ∆Gs(B) - ∆Gs(BH+)

(8)

where ∆Gpg is

and

While the gas-phase protonation energy and the free energy of solvation are expected to be the main contributors to the overall solvent-phase reaction energy, thermal and zero-point energy (ZPE) corrections are also included. Computational Aspects For the modeling of gas-phase protonation energies, standard ab initio calculations have been used. Geometry optimizations were performed using a series of common methods and basis sets: HF/3-21G*, MP2/631G*, B3LYP/3-21G*, and B3LYP/6-311++G**. All MP2 and B3LYP calculations were done using Gaussian 98.10 The thermal corrections to the free energy, the ZPEs, and the entropies were all calculated at the HF/3-21G* level. These contributions are relatively small and are not expected to change significantly with the level of modeling. To be consistent with how the gas-phase energy is calculated, the ZPE and thermal corrections are calculated as the same relative difference as that used for the protonation energy itself (eq 7). These calculations were also done using Gaussian 98. Molecular mechanics (MMFF) was used to generate an initial set of conformers. All conformers were then optimized at the HF/3-21G* level. Separate conformer searches were done for the amines and their protonated forms. The effect of the solvation models on the relative conformer stability was explored for some of the main conformers. All calculations in this work were performed on the same set of conformers. Gas-phase conformer search calculations were done with the Spartan program.12 For the calculation of solvation energies, several models are available. The continuum models such as the PCM models are probably the most common ones,13 but there are questions regarding their general applicability. Of particular importance is their failure to

explicitly include hydrogen bonding.7,9 SM continuum models have also been tested in this work. Calculations based on the explicit representation of the solvent using free-energy perturbation (FEP) simulations have also been performed. A wide variety of PCM models are available, and results have been published using a number of different basis sets. There would, however, not seem to be any clear guidelines as to whether some specific level of calculation would be more appropriate or, in general, more reliable. In this work, the IEFPCM model13 has been chosen and all calculations were performed using its default settings in Gaussian 98 with 60 tesserea per atomic sphere. These calculations will simply be referred to as PCM calculations. Most calculations were done as single-point energy calculations on gas-phase geometry. Solvent-phase geometry optimizations with the PCM models have also been performed. While the geometries did change slightly using solvent-phase optimization, the energy changes were relatively small. For larger basis sets, it was also found that solvent-phase optimization resulted in some convergence problems in the calculations. One set of results using solvent-phase geometry optimization has been included in the Results and Discussion section. The solvent-phase protonation energies (∆Gps) based on continuum models presented in the Results and Discussion section were calculated with the solvation energy calculated on the same geometry as that used to obtain the gas-phase energy. The B3LYP/6-311++G** gas-phase results were, however, added together with PCM results calculated at the B3LYP/3-21G* level. While the qualitative issues regarding gas-phase models and basis sets are fairly well understood, the solvation models are, in general, semiempirical, and it is not clear how their performance changes with the level of geometry optimization. In general, it would therefore seem best to consider solvation energy calculation and gasphase energy calculation as separate processes. While they should be calculated on the same conformer, it is not given that they should be calculated at the same level of geometry optimization. The SM models are a series of semiempirical models to calculate the free energy of solvation. The SM5.4A11 model is parametrized to work with AM1 geometries. In this work, this model has been used to calculate solvation energies using AM1 geometries in the Spartan program. In addition, SM5.42R/HF/6-31G* calculations were performed with Gamesol 3.1.15 Simulations As an alternative to the implicit solvent models (PCM and SM), classical Monte Carlo calculations were performed. Wiberg et al.16 have obtained good results combining gas-phase ab initio calculations with Monte Carlo calculations of the solvation energy to obtain free energy in solvation. In the present work a similar procedure has been adopted. Wiberg et al.16 used perturbations between the neutral forms of the molecules and between the ionic forms of the molecules; i.e., they only performed perturbations between molecules with the same charge. The molecules in the present work do, however, vary considerably in size and structure, making perturbations between them difficult. Instead, the FEP calculations were done by perturbating the protonated form of the amine to the amine itself,

4416 Ind. Eng. Chem. Res., Vol. 42, No. 19, 2003 Table 1. Experimental pKa Data no.

compd

name

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

NH3 NH2(CH3) NH(CH3)2 N(CH3)3 ethanolamine 1-amino-2-propanol 3-amino-1-propanol 2-amino-2-methylpropanol N-(2-hydroxyethyl)ethylenediamine diethanolamine diisopropanolamine morpholine diethylenediamine N-n-butylethanolamine N-methyldiethanolamine triethanolamine

typea

hydrogen bondsb

exptl pKa at 25 °C

ref

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

0 0 0 0 1 1 1 1 1 2 2 0 0 1 2 2

9.3 10.657 10.732 9.9 9.51 9.47 9.96 9.7 9.82c 8.95 8.89 8.7 9.83c 9.9 8.63 7.78

20 21 21 20 21 21 21 21 21 21 21 22 21 23 21 21

MEA MIPA MPA AMP AEEA DEA DIPA piperazine BEA MDEA TEA

a p: primary amine. s: secondary amine. t: tertiary amine. c: cyclical amine. b Number of intramolecular hydrogen bonds for the protonated form of the amine. c The first protonation constant.

Table 2. Gas-Phase Protonation Energies (All Results in kcal/mol) B3LYP/3-21G*

b

MP2/6-31G*

B3LYP/6-311++G**

compd

∆Gpga

rel ∆Gpg

∆Gpga

rel ∆Gpg

∆Gpga

rel ∆Gpg

rel ∆GExptlb

NH3 NH2(CH3) NH(CH3)2 N(CH3)3

229.89 236.08 241.26 244.80

0.00 6.19 11.38 14.92

217.17 225.64 232.29 236.42

0.00 8.47 15.12 19.25

211.87 221.55 229.29 234.23

0.00 9.69 17.43 22.37

0.00 10.87 18.52 23.69

a Thermal correction and ZPE calculated at the HF/3-21G* level included the value relative to that of NH (-9.38 kcal/mol). 3 Experimental data from Hunter and Lias.24

giving the relative difference in free energy of solvation (∆Gs) directly. These calculations were done with BOSS version 4.117 using procedures developed by Rizzo and Jorgensen.9 A single solute molecule was placed in a periodic cube with 267 TIP4P water molecules at 25 °C and 1 atm in the NPT ensemble. Periodic boundary conditions were applied. A number of water molecules corresponding to the number (n) of non-hydrogen atoms in the amine molecule were removed, giving 267 - n water molecules. The perturbations were carried out over five windows of double-wide sampling, giving 10 free-energy increments that are summed up to give the total change in free energy of solvation. Each window had 500 000 steps for equilibration and another 500 000 for sampling. Wiberg et al.16 used solution-phase B3P86/6-311+G** geometries. In the present work, similar solution-phase B3LYP/6-311++G** geometries (optimized with PCM) were used. The same conformers as those for the continuum calculations were used, and simulations were performed using rigid geometries. The intermolecular interactions between two molecules a and b were evaluated using Coulomb and Lennard-Jones terms: on aon b

∆Eab )

∑i ∑j

{

qiqje2 rij

[( ) ( ) ]}

+ 4ij

σij rij

12

-

σij rij

6

(9)

The Lennard-Jones σ and  were taken from the OPLSAll atom force field.17 Wiberg et al.16 calculated atomic charges in the gasphase and scaled these by a factor of 1.2 to obtain values appropriate for solution. In the present work, methods were chosen that directly give solution-phase atomic charges. Two different methods were tested for calculating the charges. One was the CM2 model18 found in Gamesol, while the other method used was the MerzKollmann (MK) scheme19 available in Gaussian. Both

models were used on HF/6-31G* gas-phase geometries and basis sets. For the CM2 scheme, calculations were done with the SM5.42R solvent field, while for the MK scheme, the PCM solvent field was used. It should be noted that these simulations have a statistical uncertainty, unlike the continuum models that are deterministic. On the basis of the batch means procedure available in BOSS, the statistical uncertainties were estimated to be on the order of (2 kcal/mol. This uncertainty is something that must be kept in mind when comparing results obtained by FEP and continuum models. Results and Discussion In Table 1 are shown the amines used in this study, and in the table, it is indicated whether the amines are primary (p), secondary (s), tertiary (t), or cyclic (c). Experimental pKa values at 25 °C are also shown. The quality of the experimental data would seem to vary somewhat. For some molecules, different experimental results are available and variations between these suggest uncertainties in the order of (0.1 pKa unit. The series NH3, NH2CH3, NH(CH3)2, and N(CH3)3 has been the subject of several previous studies.7-9 In Table 2, the gas-phase reaction energies for these molecules are shown together with experimental values. The B3LYP/6-311++G** results in particular are in good agreement with the experimental data. Solvation energies calculated using both continuum models and FEPs are shown in Table 3. There is reasonable qualitative agreement between both the gasphase energies and the solvation energies for all of the sets of results. In Table 4 are shown relative free energies of protonation in the solvent (∆Gps). The experimental data are based on eq 5 and data from Table 1. The errors in the prediction of the solvent-phase protonation energy are larger than the errors in the gas-

Ind. Eng. Chem. Res., Vol. 42, No. 19, 2003 4417

For the neutral amines, the most stable conformers were also found to have different forms of hydrogen bonding. Hydrogen-bonded gauche-MEA was, for example, found to be 4 kcal/mol more stable than the trans conformer (at the HF/3-21G* level). These conformer searches have been based on gasphase calculations. The intramolecular hydrogen bonds found to dominate in the gas phase will in the solvent compete with hydrogen bonding to water molecules. The calculations done with solvent models (PCM and SM5.4A) do, however, suggest that these intramolecular hydrogen bonds are favored even in the solvent, particularly for the protonated forms of the amines. Molecules 9-11 and 14-16 have many free dihedral angles and have many potential conformers. For these molecules in particular, we see that the most stable conformer can change with the level of modeling; the energy differences between the conformers are, however, expected to be relatively small because the effects of intermolecular hydrogen bonds and intramolecular hydrogen bonds cancel out. In Table 5, gas-phase energies for molecules 5-16 are shown together with experimental values. The results from the different calculations are in reasonable qualitative agreement. When compared with the experimental energies, the B3LYP/6-311++G** results are in good quantitative agreement for 3-amino-1-propanol (MPA), morpholine, and piperazine. For DEA, the protonation energies are, however, overestimated by 4 kcal/mol, suggesting that the strength of the intramolecular hydrogen bonds for the protonated form of the molecule are overestimated. For MEA, all models show too low protonation energy, suggesting that the strength of the hydrogen bond of the protonated form of the molecule in this case is underestimated. The uncertainty in the estimation of the hydrogen bond strength was also seen in the optimized geometries: BEA had an intramolecular hydrogen bond [H(O)-N] varying between 2.0 Å (B3LYP/3-21G*) and 2.3 Å (B3LYP/6-311++G**). No direct correlation was found between the gasphase protonation energy (∆Gpg) and the pKa, and this strongly suggests that the solvation energy is crucial for predicting the relative pKa for these compounds. In Table 6, the free energies of solvation calculated with various models are shown. The different PCM results can be seen to be quite similar; in particular, it can be seen that the effect of solvent-phase optimization is small. The FEP results are, however, quite different; while they show some qualitative agreement with the PCM results, the relative differences between the various molecules is much larger than those calculated with PCM. Table 7 shows calculated and experimental solventphase protonation energies. Experimental data are based on eq 5 and data in Table 1. The overall quality of the results with continuum models is quite disap-

Table 3. Solvation Energies (All Results in kcal/mol) compd

PCM/MP2a PCM/B3Lb PCM/B3Lsc FEP-CM2 FEP-MK

NH3 NH2(CH3) NH(CH3)2 N(CH3)3

75.6 65.7 61.5 56.8

76.1 65.9 60.9 56.0

76.0 66.0 61.3 56.2

76.4 67.1 58.1 50.6

74.1 61.7 60.2 55.4

a PCM/MP2/6-31G*//MP2/6-31G*. b PCM/B3LYP/3-21G*//B3LYP/ 3-21G*. c Optimization in solution: PCM/B3LYP/3-21G*//PCM/ B3LYP/3-21G*.

phase energies, suggesting that the solvation energies are not completely accurate. We would argue that this series of four molecules is too small to draw any firm conclusion as to the applicability of any single model. The energy differences that one is attempting to reproduce are also relatively small. The FEP calculations used have an uncertainty that is too large ((2 kcal/mol) to draw conclusions for this small series. Gas-phase conformer searches were done at the HF/ 3-21G* level and calculations on some of the more stable conformers were also done with the other models used. For the unprotonated forms of diisopropanolamine (DIPA), diethanolamine (DEA), MDEA, and N-n-butylethanolamine (BEA), the most stable conformers did change with the level of modeling. In these cases, the most stable conformers found at higher level have been used. The most stable conformers for molecules 5-16 are shown in Figure 1. The protonated forms of the amines were found to have a strong tendency to form hydrogen bonds between amine hydrogens and oxygen atoms on the alcohol groups. For MDEA, the most stable conformer without hydrogen bonds was 5 kcal/mol less stable than the most stable hydrogen-bonded conformer (at the HF/3-21G* level). For some of the smaller molecules such as MEA, only a hydrogen-bonded conformer was found. In Table 1, the number of such bonds found for each amine in the protonated form is indicated. On the basis of the results of the conformer searches, a general qualitative explanation for the trends seen in the experimental pKa data can be suggested. The alcohol groups in the molecules are electron-withdrawing, destabilizing the protonated form of the amine. This effect is mitigated by the alcohol groups forming hydrogen bonds to the amine protons. Most of the alkanolamines therefore have pKa values slightly lower than those of methylamines of the same order. Morpholine has an electron-withdrawing oxygen but cannot form hydrogen bonds and has therefore a relatively low pKa. Triethanolamine (TEA) has three ethanol groups that together have a strong electron-withdrawing effect. In the protonated form, there is, however, only one amine proton that these groups can bond with, limiting the stabilizing effect of the hydrogen bonding. One might think of the hydrogen-bonding effect as reaching a form of saturation, giving a significant drop in the pKa.

Table 4. Relative Solvent-Phase Protonation Energies (All Results in kcal/mol) gas-phasea MP2/6-31G*

B3LYP/6-311++G**

compd

PCM/MP2b

FEP-CM2

FEP-MK

PCM/B3Lc

FEP-CM2

FEP-MK

exptl

NH3 NH2(CH3) NH(CH3)2 N(CH3)3

0.00 -1.47 1.07 0.44

0.00 -0.77 -3.15 -6.49

0.00 -4.00 1.21 0.55

0.00 -0.53 2.14 2.21

0.00 0.44 -0.84 -3.37

0.00 -2.78 3.52 3.67

0.00 1.85 1.95 0.82

a Thermal correction and ZPE calculated at the HF/3-21G* level included the value relative to that of NH (-9.38 kcal/mol). b PCM/ 3 MP2/6-31G*//MP2/6-31G*. c PCM/B3LYP/3-21G*//B3LYP/3-21G*.

4418 Ind. Eng. Chem. Res., Vol. 42, No. 19, 2003

Figure 1. Conformers of molecules 5-16. Table 5. Gas-Phase Protonation Energies (All Results in kcal/mol) B3LYP/3-21G*

b

MP2/6-31G*

B3LYP/6-311++G**

no.

compd

∆Gpga

rel ∆Gpg

∆Gpga

rel ∆Gpg

∆Gpga

rel ∆Gpg

rel ∆Gexptlb

5 6 7 8 9 10 11 12 13 14 15 16

MEA MIPA MPA AMP AEEA DEA DIPA morpholine piperazine BEA MDEA TEA

245.43 247.30 254.02 254.33 264.68 256.53 257.50 240.69 247.71 252.90 257.85 243.54

15.55 17.41 24.14 24.45 34.80 26.65 27.62 10.80 17.83 23.01 27.96 13.65

231.96 233.42 238.44 239.02 246.83 246.73 245.48 231.23 237.71 241.45 249.06 241.89

14.79 16.25 21.27 21.85 29.67 29.56 28.31 14.07 20.54 24.28 31.89 24.72

227.55 229.27 234.96 234.56 240.43 240.25 243.17 228.52 234.76 238.98 243.61 244.92

15.69 17.40 23.09 22.69 28.56 28.39 31.31 16.65 22.89 27.11 31.74 33.05

18.59 23.49 24.14 17.26 22.87

a Thermal correction and ZPE calculated at the HF/3-21G* level included the value relative to that of NH (-9.38 kcal/mol). 3 Experimental data from Hunter and Lias.24

pointing. At the B3LYP/6-311++G** level, one can, for example, see that the molecule with the lowest experi-

mental value (TEA) in the data set has the highest value in the calculated results.

Ind. Eng. Chem. Res., Vol. 42, No. 19, 2003 4419 Table 6. Solvation Energies (All Results in kcal/mol) PCM/MP2a PCM/B3Lb PCM/B3Lsc FEP-CM2

no.

compd

5 6 7 8 9 10 11 12 13 14 15 16

MEA MIPA MPA AMP AEEA DEA DIPA morpholine piperazine BEA MDEA TEA

60.5 59.3 55.5 53.8 52.1 51.4 49.0 63.0 59.8 53.6 47.6 51.0

58.2 56.4 51.5 51.7 48.2 47.9 46.7 62.1 58.0 51.2 46.9 49.9

58.9 57.4 52.2 52.3 50.0 49.8 47.5 62.7 58.1 52.3 47.8 50.2

56.7 60.1 57.9 54.7 44.9 43.1 42.4 54.7 50.3 47.4 38.1 36.6

a PCM/MP2/6-31G*//MP2/6-31G*. b PCM/B3LYP/3-21G*//B3LYP/ 3-21G*. c Optimization in solution: PCM/B3LYP/3-21G*//PCM/ B3LYP/3-21G*.

As noted previously, this data set contains molecules with very differing bonding. Given the uncertainty in the estimation of hydrogen bonds already noted and the uncertainty regarding the PCM model’s ability to account for hydrogen bonding with the solvent, it is of interest to look at how the models perform in predicting the relative pKa values of molecules with similar hydrogen bonding. To have similar bonding, the molecules must have the same number of hydrogens on the nitrogen and the same number of intramolecular hydrogen bonds. All of the primary alkanolamines (molecules 5-8) have such a similarity, and so do the two cyclic molecules (12 and 13) and DEA and DIPA (molecules 10 and 11). These groups are marked in Table 7. The other PCM results are also reasonably good. The order between piperazine and morpholine is also predicted correctly by all models. For the order between DEA and DIPA, all of the models are wrong; the B3LYP/6-311++G** results are, for example, off by about 2 kcal/mol. Calculations with the SM continuum models, in general, gave results similar to those obtained with the PCM model. Using FEP solvation energies gave a better overall trend in the results. For the full set of 16 molecules, the FEP-CM2 results in combination with MP2/6-31G* gas-phase energies gave an overall correlation coefficient of 0.45; in combination with B3LYP/6-311++G** energies, a correlation coefficient of 0.42 was obtained. In Figure 2, this FEP set of results is shown together with the best set of results for the PCM model. The same gas-phase energy (MP2/6-31G*) together with the PCM

Figure 2. Calculated protonation energies in solution versus experimental pKa values.

solvation energy gave no overall correlation. In Table 7, however, it can be seen that the results with FEP solvation energies have larger relative differences than those seen in the experimental data set. While the B3LYP/6-311++G** gas-phase energies, in general, seem to be fairly accurate, there is an uncertainty in the estimation of the strength of intramolecular hydrogen bonds. Given the uncertainty in the gasphase energies, we cannot draw any firm conclusions as to the performance of the models used to calculate the solvation energies. The present work does, however, suggest that FEP simulations are a promising tool for the solvation energy calculations for these alkanolamines. More accurate free-energy calculations will, however, be needed to better assess the performance of these simulations. Temperature Effects Ab initio calculations can be used to calculate the molecular vibration frequencies and thereby obtain gasphase entropies. With an estimate of the entropy, the temperature changes in the pKa can be predicted by using the following equation:25

-d(pKa)/dT ) (pKa + 0.052∆S0)/T

(10)

In this work the vibration frequency calculations were

Table 7. Relative Solvent-Phase Protonation Energies (All Results in kcal/mol) gas-phasea B3LYP/3-21G*

MP2/6-31G*

B3LYP/6-311++G**

no.

compd

PCM/B3Lb

FEP-CM2

PCM/MP2c

FEP-CM2

PCM/B3Lc

FEP-CM2

exptl

5 6 7 8 9 10 11 12 13 14 15 16

MEA MIPA MPA AMP AEEA DEA DIPA morpholine piperazine BEA MDEA TEA

-2.76 -2.53 -0.72 -0.87 5.51 0.11 1.64 -3.63 -1.00 -1.67 -0.06 -9.98

-4.44 0.91 5.48 1.84 1.97 -4.87 -2.92 -11.29 -8.89 -5.68 -9.06 -23.50

-0.67 -0.28 0.97 -0.86 4.75 2.52 2.73 1.04 4.10 2.32 1.77 2.74

-5.20 -0.25 2.62 -0.76 -3.16 -6.49 -4.61 -8.03 -6.18 -4.60 -8.42 -12.43

4.25 -2.30 -1.58 -1.74 0.63 0.14 1.90 2.64 4.71 2.16 3.87 6.80

2.57 1.14 4.62 0.98 -2.91 -4.84 -2.66 -5.02 -3.18 -1.86 -5.13 -6.72

0.27 0.22 0.90 0.57 0.71 -0.46 -0.56 -0.82 0.72 0.82 -1.06 -2.10

a Thermal correction and ZPE calculated at the HF/3-21G* level included the value relative to that of NH (-9.38 kcal/mol). b PCM/ 3 B3LYP/3-21G*//B3LYP/3-21G*. c PCM/MP2/6-31G*//MP2/6-31G*.

4420 Ind. Eng. Chem. Res., Vol. 42, No. 19, 2003 Table 8. Experimental pKa Data and Calculated Entropies (Data Given in cal/mol)

a

compd

exptl pKa(20 °C)a

exptl pKa(60 °C)a

∆S(20 °C)b

∆S(60 °C)b

MDEA DMMEA [2-(dimethylamino)ethanol] DGA [2-(2-aminoethoxy)ethanol] DEMEA [2-(diethylamino)ethanol] AMP MMEA [2-(methylamino)ethanol] DIPMEA [2-(diisopropylamino)ethanol] TBAE [2-(tert-butylamino)ethanol]

8.76 9.23 9.62 9.76 9.88 9.95 10.14 10.29

7.99 8.36 8.60 8.71 8.78 8.94 9.13 9.28

-3.156 -0.593 1.046 0.336 0.844 -0.416 0.330 -0.429

-4.045 -0.699 0.961 0.247 0.07 -0.501 0.269 -0.521

Experimental data from Littel et al.26

b

Reaction entropies calculated at the HF/3-21G* level.

number of amine hydrogens and the same number of intramolecular hydrogen bonds. The full set of amines was, however, not successfully modeled with any of the continuum models tested. Reasonable results were obtained using FEPs to calculate the solvation energy. It was also found that gas-phase entropy change calculations could be used to expand the data to temperatures other than those experimentally available. We propose that the differences in temperature dependency of different amines can be attributed to differences in intramolecular hydrogen bonding. Literature Cited

Figure 3. Plot of experimental versus calculated pKa values at 60 °C.

done at the HF/3-21G* level at 20 and 60 °C using the Gaussian program. The same conformer search routine as that described previously was used for these alkanolamines. To get a reasonable estimate of the total entropy, we calculated the entropy of reaction given by eq 1 including the values for H2O and H3O+. Calculated entropies together with the experimental pKa values used are given in Table 8. The entropies were assumed to vary linearly with temperature, and eq 10 was solved numerically, doing a stepwise calculation from 20 to 60 °C. Figure 3 shows these estimated values at 60 °C plotted against experimental pKa values at 60 °C. While the agreement is very good, it should be noted that using eq 10 even without the entropy contribution also gives good results. The entropy term does, however, improve the correlation. We believe that molecules that depend on intramolecular hydrogen bonding for their high pKa are more sensitive to temperature variations. The data are, however, too limited to draw any firm conclusion. We see that the estimated pKa values are systematically lower than the experimental ones. This can be attributed to systematic errors in the entropy estimation and/or to changes in the solvent with temperature that are not accounted for in the model. Conclusions Calculations have shown that intramolecular hydrogen bonds play a crucial part in determining the pKa values of alkanolamines. These same hydrogen bonds make the accurate modeling of these molecules difficult. Continuum solvent models were found to be useful in predicting the relative pKa strengths between amines with similar solvation behavior, i.e., with the same

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Received for review October 16, 2002 Revised manuscript received July 29, 2003 Accepted August 5, 2003 IE020808N