Study of the Carbamate Stability of Amines Using ab Initio Methods

Study of the Carbamate Stability of Amines Using ab Initio Methods and Free-Energy Perturbations ... used in CO2 absorption processes have been studie...
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Ind. Eng. Chem. Res. 2006, 45, 2497-2504

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Study of the Carbamate Stability 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

The relative carbamate stability of a series of amines used in CO2 absorption processes have been studied with different solvation models and gas-phase energies calculated with the B3LYP density functional method. The solvation energies were calculated with Monte Carlo free-energy perturbations and continuum models. Comparison between calculated energies and experimental nuclear magnetic resonance (NMR) and kinetic data shows reasonable agreement. The trends in carbamate stability apparently cannot be explained, in terms of any single molecular characteristic. Introduction As a measure for preventing global warming, there is a steadily increasing interest in methods for removing carbon dioxide (CO2) from exhaust gases. Absorption with alkanolamines in mixtures with promoters has traditionally been used for the removal of CO2 from natural gas and refinery gas, and the same technology is an option for the treatment of exhaust gases. 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, the high energy demand for regeneration and relatively high degradation rates for this amine are unfavorable for large fossil fuel power plants. During the last years, new systems such as the PSR 1-31 and Mitsubishi KS 1-32 have been developed and promise improved performance, compared to the conventional MEA. At the same time, it should also be noted that improvements in performance have been reported for MEA.3 In the chemical absorption of CO2 in aqueous amine systems, the CO2 is bound as either bicarbonate or carbamate.4 If the equilibrium constants governing the formation of these species is known or can be predicted the overall performance of a solvent can be predicted, to a large extent. For the formation of carbamate, there is the following reaction:4 -

CO2 + R2NH + B h R2NCO2 + BH

+

(2)

Although no amine molecule appears in eq 2, the extent to which this reaction will proceed is, in fact, governed by the strength of the amine as a base:

BH+ + H2O h B + H3O+

HCO3- + R2NH h R2NCO2- + H2O

(3)

The present work will involve the modeling of carbamate stability. Several models are available for the base strength. If * To whom correspondence should be addressed. Tel.: +47 73594125. Fax: +47 73594080. E-mail: [email protected].

(4)

If the mole-fraction-based activity of water is assumed to be 1 and if H3O+ is written as H+, the following equilibrium constant is obtained for eq 3:

Ka )

aBaH+ aBH+

(5)

Similarly, the following equilibrium constant is obtained for the formation of carbamate (eq 4):

Kc )

aR2NCO2aR2NHaHCO3-

(6)

The carbamate equilibrium constant from eq 1 (Kc2) can be expressed as a product of the equilibrium constants of eqs 2, 3, and 4:

Kc2 )

(1)

where B indicates a base molecule and R2NH is any primary or secondary amine molecule. For bicarbonate formation, there is the following reaction:

CO2 + 2H2O h HCO3- + H3O+

the carbamate stability can be modeled in similar fashion, the performance of different amine solvents can be predicted. For the formation of carbamate, an alternative equilibrium can be set up that does not involve the base molecule:

KcK 2 Ka

(7)

where K2 is the equilibrium constant of eq 2. Therefore, the interactions between an amine species and CO2 in solution can be described by two equilibrium constants: Ka and Kc. Although there are also other reactions that occur,4 these are independent of the amine present in the system. From knowledge of these two equilibrium constants, the amount of CO2 captured and energy consumption of the process can be estimated. As will be shown in the present work, knowledge of the equilibrium constants can also be used to predict the reaction rates. Therefore, models that can predict these equilibrium constants are likely to be very useful in efforts to improve the absorption process, in terms of energy consumption and overall efficiency. The equilibrium constant Ka is usually presented in the form of the pKa (pKa ) -log Ka). Well-established methods exist for the experimental determination of the pKa value and the determination can be done with a fairly high degree of accuracy.

10.1021/ie050501z CCC: $33.50 © 2006 American Chemical Society Published on Web 07/15/2005

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Substantial data on the pKa for alkanolamines and other organic bases are also available in the literature.5 For the carbamate stability (Kc), however, the situation is very different. The carbamate species only appear in significant concentrations in systems where several other species are also present in significant concentrations. The carbamate species is also in equilibrium with solvated CO2. Because the solvated CO2 is only present in small quantities, its concentration can be difficult to establish. The only direct experimental route to obtaining this carbamate equilibrium constant seems to be nuclear magnetic resonance (NMR) techniques. However, the NMR experiments are very demanding and data have only been published for a small number of molecules.6-8 The uncertainty in the results are also much larger than for pKa measurement. To compare NMR results obtained under different conditions, estimates for activity coefficients are also required. As already noted, these systems have many components, several of them ionic, making the estimation of activity coefficients challenging. In summary, it can be observed that the experimental determination of carbamate stability is a more demanding task than the determination of the pKa value and the quality of the results that can be obtained is inferior. Although the experimental tasks of determining pKa and carbamate stability are very different, the modeling tasks are very similar. In both cases, one is attempting to calculate the free energy difference in aqueous solution between an ionic species and a closely related neutral species. The present authors have used quantum mechanical calculations and free energy perturbations to estimate trends in the pKa.9 In the present work we will use essentially the same models to predict trends in carbamate stability. Although some theoretical work has been published on carbamate species,10-13 the present work is, to our knowledge, the first modeling work on relative carbamate stability. Methods For eq 4, the following thermodynamic cycle can be constructed: On the basis of the thermodynamic cycle, the reaction energy

were conducted for the amines and the carbamate forms. The conformers that were observed to be the most stable in the gas phase were also assumed to be the most stable in solution, and all calculations in this work were performed on the same set of conformers. Gas-phase conformer search calculations were performed with PC Spartan Pro version 1.0.7.16 Calculation of gas-phase reaction energies were performed at the B3LYP/6-311++G(d,p) and MP2/6-31G(d) levels. Our previous work with pKa9 suggests that the B3LYP/6-311++G(d,p) method produces results that are in better agreement with experimental data. It has also been noted in the literature14 that this level of theory reproduces experimental properties quite well. The presence of intramolecular hydrogen bonds in the amines identified in our previous work means that they cannot reliably be modeled with the small basis set in the second-order Møller-Plesset (MP2) calculation. B3LYP and MP2 calculations were performed with their implementations in Gaussian 98.15 Thermal corrections and zero-point energies have been calculated at the HF/3-21G(d) level. Although this method is not very accurate, it should be noted that these contributions to the gas-phase energy are relatively small. These calculations were also performed with Gaussian 9815 implementations. In the calculation of solvation energy, three different models are used. One is a free-energy perturbation scheme, whereas the other two are widely used continuum models. The free-energy perturbation scheme is similar to what we have previously used in the modeling of pKa, using an approach that was modeled on work by Wiberg et al.17 In the present work, free-energy perturbations have been performed as two separate series: one between the neutral form of the amines, the second between the carbamate forms of the molecules. Therefore, all perturbations were between species of the same charge; this is the same form as that used by Wiberg et al.17 and is more accurate than the form used in our previous work on pKa. In the present work, simulations were performed on rigid gasphase B3LYP/6-311++G(d,p) geometries. The intermolecular interactions between two molecules a and b were evaluated using Coulombic and Lennard-Jones terms: on aon b

∆Eab )

in solution (∆Gcs) can be divided into two contributions:

∆Gcs ) ∆Gcg + ∆∆Gs

(8)

where ∆Gcg is

∆Gcg ) Gg(R2NCO2-) + Gg(H2O) - Gg(R2NHg) Gg(HCO3-) (9) and

∆∆Gs ) ∆Gs(R2NCO2-) + ∆Gs(H2O) ∆Gs(R2NHg) - ∆Gs(HCO3-) (10) Molecular mechanics (MMFF) was used to generate an initial set of conformers. All conformers were then optimized at the Hartree-Fock HF/6-31G(d) level. Separate conformer searches

∑i ∑j

{

qiqje2 rij

[( ) ( ) ]}

+ 4ij

σij rij

12

-

σij rij

6

(11)

The Lennard-Jones σ and  values for alcohol, alkane, and amine groups were from the OPLS-All atom force field.18,19 For CO2, the EPM220 parameters were chosen: σ(C) ) 2.757 Å, σ(O) ) 3.033 Å, (C) ) 0.066 kcal/mol, and (O) ) 0.170 kcal/mol. Partial atomic charges were determined using solvent-phase (SM 5.42R21) CM222 charges implemented in the Gamesol23 program. These charges were calculated on HF/6-31G(d) geometries. Note that atomic charges are not uniquely defined and many schemes for their calculation are available.24,25 The calculation of charges is one of the main uncertainties when using simulations to determine free energies. The perturbations were conducted between the amines closest in size. To allow smooth transitions, no more than one non-H atom was deleted in a single simulation. Therefore, series of up to three simulations were used to transform larger solutes to smaller ones. These calculations were performed with BOSS Version 4.1,26 using procedures developed by Jorgensen et al.27 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. Several

Ind. Eng. Chem. Res., Vol. 45, No. 8, 2006 2499 Table 1. Experimental pKa Data number

compound

name

typea

experimental pKa value at 25 °C

reference(s) used for kinetics/NMR data

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

ethanolamine 3-amino-1-propanol 2-(2-aminoethoxy)ethanol ethylendiamine 1-amino-2-propanol N-(2-hydroxyethyl)ethylenediamine 2-amino-2-methylpropanol 2-amino-2-methyl-1,3-propanediol 2-amino-2-ethyl-1,3-propanediol diethanolamine di-isopropanolamine 2-(methylamino)ethanol morpholine piperazine piperidine

MEA MPA DGA EDA MIPA AEEA AMP AMPD AEPD DEA DIPA MMEA

p p p p p p, s p* p* p* s s s s, c s, c s, c

9.51b 9.96b 9.46c 9.92b,d 9.46b 9.82b,d 9.7b 8.8b 8.8b 8.95b 8.89b 9.77b 8.49b 9.83b,d 11.12b

4, 31, 7,e 8e 4 4 31 4 31, 7e 31, 6,e 7e 7e 4, 6e 4 4, 8e 31 30 31

a Legend of symbols: p, primary amine; s, secondary amine; and c, cyclical amine. Asterisk symbol (*) denotes a subsituent group on an atom neighboring the amine functionality. b Data from Perrin.5 c Data from Littel et al.29 (extrapolated from data at 20 °C). d The first protonation constant. e Reference to NMR data.

water molecules corresponding to the number (n) of non-H atoms in the amine molecule were removed, giving (267 - n) water molecules. The perturbations were conducted over 10 windows of double-wide sampling, giving 20 free-energy increments that are summed to give the total change in free energy of solvation. Each window had 500 000 steps for equilibration and another 500 000 for sampling. The present free-energy perturbations have a statistical uncertainty of approximately (1 kcal/mol. This combination of B3LYP gas-phase energies and solvation energies from free-energy perturbations is essentially the same as that presented in our work on pKa. It should be emphasized that the model involves no form of adjustment to obtain agreement with the experimental data. The first of the two continuum models used to calculate the solvation energies is the IEFPCM model.28 Calculations were conducted with 60 tesserae per atomic sphere and other default settings in Gaussian 98. Calculations were performed as singlepoint calculations on gas-phase MP2/6-31G(d) geometries (IEFPCM/MP2/6-31G(d)//MP2/6-31G(d)). This model was also utilized in our work on pKa modeling.9 The other continuum model is the SM 5.42R21 model; in this case, single-point calculations on the HF/6-31G(d) level were conducted (SM 5.42R/ HF/6-31G(d)// HF/6-31G(d)). The IEFPCM and SM 5.42R calculations were conducted in Gaussian 9815 and Gamesol,23 respectively. The IEFPCM model has also been used to determine the solvation energies of HCO3-, CO2, and H2O. Results Table 1 lists the molecules studied in this report. The table indicates whether amines are primary or secondary. Tertiary amines do not form carbamate species and, therefore, are not included in the present study. It is also indicated in the table if the molecule has any substituent groups on the carbon(s) adjacent to the amine. This particular characteristic has been used to rationalize carbamate stability, and we will examine this characteristic in the discussion. Experimental pKa values are also given in Table 1; they will be used to convert the data from Kc to Kc2, and they are also relevant to the discussion of explanations given for carbamate stability. Finally, we have given some references to the amines in the CO2 absorption literature and included references to NMR results when these are available. The compounds chosen for this study covers a fairly large portion of the amines commonly used in CO2 absorption. Almost

Figure 1. Carbamate forms of ethanolamine (MEA), 2-amino-2-methylpropanol (AMP), and piperidine. Dotted lines indicate hydrogen bonds.

all amines covered in a review by Versteeg et al.4 are included. In addition, we have attempted to cover amines in the literature that seem promising or that display particularly interesting behavior. The geometries of the most-stable conformers found for the carbamate forms of MEA, 2-amino-2-methylpropanol (AMP) and piperidine are shown in Figure 1. The most-stable carbamate conformers of the other amine molecules are shown in Figure 2. For N-(2-hydroxyethyl)ethylenediamine (AEEA), conformers are shown for bonding to both amine functionalities. The conformers of the amines themselves are shown in the Supporting Information; most of these conformers were also presented in our previous work on pKa.9 To study the most likely form of intramolecular hydrogen bonding for the carbamate species, the potential conformer forms of 3-amino-1-propanol (MPA) have been studied in greater detail. There can be conformers with hydrogen bonding between the alcohol group and carbamate oxygens and between the alcohol group and the N atom, and finally there are conformers without any hydrogen bonds. In Figure 3, the conformers identified as the most stable of each type in the gas phase are shown and energies for these conformers are shown in the tables. In Table 4 (shown later in this paper), reaction energies are shown for these different carbamate conformers of MPA (all calculated relative to the same conformer of MPA itself). Results with different solvation models all suggest that the carbamate conformer determined to be most stable in the gas phase (see Table 2, presented later in this paper) remains the most stable in solution. In Figure 2, it can be seen that the carbamate molecules tend to form intramolecular hydrogen bonds between alcohol-group H atoms and CO2-group oxygens. For the amines themselves, we found intramolecular hydrogen bonding between the amine groups and the alcohol groups. In the present work, we assumed that these conformers with intramolecular hydrogen bonds also dominate in solution.

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Figure 2. Carbamate forms of amines. Dotted lines indicate hydrogen bonds. Table 2. Calculated Gas-Phase Reaction Energies ∆Gcg (kcal/mol) number

name

MP2a

B3LYPb

1 2

MEA MPA(1)c MPA(2)c MPA(3)c DGA EDA MIPA AEEA(p) AEEA(s) AMP AMPD AEPD DEA DIPA MMEA morpholine piperazine piperidine

-7.79 -8.50 -2.98 6.19 -5.60 -2.60 -7.99 -8.12 -13.41 -4.09 -12.18 -13.13 -19.66 -20.55 -9.14 -4.52 -3.20 -2.26

-6.26 -5.83 -0.90 3.31 -3.55 0.28 -5.11 -4.56 -6.87 -1.13 -8.39 -8.54 -12.99 -13.10 -5.46 -2.26 -0.53 2.14

3 4 5 6

Figure 3. Conformers of 3-amino-1-propanol (MPA) displaying different intramolecular hydrogen bonds.

However, it is clear that, in solution, this intramolecular hydrogen bonding competes with hydrogen bonding to the water molecules in the solution. Modeling32 and experimental work33,34 for ethanolamine suggest that, in the liquid form or aqueous solution, the conformers change, compared to the gas phase, the geometry changes to allow greater formation of intermolecular hydrogen bonds. However, the results also do suggest that intramolecular hydrogen bonding remains. Work on 2-(methylamino)ethanol12 (MMEA) suggests that this molecule also has some degree of intramolecular hydrogen bonding in solution. The same work also finds intramolecular hydrogen bonds in solution for the carbamate species. This is consistent with the present model results for MPA. In summary, this would suggest some degree of conformer change for neutral amines in aqueous solution, compared to the gas phase, less so for the carbamate species. Therefore, the use of conformers that are identified as the most stable in the gas phase is an approximation; however, because

7 8 9 10 11 12 13 14 15

a MP2/6-31G(d) with thermal correction and zero-point energy at the HF/3-21G(d) level. b B3LYP/6-311++G(d,p) level with thermal correction and zero-point energy at the HF/3-21G(d) level. c With different carbamate conformers as shown in Figure 3.

the conformers are likely to be similar in energy, this should not have too large of an effect on calculated energies. Table 2 shows the results for gas-phase reaction energies (∆Gcg) calculated at the B3LYP and MP2 levels. Considerable differences can be observed between the MP2 and B3LYP gasphase results. However, the differences are comparable to what we found using the same levels of theory in our work on base strength.9 As noted in the Methods section, we believe the B3LYP results to be the more-accurate. Table 3 shows the solvation energies calculated with freeenergy perturbations and the continuum models. The continuum

Ind. Eng. Chem. Res., Vol. 45, No. 8, 2006 2501 Table 3. Solvation Energies Solvation Energy (kcal/mol) FEPa number

name

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

MEA MPA(1)d MPA(2)d MPA(3)d DGA EDA MIPA AEEA(p) AEEA(s) AMP AMPD AEPD DEA DIPA MMEA morpholine piperazine piperidine

PCMb -

SMc

Am AmCO2

Am AmCO2

Am AmCO2-

-8.9 -8.7

-8.9 -8.6

-9.0 -9.2

-12.9 -11.8 -10.2 -10.3 -6.8 -7.7 -6.9 -11.2 -8.1 -5.7 -4.4 -5.7 -2.7

-67.8 -64.1 -63.0 -70.5 -68.9 -85.7 -68.9 -46.3 -54.0 -65.0 -59.9 -58.4 -60.6 -58.3 -68.8 -76.7 -86.4 -81.8

-

-10.5 -9.1 -8.1 -11.5 -7.3 -8.7 -7.7 -9.8 -10.5 -8.1 -9.1 -11.0 -5.4

-67.8 -66.8 -68.0 -75.9 -63.9 -69.2 -66.0 -64.4 -62.3 -64.4 -62.5 -60.9 -60.0 -57.3 -64.3 -70.2 -72.7 -68.5

-11.3 -9.3 -8.4 -11.0 -6.8 -9.9 -9.3 -12.9 -10.6 -7.4 -7.2 -9.1 -4.3

-72.3 -70.7 -71.8 -78.1 -68.9 -74.3 -70.7 -71.4 -67.4 -69.1 -68.3 -67.2 -66.0 -64.0 -69.6 -72.3 -75.3 -71.4

a Free-energy perturbations with CM2 charges on a B3LYP/6311++G(d,p) geometry. b IEFPCM/MP2/6-31G(d)//MP2/6-31G(d). c SM 5.42R/HF/6-31G(d)//HF/6-31G(d). d With different carbamate conformers as shown in Figure 3.

Table 4. Free Energies of Reaction in Solution Free Energy of Reaction (kcal/mol) ∆Gcsa,b

∆Gcs2a,c,d

number

name

FEP

PCM

SM

FEP

PCM

SM

1 2

MEA MPA(1)e MPA(2)e MPA(3)e DGA EDA MIPA AEEA(p) AEEA(s) AMP AMPD AEPD DEA DIPA MMEA morpholine piperazine piperidine

1.9 5.9 11.9 8.7 7.5 -6.5 3.3 26.5 16.5 7.8 6.6 7.1 4.7 3.8 -1.4 -7.5 -12.5 -11.4

1.9 3.1 6.9 3.2 10.2 7.3 4.0 9.7 9.4 8.8 4.8 5.4 3.9 7.3 5.5 3.7 4.8 6.1

-2.5 -0.2 3.6 1.4 6.0 2.4 -0.3 2.1 3.8 3.6 -2.3 0.7 1.0 0.6 -0.6 -0.2 0.3 2.2

13.6 17.0 23.0 19.8 19.3 4.7 15.1 37.8 27.8 19.3 19.2 19.7 17.1 16.4 9.9 5.6 -1.2 -1.9

13.6 14.2 18.0 14.3 21.9 18.5 15.8 21.0 27.6 20.2 17.5 18.1 16.4 19.8 16.8 16.8 16.1 15.7

9.2 10.9 14.7 12.5 17.8 13.5 11.5 13.4 22.0 15.0 10.4 13.4 13.5 13.2 10.8 12.9 11.6 11.7

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

a Gas-phase energies are given at the B3LYP/6-311++G(d,p) level with thermal correction and zero-point energy at the HF/3-21G(d) level. b Reaction energy for eq 4. c Reaction energy for eq 1. d Experimental pK a data used in calculation. e With different carbamate conformers as shown in Figure 3.

and free-energy perturbation solvation energies are mostly in reasonable agreement but do differ significantly in some cases. Finally, Table 4 shows the solvation phase energy for eqs 1 and 4. The energies are based on the B3LYP gas-phase energies, and separate sets of results are shown based on the different solvation models. To calculate the energy for Kc2 (eq 1), experimental pKa data were used, together with model data for eq 2 (given in the Supporting Information). AEEA is special among the amines in present study in that it has two nonequivalent amine functionalities. In Table 4, equilibrium constants are calculated based on bonding to both amine functionalities. The table shows that, although the freeenergy perturbation results suggest that CO2 bonded to the secondary amine functionality produces the more-stable carbamate form, the SM results suggest that primary carbamate is

more stable. All the models suggest that AEEA has a lower equilibrium constant for carbamate formation than MEA. However, the models do differ in regard to how great this difference is. Table 4 also shows that different solvation models give different relative energies for many of the other amines. The assessments of the accuracy of the different models will be based on comparison with experimental data. Before turning to comparison with experimental data, some general comments should be made on the quality of the quantum mechanical calculations and solvation energies. In our study of amine pKa values,9 we obtained results that can perhaps best be summarized as semiquantitative. In the present study, the method used is almost identical. However, the carbamate formation reaction occurs between an anionic species and a neutral species, whereas the pKa study involved cationic molecules. There are some reasons to believe that the carbamate stability calculations will be at least as accurate as the pKa calculations: the CO2 group does not vary that much in nature between the different carbamate molecules, and the intramolecular hydrogen bonds seem to have a lesser role than is the case for the protonated amines in the pKa study. Note that we do not believe the calculated absolute energies to be reliable; however, the present level of modeling should be sufficient to reasonably predict the relative stability of carbamates formed from different amines. 1. Comparison with Experimental Data. Although tertiary amines are not included in the present study, some calculations were performed on the stability of carbamate-like species from the tertiary amines triethanolamine and MDEA. No stable species involving CO2 bonding to the amine functionality were found in these calculations. This is in agreement with the established knowledge that tertiary amines do not form carbamate species.8 The calculations were performed on single solute molecules with solvation models that produce results corresponding to infinite dilution in aqueous solution. As noted in the Introduction, the carbamate is, in fact, only formed at detectable levels in systems where several other species are also present in significant concentrations, and most experimental measurements are performed in conditions far from infinite dilution. In comparing the calculated results with experimental data, we will be ignoring concentration effects; this is an approximation that should be kept in mind when studying the results. As already noted, NMR experiments offer the only direct route to finding carbamate stabilities. Sartori and Savage6 reported the following order for Kc: MEA < diethanolamine (DEA) < AMP. The results with free-energy perturbations in Table 4 reproduce this trend, as do the continuum models. Suda et al.8 gave the following order in Kc2: MEA < MMEA < MDEA. The results with free-energy perturbations give an order of MMEA < MEA < MDEA, whereas both of the continuum models produce the same trend as that observed for the experimental data. Data from Yoon and Lee7 give the following order in Kc2: MEA < 2-amino-2-methyl-1,3-propanediol (AMPD) < 2-amino2-ethyl-1,3-propanediol (AEPD) < AMP. The free-energy perturbation data in Table 4 give the following order: MEA < AMP ≈ AMPD < AEPD. The continuum models produce results in full agreement with the experimental trend. In summary, it can be observed that results based on the continuum model give the same relative carbamate stabilities

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Figure 4. Plot of the logarithm of the experimental reaction rate versus calculated energies. Dotted lines indicate the set of results for a molecule.

as do the NMR data, whereas the free-energy perturbations err in some cases. Although the NMR methods offer the only direct method for estimating carbamate stability, there are other ways to infer carbamate stability from experimental data. Carbamate formation (eq 1) is a much faster reaction than bicarbonate formation; therefore, high reaction rates are evidence of carbamate formation, and it would seem reasonable to expect a correlation between the reaction rate and the stability of the carbamate formed (i.e., the reaction energy). Available kinetic data are taken from experiments on a single amine species in aqueous solution. In this case, eq 1 represents the reaction that happens. For molecules that undergo the same reaction, we can assume that there is a linear relation between the logarithm of the rate of reaction and the reaction energy. In Figure 4, calculated ∆Gcs2 from Table 4 is plotted against the logarithm of experimental kinetic parameters for second-order reaction (k2, in units of m3 mol-1 s-1). Experimental data are taken from the references given in Table 1, and the chosen values are given in the Supporting Information. The data are obtained at 25 °C, and where several values are available, the most representative values have been chosen. Note that there are inconsistencies and uncertainties in the experimental kinetics data; however, these should not affect the overall trends in the results. The experimental value for AMPD was very low and was considered to be relatively uncertain; therefore, this value was omitted from the plot. Figure 4 shows good overall correlation between calculated reaction energies with free-energy perturbation solvation energies and the kinetic data; however, the trend line might overstate the relative energy differences. The outlying points in the freeenergy perturbation based plot in Figure 4 are for MPA and diglycolamine (DGA). The results with the continuum solvation models, in this case, show somewhat poorer correlation with the experimental data. It would seem that both of the continuum models underestimate the solvation energy of the carbamate forms of the cyclical amines. This suggests that, although the continuum models are more reliable for molecules with similar structures, they are not as good as the free-energy perturbations in regard to predicting the relative solvation energies of species with different structures.

Generally, the calculations seem to be in reasonably good agreement with trends in the experimental data. The models clearly are not completely accurate, and the solvation energies seem to be the main source of uncertainty. A final possibility to extract information on relative carbamate stability from experimental data is to look at the amount of CO2 absorbed in the system. This is usually measured as the loading, in terms of moles of CO2 per mole of amine in solution. Carbamate formation consumes amine and CO2 at a stoichiometry of 2:1, whereas bicarbonate formation has a stoichiometry of 1:1. Therefore, systems where carbamate formation dominate will have loadings that are not much higher than 0.5, whereas systems with only bicarbonate formation can have loadings close to 1. Such an analysis can, however, be ambiguous, because a low loading can indicate either carbamate formation or a low overall equilibrium. Although comparison with such data is not included in the present work, it is an option for systems where other experimental data are not available. 2. Contributions to Carbamate Stability. Some efforts have been made to rationalize the observed trends in carbamate stability. It is interesting to determine if the results from the present work validate such rationalizations or if any new general correlations can be identified. Versteeg et al.4 observed a correlation between the pKa and the reaction rate for a series of amines. A similar plot for the molecules in Figure 4 is given in the Supporting Information. Little overall correlation is observed in this plot. The correlation observed by Versteeg et al.4 can be seen for a group of nine molecules; however, the data for piperidine, morpholine, and AMP do not fit this correlation. The fact that the previously observed correlation does not hold for all primary and secondary molecules is not at all surprising. The base strength and carbamate stability are two separate equilibrium constants representing the stability ratio between different chemical species, and, a priori, it is not at all evident, but rather surprising, that there should be any such correlation at all. Although the correlation observed by Versteeg et al.4 is interesting, it would therefore not seem likely that it has predictive value. We see no apparent explanation for the correlation observed for some amines. Some molecular characteristics might be favorable to the formation of both anionic and cationic species. Sartori and Savage6 showed that a series of amines with substituent groups on the carbon bonded to the amine functionality formed carbamate to a lesser extent than other primary and secondary amines. They referred to these amines as “sterically hindered”. Although these amines do have some degree of steric hindrance, we would caution that the name conveys an overly simple physical interpretation of carbamate stability. The effect of a substituent group on the stability of a species can take several forms. There are the effects of donating or withdrawing electrons through bonds, and there can be energetically favorable or unfavorable interactions to groups to which the substituent is not directly bonded. Steric hindrance refer to the latter of these interactions. In addition, a substituent group can also affect the accessibility of the solvent to various parts of the molecular surface, thereby changing the solvation energy. Examination of the geometry of AMP-carbamate (see Figure 1 and the Supporting Information) shows that there is some steric interaction between a methyl substituent and the CO2 carbon. In particular, the N-C-C(OH) angle tightens from 114.53° in MEA-carbamate to 111.38° in AMP-carbamate, suggesting that the N atom, together with the carbamate functionality, is forced away from one of the methyl groups. Although this effect

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is significant for AMP, it will however not always necessarily be the dominant factor. When estimating the reactivity of an amine, all of these effects must be considered together; for example, AMPD and AEPD are clearly no less sterically hindered than AMP, but, nevertheless, the experimental results strongly suggest that they have more-stable carbamate forms. One group of amines that stand out, in terms of the rate of carbamate formation, is the cyclical amines. There would seem to be two factors that can account for these amines having a strong tendency to form carbamate species. The carbamate group on the cyclical molecules are completely accessible to solvent, leading to high solvation energies for the carbamate form. The solvation energy of the neutral amines themselves is also relatively low. Together, these two solvent effects contribute to the carbamate formation being favored. However, these effects will vary with the structure of the cyclical amine, and this should not be considered to be some form of general rule. Therefore, it would not seem that the carbamate stability can be explained in terms of a single molecular property. Although steric effects do have a role, other factors (such as intramolecular hydrogen bonding and variations in solvation energy) can dominate. 3. Temperature Effects. In the earlier work on pKa calculations,9 it was found that entropies from quantum mechanical calculations, together with pKa values, can be used to predict changes in pKa with temperature. The equation presented for pKa in that work can be written in a more general form:

d(ln K) (∆Sreaction/R) - ln K ) dT T

This shows that carbamate stability can be predicted with a reasonable accuracy. Together with similar models for calculating amine basicity, the present work can be utilized to predict the chemistry and overall performance of different amine solvents in CO2 absorption. Different solvent models produced results in reasonable overall agreement. However, the results obtained from different models did vary, and none of the models were completely accurate. The carbamate species seem to form hydrogen bonds between alcohol groups and carbamate functionality O atoms. The model results suggest that steric hindrance is only one of several effects contributing to relative carbamate stability. The high carbamate stability of some cyclical amines seems to be caused by the high solubility of the carbamate functionality. Acknowledgment This work has received support from the Research Council of Norway through a grant of computing time. Supporting Information Available: Underlying values for data in Table 2, conformers of amine molecules, details of MEA and AMP carbamate geometry, rate constants for Figure 4, and a plot of experimental pKa versus reaction rate (PDF). This material is available free of charge via the Internet at http:// pubs.acs.org. Literature Cited

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Using this equation, it should also be possible to estimate how the carbamate stability changes over temperature. The lack of accurate carbamate equilibrium constants, even at room temperature, means that the same level of accuracy in prediction cannot be achieved. There is also very little experimental data for carbamate to validate model results. 4. Solvation Energy. In this work, free energies of solvation have been used to calculate equilibrium constants; however, they are also of intrinsic interest. The free energy of solvation represents the partitioning of a species between the gas phase and the liquid phase, and it is directly related to the partial pressure of a component in the gas phase.35 Negative values indicate a preference for the solute to stay in the liquid phase. For the amines used in aqueous solution, it is preferable if they are soluble in large quantities and do not evaporate. The solubility is one of the factors that must be considered when selecting solvents for industrial application. High solubility is perhaps the main reason alkanolamines are usually chosen for CO2 absorption processes. The solvation models used in this work can give indications of which amines have high solubility. Examination of the data for neutral amines in Table 3 shows that piperidine has low solubility and AMP has relatively low solubility. This is consistent with what is known about these amines experimentally. New solvents for this process should ideally have solvation energies that are comparable to MEA (see Table 3). Conclusions In the present work, the carbamate stability of a series of amines has been calculated with quantum mechanical gas-phase energies and various solvation models. The results are in good overall agreement with trends in available experimental data.

(1) Chakma, A.; Tontiwachiwuthikul, P. Designer Solvents for Efficient CO2 Separation from Flue Gas Streams. Greenhouse Gas Control Technol., Proc. Int. Conf., 4th 1999, 35. (2) Mimura, T.; Satsumi, S.; Iijima, M.; Mitsuoka, S. Development on Energy Saving Technology for Flue Gas CO2 Recovery by the Chemical Absorption Method in Power Plant. Greenhouse Gas Control Technol., Proc. Int. Conf., 4th 1999, 71. (3) Reddy, S.; Scherffius, J.; Freguia, S.; Roberts, C. Fluor’s Econamine FG Plus Technology. Presented at the Second International Conference on Carbon Sequestration, U.S. Department of Energy (DOE), Alexandria, VA, 2003. (4) Versteeg, G. F.; van Dijck, L. A. J.; van Swaaij, W. P. M. On the kinetics between CO2 and alkanolamines both in aqueous and nonaqueous solutions. An overview. Chem. Eng. Commun. 1996, 144, 113. (5) Perrin, D. D. Dissociation Constants of Organic Bases in Aqueous Solution. Butterworths: London, 1965 (and Supplement, 1972). (6) Sartori, G.; Savage, D. W. Sterically Hindered Amines for CO2 Removal from Gases. Ind. Eng. Chem. Fundam. 1983, 22, 239. (7) Yoon, S. J.; Lee, H. Substituent Effect in Amine-CO2 interaction investigated by NMR and IR Spectroscopies. Chem. Lett. 2003, 32, 344. (8) Suda, T.; Iwaki, T.; Mimura, T. Facile Determination of dissolved species in CO2-amine-H2O-system by NMR spectroscopy. Chem. Lett. 1996, 25, 777. (9) da Silva, E. F.; Svendsen, H. F. Prediction of the pKa Values of Amines Using ab Initio Methods and Free-Energy Perturbations. Ind. Eng. Chem. Res. 2003, 42, 4414. (10) Jamroz, M. H.; Dobrowolski, J.; Borowiak, M. Ab initio study on the 1:2 reaction of CO2 with dimethylamine. J. Mol. Struct. 1997, 404, 105. (11) Chakraborty, A. B.; Bischoff, K. B.; Astarita, G.; Damewood, J. R. Molecular Orbital Approach to Substituent Effects in Amine-CO2 Interactions. J. Am. Chem. Soc. 1988, 110, 6947. (12) Ohno, K.; Inoue, Y.; Yoshida, H.; Matsuura, H. Reaction of Aqueous 2-(N-Methylamino)ethanol Solutions with Carbon Dioxide. Chemical Species and Their Conformations Studied by Vibrational Spectroscopy and ab Initio Theories. J. Phys. Chem. A 1999, 103, 4283. (13) da Silva, E. F.; Svendsen, H. F. Ab Initio Study of the Reaction of Carbamate Formation from CO2 and Alkanolamines. Ind. Eng. Chem. Res. 2004, 43, 3413. (14) Lukin, O.; Leszczynski, J. Rationalizing the Strength of HydrogenBonded Complexes. Ab Initio HF and DFT Studies. J. Phys. Chem. A 2002, 106, 6775-6782.

2504

Ind. Eng. Chem. Res., Vol. 45, No. 8, 2006

(15) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Zakrzewski, V. G.; Montgomery, J. A., Jr.; Stratmann, R. E.; Burant, J. C.; Dapprich, S.; Millam, J. M.; Daniels, A. D.; Kudin, K. N.; Strain, M. C.; Farkas, O.; Tomasi, J.; Barone, V.; Cossi, M.; Cammi, R.; Mennucci, B.; Pomelli, C.; Adamo, C.; Clifford, S.; Ochterski, J.; Petersson, G. A.; Ayala, P. Y.; Cui, Q.; Morokuma, K.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Cioslowski, J.; Ortiz, J. V.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Gomperts, R.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Gonzalez, C.; Challacombe, M.; Gill, P. M. W.; Johnson, B. G.; Chen, W.; Wong, M. W.; Andres, J. L.; Head-Gordon, M.; Replogle, E. S.; Pople, J. A. Gaussian 98, revision A.9; Gaussian, Inc.: Pittsburgh, PA, 1998. (16) PC SPARTAN Version 1.0.7, Wavefunction, Inc., Irvine, CA. (17) Wiberg, K. B.; Clifford, S.; Jorgensen, W. L.; Frisch, M. J. Origin of the Inversion of the Acidity Order for Haloacetic Acids on going from the Gas phase to Solution. J. Phys. Chem. A 2000, 104, 7625. (18) Rizzo, R. C.; Jorgensen, W. L. OPLS All-Atom Model for Amines: Resolution of the Amine Hydration Problem. J. Am. Chem. Soc. 1999, 121, 4827. (19) Jorgensen, W. L.; Maxwell, D. S.; Tirado-Rives, J. Development and Testing of the OPLS All-Atom Force Field on Conformational Energetics and Properties of Organic Liquids. J. Am. Chem. Soc. 1996, 118, 11225. (20) Harris, J. G.; Yung, K. H. Carbon dioxide’s liquid-vapor coexistence curve and critical properties as predicted by a simple molecular model. J. Phys. Chem. 1995, 99, 12021. (21) Hawkins, G. D.; Zhu, T.; Li, J.; Chambers, C. C.; Giesen, D. J.; Liotard, D. A.; Cramer, C. J.; Truhlar, D. G. Universal Solvation Models. In Combined Quantum Mechanical and Molecular Mechanical Methods; Gao, J., Thompson, M. A., Eds.; ACS Symposium Series 712; American Chemical Society: Washington, DC, 1998; pp 201-219. (22) Li, J.; Zhu, T.; Cramer, C. J.; Truhlar, D. G. New Class IV Charge Model for Extracting Accurate Partial Charges from Wave Functions J. Phys. Chem. A 1998, 102, 1820-1831. (23) Xidos, J. D.; Li, J.; Zhu, T.; Hawkins, G. D.; Thompson, J. D.; Chuang, Y.-Y.; Fast, P. L.; Liotard, D. A.; Rinaldi, D.; Cramer, C. J.; Truhlar, D. G. Gamesol-version 3.1, University of Minnesota, Minneapolis, MN, 2002. (Based on the General Atomic and Molecular Electronic Structure System (GAMESS), as described in Schmidt, M. W.; Baldridge,

K. K.; Boatz, J. A.; Elbert, S. T.; Gordon, M. S.; Jensen, J. H.; Koseki, S.; Matsunaga, N.; Nguyen, K. A.; Su, S. J.; Windus, T. L.; Dupuis, M.; Montgomery, J. A. J. Comput. Chem. 1993, 14, 1347.) (24) Cramer, C. J. Essentials of Computational Chemistry; Wiley: New York, 2002. (25) Sigfridsson, E.; Ryde, U. Comparison of Methods for Deriving Atomic Charges from the Electrostatic Potential and Monomers. J. Comput. Chem. 1998, 19, 377. (26) Jorgensen, W. L. BOSS, Version 4.3, Yale University, New Haven, CT, 1989. (27) Jorgensen, W. L.; Ravimohan, C. Monte Carlo simulation of differences in free energies of hydration. J. Chem. Phys. 1985, 83, 3050. (28) Cances, M. T.; Mennucci, V.; Tomasi, J. A new integral equation formalism for the polarizable continuum model: Theoretical background and applications to isotropic and anisotropic dielectrics. Chem. Phys. 1997, 107, 3032. (29) Littel, R. J.; Bos, M.; Knoop, G. J. Dissociation constants of some alkanolamines at 293, 303, 318, and 333 K. J. Chem. Eng. Data 1990, 35, 276. (30) Bishnoi, S. Dissertation, University of Texas, Austin, TX, 2000. (31) Sharma, M. M. Kinetics of Reactions of Carbonyl Sulphide and Carbon Dioxide with Amines. Trans. Faraday Soc. 1965, 61, 681. (32) Alejandro, J.; Rivera, J. L.; Mora, M. A.; de la Garza, V. Force Field of Monoethanolamine. J. Phys. Chem. B 2000, 104, 1332. (33) Tubergen, M. J.; Torok, C. R.; Lavrich, R. J. Effect of solvent on molecular conformation: Microwave spectra and structures of 2-aminoethanol van der Waals complexes. J. Chem. Phys. 2003, 119, 8397. (34) Silva, C. F. P.; Duarte, M. L. T. S.; Fausto, R. A concerted SCFMO ab initio and vibrational spectroscopic study of the conformational isomerism in 2-aminoethanol. J. Mol. Struct. 1999, 483, 591. (35) Winget, P.; Hawkins, G. D.; Cramer, C. J.; Truhlar, D. G. Prediction of Vapor Pressures from Selv-Solvation Free Energies Calculated by the SM5 Series of Universal Solvation Models. J. Phys. Chem. B 2000, 104, 4726.

ReceiVed for reView April 27, 2005 ReVised manuscript receiVed June 7, 2005 Accepted June 9, 2005 IE050501Z