i n t e r n a t i o n a l j o u r n a l o f g r e e n h o u s e g a s c o n t r o l 1 ( 2 0 0 7 ) 1 5 1 – 1 5 7

Computational chemistry study of reactions, equilibriumand kinetics of chemical CO2 absorption

Eirik F. da Silva a,b,*, Hallvard F. Svendsen a

aThe Norwegian University of Science and Technology (NTNU), NO-7491 Trondheim, Norwayb SINTEF Materials and Chemistry, NO-7465 Trondheim, Norway

a r t i c l e i n f o

Article history:

Received 7 August 2006

Received in revised form

22 November 2006

Accepted 26 January 2007

Published on line 13 March 2007

Keywords:

CO2 absorption

Solvents

Reaction mechanism

Computational chemistry

a b s t r a c t

The chemical reactions involved in CO2 absorption in amine systems are studied. For each

mechanism, available experimental data are considered and quantum mechanical calcula-

tions carried out. Base-catalyzed bicarbonate formation is found to be a likely mechanism

for all amine bases, not only tertiary amines. Direct formation of bicarbonate species from

carbamate species is found to be unlikely. The carbamate formation has been proposed to

take place through a single-step termolecular reaction, or through a two step mechanism

with a zwitterionic intermediate. Quantum mechanical calculations suggest that if there is

such a zwitterionic intermediate, it is likely to be short-lived.

Quantum mechanical calculations together with solvation models are shown to predict

the base strength and carbamate stability of different amine solvents with a useful degree of

accuracy. Solvent effects and electron donation and withdrawal through bonds are identi-

fied as important factors in determining the overall reactivity of different amine solvents.

Results suggest a strong correlation between the carbamate stability and base strength of

amine solvents and their reaction kinetics.

# 2007 Elsevier Ltd. All rights reserved.

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1. Introduction

There is at present great interest both in finding optimal

solvents for CO2 absorption and in finding the optimal process

conditions for a given solvent. Detailed understanding of the

chemistry is of great value in accomplishing both of these

tasks. For simple aliphatic amines, the species formed are

known and the overall reactions are reasonably well under-

stood (Versteeg et al., 1996). There is, however, uncertainties

regarding some mechanisms that have not been resolved by

experimental work (Versteeg et al., 1996). Quantum mechan-

ical calculations can be used to directly study a given reaction

mechanism, thereby providing new insight into which

reaction mechanisms are most likely.

Over the years a number of different amine solvents have

been studied in the context of CO2 absorption. Kinetic and

* Corresponding author.E-mail address: eirik.silva@sintef.no (E.F. da Silva).

1750-5836/$ – see front matter # 2007 Elsevier Ltd. All rights reserveddoi:10.1016/S1750-5836(07)00022-9

equilibrium data have been reported and in many cases there

is a good understanding of the chemistry. There has, however,

been a limited understanding of the relationship between the

molecular structure of the solvent and chemical equilibrium.

2. Computational chemistry

Quantum mechanics offers the possibility of calculating a

large number of chemical properties from first principles, with

little or no experimental input. As availability of computa-

tional resources has increased, the application of quantum

mechanical calculations has grown. Such calculations are

today successfully used to study and predict molecular

structure, reaction mechanisms, thermodynamics and spec-

troscopic properties. A general presentation on main the

.

Fig. 1 – Species formed in solution.

i n t e r n a t i o n a l j o u r n a l o f g r e e n h o u s e g a s c o n t r o l 1 ( 2 0 0 7 ) 1 5 1 – 1 5 7152

applications of quantum mechanics and other forms of

computational chemistry can be found in the textbook

‘‘Essentials of computational chemistry’’ (Cramer, 2002).

The computation time for quantum mechanical calcula-

tions increases with the quality of calculations and the size of

the system. Such calculations are therefore quite successful in

calculating gas phase reaction energies (examples are work by

Smith and Radom, 1993; East et al., 1997; da Silva, 2005).

Determining reaction energies in solution directly from

quantum mechanical calculations is, however, a very challen-

ging task. In a solution, there are very large numbers of

molecules interacting and experimentally observed properties

represent averages over large ensembles, accurate calcula-

tions on such large systems are extremely time-consuming. A

widely used approach to calculate reaction energies in

solution is to first calculate reaction energies in gas phase

and then calculate the solvation energy with some form of

solvation model (Cramer, 2002). Solvation models are based on

some simplified representation of the solvent, common forms

are continuum models, where the solvent is represented as a

dielectric continuum, and explicit models where solvent

molecules are usually given a simplified molecular mechanics

representation (some form of ball-and-stick model with fixed

charges). Orozco and Luque (2000) provide a broad review of

solvation models. In calculations, where quantum mechanical

calculations and solvation models are combined, the solvation

models are usually expected to be the main source of

uncertainty.

Fig. 2 – Transition state of bicarbonate formation.

3. Methods

In the present work, reaction mechanisms are studied by

calculations in vacuum, solvent molecules are added to

capture their direct contribution to reactions. This is quali-

tative approach, intended to address the likelihood of a

reaction taking place. These calculations were carried at the

Hartree-Fock level in the Spartan 04 program.

For the calculation of basicity in solution (pKa of the

conjugate base of a amine) a combination of quantum

mechanical gas phase energies and a continuum solvation

model is utilized. Gas phase energies were calculated at the

B3LYP/6-311++G(d,p) level, while the zero-point energy and

thermal corrections were calculated at the HF/6-31G(d) level.

This level of theory has been shown to be reasonably accurate

for the calculation of gas phase basicities (da Silva, 2005).

Solvation energies were calculated with the SM 5.42 R model

(Li et al., 1999) on HF/6-31G(d) level geometries. The reported

mean absolute error for neutral solutes for this model is

0.46 kcal/mol, while it is 3.8 kcal/mol for ions (Li et al., 1999).

The present basicity calculations are an extension to pre-

viously published work by the present authors (da Silva and

Svendsen, 2003). Gas phase energies were calculated in

Gaussian98 (Frisch et al., 1998) while solvation energies were

calculated in the Gamesol program (Xidos et al., 2002).

Many of the amines in the present study are highly flexible

molecules that may take on a number of conformers in

aqueous solution. As in our previous work, the overall

approach has been to assume that conformers identified as

the most stable in the gas phase, are also the most stable in

solution. While it is a reasonable assumption, it does add a

layer of uncertainty to the results.

4. Reaction mechanisms

4.1. Bicarbonate formation

CO2 reacts in aqueous amine systems to form either

bicarbonate or carbamate. These species are shown in

Fig. 1. The R groups in NR2 can be a proton or any form of

substituent group.

The formation of bicarbonate from CO2 and water is a well

known reaction in chemistry. There are three (related)

mechanisms for this reaction.

CO2 þH2OÐH2CO3 (1)

CO2 þOH�ÐHCO�3 (2)

H2CO3 þOH�ÐHCO�3 þH2O (3)

Bicarbonate can again be deprotonated by a base molecule

(B).

HCO�3 þ BÐCO�23 þ BHþ (4)

The base molecule is usually an amine molecule or a

hydroxyl ion (OH�). By itself bicarbonate formation is,

however, a rather slow reaction. It has been observed that

this reaction proceeds more quickly in the presence of amine

molecules, an effect beside the direct effect of the amines as

bases (Donaldsen and Nguyen, 1980). It is also known that

Fig. 3 – Mechanism of catalyzed bicarbonate formation.

Fig. 4 – Zwitterion mechanism. Water as base molecule.

Fig. 6 – Ethanolamine carbamate interacting with a water

molecule.

i n t e r n a t i o n a l j o u r n a l o f g r e e n h o u s e g a s c o n t r o l 1 ( 2 0 0 7 ) 1 5 1 – 1 5 7 153

Brønsted bases can act to catalyze the formation of bicarbo-

nate (Sharma and Danckwerts, 1963).

Calculations for this mechanism were performed with one

water molecule and one CO2 molecule in the presence of an

Ethanolamine molecule. The determined transition-state

geometry at the HF/6-31G(d,p) level is shown in Fig. 2.

This transition state is consistent with the mechanism

proposed by Donaldsen and Nguyen (1980) (Fig. 3):

This reaction may be written in the following form:

CO2 þH2Oþ BÐHCO�3 þ BHþ (5)

At the HF/6-31G(d,p) level, the barrier to bicarbonate

formation with Ethanolamine as a base was found to be

29.5 kcal/mol. For the bicarbonate formation in water a

reaction-barrier of 42.5 kcal/mol has been reported with the

same type of calculation at the same level of theory (Nguyen

et al., 1997). While neither of these calculations is quantitative

in nature, the results do suggest that the presence of

Ethanolamine significantly lowers the reaction barrier.

While this mechanism is usually mentioned in the context

of tertiary amines, it is probably not unique to this class of

molecules. The calculations suggest that this reaction will take

place as long as the base functionality is of appropriate

strength and accessible to the solvent water molecules.

4.2. Carbamate formation

The carbamate formation is one of the main reactions of CO2

absorption. Two mechanisms have been proposed for this in

the literature. One is the zwitterion mechanism originally

proposed by Caplow (1968) (Fig. 4).

In this mechanism, CO2 forms a bond to the amine

functionality in a first step. In a second step, an amine-proton

is transferred to a base molecule. Crooks and Donnellan (1989)

proposed the following single-step mechanism (Fig. 5).

Fig. 5 – Single-step carbamate formation mechanism.

Here, B is a base molecule. In this mechanism, the bonding

between amine and CO2 and the proton transfer take place

simultaneously.

The present authors have in previous work concluded that

experimental data can be accounted for by both mechanisms

(da Silva and Svendsen, 2004). Quantum mechanical calcula-

tions suggest that any zwitterion species is likely to be

unstable (da Silva and Svendsen, 2004; Ohno et al., 1999). This

suggests three possible mechanisms, depending on the nature

of the zwitterion. The zwitterion may be an entirely transient

state (giving a single-step mechanism), it may be a short-lived

species or it may be a transition state. The overall reaction may

in general be written in the following form:

CO2 þAmþ BÐAmCO�2 þ BHþ (6)

4.3. Carbamate as reaction intermediate

It has been suggested that carbamate undergoes a direct

hydrolysis reaction (Smith and Quinn, 1979), meaning a direct

reaction with water to form bicarbonate and amine. In

quantum mechanical, calculations no reaction path or

transition-state was found for such a mechanism. Fig. 6

shows a HF/3-21G(d) geometry of a water molecule interacting

with a carbamate species. Other forms of interaction were also

considered, but the general conclusion from the calculations is

that the carbamate CO2-group carbon is unlikely to participate

in any reaction except reversal back to CO2 and amine.

It is known that in a CO2–water–amine system there may be

shifts in concentration between carbamate and bicarbonate

species. Such shifts can, however, readily be accounted for by

reactions (1)–(6), all of which are reversible.

4.4. Alcohol-group bonding to CO2

It has been suggested that at very high pH values, CO2 can

bond to alcohol-groups (Jørgensen and Faurholt, 1954).

Calculations at the HF/3-21G(d) level with Ethanolamine as

reactant and base suggest a mechanism analog to that of

carbamate formation (Fig. 7):

Fig. 7 – CO2 bonding to alcohol groups. Fig. 8 – General reaction with CO2.

i n t e r n a t i o n a l j o u r n a l o f g r e e n h o u s e g a s c o n t r o l 1 ( 2 0 0 7 ) 1 5 1 – 1 5 7154

This reaction is, however, in general not expected to play a

significant role in industrial CO2 absorption processes as the

pH of the system is usually not high enough for this reaction to

take place (Versteeg et al., 1996).

4.5. Other reactions

The amines are organic bases that may undergo the following

reaction:

BþH2OÐBHþ þOH� (7)

Finally, there is the self-dissociation of water:

H2OÐHþ þOH� (8)

Table 1 – Experimental and calculated basicity data

No. Compound Acronym Exp

1 Ammonia

2 Methylamine

3 Dimethylamine

4 Trimethylamine

5 Piperidine

6 Piperazine

7 Morpholine

8 Pyrrolidine

9 Ethyleneamine

10 2,2,6,6 Tetramethyl-4-piperidinol TMP

11 Ethanolamine MEA

12 2-Amino-2-methylpropanol AMP

13 1-Amino-2-Propanol MIPA

14 N-N-Butylethanolamine BEA

15 2-Methylaminoethanol MMEA

16 3-Amino-1-propanol MPA

17 Ethylenediamine EDA

18 Diethanolamine DEA

19 Diisopropanolamine DIPA

20 N-Methyldiethanolamine MDEA

21 Diglycolamine DGA

22 Triethanolamine TEA

23 o-Methylhydroxylamine

24 Ethanimidamine

25 Diethylaminoethanol DEMEA

26 N-(2-hydroxyethyl) ethylenediamine AEEA

27 Diethanoltriamine DETA

28 N,N-Dimethylethanolamine DMMEA

29 2-Diisopropylaminoethanol DIPMEA

a Relative gas phase protonation energies. Energies calculated at B3LYP/6

calculated at HF/6-31G(d) level.b Solvation energy of amine. Calculation is SM 5.42R/HF/6-31G(d)//HF/6-3c Solvation energy of protonated amine. Calculation is SM 5.42R/HF/6-31d Relative protonation energies (basicity) in solution.e First protonation constant: 1, Pearson (1986); 2, Perrin (1965); 3, Hoff (2

4.6. Reaction summary

It is noteworthy that all the reviewed reactions with the CO2

molecule can be summarized as a nucleophile attack on the

CO2-carbon (Fig. 8).

B is again a base molecule and AH is any molecule with a

free-electron pair and a hydrogen atom on the same site.

5. Equilibrium constants and structure

In Table 1, experimental basicity data are shown together with

calculated values for gas phase basicity, solvation energies

tl pKa at 25 8C DGpga DGs

b DGs(H+)c DGps

d

9.31 0.0 �4.9 �87.2 0.0

10.652 10.2 �5.1 �76.4 �0.9

10.82 17.9 �3.8 �67.1 �1.1

9.82 22.2 �3.0 �59.4 �3.7

11.122 24.2 �4.3 �61.7 �0.8

9.832e 23.3 �9.0 �66.2 �1.9

8.4922 17.0 �7.2 �67.7 �4.8

11.32 23.6 �6.0 �63.9 �0.9

10.782 14.3 �4.9 �72.7 �0.2

10.052 29.7 �5.6 �56.2 �2.0

9.52 16.2 �9.0 �70.7 �4.4

9.722 23.6 �7.0 �64.0 �1.7

9.462 17.9 �8.4 �70.3 �2.5

9.93 27.6 �6.3 �60.2 �0.9

9.82 23.0 �7.4 �64.6 �2.2

10.02 23.4 �9.2 �67.6 �0.5

9.922 22.7 �9.3 �69.3 0.4

8.962 28.2 �12.9 �61.5 �5.5

8.892 31.8 �10.7 �57.3 �3.9

8.522 32.2 �11.2 �56.6 �4.7

9.462 26.6 �11.3 �66.0 �1.0

7.762 32.7 �17.9 �60.0 �3.0

4.62 �3.3 �4.8 71.9 �13.7

12.42 31.4 �10.0 �65.6 4.7

9.752 31.6 �4.6 �52.8 �2.5

9.822e 28.6 �11.1 �64.6 �0.2

9.82 32.6 �11.1 �61.0 0.2

9.232 27.0 �6.0 �57.7 �3.6

9.972 34.7 �2.9 �48.1 �2.4

-311++G(d,p) level with thermal corrections and zero-point energies

1G(d) level.

G(d)//HF/6-31G(d) level.

003).

Fig. 9 – Calculated basicity vs. experimental basicity. Gray

crosshairs are flexible amines, with potential uncertainty

in conformer form, while black crosshairs are rigid

molecules.

Fig. 10 – Plot of logarithm of experimental reaction rate vs.

calculated carbamate stability (da Silva and Svendsen,

2006).

i n t e r n a t i o n a l j o u r n a l o f g r e e n h o u s e g a s c o n t r o l 1 ( 2 0 0 7 ) 1 5 1 – 1 5 7 155

and basicity in solution. The computational results are only

used to predict basicites, and basicity results are shown as

values relative to ammonia. For the solvation energies of the

amines and their protonated forms the absolute values are

shown (more negative values indicating higher solvability).

In Fig. 9, basicites from computational chemistry calcula-

tions are plotted against experimental values. In the plotted

results, piperazine is given it’s experimental pKa value and all

calculated values are relative to this value. The grey line

indicates the theoretical relationship between calculated and

experimental values, i.e. if the model had been perfect all

points should fall on this line. While most of the amines in the

study are of direct relevance to CO2 absorption, o-methylhy-

droxylamine (lowest pKa in plot) and ethanimidamine (highest

pKa in the plot) are mainly included to show the overall

robustness of the predictions. While the calculations are not

entirely accurate, they are capable of predicting if a base is

very strong or very weak.

Fig. 10 shows a previously published plot (da Silva and

Svendsen, 2006) of calculated carbamate stabilities versus the

logarithm of experimental reaction rates (second-order rate

constant). There is very little reliable experimental data

available on the equilibrium constants of carbamate forma-

tion and logarithm of the rate of reaction was chosen as a

proxy variable for carbamate stability. The underlying

assumption is that the rate of reaction increases proportion-

ally with increasing stability of the carbamate species. The

calculated energy (DGc2s) is for the reaction given in Eq. (6),

where the base molecule is a second amine molecule.

Both Figs. 9 and 10 show fairly good correlation between

modeled values and experimental data. While not entirely

accurate, the models give a good qualitative picture of the

relationship between molecular structure and the stability of

different species formed.

The contributions to stability of species in solution can be

separated into stability through bonds, steric repulsion

between non-bonded groups, intramolecular hydrogen bond-

ing and solvation effects. The stabilizing effect of the solvent

depends on the accessibility of the solute surface to the

solvent, this is of particular importance for ions. Examples of

this can be seen in Table 1; ammonia is a relatively weak base

in gas phase, but protonated ammonia has a high degree of

solvent stabilization resulting in fairly strong basicity in

solution. Triethanolamine is on the other hand, a strong base

in the gas phase, but as a tertiary amine it has a congested

amine functionality resulting in low solvability for the

protonated form and relatively low basicity.

Alcohol groups in the molecular structure tend to reduce

the basicity of amines, while alkane groups tend to increase

the basicity. By adding an alcohol group to ethyleneamine

ethanolamine is formed, the addition of this groups leads to a

drop in base strength of over 1 pKa unit. Ethylamine, having a

methyl group more than methylamine, has a somewhat

higher pKa. These effects are mainly due to stabilization

through bonds.

There has in the literature on CO2 absorption been a

tendency to only consider sterical hindrance when discussing

differences in reactivity towards CO2 between different

solvents. While sterical hindrance may play a role in affecting

reactivity, other effects such as electron donation through

bonds and solvation effects are in many cases likely to be at

least as important in accounting for overall reactivity. This

conclusion is in part supported by the breakdown of

contributions to stability in the computational chemistry

models. Experimental data also show large variations in

i n t e r n a t i o n a l j o u r n a l o f g r e e n h o u s e g a s c o n t r o l 1 ( 2 0 0 7 ) 1 5 1 – 1 5 7156

activity towards CO2 between amines that are not sterically

hindered.

6. Reaction kinetics

The kinetics of CO2 in aqueous amine systems is of great

importance in determining the viability of a given solvent. Fast

kinetics is by itself preferable as a given degree of CO2

separation can be achieved with a smaller absorption column

than would be the case with slower kinetics. General insight

into differences in kinetics between different amines is

therefore of importance in solvent selection.

We suggest that that there is a simple overall correlation

between the kinetics and the free energy for the main

reactions of CO2 absorption, these reactions being carbamate

formation and bicarbonate formation. The kinetics of carba-

mate formation is significantly faster than that of bicarbonate

formation (Versteeg et al., 1996), and for a carbamate forming

system we would therefore expect the carbamate formation

kinetics to dominate. The results in Fig. 10 do strongly suggest

such a correlation between overall kinetics and free energy for

carbamate formation. For amines that do not form carbamate

the main reaction is bicarbonate formation, the free energy of

reaction is in this case a function of the base strength of the

amine. In Fig. 11, the base strength of tertiary amines (that do

not form carbamate) are plotted against kinetic data (second-

order rate constants, data from Versteeg et al., 1996). Again a

fairly strong correlation can be seen between the free energy of

reaction and rate of reaction. These observed correlations

between free energies of reaction and kinetics, suggest that

reaction kinetics can be predicted from equilibrium data.

This observed relationship between chemical equilibrium

and kinetics do have implications for the search for solvents

with optimal properties. Ideally, one might want a solvent

with fast kinetics and low reaction energies. Since these

characteristics are inversely proportional the focus should

Fig. 11 – Brønsted plot for tertiary amines in aqueous

solutions. Data from Versteeg et al. (1996).

perhaps be on finding the optimal tradeoff between desired

kinetics and reaction energies.

7. Conclusion

The review of reaction mechanisms suggest that the absorp-

tion of CO2 in aqueous amine systems can be accounted for

with a small set of reactions. Base-catalyzed bicarbonate

formation is found to be a likely mechanism for all amines

with appropriate base strength. It would seem unlikely that

the carbamate species undergo direct conversion to bicarbo-

nate species. Carbamate formation seems likely to proceed

either as a single-step termolecular reaction or through a two

step reaction, with a short-lived zwitterion intermediate.

The strength of amines as bases and the stability of the

carbamate species they form are determined by a number of

factors. Solvent stabilization, electron donation and with-

drawal through bonds, and sterical effects all play a part. In the

literature on CO2 absorption, too much attention has perhaps

been given to sterical effects in explaining variations in

reactivity.

There appears to be strong correlations between carbamate

stability, base strength and the reaction kinetics of different

amine solvents. For carbamate forming solvents, the reaction

kinetics can be estimated from the reaction energy of

carbamate formation. For solvents that do not form carbamate

(mainly tertiary amines) the kinetics can be estimated from

the base strength. The correlation between equilibrium and

kinetics should be taken into account in the search for optimal

solvents for a given absorption process.

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