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Synlett 2013; 24(19): 2519-2524
DOI: 10.1055/s-0033-1339545
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© Georg Thieme Verlag Stuttgart · New York

Is the Isodesmic Reaction Approach a Better Model for Accurate Calculation of pK a of Organic Superbases? A Computational Study

Abul Kalam Biswas
a   Computation and Simulation Unit (Analytical Discipline and Centralized Instrument Facility), CSIR-Central Salt & Marine Chemicals Research Institute, Bhavnagar, Gujarat, 364 002, India
b   Academy of Scientific and Innovative Research, CSIR-Central Salt & Marine Chemicals Research Institute, Bhavnagar, Gujarat, 364 002, India   Fax: +91(278)2567562   Email: ganguly@csmcri.org
,
Rabindranath Lo
a   Computation and Simulation Unit (Analytical Discipline and Centralized Instrument Facility), CSIR-Central Salt & Marine Chemicals Research Institute, Bhavnagar, Gujarat, 364 002, India
,
Bishwajit Ganguly*
a   Computation and Simulation Unit (Analytical Discipline and Centralized Instrument Facility), CSIR-Central Salt & Marine Chemicals Research Institute, Bhavnagar, Gujarat, 364 002, India
b   Academy of Scientific and Innovative Research, CSIR-Central Salt & Marine Chemicals Research Institute, Bhavnagar, Gujarat, 364 002, India   Fax: +91(278)2567562   Email: ganguly@csmcri.org
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Further Information

Publication History

Received: 16 July 2013

Accepted: 18 July 2013

Publication Date:
27 August 2013 (online)

 
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Abstract

The acid-base dissociation constant (pK a) can be related to the solubility and binding of drugs. However, measuring accurate pK a values is a challenging task. In this study, we have examined the pK a of various organic superbases: naphthalenes, cyclic guanidines, vinamidines, and acyclic guanidines computationally. We have calculated the pK a of such superbases by employing two methods: a conventional thermodynamic cycle and a second method based on an isodesmic reaction. The thermodynamic cycle involves computation of solvation free energy by using gas-phase free energy and the difference in solvation free energies (∆Gsolv) between products and reactants. Calculations performed with the isodesmic reaction approach do not use the free energy of solvation; hence, the accuracy of the approach is less sensitive to solvent molecules and global charges of the calculated species. The root-mean-square errors (RMSE) predict that the pK a of the studied organic superbases are more accurate when calculated with the isodesmic reaction approach.


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Key words

basicity - dissociation constant - organic superbases - isodesmic reactions

Neutral organic superbases have become prominent in organic synthesis over the last two decades.[1] [2] [3] [4] [5] [6] [7] Various types of organic superbases containing amines, imines, guanidines, phosphazenes, or quinoimines have been prepared.[8–18] The extraordinary basicity of these compounds is attained by a range of strategies including strong lone-pair repulsion, relief of lone-pair repulsion in the protonated form, strong intramolecular hydrogen bonding in the resulting conjugate acids, or noncovalent interactions.[16,17] A general feature of all organic superbases is the presence of two basic centers in the molecule (in general nitrogen atoms), that are oriented in such a way that the incoming proton forms a strong intramolecular hydrogen bond.[16] [17] Organic superbases have a wide range of applications in base-mediated transformations,[19] carbon dioxide storage,[20] and polymerization.[21]

The basicity of a superbase can be measured in the gas phase, but the measurement of gas-phase basicity is difficult due to a lack of suitable reference bases,[8a] the low volatility of the bases, and their tendency to undergo decomposition during measurement.[22] In the condensed phase, the basicity of organic superbases can be measured in terms of acidity constant (K a) or its negative logarithmic form (pK a). The acid equilibrium constant (K a, pK a = –log K a) is an important property of organic and inorganic compounds. In particular, aqueous pK a values are useful because of their environmental and pharmacological applications[23] such as evaluating solubility, extent of binding, and rate of absorption. In addition, the determination of dosage and the regimes of drug use are also related to pK a values.[23b]

A number of experimental methods have been employed to predict pK a values of organic superbases.[24] However, the measurement of basicity of a superbase in a protic solvent is also difficult because the bases undergo association and decomposition. The basicity of superbases can be readily measured in aprotic solvents such as dimethylsulfoxide, tetrahydrofuran and acetonitrile.[25] [26] The advantages of the use of dipolar aprotic solvents are that the intrinsic properties of the bases are expressed to a higher extent. For practical purposes, acetonitrile has commonly been used because it is weakly basic with a high dielectric constant (36.0) and is chemically inert,[27] favoring the dissociation of ion pairs into free ions.

Several theoretical models have been proposed to calculate pK a values of species in solution.[28] The estimation of pK a values of various superbases in acetonitrile has been carried out by correlating the proton affinities in the solvent with the experimental pK a(MeCN). Theoretical pK a calculations using the proton affinity values calculated in the isodensity polarized continuum model (IPCM) show good agreement with the available measured data for guanidines, polyguanidines and related polycyclic compounds.[29] However, the prediction of pK a(MeCN) using such linear relationships fails for molecules possessing multiple intramolecular hydrogen bonds. Furthermore, the calculated linear relationships are system dependent and the pK a values for different organic superbases are calculated using different linear relationships.[10b] [29] [30] Therefore, a more reliable approach for accurate pK a calculation of various superbases is warranted.

The purpose of the present work was to compare different computational methods for pK a estimation of organic superbases against experimental pK a values. The series of organic superbases involving naphthalene frameworks, cyclic guanidines, vinamidines and acyclic guanidines chosen for examination is shown in Figure [1].

Zoom Image
Figure 1 Organic superbases examined

The experimental pK a values in acetonitrile at 25 °C of these organic superbases are available for comparison with the calculated results. Herein, we report the use of two methods: the conventional method using the thermodynamic cycles[13a] [b] and a method based on the isodesmic reaction approach.[31] In the conventional method, the pK a value is calculated by using the gas-phase free energy and solvation-phase free energy of the bases under study. In the second method, an isodesmic reaction is used to calculate the pK a values of organic superbases. This method has been used to calculate the pK a of substituted pyridines and carbon acids, giving results that are in good agreement with the corresponding experimentally measured values.[31]

All the superbases examined have pK a values that are reported in the literature.[32] In the thermodynamic cycle method, pK a values were calculated by using the change of Gibbs free energies for the dissociation of acids in solution (see Eq. 1 in the Supporting Information). The free energy change for the reaction was computed by using gas-phase free energies and solvation energies, the latter was calculated by using the continuum solvation model. In general, the solvation free energy for neutral and charged species can be predicted with an average error of 1 and 5 kcal mol–1, respectively.[33] In this thermodynamic cycle method, the solvation free energies contribute to the larger error in the pK a calculations. However, the pK a calculations for small amines, imines and carbenes are in good agreement with the corresponding experimentally measured values.[13] [20b] In the isodesmic reaction approach, the error in the calculation of Gibbs free energies in solution (∆Gsoln) is cancelled due to subtraction of the gas-phase and solvation free energies of the reactants and products. This method predicts the pK a values accurately for compounds that also undergo large conformational changes during the solvation process and species such as zwitterionic tautomers that are unstable in the gas phase.[31] The accuracy of the results is less sensitive to the presence of explicit water molecules and charged molecules because the method does not use the free energy of solvation and also predicts the basicity of the molecules that undergo large conformational changes.[31]

The first naphthalene-based superbase, 1,8-bis(dimethylamino)naphthalene (DMAN; Figure [2]) was reported by Alder et al.[34] and has found a range of applications including conversion of optically active alcohols into ethers, debromination, and cyclization reactions.[35] This compound has a basicity of ca. 106 times higher than other similar organic amines.[34] It has been reported that the basicity can be enhanced by the inclusion of various electron-donating groups at the ortho- and para-positions of the naphthalene nucleus and also at the nitrogen centers.[32a] The π-electron-releasing NMe2 group at the para-position of the naphthalene nucleus increases the electron density on the protonation site through π-resonance and results in a greater pK a for compound 1. Furthermore, the introduction of the more inductively electron-donating ethyl group on the nitrogen centers in 2 and 3 increases the pK a values of the systems compared with the parent DMAN. However, the electron-withdrawing NHCOMe group present at the para-position of the naphthalene nucleus decreases the electron density at the nitrogen center of compound 4. Consequently, compound 4 shows the lowest basicity (pK a 18.35) in this series. Finally, ortho-chloro-substituted DMAN 5 shows an enhanced pK a value due to the ‘buttressing effect’ created by the ortho substituent (Table [1]),[32a] which forces both dialkylamino groups towards each other, resulting in greater steric strain in the unprotonated system that is relieved upon protonation.

Zoom Image
Figure 2 Reference compounds used in the isodesmic reaction approach

We compared the pK a values of compounds 1–5 calculated by the thermodynamic cycle method against their experimentally determined pK a values (Table [1]) and found that the calculated pK a values of these compounds showed large absolute error from the experimental values. The largest and smallest errors were –1.65 pK a unit (compound 4) and –0.07 pK a unit (compound 1), respectively. The calculated RMSE value for compounds 1–5 was 1.07 pK a unit (Table [1]).

We then calculated the pK a values of compounds 1–5 by using the isodesmic reaction approach. A reference system is required for the pK a calculation using this method, and 1,8-bis(dimethylamino)naphthalene was used as such a reference compound (Figure [2]). The calculated pK a value of compound 1 by using the isodesmic reaction approach was 19.97, which is in very good agreement with the experimental value (19.15; Table [1]). Furthermore, we have calculated the pK a values of compounds 2–5 (Table [1]) and found that the calculated and experimental pK a values were in good agreement. The absolute errors vary from 0.82 to –0.07 pK a units. The RMSE value for compounds 1–5 obtained by using the isodesmic reaction approach is much lower (0.48 pK a unit) compared with those obtained by using the thermodynamic cycle method (Table [1]). These pK a calculations suggest that the pK a of compounds 1–5 can be better described by the isodesmic reaction approach than by the conventional thermodynamic cycle method.

Table 1 Calculated and Experimental pK a Values of Five Naphthalene Superbases

Compound

Thermodynamic cycle methoda

Isodesmic reaction approacha

Experimental values[32a]

1

19.08 (_0.07)

19.97 (+0.82)

19.15

2

17.78 (_0.72)

18.68 (+0.18)

18.50

3

17.73 (_0.97)

18.63 (_0.07)

18.70

4

16.70 (_1.65)

17.79 (_0.56)

5

17.10 (_1.25)

17.99 (_0.36)

MAXE

_1.65

 0.82

MUE

 0.93

 0.40

MSE

–0.93

 0.00

RMSE

 1.07

 0.48

a Numbers shown in parentheses are the deviations of the calculated values compared to the experimental values.

Table 2 Calculated and Experimental pK a Values of Three Cyclic Guanidine Superbases

Compound

Thermodynamic cycle methoda

Isodesmic reaction approacha

Experimental values[32d]

6

24.66 (0.11)

23.36 (_1.19)

24.55

7

27.96 (2.00)

26.70 (0.74)

25.96

8

28.27 (2.84)

26.99 (1.56)

25.43

MAXE

 2.00

 1.56

MUE

 1.65

 1.16

MSE

 1.65

 0.37

RMSE

 2.01

 1.21

a Numbers shown in parentheses are the deviations of the calculated values compared to the experimental values.

We next examined the pK a values for the cyclic guanidine systems containing both imine and amine functionality. The experimental pK a value of compound 6 in acetonitrile is 24.55 (Figure [1, ]Table [2]). However, five-membered-ring containing guanidines are weaker bases than those possessing six- and seven-membered rings, which has been shown to be associated with smaller ring strain.[36] Cyclic guanidine 7 shows higher basicity than 6 due to relief of the strain (Figure [1, ]Table [2]).[36] The methylation product of 1,5,7-triazabicyclo[4,4,0]dec-5-ene (TBD), MTBD shows a lower basicity than TBD. These compounds are extensively used in organic synthesis as catalysts.[37]

The pK a values of cyclic guanidines 6–8 were calculated by employing the thermodynamic cycle method and compared with the experimental values (Table [2]). For cyclic guanidine systems 6–8, the absolute errors are high and the calculated RMSE value is 2.01 (Table [2]).

We then examined pK a values by using the isodesmic reaction approach, with 5,6,7,8-tetrahydroimidazo[1,2-a]pyrimidine as the reference (experimental pK a 23.79; Figure [2]).[32d] The variations in the absolute errors is lower for compounds 6–8 than those obtained with the thermodynamic cycle method (Table [2]). The RMSE values calculated by using the thermodynamic cycle method showed higher values than those obtained with the isodesmic reaction approach (Table [2]).

We then extended our study to polycyclic amidine systems (vinamidines). Such compounds, which were first reported by Schwesinger et al.,[32c] possess very high basicity. The high basicity of these compounds is due to destabilization of the lone pair interactions of the chelate forming nitrogen atoms being diminished on protonation because the nitrogen atoms are closer in the protonated form, enhancing conjugation.[37] The introduction of a double bond into the imidazoline ring increases the basicity of compound 10 compared with 9 due to the greater extent of π-conjugation in the protonated form.[37] The basicity of compound 11 is greater than 9 due to the inclusion of an additional methylene unit in the ring, as a result the nitrogen atoms become closer to each other.

We calculated the pK a value of compounds 9–11 by employing the thermodynamic cycle method and compared the results to the experimental values (Table [3]). The calculated RMSE value is 4.86 pK a units (Table [3]).

The methyl derivative of pentacyclic vinamidine was used as the reference in the isodesmic reaction approach (experimental pK a 30.03; Figure [2]).[32c] We calculated the pK a value of compounds 9–11 and compared these with the experimental values. The calculated RMSE of compounds 9–11 were found to be 1.28 pK a units (Table [3]).

Table 3 Calculated and Experimental pK a Values of Three Vinamidine Superbases

Compound

Thermodynamic cycle methoda

Isodesmic reaction approacha

Experimental values[32c]

 9

34.97 (+5.77)

28.25 (_0.95)

29.20

10

37.15 (+5.21)

30.35 (_1.16)

31.94

11

32.77 (+3.26)

25.96 (_3.55)

29.51

MAXE

 5.77

–3.55

MUE

 4.74

 1.87

MSE

 4.74

–1.87

RMSE

 4.86

 1.28

a The numbers shown in parentheses are the deviations of the calculated values compared to the experimental values.

Finally, pK a calculations were performed on the flexible acyclic guanidine superbases. These superbases contain multiple intramolecular hydrogen bonds formed through corona effects.[12b] [38] Proton affinities calculated in acetonitrile medium are less accurate for such flexible molecules and hence the predictions of pK a values are also less reliable.[30] The high basicity of these guanidine derivatives is due to the construction of highly effective conjugation systems after protonation under the reversible conditions, stabilization by intramolecular hydrogen bonding, and because of the effect of solvation on the stability of the protonated form.[39] The basic amino acid arginine, having a guanidine group in the side chain, can act as a base catalyst for enzymatic reactions.[40]

The introduction of an inductively electron-donating methyl group at the imine nitrogen atom of N,N,N',N'-tetra­methylguanidine (TMG, 12) increases the basicity of the resulting pentamethylguanidine (PMG, 13; Table [4]).[32b] Additionally, the introduction of heteroalkyl chains into the guanidine systems enhances their basicity further due to the ability to form multiple intramolecular hydrogen bonds in the protonated forms. The incorporation of a dimethylaminopropyl chain at the imine nitrogen atom and the double replacement of the methyl group at the amine nitrogen atom of TMG by hydrogen and propyl groups leads to a considerable increase in the pK a value (25.85) of 14. The presence of a propyl group at the imine nitrogen and a dimethylaminopropyl chain at the amine nitrogen atom of TMG leads to compound 15, with an even greater pK a value of 26.63. Finally, the introduction of a dimethylaminopropyl chain at the imine and amine nitrogen atoms of TMG results in 16, with the highest pK a value in the series due to the greater stabilization of the protonated form through three intramolecular hydrogen bonds. The gas-phase basicity of compound 16 was found to be comparable to that of P2 phosphazene;[41] whereas the presence of a methoxypropyl chain in TMG leads, in 17, to a decrease in the pK a value compared to 16 (Table [4]).

The calculated pK a values of compounds 12–17 obtained by employing the thermodynamic cycle method showed high absolute errors with respect to the experimental results (Table [4]). The absolute errors vary from 3.11 to 0.07 pK a units and the calculated RMSE is 1.30 pK a units (Table [4]).

N'-Propyl-N''-di(3-methoxypropyl)guanidine was chosen as a reference system for the isodesmic reaction approach (experimental pK a 24.84; Figure [2]).[32b] The calculated pK a values of compounds 12–17 were in good agreement with the experimental values (Table [4]). In this case, the absolute errors vary from _0.99 to _0.05 pK a units and the calculated RMSE value is 0.53 pK a units. Based on these values, it appears that the isodesmic reaction approach is more accurate for predicting the pK a than the thermodynamic cycle method for acyclic superbases such as guanidines.

Table 4 Calculated and Experimental pK a Values of Six Acyclic Guanidine Superbases

Compound

Thermodynamic cycle methoda

Isodesmic reaction approacha

Experimental values[32b]

12

23.37 (0.07)

22.90 (_0.40)

23.30

13

25.40 (0.40)

24.90 (_0.10)

25.00

14

26.27 (0.42)

25.80 (_0.05)

25.85

15

26.42 (_0.21)

25.94 (_0.69)

26.63

16

30.26 (3.11)

26.16 (_0.99)

27.15

17

25.04 (0.30)

24.56 (–0.18)

24.74

MAXE

–3.11

–0.99

MUE

0.75

0.40

MSE

–0.35

–0.40

RMSE

1.30

0.53

a Numbers shown in parentheses are the deviations of the calculated values compared to the experimental values.

In conclusion, we have calculated the pK a values of a range of nitrogen-containing organic superbases by employing two different approaches. The superbases studied cover nitrogen bases including amines, imines and guanidines. The isodesmic reaction approach is more accurate in describing the pK a of naphthalene-based superbases, cyclic guanidines, and vinamidines compared with the more studied thermodynamic cycle method. The RMSE values calculated with the isodesmic reaction approach are lower than with the thermodynamic cycle method. The isodesmic approach appears to predict the pK a values with good accuracy for the acyclic systems with multiple intramolecular hydrogen bonds, which is a concern that has been highlighted previously in the literature. These analyses suggest that the isodesmic reaction approach can be an important tool that can be used to calculate the pK a of designed organic superbases.


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Acknowledgment

A.K.B. is grateful to UGC, New Delhi, India, for the award of a Junior Research Fellowship, R.L. is grateful to UGC, New Delhi, India, for the award of a Senior Research Fellowship, and B.G. thanks DST, New Delhi, and MSM, SIP for financial support of this work.

Supporting Information

    for this article is available online at http://www.thieme-connect.com.accesdistant.sorbonne-universite.fr/ejournals/toc/synlett.
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Zoom Image
Figure 1 Organic superbases examined
Zoom Image
Figure 2 Reference compounds used in the isodesmic reaction approach