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First principles prediction of aqueous acidities of some benzodiazepine drugs
Accepted Manuscript Research paper First principles prediction of aqueous acidities of some benzodiazepine drugs Bahram Ghalami-Choobar, Ali Ghiami-Shomami, Soheila AsadzadehKhanghah PII: DOI: Reference:
S0009-2614(18)30524-4 https://doi.org/10.1016/j.cplett.2018.06.044 CPLETT 35743
To appear in:
Chemical Physics Letters
Received Date: Accepted Date:
11 March 2018 20 June 2018
Please cite this article as: B. Ghalami-Choobar, A. Ghiami-Shomami, S. Asadzadeh-Khanghah, First principles prediction of aqueous acidities of some benzodiazepine drugs, Chemical Physics Letters (2018), doi: https://doi.org/ 10.1016/j.cplett.2018.06.044
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First principles prediction of aqueous acidities of some benzodiazepine drugs
Bahram Ghalami-Choobar*, Ali Ghiami-Shomami, and Soheila Asadzadeh-Khanghah Department of Chemistry, Faculty of Science, University of Guilan, P.O. Box: 19141, Rasht, Iran
*Corresponding author: E-mail: [email protected] , Phone: +0981333367262
Abstract In this study, aqueous acidities of several benzodiazepine (BZD) drugs including Oxazepam, Clonazepam, Nitrazepam, Flunitrazepam, Diazepam, Alprazolam, Estazolam, Temazepam, Medazepam
and
Bromazepam
were
successfully
computed
using
two
common
thermodynamic cycles. To that, calculated gas phase Gibbs free energies at PBE1PBE/6311+G(d,p) level of theory and computed solvation Gibbs free energies at (CPCM/IEF-PCM: UAKS, UAHF and UA0)/HF/6-31+G(d) levels of theory were combined. The most accurate pKa values were obtained with thermodynamic cycle involving water and using CPCM-UA0 solvation model with MAD = 0.4. Moreover, for the first time, aqueous pKa value of Halazepam was predicted using the best method equal to 3.1.
Keywords: Benzodiazepine; pKa; Thermodynamic cycle; Solvation model; Cavity model.
1
1. Introduction
The exact determination and estimation of the acidity of chemical compounds is a significant subject of general interest for chemists as well as a matter of practical interest for chemical and pharmaceutical industries [1]. Most drugs are weak acids or bases and the pKa value of a drug influences its lipophilicity, solubility, protein binding and permeability which in turn directly affect its pharmacokinetic characteristics such as absorption, distribution, metabolism and excretion [2,3]. Therefore, the pKa measurement or prediction is the most important parameter in the drug development process [4]. The pKa values are usually measured through various experimental methods such as voltammetry [5], spectroscopy [6], potentiometry [7], conductometry [8] and capillary electrophoresis [9]. However, the experimental pKa measurements of drugs may involve some approximations and are not always practical [9,10]. Thus, an alternative computational method is needed for predicting pKa values in various chemical systems. In addition, the link between theoretical and experimental data can facilitate the development of predictive models to determine the pKa of compounds for which experimental data are not yet available [11–17]. Therefore, first principles prediction of the pKa of chemical compounds and drugs in aqueous solution has received a considerable amount of attention in recent years. For instance, several works have been performed to accurately model acid–base equilibria in gas and/or liquid phases for several small organic acids [18-20], inorganic acids [20-26], phenols [27-30],
carboxylic acids [30,31], peptides [32], alkyl phosphates [33], alcohols [27,28], amines [3436] and some drugs [37] using various computational methods. Along with our previous studies about the pKa calculations of organic compounds and drugs [11–13, 38], in the present study, a theoretical method has been applied to determine pKa values of ten benzodiazepine (BZD) drugs including Oxazepam, Clonazepam, Nitrazepam, Flunitrazepam,
Diazepam,
Alprazolam,
Estazolam,
2
Temazepam,
Medazepam
and
Bromazepam in aqueous solution (see Fig 1). The pKa value refers to the deprotonation of the N-4 position in the cationic form of the parent. These BZDs are the most widely prescribed minor tranquilizers in current use. They are known to act on the central nervous system and to have hypnotic, tranquillizing and anticonvulsant properties. They are also used in the management of many psychiatric disorders [39]. To find the pKa values of the BZDs, two kinds of thermodynamic cycles, two types of solvation models, and several cavity models were applied. Then, the correlation equation between experimental and calculated pKa values of the investigated BZDs was found. Also, the aqueous pKa value of Halazepam, for which there is currently no experimental data, was predicted using the most accurate computational method.
2. Methods 2.1. Theoretical model Various theoretical methods such as Hammett equation [40], quantitative structure–property relationship (QSPR) model [41] and thermodynamic cycles [42] have been presented to predict the pKa values of compounds. Among the mentioned methods, the last method is popular and presents an effective way to indirectly evaluate the condensed phase free energy change of the acid dissociation reaction, a quantity which solely determines the acidity constant [19]. In this work, the pKa values of the BDZ drugs in aqueous solution were calculated using the thermodynamic cycles A and B (See Figs. 2a and 2b).
2.1.1 Thermodynamic cycle A In the thermodynamic cycle A, the pKa values of investigated drugs in aqueous solution were computed in according to the following equation [19,37]:
pK a
G *s ln 2.303RT
(1)
3
where, G *s ln , indicates the overall change in Gibbs free energy of protonated molecule in aqueous solution that is equal to the sum of the two expressions in according to the equation 2: G*s ln G g G*solv
(2)
where, G g , represents the change in the gas phase Gibbs free energy, and G *solv , is the change in Gibbs free energy of solvation, in according to the equations 2 and 3. G g G g ,H G g ,B G g ,BH
(3)
G *solv G *solv,H G *solv,B G *solv,BH
(4)
An experimental value taken from the literature was used for G *solv,H in water equal to 265.9 kcal mol-1 [12]. As well, G g ,H was calculated from the Sackur–Tetrode equation for gas phase mono atomic species. This value was obtained for G g ,H equal to – 6.28 kcal mol-1 at 298.15 K and 1 atm [19]. Also, a correction of –RTln24.46 was also included in the calculations, to convert from a standard state of 1 atm to 1 M [37]:
G*g (1M) G g (1atm) RT ln 24.46
(5)
Therefore, the Gibbs free energy of a protonated molecule in aqueous solution can be calculated according to equation (6). G *s ln G g,B G g ,BH G *solv,B G *solv,BH 270.29
(6)
Cycle A is by far the most commonly used because of its simplicity [43].
2.1.2 Thermodynamic cycle B Thermodynamic cycle B is based on a transfer of proton to water and has some advantages over cycle A. Specifically, the use of water as a co-reactant is sometimes necessary for an accurate representation of the actual chemistry occurring in solution [43]. In fact, such cycle 4
is used to represent the real chemistry occurring in a solution. Therefore, aqueous pKa values of the studied drugs were calculated based on the thermodynamic cycle B using the equations (7–9): pK a
G*s ln log[H 2O] 2.303RT
(7)
G g G g ,H O G g ,B G g ,BH G g ,H2O
(8)
3
G *solv G *solv,H O G *solv,B G *solv,BH G *solv,H2O
(9)
3
Where, the empirical values were used for G *solv,H O and G*solv,H 2O are equal to -110.30 kcal 3
mol-1 and -6.32 kcal mol-1, respectively [11].
2.2. Computational details Firstly, gas phase geometries of all the B and BH+ species were optimized at PBE1PBE/6311+G(d,p) level of theory at 298.15 K. Recently, it has been found that this level of theory is a reliable level with a reasonable computational cost for the calculations of gas phase basicities and acidities for a series of compounds containing neutral bases [44]. Then, frequency calculations were also performed at the same level of theory to characterize the stationary points obtained and to calculate the gas phase thermal and entropic corrections. After that, the gas phase Gibbs free energies changes, G g , were calculated using equations (3) and (8). Also, to assess solvation and cavity model effects on solvation Gibbs free energies and also pKa values, CPCM and IEFPCM solvation models and UAKS, UAHF, and UA0 cavities were selected. These calculations were performed on the optimized structures in gas phase and at the HF/6-31+G(d) level of theory, since continuum solvation models are parameterized at low levels of theory [43]. Finally, the solution phase Gibbs free energies and hence pKa values were determined through a combination of gas phase and solvation Gibbs
5
free energies based on thermodynamic cycles A and B, and the use of equations (1) and (7). All calculations were performed using the Gaussian 09 software [45].
3. Results and discussion 3.1. Calculation of pKa values of the BZDs Table 1 indicates the calculated Gibbs free energies in gas phase for studied compounds and its cationic forms at the PBE1PBE/6-311+G(d,p) level of theory. The optimized structures of the BZDs and their corresponding cationic forms are given in Tables S1-S11 in the supporting information. Also, Table 2 illustrates the computed solvation Gibbs free energies of investigated drugs and their corresponding cationic forms in water solvent with the CPCM and IEF-PCM solvation models together with UAHF, UAKS and UA0 cavities at the HF/631+G(d) level of theory. The obtained results show that calculated solvation Gibbs free energies using UAKS cavity are larger (more negative) than other cavities. Also, the IEFPCM solvation model led to more positive solvation Gibbs free energies than the CPCM solvation model. Also, Table 3 shows the calculated pKa values of BZD drugs using DFT method in gas phase and various solvation models in liquid phase based on thermodynamic cycles A and B. To assess the accuracy of the results, mean absolute deviations (MAD) values were computed using the available experimental pKa values. Table 3 demonstrates that the calculated pKa values using thermodynamic cycle B are more accurate than those obtained using thermodynamic cycle A. It is notable that this trend is there in all cavity types and solvation models. Therefore, obtained MAD values show that consideration of water in thermodynamic cycle can describe the studied process more accurately. Also, the results indicate that there is a little difference between CPCM and IEF-PCM solvation models as it is about 0.1 pKa units. Also, among cavity models, UA0 radii led to more reliable results than UAHF and UAKS cavities. Moreover, to analyze the results in more details, the correlations
6
between the calculated and experimental pKa values of the BZDs were established for the best methods (see Figs. 3a and 3b). The comparison of the corresponding squared correlation coefficients in equations (10) and (11) indicate that the CPCM solvation model based on the thermodynamic cycle B is more accurate than the IEF-PCM solvation model. pKa (Corr) = 0.772 pKa (CPCM-UA0-Cycle B) + 0.733
R2 = 0.971
(10)
pKa (Corr) = 0.763 pKa (IEF-PCM-UA0-Cycle B) + 0.812
R2 = 0.970
(11)
Consequently, applied thermodynamic cycle B with CPCM- UA0 solvation model with MAD = 0.4 and very good squared correlation coefficients (R2=0.971) was selected as the most reliable method for calculation of pKa of the BZDs (see Fig 3, a). Also, the same thermodynamic cycle with IEF-PCM-UA0 solvation model with MAD = 0.5 and very good squared correlation coefficients (R2= 0.970) can be considered as an alternative choice (see Fig 3, b).
3.2. Prediction of aqueous pKa value for the Halazepam drug In order to extend the available pKa data for BZD drugs, Halazepam drug as a BZD derivative was selected and its pKa value was predicted. Halazepam is a 1, 4-benzodiazepine which has anxiolytic properties and can be considered as a derivative of the Diazepam drug with CF3 substitution, a strong electron withdrawing group. To the best of our knowledge, there is not any literature reporting its pKa and the current study is the first one. For this aim, the best computational method confirmed in the previous section was used. In gas phase, the Halazepam and its corresponding cationic form were optimized at PBE1PBE/6-311+G(d,p) level of theory and in aqueous phase, CPCM-UA0/HF/6-31+G(d) level of theory was applied. Then, pKa values of the Halazepam were predicted using equations 7 and 10. Table 4 shows the computed gas phase and solvation Gibbs free energies for the Halazepam and its cationic form through our proposed method. The predicted pKa value of the Halazepam drug using the
7
best method and its corresponding correlation equation are 3.1. These predictions are reasonable, because CF3 substituent makes the Halazepam more acidic than the Diazepam drug.
Conclusions In this work, the aqueous pKa values of ten benzodiazepine derivatives have been successfully obtained. For this aim, the calculated gas phase Gibbs free energies at PBE1PBE/6311+G(d,p) level of theory and the computed solvation Gibbs free energies utilizing CPCM and IEF-PCM solvation models and UAKS, UAHF and UA0 cavity models at HF/6-31+G(d) level of theory were combined through two various thermodynamic cycles. The results indicated that CPCM-UA0 and IEF-PCM-UA0 solvation models based on thermodynamic cycle involving water provide the highest accuracies with (MAD = 0.4, R2 = 0.971) and (MAD = 0.5, R2 = 0.970), respectively. Also, among the cavity models, the UA0 radius was the best one to calculate the pKa values for the BZDs. It can be concluded that the type of cavity model plays a very important role in the obtained pKa values. As well, comparison of results shows a good agreement between the experimental and the calculated pKa values of the investigated drugs. Therefore, to extend pKa database for the BZDs, the pKa value of the Halazepam drug as a BZD derivative in water solvent was predicted using the optimized method and also its corresponding correlation equation. This work, for the first time, predicted the pKa value for the Halazepam drug equal to 3.1. It can be concluded that the theoretical methods proposed in the current study are predictive and can act as a useful tool for prediction of pKa values of the compounds with similar structures to the BZDs.
Acknowledgments
8
We gratefully acknowledge the graduate office of University of Guilan for supporting of this work. The Authors also would like to thank Professor Michelle L. Coote (Research School of Chemistry, Australian National University) for her helpful comments about the work. In addition, Authors would like to thank Miss Mona Ashtari-Delivand (PhD. Student in physical chemistry in University of Guilan) for her contribution.
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Gomperts, R. E. Stratmann, O. Yazyev, A. J. Austin, R. Cammi, C. Pomelli, J. W. Ochterski, R. L. Martin, K. Morokuma, V. G. Zakrzewski, G. A. Voth, P. Salvador, J. J. Dannenberg, S. Dapprich, A. D. Daniels, O. Farkas, J. B. Foresman, J. V. Ortiz, J. Cioslowski, and D. J. Fox, Gaussian, Inc., Wallingford CT, 2009. [46] N. J. K. Simpson, Solid-phase extraction: principles, techniques, and applications, Marcel Dekker, New York, 2000. [47] J. Karppi, S. Akerman, K. kerman, A. Sundell, K. Nyyssonen, I. Penttila, Eur. J. Pharm. Biopharm. 2007, 67, 562–568. [48] R. J. Prankerd, Profiles of drug substances, excipients, and related methodology, 2007, 33, 1–33. [49] Recommended Methods for the Detection and Assay of Barbiturates and Benzodiazepines in Biological Specimens: Manual for Use by National Laboratories, United Nations, New York, 1997.
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Figures Captions:
Fig 1. The Structures of the studied BZD drugs Fig 2. The thermodynamic cycles A (a) and B (b) applied in this work. Fig 3. Correlations between experimental and calculated pKa values obtained using (a) CPCM-UA0 and (b) IEF-PCM-UA0 solvation models based on thermodynamic cycle B.
(Oxazepam)
(Clonazepam)
(Nitrazepam)
(Flunitrazepam)
(Diazepam)
(Alprazolam)
(Estazolam)
(Temazepam)
13
(Medazepam)
(Bromazepam)
Fig 1.
(a)
(b)
Fig 2.
14
8
pKa(Corr) = 0.772 pKa (CPCM-UA0-B) + 0.733 R2=0.971 MAD = 0.4
7 pKa (Corr)
6 5 4 3 2 1
0 0
1
2
3
4
pKa (CPCM-UA0-B)
(a)
15
5
6
7
8
8
pKa(Corr) = 0.763 pKa (IEFPCM-UA0-B) + 0.812 R2=0.970 MAD = 0.5
7 pKa (Corr)
6 5 4 3 2 1
0 0
1
2
3
4
5
6
7
8
pKa (IEFPCM-UA0-B)
(b)
Fig 3.
Table Captions: Table 1. Calculated gas phase Gibbs free energies (in kcal mol-1) of drugs and its cationic forms at PBE1PBE/6-311+G(d,p) level of theory. Table 2. Computed solvation Gibbs free energies (in kcal mol-1) of BZDs and its cationic forms in water solvent using CPCM and IEF-PCM solvation models with UAKS, UAHF and UA0 cavities at HF/6-31+G(d) level of theory. Table 3. Calculated pKa values of BZDs using thermodynamic cycles A and B together with their corresponding MADs values. Table 4. Structure, gas phase and solvation Gibbs free energies (in kcal mol-1) for Halazepam drug with its predicted pKa value.
16
Table 1. G°g(kcal mol-1)
Drugs BH+
B
Oxazepam
-814298.4
-814073.8
Clonazepam
-895363.0
-895137.3
Nitrazepam
-607042.5
-606816.3
Flunitrazepam
-693904.5
-693679.3
Diazepam
-791758.6
-791526.0
Alprazolam
-837110.8
-836881.1
Estazolam
-812474.9
-812246.9
Temazepam
-838929.1
-838696.9
Medazepam
-745322.9
-745082.8
Bromazepam
-837110.8
-836881.1
Water
-48087.0
-47921.7
Table 2
UAKS
G *solv (kcal .mol-1) UAHF
UA0
Oxazepam BH+ B
-64.9 (-64.6)a -16.4 (-16.1)
-61.6 (-61.3) -14.0 (-13.8)
-61.0 (-60.7) -12.5 (-12.3)
Clonazepam BH+ B
-65.2 (-64.9) -16.7 (-16.5)
-60.9 (-60.7) -13.4 (-13.2)
-58.8 (-58.6) -11.1 (-10.9)
Nitrazepam BH+
-68.1 (-67.8)
-63.7 (-63.5)
-61.1 (-60.8)
Drugs
17
B
-17.6 (-17.3)
-14.3 (-14.1)
-11.6 (-11.3)
Flunitrazepam BH+ B
-62.2 (-61.9) -12.4 (-12.3)
-59.0 (-58.8) -10.4 (-10.2)
-51.5 (-51.2) -3.3 (-3.2)
Diazepam BH+ B
-55.2 (-54. 9) -9.4 (-9.2)
-53.2 (-53.0) -8.4 (-8.2)
-45.6 (-45.9) -1.4 (-1.2)
Alprazolam BH+ B
-60.69 (-60.42) -14.64 (-14.44)
-58.43 (-58.18) -13.24 (-13.06)
-50.17(-49.91) -5.13 (-4.94)
Estazolam BH+ B
-62.92 (-62.65) -15.44 (-15.24)
-60.69 (-60.44) -14.13 (-13.95)
-55.56 (-55.30) -9.02 (-8.82)
Temazepam BH+ B
-53.53 (-53.28) -11.76 (-11.57)
-51.66 (-51.42) -10.65 (-10.47)
-46.48 (-46.25) -4.91 (-4.73)
Medazepam BH+ B
-48.02 (-47.89) -5.58 (-5.46)
-46.97 (-46.85) -5.17 (-5.06)
-38.89 (-38.69) 2.29 (2.41)
Bromazepam BH+ B
-64.45 (-64.17) -15.47 (-15.28)
-60.74 (-60.50) -13.01 (-12.84)
-56.26 (-56.01) -8.88 (-8.71)
a. The values in parentheses are calculated from IEF-PCM solvation model and the others are computed from CPCM solvation model.
Table 3.
18
Drugs
pKa (calc)
pKa (Exp)
UAKS
UAHF
UA0
Oxazepam
2.1 (2.1)a
1.4 (1.3)
2.1 (2.1)
1.7b
Clonazepam
2.9 (2.8)
2.2 (2.1)
2.3 (2.2)
1.5b
Nitrazepam
4.7 (4.7)
3.9 (3.9)
4.0 (4.0)
3.2b
Flunitrazepam
3.5 (3.4)
2.6 (2.5)
2.3 (2.2)
1.8c
Diazepam
5.9 (5.9)
5.2 (5.2)
4.8 (4.7)
3.3b
Alprazolam
4.1 (4.0)
3.4 (3.4)
3.3 (3.3)
2.4b
Estazolam
3.8 (3.8)
3.1 (3.1)
3.1 (3.1)
2.8d
Temazepam
2.6 (2.6)
2.1 (2.0)
2.5 (2.5)
1.6b
Medazepam
9.0 (8.9)
8.5 (8.4)
8.1 (8.0)
6.2b
Bromazepam
4.9 (4.8)
4.0 (3.9)
3.7 (3.7)
2.9e
MAD
1.6 (1.6)
1.0 (0.9)
0.9 (0.8)
Oxazepam
1.1 (1.0)
0.3 (0.3)
1.1 (1.0)
1.7b
Clonazepam
1.8 (1.8)
1.1 (1.1)
1.2 (1.2)
1.5b
Nitrazepam
3.7 (3.6)
2.9 (2.9)
3.0 (2.9)
3.2b
Flunitrazepam
2.4 (2.4)
1.6 (1.5)
1.3 (1.2)
1.8c
Diazepam
4.9 (4.9)
4.2 (4.2)
3.8 (3.7)
3.3b
Alprazolam
3.0 (3.0)
2.4 (2.3)
2.3 (2.2)
2.4b
Estazolam
2.8 (2.7)
2.1 (2.1)
2.1 (2.0)
2.8d
Temazepam
1.6 (1.6)
1.1 (1.0)
1.5 (1.4)
1.6b
Medazepam
8.0 (8.0)
7.5 (7.5)
7.0 (7.0)
6.2b
Bromazepam
3.9 (3.8)
2.9 (2.9)
2.7 (2.6)
2.9e
MAD
0.7 (0.7)
0.6 (0.6)
0.4 (0.5)
Cycle A
Cycle B
a. The values in parentheses are calculated from IEF-PCM solvation model and the others are computed from CPCM solvation model.. b. The values are taken from ref [46]. c. The values are taken from ref [47]. d. The values are taken from ref [48]. e. The values are taken from ref [49].
19
Table 4 Halazepam
Gºg ( kcal mol-1)a G *solv (kcal mol-1)b
pKa (Cal)c pKa (Corr)
d
BH+
B
-607042.5
-606816.3
-45.83
-1.45
3.1
-
3.1
-
a. Calculated at PBE1PBE/6-311+G(d,p) level of theory. b. Computed at CPCM-UA0/HF/6-31+G(d) level of theory. c. Obtained using thermodynamic cycle B. d. Obtained using correlation equation 10.
Highlights Aqueous acidities of BZD drugs were successfully computed with MAD = 0.4 pKa unit. Thermodynamic cycle involving water was found appropriate for process description. The UA0 radius was known as the best cavity among united atom topological models. pKa database for BZD drugs was extended through the proposed computational method. For the first time, pKa value of Halazepam drug was predicted equal to 3.1.
20
Graphical
21
S0009-2614(18)30524-4 https://doi.org/10.1016/j.cplett.2018.06.044 CPLETT 35743
To appear in:
Chemical Physics Letters
Received Date: Accepted Date:
11 March 2018 20 June 2018
Please cite this article as: B. Ghalami-Choobar, A. Ghiami-Shomami, S. Asadzadeh-Khanghah, First principles prediction of aqueous acidities of some benzodiazepine drugs, Chemical Physics Letters (2018), doi: https://doi.org/ 10.1016/j.cplett.2018.06.044
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First principles prediction of aqueous acidities of some benzodiazepine drugs
Bahram Ghalami-Choobar*, Ali Ghiami-Shomami, and Soheila Asadzadeh-Khanghah Department of Chemistry, Faculty of Science, University of Guilan, P.O. Box: 19141, Rasht, Iran
*Corresponding author: E-mail: [email protected] , Phone: +0981333367262
Abstract In this study, aqueous acidities of several benzodiazepine (BZD) drugs including Oxazepam, Clonazepam, Nitrazepam, Flunitrazepam, Diazepam, Alprazolam, Estazolam, Temazepam, Medazepam
and
Bromazepam
were
successfully
computed
using
two
common
thermodynamic cycles. To that, calculated gas phase Gibbs free energies at PBE1PBE/6311+G(d,p) level of theory and computed solvation Gibbs free energies at (CPCM/IEF-PCM: UAKS, UAHF and UA0)/HF/6-31+G(d) levels of theory were combined. The most accurate pKa values were obtained with thermodynamic cycle involving water and using CPCM-UA0 solvation model with MAD = 0.4. Moreover, for the first time, aqueous pKa value of Halazepam was predicted using the best method equal to 3.1.
Keywords: Benzodiazepine; pKa; Thermodynamic cycle; Solvation model; Cavity model.
1
1. Introduction
The exact determination and estimation of the acidity of chemical compounds is a significant subject of general interest for chemists as well as a matter of practical interest for chemical and pharmaceutical industries [1]. Most drugs are weak acids or bases and the pKa value of a drug influences its lipophilicity, solubility, protein binding and permeability which in turn directly affect its pharmacokinetic characteristics such as absorption, distribution, metabolism and excretion [2,3]. Therefore, the pKa measurement or prediction is the most important parameter in the drug development process [4]. The pKa values are usually measured through various experimental methods such as voltammetry [5], spectroscopy [6], potentiometry [7], conductometry [8] and capillary electrophoresis [9]. However, the experimental pKa measurements of drugs may involve some approximations and are not always practical [9,10]. Thus, an alternative computational method is needed for predicting pKa values in various chemical systems. In addition, the link between theoretical and experimental data can facilitate the development of predictive models to determine the pKa of compounds for which experimental data are not yet available [11–17]. Therefore, first principles prediction of the pKa of chemical compounds and drugs in aqueous solution has received a considerable amount of attention in recent years. For instance, several works have been performed to accurately model acid–base equilibria in gas and/or liquid phases for several small organic acids [18-20], inorganic acids [20-26], phenols [27-30],
carboxylic acids [30,31], peptides [32], alkyl phosphates [33], alcohols [27,28], amines [3436] and some drugs [37] using various computational methods. Along with our previous studies about the pKa calculations of organic compounds and drugs [11–13, 38], in the present study, a theoretical method has been applied to determine pKa values of ten benzodiazepine (BZD) drugs including Oxazepam, Clonazepam, Nitrazepam, Flunitrazepam,
Diazepam,
Alprazolam,
Estazolam,
2
Temazepam,
Medazepam
and
Bromazepam in aqueous solution (see Fig 1). The pKa value refers to the deprotonation of the N-4 position in the cationic form of the parent. These BZDs are the most widely prescribed minor tranquilizers in current use. They are known to act on the central nervous system and to have hypnotic, tranquillizing and anticonvulsant properties. They are also used in the management of many psychiatric disorders [39]. To find the pKa values of the BZDs, two kinds of thermodynamic cycles, two types of solvation models, and several cavity models were applied. Then, the correlation equation between experimental and calculated pKa values of the investigated BZDs was found. Also, the aqueous pKa value of Halazepam, for which there is currently no experimental data, was predicted using the most accurate computational method.
2. Methods 2.1. Theoretical model Various theoretical methods such as Hammett equation [40], quantitative structure–property relationship (QSPR) model [41] and thermodynamic cycles [42] have been presented to predict the pKa values of compounds. Among the mentioned methods, the last method is popular and presents an effective way to indirectly evaluate the condensed phase free energy change of the acid dissociation reaction, a quantity which solely determines the acidity constant [19]. In this work, the pKa values of the BDZ drugs in aqueous solution were calculated using the thermodynamic cycles A and B (See Figs. 2a and 2b).
2.1.1 Thermodynamic cycle A In the thermodynamic cycle A, the pKa values of investigated drugs in aqueous solution were computed in according to the following equation [19,37]:
pK a
G *s ln 2.303RT
(1)
3
where, G *s ln , indicates the overall change in Gibbs free energy of protonated molecule in aqueous solution that is equal to the sum of the two expressions in according to the equation 2: G*s ln G g G*solv
(2)
where, G g , represents the change in the gas phase Gibbs free energy, and G *solv , is the change in Gibbs free energy of solvation, in according to the equations 2 and 3. G g G g ,H G g ,B G g ,BH
(3)
G *solv G *solv,H G *solv,B G *solv,BH
(4)
An experimental value taken from the literature was used for G *solv,H in water equal to 265.9 kcal mol-1 [12]. As well, G g ,H was calculated from the Sackur–Tetrode equation for gas phase mono atomic species. This value was obtained for G g ,H equal to – 6.28 kcal mol-1 at 298.15 K and 1 atm [19]. Also, a correction of –RTln24.46 was also included in the calculations, to convert from a standard state of 1 atm to 1 M [37]:
G*g (1M) G g (1atm) RT ln 24.46
(5)
Therefore, the Gibbs free energy of a protonated molecule in aqueous solution can be calculated according to equation (6). G *s ln G g,B G g ,BH G *solv,B G *solv,BH 270.29
(6)
Cycle A is by far the most commonly used because of its simplicity [43].
2.1.2 Thermodynamic cycle B Thermodynamic cycle B is based on a transfer of proton to water and has some advantages over cycle A. Specifically, the use of water as a co-reactant is sometimes necessary for an accurate representation of the actual chemistry occurring in solution [43]. In fact, such cycle 4
is used to represent the real chemistry occurring in a solution. Therefore, aqueous pKa values of the studied drugs were calculated based on the thermodynamic cycle B using the equations (7–9): pK a
G*s ln log[H 2O] 2.303RT
(7)
G g G g ,H O G g ,B G g ,BH G g ,H2O
(8)
3
G *solv G *solv,H O G *solv,B G *solv,BH G *solv,H2O
(9)
3
Where, the empirical values were used for G *solv,H O and G*solv,H 2O are equal to -110.30 kcal 3
mol-1 and -6.32 kcal mol-1, respectively [11].
2.2. Computational details Firstly, gas phase geometries of all the B and BH+ species were optimized at PBE1PBE/6311+G(d,p) level of theory at 298.15 K. Recently, it has been found that this level of theory is a reliable level with a reasonable computational cost for the calculations of gas phase basicities and acidities for a series of compounds containing neutral bases [44]. Then, frequency calculations were also performed at the same level of theory to characterize the stationary points obtained and to calculate the gas phase thermal and entropic corrections. After that, the gas phase Gibbs free energies changes, G g , were calculated using equations (3) and (8). Also, to assess solvation and cavity model effects on solvation Gibbs free energies and also pKa values, CPCM and IEFPCM solvation models and UAKS, UAHF, and UA0 cavities were selected. These calculations were performed on the optimized structures in gas phase and at the HF/6-31+G(d) level of theory, since continuum solvation models are parameterized at low levels of theory [43]. Finally, the solution phase Gibbs free energies and hence pKa values were determined through a combination of gas phase and solvation Gibbs
5
free energies based on thermodynamic cycles A and B, and the use of equations (1) and (7). All calculations were performed using the Gaussian 09 software [45].
3. Results and discussion 3.1. Calculation of pKa values of the BZDs Table 1 indicates the calculated Gibbs free energies in gas phase for studied compounds and its cationic forms at the PBE1PBE/6-311+G(d,p) level of theory. The optimized structures of the BZDs and their corresponding cationic forms are given in Tables S1-S11 in the supporting information. Also, Table 2 illustrates the computed solvation Gibbs free energies of investigated drugs and their corresponding cationic forms in water solvent with the CPCM and IEF-PCM solvation models together with UAHF, UAKS and UA0 cavities at the HF/631+G(d) level of theory. The obtained results show that calculated solvation Gibbs free energies using UAKS cavity are larger (more negative) than other cavities. Also, the IEFPCM solvation model led to more positive solvation Gibbs free energies than the CPCM solvation model. Also, Table 3 shows the calculated pKa values of BZD drugs using DFT method in gas phase and various solvation models in liquid phase based on thermodynamic cycles A and B. To assess the accuracy of the results, mean absolute deviations (MAD) values were computed using the available experimental pKa values. Table 3 demonstrates that the calculated pKa values using thermodynamic cycle B are more accurate than those obtained using thermodynamic cycle A. It is notable that this trend is there in all cavity types and solvation models. Therefore, obtained MAD values show that consideration of water in thermodynamic cycle can describe the studied process more accurately. Also, the results indicate that there is a little difference between CPCM and IEF-PCM solvation models as it is about 0.1 pKa units. Also, among cavity models, UA0 radii led to more reliable results than UAHF and UAKS cavities. Moreover, to analyze the results in more details, the correlations
6
between the calculated and experimental pKa values of the BZDs were established for the best methods (see Figs. 3a and 3b). The comparison of the corresponding squared correlation coefficients in equations (10) and (11) indicate that the CPCM solvation model based on the thermodynamic cycle B is more accurate than the IEF-PCM solvation model. pKa (Corr) = 0.772 pKa (CPCM-UA0-Cycle B) + 0.733
R2 = 0.971
(10)
pKa (Corr) = 0.763 pKa (IEF-PCM-UA0-Cycle B) + 0.812
R2 = 0.970
(11)
Consequently, applied thermodynamic cycle B with CPCM- UA0 solvation model with MAD = 0.4 and very good squared correlation coefficients (R2=0.971) was selected as the most reliable method for calculation of pKa of the BZDs (see Fig 3, a). Also, the same thermodynamic cycle with IEF-PCM-UA0 solvation model with MAD = 0.5 and very good squared correlation coefficients (R2= 0.970) can be considered as an alternative choice (see Fig 3, b).
3.2. Prediction of aqueous pKa value for the Halazepam drug In order to extend the available pKa data for BZD drugs, Halazepam drug as a BZD derivative was selected and its pKa value was predicted. Halazepam is a 1, 4-benzodiazepine which has anxiolytic properties and can be considered as a derivative of the Diazepam drug with CF3 substitution, a strong electron withdrawing group. To the best of our knowledge, there is not any literature reporting its pKa and the current study is the first one. For this aim, the best computational method confirmed in the previous section was used. In gas phase, the Halazepam and its corresponding cationic form were optimized at PBE1PBE/6-311+G(d,p) level of theory and in aqueous phase, CPCM-UA0/HF/6-31+G(d) level of theory was applied. Then, pKa values of the Halazepam were predicted using equations 7 and 10. Table 4 shows the computed gas phase and solvation Gibbs free energies for the Halazepam and its cationic form through our proposed method. The predicted pKa value of the Halazepam drug using the
7
best method and its corresponding correlation equation are 3.1. These predictions are reasonable, because CF3 substituent makes the Halazepam more acidic than the Diazepam drug.
Conclusions In this work, the aqueous pKa values of ten benzodiazepine derivatives have been successfully obtained. For this aim, the calculated gas phase Gibbs free energies at PBE1PBE/6311+G(d,p) level of theory and the computed solvation Gibbs free energies utilizing CPCM and IEF-PCM solvation models and UAKS, UAHF and UA0 cavity models at HF/6-31+G(d) level of theory were combined through two various thermodynamic cycles. The results indicated that CPCM-UA0 and IEF-PCM-UA0 solvation models based on thermodynamic cycle involving water provide the highest accuracies with (MAD = 0.4, R2 = 0.971) and (MAD = 0.5, R2 = 0.970), respectively. Also, among the cavity models, the UA0 radius was the best one to calculate the pKa values for the BZDs. It can be concluded that the type of cavity model plays a very important role in the obtained pKa values. As well, comparison of results shows a good agreement between the experimental and the calculated pKa values of the investigated drugs. Therefore, to extend pKa database for the BZDs, the pKa value of the Halazepam drug as a BZD derivative in water solvent was predicted using the optimized method and also its corresponding correlation equation. This work, for the first time, predicted the pKa value for the Halazepam drug equal to 3.1. It can be concluded that the theoretical methods proposed in the current study are predictive and can act as a useful tool for prediction of pKa values of the compounds with similar structures to the BZDs.
Acknowledgments
8
We gratefully acknowledge the graduate office of University of Guilan for supporting of this work. The Authors also would like to thank Professor Michelle L. Coote (Research School of Chemistry, Australian National University) for her helpful comments about the work. In addition, Authors would like to thank Miss Mona Ashtari-Delivand (PhD. Student in physical chemistry in University of Guilan) for her contribution.
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Gomperts, R. E. Stratmann, O. Yazyev, A. J. Austin, R. Cammi, C. Pomelli, J. W. Ochterski, R. L. Martin, K. Morokuma, V. G. Zakrzewski, G. A. Voth, P. Salvador, J. J. Dannenberg, S. Dapprich, A. D. Daniels, O. Farkas, J. B. Foresman, J. V. Ortiz, J. Cioslowski, and D. J. Fox, Gaussian, Inc., Wallingford CT, 2009. [46] N. J. K. Simpson, Solid-phase extraction: principles, techniques, and applications, Marcel Dekker, New York, 2000. [47] J. Karppi, S. Akerman, K. kerman, A. Sundell, K. Nyyssonen, I. Penttila, Eur. J. Pharm. Biopharm. 2007, 67, 562–568. [48] R. J. Prankerd, Profiles of drug substances, excipients, and related methodology, 2007, 33, 1–33. [49] Recommended Methods for the Detection and Assay of Barbiturates and Benzodiazepines in Biological Specimens: Manual for Use by National Laboratories, United Nations, New York, 1997.
12
Figures Captions:
Fig 1. The Structures of the studied BZD drugs Fig 2. The thermodynamic cycles A (a) and B (b) applied in this work. Fig 3. Correlations between experimental and calculated pKa values obtained using (a) CPCM-UA0 and (b) IEF-PCM-UA0 solvation models based on thermodynamic cycle B.
(Oxazepam)
(Clonazepam)
(Nitrazepam)
(Flunitrazepam)
(Diazepam)
(Alprazolam)
(Estazolam)
(Temazepam)
13
(Medazepam)
(Bromazepam)
Fig 1.
(a)
(b)
Fig 2.
14
8
pKa(Corr) = 0.772 pKa (CPCM-UA0-B) + 0.733 R2=0.971 MAD = 0.4
7 pKa (Corr)
6 5 4 3 2 1
0 0
1
2
3
4
pKa (CPCM-UA0-B)
(a)
15
5
6
7
8
8
pKa(Corr) = 0.763 pKa (IEFPCM-UA0-B) + 0.812 R2=0.970 MAD = 0.5
7 pKa (Corr)
6 5 4 3 2 1
0 0
1
2
3
4
5
6
7
8
pKa (IEFPCM-UA0-B)
(b)
Fig 3.
Table Captions: Table 1. Calculated gas phase Gibbs free energies (in kcal mol-1) of drugs and its cationic forms at PBE1PBE/6-311+G(d,p) level of theory. Table 2. Computed solvation Gibbs free energies (in kcal mol-1) of BZDs and its cationic forms in water solvent using CPCM and IEF-PCM solvation models with UAKS, UAHF and UA0 cavities at HF/6-31+G(d) level of theory. Table 3. Calculated pKa values of BZDs using thermodynamic cycles A and B together with their corresponding MADs values. Table 4. Structure, gas phase and solvation Gibbs free energies (in kcal mol-1) for Halazepam drug with its predicted pKa value.
16
Table 1. G°g(kcal mol-1)
Drugs BH+
B
Oxazepam
-814298.4
-814073.8
Clonazepam
-895363.0
-895137.3
Nitrazepam
-607042.5
-606816.3
Flunitrazepam
-693904.5
-693679.3
Diazepam
-791758.6
-791526.0
Alprazolam
-837110.8
-836881.1
Estazolam
-812474.9
-812246.9
Temazepam
-838929.1
-838696.9
Medazepam
-745322.9
-745082.8
Bromazepam
-837110.8
-836881.1
Water
-48087.0
-47921.7
Table 2
UAKS
G *solv (kcal .mol-1) UAHF
UA0
Oxazepam BH+ B
-64.9 (-64.6)a -16.4 (-16.1)
-61.6 (-61.3) -14.0 (-13.8)
-61.0 (-60.7) -12.5 (-12.3)
Clonazepam BH+ B
-65.2 (-64.9) -16.7 (-16.5)
-60.9 (-60.7) -13.4 (-13.2)
-58.8 (-58.6) -11.1 (-10.9)
Nitrazepam BH+
-68.1 (-67.8)
-63.7 (-63.5)
-61.1 (-60.8)
Drugs
17
B
-17.6 (-17.3)
-14.3 (-14.1)
-11.6 (-11.3)
Flunitrazepam BH+ B
-62.2 (-61.9) -12.4 (-12.3)
-59.0 (-58.8) -10.4 (-10.2)
-51.5 (-51.2) -3.3 (-3.2)
Diazepam BH+ B
-55.2 (-54. 9) -9.4 (-9.2)
-53.2 (-53.0) -8.4 (-8.2)
-45.6 (-45.9) -1.4 (-1.2)
Alprazolam BH+ B
-60.69 (-60.42) -14.64 (-14.44)
-58.43 (-58.18) -13.24 (-13.06)
-50.17(-49.91) -5.13 (-4.94)
Estazolam BH+ B
-62.92 (-62.65) -15.44 (-15.24)
-60.69 (-60.44) -14.13 (-13.95)
-55.56 (-55.30) -9.02 (-8.82)
Temazepam BH+ B
-53.53 (-53.28) -11.76 (-11.57)
-51.66 (-51.42) -10.65 (-10.47)
-46.48 (-46.25) -4.91 (-4.73)
Medazepam BH+ B
-48.02 (-47.89) -5.58 (-5.46)
-46.97 (-46.85) -5.17 (-5.06)
-38.89 (-38.69) 2.29 (2.41)
Bromazepam BH+ B
-64.45 (-64.17) -15.47 (-15.28)
-60.74 (-60.50) -13.01 (-12.84)
-56.26 (-56.01) -8.88 (-8.71)
a. The values in parentheses are calculated from IEF-PCM solvation model and the others are computed from CPCM solvation model.
Table 3.
18
Drugs
pKa (calc)
pKa (Exp)
UAKS
UAHF
UA0
Oxazepam
2.1 (2.1)a
1.4 (1.3)
2.1 (2.1)
1.7b
Clonazepam
2.9 (2.8)
2.2 (2.1)
2.3 (2.2)
1.5b
Nitrazepam
4.7 (4.7)
3.9 (3.9)
4.0 (4.0)
3.2b
Flunitrazepam
3.5 (3.4)
2.6 (2.5)
2.3 (2.2)
1.8c
Diazepam
5.9 (5.9)
5.2 (5.2)
4.8 (4.7)
3.3b
Alprazolam
4.1 (4.0)
3.4 (3.4)
3.3 (3.3)
2.4b
Estazolam
3.8 (3.8)
3.1 (3.1)
3.1 (3.1)
2.8d
Temazepam
2.6 (2.6)
2.1 (2.0)
2.5 (2.5)
1.6b
Medazepam
9.0 (8.9)
8.5 (8.4)
8.1 (8.0)
6.2b
Bromazepam
4.9 (4.8)
4.0 (3.9)
3.7 (3.7)
2.9e
MAD
1.6 (1.6)
1.0 (0.9)
0.9 (0.8)
Oxazepam
1.1 (1.0)
0.3 (0.3)
1.1 (1.0)
1.7b
Clonazepam
1.8 (1.8)
1.1 (1.1)
1.2 (1.2)
1.5b
Nitrazepam
3.7 (3.6)
2.9 (2.9)
3.0 (2.9)
3.2b
Flunitrazepam
2.4 (2.4)
1.6 (1.5)
1.3 (1.2)
1.8c
Diazepam
4.9 (4.9)
4.2 (4.2)
3.8 (3.7)
3.3b
Alprazolam
3.0 (3.0)
2.4 (2.3)
2.3 (2.2)
2.4b
Estazolam
2.8 (2.7)
2.1 (2.1)
2.1 (2.0)
2.8d
Temazepam
1.6 (1.6)
1.1 (1.0)
1.5 (1.4)
1.6b
Medazepam
8.0 (8.0)
7.5 (7.5)
7.0 (7.0)
6.2b
Bromazepam
3.9 (3.8)
2.9 (2.9)
2.7 (2.6)
2.9e
MAD
0.7 (0.7)
0.6 (0.6)
0.4 (0.5)
Cycle A
Cycle B
a. The values in parentheses are calculated from IEF-PCM solvation model and the others are computed from CPCM solvation model.. b. The values are taken from ref [46]. c. The values are taken from ref [47]. d. The values are taken from ref [48]. e. The values are taken from ref [49].
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Table 4 Halazepam
Gºg ( kcal mol-1)a G *solv (kcal mol-1)b
pKa (Cal)c pKa (Corr)
d
BH+
B
-607042.5
-606816.3
-45.83
-1.45
3.1
-
3.1
-
a. Calculated at PBE1PBE/6-311+G(d,p) level of theory. b. Computed at CPCM-UA0/HF/6-31+G(d) level of theory. c. Obtained using thermodynamic cycle B. d. Obtained using correlation equation 10.
Highlights Aqueous acidities of BZD drugs were successfully computed with MAD = 0.4 pKa unit. Thermodynamic cycle involving water was found appropriate for process description. The UA0 radius was known as the best cavity among united atom topological models. pKa database for BZD drugs was extended through the proposed computational method. For the first time, pKa value of Halazepam drug was predicted equal to 3.1.
20
Graphical
21