Electronic structure and dosage correlation of 1,4-benzodiazepines European Journal of Chemistry 10 (2) (2019) 108-112 European Journal of Chemistry View Journal Online View Article Online Electronic structure and dosage correlation of 1,4-benzodiazepines Raghdaa Adel Massoud and Mohamed Abdalla Makhyoun * Chemistry Department, Faculty of Science, Alexandria University, 21525 Alexandria, Egypt raghdaamassoud@yahoo.com (R.A.M.), makhyoun2@yahoo.com (M.A.M.) * Corresponding author at: Chemistry Department, Faculty of Science, Alexandria University, 21525 Alexandria, Egypt. Tel: +20.03.9547455 Fax: +20.03.5932488 e-mail: makhyoun2@yahoo.com (M.A. Makhyoun). 10.5155/eurjchem.10.2.108-112.1831 Received: 01 February 2019 Received in revised form: 19 March 2019 Accepted: 23 March 2019 Published online: 30 June 2019 Printed: 30 June 2019 Density functional theory was used to calculate the electronic structure of 20 selected 1,4- benzodiazepine derivatives. Certain parameters were extracted from the theoretical calculations, including the proton affinity of N1, the total energy, HOMO and LUMO energies, the total positive atomic charge, dipole moment and molecular volume. These parameters were used for the correlation with the minimum effective dose acting on human. The correlation was performed by applying linear least square method. Seven parameters were found to afford good fit. Clorazepate, one of the benzodiazepines, was studied extensively, it contains a carboxylate group, which can act as an ordinary molecule or zwitterions, where the ionisable proton migrates to N1. The energy gap between the two forms was found to be strongly dependent on the solvent dielectric constant. Solvent effect Proton transfer DFT calculations 1,4-Benzodiazepines Least square method Intrinsic reaction coordinate Cite this: Eur. J. Chem. 2019, 10(2), 108-112 Journal website: www.eurjchem.com 1. Introduction Benzodiazepines are a class of chemical compounds with wide medical applications. They contain a benzene ring fused to a diazepine ring. They are known since 1955, when Dr. Leo Sternbach discovered the drug chlordiazepoxide. The impor- tance of benzodiazepines made them the most prescribed medications [1]. Benzodiazepines primarily used as anxiolytic, some of them can be used as hypnotic. They are known also for muscle relaxant indications. The mechanism of action is through binding with GABA-A (Gama-aminobutyric acid type A) receptor which potentiates GABAergic neurotransmission [2]. Their half-life in human blood may be short, intermediate, or long. Short and intermediate half-lives are preferred for the treatment of insomnia; longer half-life usually used for the treatment of anxiety [3]. Common types of benzodiazepines are i) Keto compounds, where keto oxygen is attached to C3 (Clorazepate, diazepam and flurazepam), ii) Hydroxy group attached to C2 (Lora- zepam, lormetazepam and oxazepam), iii) Nitro group attached to C8 (Nitrazepam, flunitrazepam and nimetazepam) and iv) Imidazole fused to N2 and C3 (Climazolam, loprazolam, midazolam) (Figure 1) [4,5]. Figure 1. Benzodiazepine nucleus numbering scheme with groups X1, X2, X3 and X4. There is a discrepancy regarding the minimum effective doses [6-8] of benzodiazepines acting on human. This dose does not calibrate among the different compounds. In this work, we propose a procedure to calculate calibrated doses by connecting the minimum effective dose with certain molecular parameters. From the linear coefficients obtained from applying least square procedure to the linear equation, we can calculate back the proper doses. ABSTRACT RESEARCH ARTICLE KEYWORDS European Journal of Chemistry ISSN 2153-2249 (Print) / ISSN 2153-2257 (Online) – Copyright © 2019 The Authors – Atlanta Publishing House LLC – Printed in the USA. This work is published and licensed by Atlanta Publishing House LLC – CC BY NC – Some Rights Reserved. http://dx.doi.org/10.5155/eurjchem.10.2.108-112.1831 http://dx.doi.org/10.5155/eurjchem.10.2.108-112.1831 https://crossmark.crossref.org/dialog/?doi=10.5155/eurjchem.10.2.108-112.1831&domain=pdf&date_stamp=2019-06-30 http://www.eurjchem.com/ http://dx.doi.org/10.5155/eurjchem.10.2.108-112.1831 mailto:raghdaamassoud@yahoo.com mailto:makhyoun2@yahoo.com mailto:makhyoun2@yahoo.com http://www.eurjchem.com/ https://en.wikipedia.org/wiki/Benzene https://en.wikipedia.org/wiki/Diazepine https://en.wikipedia.org/wiki/Chlordiazepoxide https://en.wikipedia.org/wiki/Benzodiazepine%23cite_note-2 https://en.wikipedia.org/wiki/Benzodiazepine%23cite_note-sddat-5 https://crossmark.crossref.org/dialog/?doi=10.5155/eurjchem.10.2.108-112.1831&domain=pdf&date_stamp=2019-06-30� Massoud and Makhyoun / European Journal of Chemistry 10 (2) (2019) 108-112 109 Table 1. Used theoretical parameters and the calculated dose according to Equation (1). Compound HOMO LUMO D MV MM CT NA PA ET t½ a Dose b Calc.c Drec.d 1 -0.2091 -0.0995 3.95 183 316 0.802 29 251 -91.3 12 3.00 6.94 5.0 2 -0.2244 -0.1084 5.61 212 358 0.923 35 241 -41.6 9 20.00 18.60 20.0 3 -0.2121 -0.1158 7.51 194 315 0.966 32 242 -38.4 18 0.25 3.40 3.0 4 -0.2230 -0.1273 2.39 193 316 0.990 32 239 -38.9 48 10.00 11.40 10.0 5 -0.2111 -0.0986 3.52 198. 304 0.879 30 254 -45.8 60 0.50 0.15 0.5 6 -0.2052 -0.0957 2.63 182 285 0.775 33 244 -34.4 20 5.00 5.93 5.0 7 -0.2066 -0.0968 3.68 199 319 0.909 33 245 -46.9 42 2.00 3.89 5.0 8 -0.2164 -0.1034 5.44 214 349 0.939 38 245 -42.2 3 10.00 9.00 10.0 9 -0.2101 -0.0978 3.37 183 333 0.810 30 254 -93.5 10.6 4.00 3.50 4.0 10 -0.1801 -0.0956 3.54 242 388 1.142 50 247 -43.9 40 15.00 15.00 15.0 11 -0.2055 -0.0949 3.55 219 343 0.960 40 254 -40.2 60 10.00 9.90 10.0 12 -0.2151 -0.1015 3.09 206 353 0.940 36 240 -43.5 14 20.00 11.70 10.0 13 -0.2168 -0.1020 5.02 194 321 0.923 31 244 -47.8 10 1.00 0.47 0.5 14 -0.2127 -0.1000 5.23 202 335 0.947 34 252 -48.9 10 1.50 -0.27 - 15 -0.1968 -0.1201 1.50 186 295 0.881 32 231 -26.3 14 10.00 11.00 10.0 16 -0.2235 -0.1262 1.52 176 281 0.853 32 238 -26.4 16 10.00 6.00 5.00 17 -0.2100 -0.0974 2.60 177 271 0.745 30 243 -33.3 36 10.00 5.40 5.00 18 -0.2164 -0.1007 3.95 182 287 0.786 31 236 -35.3 5 15.00 11.40 10.00 19 -0.2109 -0.0986 3.51 196 350 0.876 30 254 -103.3 6 10.00 6.90 10.00 20 -0.2125 -0.0988 4.18 192 301 0.810 34 244 -36.4 8 10.00 12.90 10.00 a Minimum biological half-life [5]. b Estimated minimum initial dose (mg) [6-8]. c Calc.: Re-calculated values using Equation (1) utilizing linear coefficients in Table 3. d Recommended initial dose. Table 2. Molecular structure of 1,4-benzodiazepines [5]. Compound Name X1 X2 X3 X4 1 Bromazepam H H Br HC15X4=N 2 Cinolazepam CH2CN OH Cl F 3 Clonazepam H H NO2 Cl 4 Clorazepate H COOH H H 5 Delorazepam H H Cl Cl 6 Diazepam CH3 H Cl H 7 Diclazepam CH3 H Cl Cl 8 Doxefazepam CH2CH2OH OH Cl F 9 Flubromazepam H H Br F 10 Fluarazepam CH2CH2N (eth)2H Cl F - 11 Flutoprazepam cyclopropylmeth H Cl F - 12 Halazepam CH2CF3 H Cl H 13 Lorazepam H OH Cl Cl 14 Lormetazepam CH3 OH Cl Cl 15 Nimetazepam CH3 H NO2 H 16 Nitrazepam H H NO2 H 17 Nordazepam H H Cl H 18 Oxazepam H OH Cl H 19 Phenazepam H H Br Cl 20 Temazepam CH3 OH Cl H 2. Method of calculations All electronic structure calculations are based on Density Functional Theory [9]. The calculations exploit the BP86 functional and cc-pVDZ basis set. BP86 functional includes Becke’s 88 exchange and Perdew’s 86 correlations [10, 11]. cc- pVDZ basis set (correlation consistent polarized double zeta) was developed by Dunning [12]. The software used is Orca program [13]. Molecular volume was calculated as in the COSMO solvent scheme [14]. All parameters extracted from calculations were performed on an optimized geometry of the molecules. We assumed that the minimum effective doses for human and the biological half-life of the different derivatives of benzodiazepines are related to some parameters extracted from the theoretical calculations. We select nine parameters satisfying the linear Equation (1). Dose = a0 + a1 X1 + a2 X2 ……………+ a9 X9 (1) where X1 , X2……X9 are the nine selected parameters in the Equation (1). a0, a1, …., a9 are the corresponding linear coefficients. The nine selected parameters for each compound are 1, HOMO energy in a.u. (HOMO); 2, LUMO energy in a.u. (LUMO); 3, Dipole moment in Debye (D); 4, Molecular volume in angstrom3 (MV), 5, Molar mass in grams (MM); 6, The sum of positive charge over all atoms (CT); 7, Number of atoms in the molecule (NA); 8, Proton affinity at N1 (PA); and 9, Total energy in KeV (ET). The theoretically calculated parameters in addition to molar mass and number of atoms for the 20 derivatives are gathered in Table 1. 3. Results and discussion The chosen 20 compounds are given in Table 2 and their structures are based on Figure 1. By applying linear least square regression analysis procedure to Equation (1), for different possible combinations of parameters, we found that the best fit achieved was with seven parameters out of nine which are LUMO energy, dipole moment, molecular volume, total positive charge, number of atoms, proton affinity and total energy. We notice that the HOMO energy and molar mass are missing. This indicates that the LUMO is more important than the HOMO in the linear fit. Also, the molecular volume is superior over the molar mass. The same procedure was applied using Equation (1), with the same nine parameters, but with t1/2 as a dependent variable. Where t1/2 is the biological half-life of the drug in the human body. In this case, we came to the conclusion that the same seven parameters are giving the best fit to Equation (1). 2019 – European Journal of Chemistry – CC BY NC – DOI: 10.5155/eurjchem.10.2.108-112.1831 110 Massoud and Makhyoun / European Journal of Chemistry 10 (2) (2019) 108-112 Table 3. Linear square regression coefficients of best fit. (R = Correlation coefficient). Parameter R Error a0 HOMO LUMO D MV MM CT NA PA ET Minimum dose 0.9359 2.70 41.25 0.0 -490.15 0.7537 0.8291 0.0 -140.50 0.6345 -0.6229 -0.1394 Biological half-life 0.8120 19.10 113.90 0.0 1335.00 -1.3420 -1.2170 0.0 165.10 4.4560 707.1 0.2932 Table 4. Energy gap between carboxylate and zwitterion form of clorazepate as in Figure 2. Solvent Dielectric constant Refractive index Gap (eV) Hypothetical 200.00 1.330 0.20 H2O 80.40 1.330 4.85 DMSO 47.20 1.479 5.07 CH3OH 32.63 1.329 5.29 Acetone 20.70 1.359 5.71 Cl-CH2-CH2-Cl 10.36 1.445 6.68 Cl-CH2-Cl 9.08 1.424 6.93 THF 7.25 1.407 ∞ Gas phase - - ∞ Figure 2. Different proton migrations of clorazepate molecule. X = Phenyl. The linear coefficients of the Equation (1) with the best fit are given in Table 3 for minimum dose (first row) and for biological half-life (second row). The importance of each parameter in the fit is proportional to its numerical value. For example, the LUMO energy has more weight than the total charge and so on. The importance of these coefficients is that, we can use them approximately to estimate the minimum dose or the biological half-life for a newly prepared derivative. On the other hand, we can find the contribution of each parameter in estimating the required properties. For example looking in Table 3, it is clear that the magnitude of the LUMO coefficient makes it the largest contributor to the minimum dose value. The negative sign of the coefficient indicates an inversely relation. Since the protein binding abilities of these benzo- diazepines do not vary considerably among them [5], so that the values of calculated coefficients (Table 3) will be expected to be of little significance. The strength of pharmacological activities [15], which reflect the expected alteration of the magnitude of binding of benzodiazepines with GAMA-type A receptor. Accordingly, the minimum dose and smaller dose indicate a stronger binding. Also, it is connected to the biological half-life of the compound; larger half-life will indicate stronger binding affinity. From Table 3, we can decide which structure parameters having the larger effect on the magnitude of the binding strength between the benzodia- zepines and the GABA-type A receptor. As a first argument the strength of binding with GABA-type A receptor will be expected to be influenced by parameters like MV (related to the receptor cavity), dipole moment and CT assuming the receptor is polar. Also, LUMO energy assuming a possible electron transfer from the receptor to the LUMO empty level. For example, looking at Table 3, taking in your account the above discussion relating the minimum dose to the binding capacity with the receptor, it is obvious that as the molecular volume increases binding strength decreases and as the CT and LUMO energy increase the binding capacity increases. We used the calculated linear coefficients to estimate back the expected doses of our compounds which are given in Table 2. Most of the calculated doses are close enough to the value of the original doses (minimum initial dose) extracted from literature [6-8]. Some of the doses are far from the values of the original doses and one of them has an unacceptable negative value. The latter value can be explained on the basis that the original value is rather small compared to the overall error of the calculations (∼2.60) (Table 3). Since the original doses were unreliably estimated as best as random, we assume that our calculated values are close enough to hypothetical recommended values. The recommended values are based on both calculated and to some extent actual dose. These are given also in Table 1. 3.1. Clorazepate molecule The clorazepate molecule (Figure 2) is an interesting case as it contains a carboxylate group and a free lone pair on neighboring N1 making the possibility for the proton of the carboxylate to migrate to N1 forming a zwitterion. Since the latter is a strongly polar compound, we studied the calculated total energy of the two separated forms in different solvents using the COSMO model. The calculated energy gap [Etotal (Zwitterion) – Etotal (Carboxylate)], in differ- rent solvents, are given in Table 4. Since the total energy has a negative value, a positive energy gap indicates that the carboxylate form of clorazepate molecule is the more stable, which is true for all cases. But the energy gap decreases as the dielectric constant increases and reaches a very small value (0.20 eV) for the very polar hypothetical solvent. We assumed that equilibrium between the two forms is established in solution. The equilibrium is more shifted to the zwitterion form as the dielectric constant increases. The ∞ gap (Table 4) means that the carboxylate form is the only possible form under any circumstances. This happens for solvents of low dielectric constants and for the gas phase. 2019 – European Journal of Chemistry – CC BY NC – DOI: 10.5155/eurjchem.10.2.108-112.1831 Massoud and Makhyoun / European Journal of Chemistry 10 (2) (2019) 108-112 111 Figure 3. Structure of bromazepam molecule where N1 and N3 are located. Figure 4. Reaction path of proton transfer between N1 and N3 in bromazepam ion. 3.2. Bromazepam molecule The bromazepam molecule contains an extra aza nitrogen atom at position N3, due to the attachment of a pyridine molecule at C1 (Figure 3). The protonated molecule has two possibilities, where the proton is attached to either N1 or N3. The N1H+ form was found to be (by calculations) more stable than the N3H+ form. Nevertheless a proton transfer is possible between the two forms making an intermediate transition state at certain point in the reaction path (Figure 4). The transition state energy is located at the maximum of the curve representing the reaction path. The energy of the N1H+ form is located at the right end of the curve. It is clear from the curve (Figure 4) that N1H+ is the most stable form. The reaction path of curve in Figure 4 was calculated by a well-known procedure [16]. 4. Conclusion A scheme was proposed to find a correlation between the minimum effective dose of the different derivatives known as 1-4 benzodiazepines with certain theoretically calculated parameters. These parameters were calculated using quantum mechanics DFT approach. The correlation was found reasonable for some molecules. A special studies were devoted to two interesting molecules namely clorazepate and bromazepam. We discussed the proton transfer in both cases. Acknowledgement We are deeply appreciating the support given by the Chemistry Department, Faculty of Science, Alexandria University, Egypt. Disclosure statement Conflict of interests: The authors declare that they have no conflict of interest. Author contributions: All authors contributed equally to this work. Ethical approval: All ethical guidelines have been adhered. Sample availability: Samples of the compounds are available from the author. ORCID Raghdaa Adel Massoud http://orcid.org/0000-0002-8389-0576 Mohamed Abdalla Makhyoun http://orcid.org/0000-0002-8249-3528 References [1]. US Drug Enforcement Administration. (2003). https://www.dea.gov/factsheets/benzodiazepines [Accessed Date: March 19, 2019]. [2]. Bertilsson, L. Acta Psychiatr. Scand. Suppl. 1978, 274, 19-26. [3]. http://www.psyweb.com/drughtm/jsp/librium.html [Accessed Date: March 19, 2019]. [4]. Carlo, P.; Finallo, R.; Ledda, A.; Brambilla, G. Fundam. Appl. Toxicol. 1989, 12, 34-41. [5]. https://en.wikipedia.org/wiki/Benzodiazepine/ [Accessed Date: March 19, 2019]. [6]. https://drugs-forum.com/wiki/Drugs_Wiki_main_page [Accessed Date: March 19, 2019]. [7]. https://en.wikipedia.org/wiki/List_of_benzodiazepines/ [Accessed Date: March 19, 2019]. [8]. https://globalrph.com/medcalcs/benzodiazepine-converter-dosage- conversions/ [Accessed Date: March 19, 2019]. [9]. Parr, G. 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G.; Dapprich, S.; Daniels, A. D.; Strain, M. C.; Farkas, O.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Ortiz, J. V.; Cui, Q.; Baboul, A. G.; Clifford, S.; Cioslowski, J.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Gonzalez, C.; Pople, J. A. Gaussian, Inc., Pittsburgh PA, 2003. Copyright © 2019 by Authors. This work is published and licensed by Atlanta Publishing House LLC, Atlanta, GA, USA. The full terms of this license are available at http://www.eurjchem.com/index.php/eurjchem/pages/view/terms and incorporate the Creative Commons Attribution-Non Commercial (CC BY NC) (International, v4.0) License (http://creativecommons.org/licenses/by-nc/4.0). By accessing the work, you hereby accept the Terms. This is an open access article distributed under the terms and conditions of the CC BY NC License, which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited without any further permission from Atlanta Publishing House LLC (European Journal of Chemistry). No use, distribution or reproduction is permitted which does not comply with these terms. Permissions for commercial use of this work beyond the scope of the License (http://www.eurjchem.com/index.php/eurjchem/pages/view/terms) are administered by Atlanta Publishing House LLC (European Journal of Chemistry). 2019 – European Journal of Chemistry – CC BY NC – DOI: 10.5155/eurjchem.10.2.108-112.1831 http://www.eurjchem.com/index.php/eurjchem/pages/view/terms http://creativecommons.org/licenses/by-nc/4.0 http://www.eurjchem.com/index.php/eurjchem/pages/view/terms 1. Introduction 2. Method of calculations 3. Results and discussion 3.1. Clorazepate molecule 3.2. Bromazepam molecule 4. Conclusion Acknowledgement Disclosure statement ORCID References PrintField10: PrintField11: PrintField12: PrintField13: PrintField14: PrintField20: PrintField21: PrintField22: PrintField23: PrintField24: