One pot synthesis of novel pregnane-sulphur prodrugs, spectroscopic investigation, conformational analysis, chemical reactivity, Fukui function and their mathematical model

Journal of Molecular Structure 1201 (2020) 127136

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Journal of Molecular Structure journal homepage: http://www.elsevier.com/locate/molstruc

One pot synthesis of novel pregnane-sulphur prodrugs, spectroscopic investigation, conformational analysis, chemical reactivity, Fukui function and their mathematical model Arun Sethi a, *, Ranvijay Pratap Singh a, Rachana Pathak b, Dolly Shukla a, Amandeep a, Priyanka Yadav a a b

Department of Chemistry, University of Lucknow, Lucknow, 226007, India Department of Applied Science (Mathematics), Faculty of Engineering, University of Lucknow, New Campus, Lucknow, 226031, India

a r t i c l e i n f o

a b s t r a c t

Article history: Received 29 March 2019 Received in revised form 25 August 2019 Accepted 25 September 2019 Available online 30 September 2019

Novel sulphur derivatives have been synthesized for the first time from 16-Dehydropregnenolone acetate (16-DPA) by adopting thia-Michael addition reaction yielding 2-[(3b-acetoxy) pregne5-ene-20-one
16 ethio] propanoic acid, 2-[(3b-acetoxy) pregne5-ene-20-onee16ethio] ethanoic acid, 3b-acetoxy 16a-(2hydroxyethylthio)-pregn-5-ene-20-one and 3b-acetoxy-16b-(2-amino phenylthio)-pregn-5-ene-20-one. All the compounds were characterized with the help of 1H, 13C NMR, FT-IR spectroscopy and mass spectrometry. The molecular geometry and vibrational frequency of these compounds were calculated in ground state by density functional theory (DFT/B3LYP) using 6-31G (d, p) basis set. Conformational analysis of all the compounds was carried out to determine the most stable conformation. The electronic properties such as HOMO-LUMO energy were calculated by using time dependent density functional theory (TD-DFT). The topological parameters-electron density (rBCP), Laplacian of electron density (V2r(rBCP)), energy parameters-kinetic electron energy density (GBCP), potential electron density (VBCP) and the total electron energy density (HBCP) at the bond critical points (BCP) were analyzed by ‘Atoms in
0 þ
0 molecules’ AIM theory. Local reactivity descriptors like Fukui functions (fþ k , fk , fk), local softness (sk , Sk, Sk)
0 and local electrophilicity indices (uþ k , uk , uk) analysis were performed to find out the reactive sites within the molecules. Molecular electrostatic potential of the synthesized compounds were also determined. Lastly a nonlinear mathematical model has been proposed and analyzed to study the effect of catalysts on these reactions. Local and global stability analysis of the mathematical model along with the persistence of the system was checked using theory of nonlinear ordinary differential equations. © 2019 Elsevier B.V. All rights reserved.

Keywords: 16-DPA Thia-Michael addition Lewis acids Reactivity descriptors Mathematical model

1. Introduction 16-Dehydropregnenolone acetate (16-DPA), which possesses ab unsaturated carbonyl group, finds increasing application as a versatile scaffold and building block for the synthesis of different steroidal drugs like dexamethasone, b-methasone, 5a-reductase inhibitor and other related steroidal pharmacophores [1]. The most practical and widely used route for the synthesis of b-sulfido carbonyl compounds is the conjugative addition of thiols to a-b unsaturated carbonyl compounds. Thia-Michael addition is an important transformation and, apart from its versatile applications

* Corresponding author. E-mail address: [email protected] (A. Sethi). https://doi.org/10.1016/j.molstruc.2019.127136 0022-2860/© 2019 Elsevier B.V. All rights reserved.

in synthetic organic chemistry, it plays a crucial role in biosynthesis and synthesis of bioactive compounds [2,3]. Introduction of heteroatom affects the chemical properties of steroids, often resulting in alteration of its biological activity. Some of the sulphur containing compounds have shown cytotoxic activity [4], antimicrobial [5], anti-inflammatory [6], anti-proliferative [7], antineoplastic agent [8] and antitumor [9] activity. Taking this into account, we planned to synthesize b-sulfido carbonyl compounds for the first time by using thia-Michael addition reaction (Scheme 1). These newly synthesized pregnane-sulphur prodrugs were characterized with the help of 1H, 13C NMR, IR, spectroscopy and Mass spectrometry. Geometry of these compounds was optimized and their vibrational frequencies were calculated using density functional theory (DFT) with the help of B3LYP functional and 6e31 G (d, p) basis set. HOMO-LUMO analysis was also carried out

2

A. Sethi et al. / Journal of Molecular Structure 1201 (2020) 127136

Scheme 1. Synthesis of novel pregnane-sulphur prodrugs.

to predict various transitions using time dependent TD-DFT approach. Atoms in molecules theory (AIM) was used to analyze the H-bonding interactions in various systems [10]. In the present paper we also calculated the chemical reactivity of newly synthesized pregnane sulphur prodrugs [11]. The Molecular Electrostatic Potential (MEP) was also studied to determine the electrophilic and nucleophilic sites within the molecule [12]. Mathematics has always benefited from its involvement with developing sciences. In this paper, we have developed and analyzed a non-linear mathematical model for a chemical reaction and compared its results with output of the chemical reaction carried out in the laboratory.

2. Experimental section 2.1. Materials and methods All reagents used for synthesis were purchased from Sigma Aldrich (St. Louis, MO) and used without further purification. Thin layer chromatography (TLC) was performed on silica gel G coated plates to detect completion of reaction. The compounds were purified by column chromatography. Melting point was determined using open capillary tube method and are uncorrected.1H NMR spectra was recorded on a Bruker DRX-300 MHz spectrometer, 13C NMR was recorded on JOEL AL 300 FTNMR (75 MHz) Varian Inova spectrometer using CDCl3 (deuterated chloroform) as the solvent where the chemical shifts were reported in parts per million (ppm) units with respect to TMS (tetramethyl silane) as internal standard, FT-IR spectra were recorded on PerkinElmer spectrum-two FT-IR spectrometer with the range of IR spectrum from 4000 to 450 cm
1. The spectra were analyzed using Spectrum™ Software suite. The spectra were measured with 4 cm
1 resolution and 1 scan coaddition. ESI-MS was recorded on Agilent 6520 Q-TOF mass spectrometer. Elemental analysis was performed on a EuroeE 3000 elemental analyzer. Ultraviolet absorption spectra were obtained (in the range of 200e400 nm) using ELICO BL-200 UVeVis spectrophotometer equipped with a 10 mm quartz cell in dichloromethane.

2.2. Synthesis of 3b-acetoxy-5, 16-pregnadiene-20-one (2) Diosgenin was converted into compound 2 by reported method [13] and identified [14] by it m.p. 172  C, 1H NMR and ESI-MS. 2.3. Representative method for the preparation of sulphur derivative of 16-dehydropregnenolone acetate A solution of 100 mg of 16-dehydropregnenolone acetate was dissolved in freshly distilled chloroform (10 mL), and then boron trifluoride etherate was added to it, further 0.5 mL of 2mercaptopropanoic acid (or thioglycollic acid, 2-mercapto ethanol, ortho-amino thiophenol) was added to it. The reaction mixture was stirred at 30  C for 3e4.0 h. During this period the reaction mixture was monitored by TLC. Ice cold water was added to the reaction mixture and the precipitated derivative was extracted with chloroform (3  15 mL), washed with water and dried over anhydrous sodium sulphate. The crude concentrated reaction mixture was purified by column chromatography on silica gel using mixture ethyl acetate-hexane as eluting solvent to give the desired compounds 3, 4, 5 and 6. 2.3.1. 2-[(3b-acetoxy) pregne5-ene-20-one
16 ethio] propanoic acid (3) The crude material was purified by column chromatography on silica gel using mixture ethyl acetate-hexane (15: 85) as eluting solvent to give pure compound 3 in 75% yield as solid, Molecular formula: C26H38O5S, m.p ¼ 492 K, 1H NMR (300 MHz,CDCl3) d (ppm):5.37 (m, 1H, H e 6), 4.61 (m, 1H, H e 3), 3.92 (m, 1H, H e 16), 3.44 (q, 1H, H e 24, J ¼ 6.9 Hz),2.55 (d, 1H, H-17, J ¼ 8.7 Hz.), 2.33 (2H,s, H-4), 2.15 (s, 3H, CH3-21), 2.03 (s, 3H, CH3-23), 1.42 (d, 3H,CH3-25, J ¼ 6.9 Hz),1.01 (s, 3H, CH3-19), 0.642 (s, 3H, CH3-18). 13C NMR (CDCl3, 75 MHz, d(ppm): 207.52 (C-20), 178.41(C-22), 170.84 (C-26), 139.82 (C-5), 122.26 (C-6), 73.99 (C-3), 72.17 (C-17), 55.27 (C-14), 49.83 (C-9), 45.52 (C-13), 42.80 (C-4), 41.03 (C-12), 38.87 (C1), 38.20 (C-10), 37.09 (C-24), 35.54 (C-16), 34.94 (C-8), 31.82 (C-7), 31.97 (C15), 31.70 (C-2), 29.86 (C-23), 27.86 (C-21), 21.58 (C-11), 19.46 (C-25), 17.59 (C-19). 14.02 (C-18). I.R. nmax in (cm
1): 34002400 (hydrogen bonded OeH), 3030.06, 2971.28, 2936.55, 2890.10,

A. Sethi et al. / Journal of Molecular Structure 1201 (2020) 127136

2849.16, 1735.41, 1701.22, 1687.47, 1452.27, 1356.90, 1319.39, 1234.08, 840.88. ESI-MS: m/z 485 [Mþ þ Na]. 2.3.2. 2[(3-b acetoxy) pregn
5 ene
20-one e 16 ethio] ethanoic acid (4) The crude material was purified by column chromatography on silica gel using mixture ethyl acetate-hexane (15: 85) as eluting solvent to give pure compound 4 in 75% yield as solid, Molecular formula: C25H36O5S, m.p ¼ 483 K,1H NMR (300 MHz,CDCl3) d (ppm): 5.36 (m, 1H, H e 6), 4.70 (m, 1H, H e 3), 3.85 (m, 1H, H e 16), 3.29 (s, 2H, H e 24), 2.59 (d, 1H, H-17, J ¼ 8.1 Hz.), 2.17 (s, 3H, CH3-21), 2.03 (s, 3H, CH3-23), 1.01 (s, 3H, CH3-19), 0.63 (s, 3H, CH318).13C NMR (CDCl3, 75 MHz, d(ppm): 207.88 (C-20), 180.97 (C-22), 170.86 (C-25), 139.81 (C-5), 122.27 (C-6), 73.97 (C-3), 72.30 (C-17), 55.13 (C-14), 49.79 (C-9), 45.75 (C-13), 42.01 (C-4), 38.84 (C-12), 38.20 (C-1), 37.08 (C-10), 36.75 (C-24), 34.81 (C-16), 34.34 (C-8), 31.69 (C-7), 31.81 (C15), 31.53 (C-2), 27.86 (C-23), 21.64 (C-21), 21.01 (C-11), 19.48 (C-19). 14.03 (C-18). I.R. nmax in (cm
1): 3400-2400 (hydrogen bonded OeH), 2970.35, 2937.96, 2891.56, 2845, 1728.55, 1702.24, 1437.97, 1363.71, 1247.24, 736,715. ESI-MS: m/z 471 [Mþ þ Na]. 2.3.3. 3b-acetoxy 16a-(2-hydroxyethylthio)-pregn-5-ene-20-one (5) The crude material was purified by column chromatography on silica gel using mixture ethyl acetate-hexane (9: 91) as eluting solvent to give pure compound 5 in 74% yield as viscous, Molecular formula: C25H38O4S, 1H NMR (300 MHz,CDCl3) d (ppm): 5.38 (1H, br d, H-6, J ¼ 5.1 Hz), 4.69e4.57 (1H, m, H-3), 4.21e4.25 (1H, m, H-16), 3.78e3.72 (2H, m, H-25), 2.76e2.65 (4H, m, H-24 & H-4), 2.56 (1H, d, H-17, J ¼ 8.4 Hz), 2.21 (3H, s, CH3-21), 2.09 (3H, s, CH3-23), 1.01 (3H, s, CH3-19), 0.69 (3H, s, CH3-18). 13C NMR (CDCl3, 75 MHz, d(ppm): 207.73 (C-20), 170.78 (C-22), 140.91 (C-5), 122.28 (C-6), 73.94 (C-3), 72.50 (C-17), 60.92 (C-25), 55.17 (C-14), 49.93 (C-9), 45.56 (C-13), 40.31 (C-4), 38.89 (C-10), 38.20 (C-12), 37.10 (C-24), 36.76 (C-16), 35.72 (C-8), 35.17 (C-1), 31.96 (C-7), 31.72 (C-21), 31.56 (C-2), 27.87 (C-15), 21.64 (C-19), 21.04 (C-11), 19.48 (C-23), 13.98 (C18). I.R. nmax in (cm
1): 3413, 2936, 2850, 1730, 1703, 1664, 1587, 1467, 1454, 1439, 1373, 1362, 1318, 1244, 1202, 1167, 1136, 1097, 1031, 981, 953, 907, 879, 841, 813, 736, 650, 603, 533, 510. ESI-MS: m/z 418, m/z 389. 2.3.4. 3b-acetoxy-16b-(2-amino phenylthio)-pregn-5-ene-20-one (6) The crude material was purified by column chromatography on silica gel using mixture ethyl acetate-hexane (12: 82) as eluting solvent to give pure compound 6 in 83% yield as amorphous, Mo1 lecular formula: C29H39NO3S, m.p ¼ 463 K, H NMR (300 MHz,CDCl3) d (ppm): 7.36 (1H, t, H-29, J ¼ 7.2 Hz), 7.15e7.10 (1H, m, H-27), 6.70e6.62 (2H, m, H-26 & H-28), 5.37 (1H, d, H-6, J ¼ 4.5 Hz), 4.62e4.55 (1H, m, H-3), 4.42e4.31 (2H, NH2), 4.08 (1H, t, H-16, J ¼ 6.6 Hz), 2.60 (1H, d, H-17, J ¼ 8.4 Hz), 2.03 (3H, s, CH3-21), 1.95 (3H, s, CH3-23), 0.99 (3H, s, CH3-19), 0.602 (3H, s, CH3-18). I.R. nmax in (cm
1): 3439, 3358, 2924, 2854, 1731, 1701, 1641, 1608, 1509, 1456, 1366, 1246, 1033, 750, 650. ESI-MS: m/z ¼ 482, 480, 483, 357, 325, 282. 3. Computational study The molecular geometry optimization for compounds 3, 4, 5 and 6 were carried out with Gaussian 09 [15] program package using B3LYP functional with the standard 6-31G (d, p) basis set. Electronic transitions and electronic properties such as HOMO-LUMO were further computed with the help of time-dependant DFT (TD-DFT) method. Presentation graphics including visualization of the

3

molecular structures were done with the help of Gauss View [16] and intramolecular interactions analyzed by AIM approach [17].

4. Results and discussion 4.1. Catalyst, 1H,

13

C NMR and FT-IR spectroscopy

Thia-Michael addition reaction on 16-Dehydropregnenolone acetate with different nucleophilic sulphur reagents in presence of Lewis acid catalyst BF3$Et2O (other catalyst like AlCl3& FeCl3 were also used to find the relative yield as given in Table 1) resulted in the formation of compounds 3, 4, 5 and 6. The prodrugs have been characterized by 1H, 13C NMR and FT-IR spectra (Figs. S1eS17 in supporting information). Experimental FTIR spectrum of synthesized compound was recorded in the range of 4000-450 cm
1. The calculated (by DFT method) and experimental FT-IR wave-numbers for synthesized prodrugs with their assignments are gathered in supporting information (Tables S1eS4). The calculated wave numbers were scaled down by a single scaling factor 0.9608 [18]. The 1H NMR spectrum of compound 3 showed the absence of H-16 vinylic proton signal (d 6.7 in compound 2) and appearance of one proton multiplet at d 3.92, three proton doublet at d 1.42, together with one proton quartet at d 3.44 suggested the introduction of 2-mercaptopropanoic acid at C-16 position. In the 13 C NMR spectrum of compound 3, appearance of the carbon signal of the carboxylic group at d 170.84 (C-26) along with the signal at d 37.09, 35.54 and 19.46 for C-24, C-16 and C-25, confirmed the introduction of a 2-mercaptopropnoic acid at C-16 position. In the FT-IR spectrum of compound 3, high intensity bands observed at 1735.41 and 1701.22 cm
1 (1752 and 1718 cm
1 calculated) were for stretching vibration of carbonyl groups (C]O) present at C-22 (C-26, dimeric carboxylic C]O stretch) and C20. The most characteristic feature of the spectrum was the presence of the broad band from 3400 to 2400 cm
1 for OeH of carboxylic acid. This broad band centered around 3200 cm
1 (3606 cm
1 calculated) was attributed to the strong hydrogen bonding. The presence of sulphur in the compound was confirmed by the observed weak bands at 664.79 and 599.31 cm
1 for the SeC24 and C16eS respectively. The 1H NMR spectrum of compound 4 showed the appearance of one proton multiplet at d3.85 at C-16 along with sharp singlet of two protons at d 3.29 for H-24 suggested the introduction of a thioglycollic acid at C-16 position. In the 13C NMR spectrum of compound 4, presence of carboxylic group was confirmed by the presence of signal for the carbonyl group at d 170.86 (C-25) along with the signal at d 36.75 & 34.81 for C-24 and C-16, suggested the introduction of a thioglycollic acid at C-16 position. In FT-IR Spectrum of compound 4, appearance of band at 3330-2500 cm
1 for OH stretching of hydrogen bonded acid group centered around 3000 cm
1 (3601 cm
1 calculated) suggested the dimeric nature of the newly introduced carboxylic group, besides the presence of

Table 1 Yield of Michael prodrugs under different catalyst and conditions. Prodrugs

Catalyst

Time (h)

Tem. ( C)

Yield (%)

3&4

BF3$Et2O AlCl3 FeCl3 BF3$Et2O AlCl3 FeCl3 BF3$Et2O AlCl3 FeCl3

3e3.5 3e3.5 3e3.5 3e3.5 3e3.5 3.3.5 3e3.5 3e3.5 3.3.5

30 30 30 30 30 30 30 30 30

75 60 45 74 55 43 83 72 57

5

6

4

A. Sethi et al. / Journal of Molecular Structure 1201 (2020) 127136

band at 715 cm
1 for CeS stretching confirmed the conjugation of sulphur at C-16. In the 1H NMR spectrum of compound 5, presence of one proton multiplet in the range of d 4.21e4.25 for C-16 methine proton together with two mulptiplets of two proton each in the range of d 3.78e3.72 and d 2.76e2.65 for H-25 and H-24 methylene protons respectively and a doublet at d 2.56 (J ¼ 8.4 Hz) due to the H-17 proton suggested the introduction of 2-hydroxyethyl mercaptan at C-16 position. The magnitude of the coupling of H-17 proton doublet (J ¼ 8.4 Hz), due to J16bH-17aH confirmed the orientation of the side chain at C-16 to be a. In the 13C NMR spectrum of 5, appearance of the carbon signal for C-25, C-24 andC-16at d 60.92, d 37.10 and d 36.76 respectively confirmed the presence of 2hydroxyethyl mercaptan at C-16 position. In the FT-IR spectrum 5, the observed band at 3413 cm
1 (3656 cm
1 calculated) is due intermolecular hydrogen bonded hydroxyl group present at C-25. The presence of sulphur in the compound was confirmed by the observed weak bands at 736 and 650 cm
1 for the SeC24 and C16eS respectively. In the 1H NMR of the compound 6, appearance of one proton triplet at d 4.08 (J ¼ 6.6 Hz) together with aromatic protons at d 7.36 (1H, t, H-29, J ¼ 7.2 Hz), d 7.15e7.10 (1H, m, H-27), d 6.70e6.62 (2H, m, H-26 & H-28) and a well defined doublet at d 2.60 (J ¼ 8.4 Hz) due to the H-17 suggested the introduction of 2-amino thiophenol at C-16. Since four aromatic protons were observed, hence this reaction could proceed either by Thia-Michael reaction or azaMichael reaction. If the reaction had taken place via thia-Michael reaction then C-16 proton would have been observed in the range of d 3.90e4.10 and if the reaction had taken place via aza Michael reaction then C-16 proton would be observed in the range of d 4.2e4.5. But since C-16 proton is observed as a triplet at d 4.08 (J ¼ 6.6 Hz), hence reaction had proceeded via thia-Michael addition. In addition to this, if the reaction had proceeded aza-Michael reaction, then the proton of free thio group would have appeared in the region d 3.00e4.00 but as two proton doublet in the range of d 4.42e4.31 was observed for NH2 group (normally one broad singlet for NH2 group is observed in this region when the nitrogen inversion is rapid, however if the inversion is slow then a doublet for NH2 is observed), hence it was concluded that reaction had taken place via thia-Michael addition reaction. The magnitude of the coupling of H-17 proton doublet (J ¼ 8.4 Hz), due to J16bH-17aH confirm the orientation of the side chain at C-16 to be a (This has been proved with the help of NOESY as given in Fig. 1). NOESY is a powerful tools used for the identification of relative stereochemistry of the molecule. The NOESY correlation between CH3-18/H-16 revealed the b-orientations of CH3-18 and H-16 as shown by arrow in Fig. 1. In the IR spectrum of the compound 6, after the addition of 2-

aminothiophenol at the C-16 position of unsaturated ketone of compound 2, the unsaturated ketone became saturated in compound 6, hence the C]O stretching vibration of saturated ketone was now observed at higher frequency at 1701 cm
1 (1701 cm
1 calculated) confirming that Michael addition reaction has taken place. If the aza-Michael addition reaction had taken place then a single band around 3400-3500 cm
1 would be observed due to NeH stretching but since two distinct bands were observed at 3439 and 3358 cm
1 (3511 and 3395 cm
1 calculated) for asymmetric and symmetric stretching vibration of free eNH2 group further confirming that thia-Michael reaction had taken place. The NeH bending for primary amine was observed at 1608 cm
1 (1595 cm
1 calculated). The presence of sulphur in the compound was confirmed by the observed weak bands at 750 and 650 cm
1 for the SeC24 and C16eS respectively. 4.2. Conformational analysis The different spatial arrangements that a molecule can adopt due to rotation about s bonds are called their conformations and phenomenon is called conformational isomerism [19]. For the rotation, activation energy is required, whose value is plotted in potential energy surface. The potential energy surface (PES) is the mathematical or graphical relationship between the energy of a molecule and its geometry [20]. Conformational analysis of all the synthesized prodrugs 3, 4, 5, and 6 was carried out to determine their most stable conformer. The potential energy curves as well as most stable conformer for prodrugs 3, 4 and 5 have been mentioned in supporting information (Fig. S18) whereas the most stable conformer of 6 mentioned in Fig. 2. The most stable conformers obtained from conformational analysis were optimized to fix their torsion angle and all the theoretical calculations were carried out with these stable conformers. In compound 3, the most stable conformer was conformer-X (due to formation of intramolecular hydrogen bonding between H24 …. .O3, also confirmed by AIM), in case of compound 4, conformer-II (due to formation of intramolecular hydrogen bonding between H24A …. .O3, also confirmed by AIM) was the most stable, in case of compound 5, conformer-V (due to interamolecular interactions between H21A …. S and H12A …. O3, as given in AIM approach) was the most stable and in case of compound 6, conformer-IV (stability explain in next paragraph) was the most stable with energy
1788.04 hartree,
1748.73 hartree,
1674.68 hartree and
1807.26 hartree respectively. The potential energy was determined by calculating the variation in the total energy of the molecule with change in dihedral angle t (C17eC16eSeC24) at intervals of 10 by DFT/631G (d, p) method and is given in Fig. 2(a). The conformational analysis of one of the prodrug 6 is discussed

Fig. 1. Nuclear Overhauser Effect Spectroscopy (NOESY) correlation for 6.

A. Sethi et al. / Journal of Molecular Structure 1201 (2020) 127136

Fig. 2. (a). The potential energy curve of conformers for 6. (b). Most stable conformer’s prodrugs 3, 4, 5 and 6.

5

6

A. Sethi et al. / Journal of Molecular Structure 1201 (2020) 127136

here. Four minima were observed in the potential energy curve, which correspond to the conformers I, II, IV and VI. The relative energy values of these conformers were
1807.2626 hartree,
1807.2628 hartree,
1807.2661 hartree, and
1807.2655 hartree. From potential energy curve it was observed that conformer IV was the most stable of the all, as its potential energy was the lowest. This probably is due to the orientation of NeH and C]O group such that hydrogen of the eNH group at aromatic ring is pointing towards the oxygen of the keto (C]O) group present at C-20 and there may be intramolecular hydrogen bonding (O …. .HeN, 2.361 Å) between O atom of keto group and H atom of amino group, which leads to stabilization of conformer IV (the intramolecular hydrogen bonding between O atom of keto group and H atom of amino group is also confirmed by AIM approach). The next more stable conformation is conformer VI, in which the eNH group at aromatic ring is away from the keto (C]O) group present at C-20. The optimized structure of conformers IV is given in Fig. 2(b).

H12A …. O3 (in 5&6), H21A …. S (in 5), O3 … …S, H24 …. .O3 (presented as H24a …. .O3 in compound 4), H16 …. .O4 and S … … NHA, NHA …. O3 (in compound 6) suggested that the interactions are weak. All the interactions possess positive values of V2r(r) at BCP indicating that G(r) is greater than V(r) and shows depletion of electronic charge along the bond path, which is specification of closed-shell interactions. The ratio of
G(rBCP)/V (rBCP) for all the interactions in compounds 3, 4, 5 and 6, are greater than unity and shows that hydrogen bonds or interactions are non covalent in nature. According to AIM calculation, the total energy of intramolecular interaction for compounds 3, 4, 5 and 6 were calculated as
16.26 kcal/mol and
16.26 kcal/mol,
10.95 kcal/mol and
7.83 kcal/mol respectively. From the above findings we conclude that compounds 3 and 4 are more stabilized in comparison to compound 5 and 6 (higher the negative value of interaction energy higher the stabilization of the molecule). 4.4. Electronic transitions and frontier molecular orbital

4.3. AIM approach In the topological theory of AIM (atom in molecule), when two neighbouring atoms are chemically bonded, a bond critical point appears between them and the nature of chemical bonds and molecular reactivity are described by total electronic density, r(r), and its corresponding Laplacian, V2r(r). Laplacian of total electronic density is related to energetic topological parameters by a local expression of the virial theorem at critical points [21]:

1 2 V rðrÞ ¼ 2G ðrÞ þ V ðrÞ 4 Where, G(r) and V(r) are the kinetic and potential electron energy densities at critical points respectively. In the characterization of IHB (Intramolecular Hydrogen Bonding), bond critical point (BCP) in the hydrogen bond and ring critical point (RCP) in the ring are useful. Positive values of V2r(r)at BCP indicate that G(r) is greater than that of V(r) and shows depletion of electronic charge along the bond path, which is specification of closed-shell interactions such as hydrogen bonds, but negative values show excess potential energy at BCP which is the specialty of shared interactions, such as covalent bonds. In the later case, electronic charge is focused in the internuclear region and shared by two nuclei [22]. As Rozas et al. [23] explained; hydrogen bonds can be classified as (1)Weak hydrogen bonds V2r(rBCP) > 0 and G(rBCP) þ V(rBCP) > 0; (2) Medium hydrogen bonds V2r(rBCP) > 0 and G(rBCP) þ V(rBCP) < 0; (3) Strong hydrogen bonds V2r(rBCP) < 0 and G(rBCP) þ V(rBCP) < 0; Where G(rBCP)þV(rBCP) is also known as total electron energy density, H(rBCP). The typical ranges of r(r) and V2r(r) for hydrogen bond in BCP are 0.002e0.035 e/a3◦and 0.02e0.139 e/a5◦, respectively [24]. The nature of IHB can be determined using ratio of
G(rBCP)/V (rBCP), which for
G(rBCP)/V(rBCP) > 1, the IHB has non-covalent nature, while for 0.5 <
G(rBCP)/V(rBCP) < 1 is partly covalent [25]. Several theoretical methods [26,27] have been proposed to estimate hydrogen bond energy. One of the most useful of these methods has been explained by Espinosa et al. [28] who found that IHB energy may be correlated with the potential electron energy density at critical point by the expression EIHB ¼ 1/2V (rBCP). Molecular graph of the compounds 3, 4, 5 and 6, using AIM program at B3LYP/6- 31G (d, p) level are shown in supporting information (Figs. S19eS22). For compounds 3, 4, 5 and 6, geometrical and topological parameters for bonds of interacting atoms are given in supporting information (Tables S5eS8) and on the basis of above criteriaV2r (rBCP) and HBCP parameters are greater than zero for bond H19b …. .H8 (absent in compound 5), H19b …. .H11b, H1b …. .H11a, H11b …. .H18b, H12b …. .C21, H18c …. .H21b, H18a …. .S,

HOMO-LUMO analysis was also carried out to predict various transitions using time dependent TD-DFT approach. TD-DFT is used to investigate the properties and dynamics of many-body systems in the presence of time-dependent potentials, such as electric or magnetic fields. The electronic spectrum (calculated by TD-DFT) of synthesized compounds are mentioned in supporting information (Fig. S23). The electronic transitions, lmax, energy gap and molecular orbitals participation of synthesized prodrugs are summarized in supporting information (Table S9). From the data given in Table S9, we conclude that in all the compounds the highest lmax is represented by n/p* transition and lowest by p /p* transition. The frontier orbitals, HOMO and LUMO determines (Fig. 3) the way how the molecule interacts with other species and helps to characterize the chemical reactivity and kinetic stability of the molecule on the basis of energy gap. The energy gap between the HOMO and LUMO is very important in determining the chemical reactivity of the molecule. A small HOMO-LUMO energy gap implies low kinetic stability, because it is energetically favourable to add electrons to a low-lying LUMO and to receive electrons from a high-lying HOMO. Thus, molecules with low frontier orbital gap are more polarisable and associated with high chemical reactivity. For compound 3, HOMO lying at
5.93 eV (computed by TD-DFT) whereas the LUMO lying at
0.51eV. The energy difference between the HOMO and LUMO was obtained as 5.41eV in the gas phase calculations. For compound 4, the HOMO lying at
5.98eV whereas the LUMO lying at
0.52eV. The energy difference between the HOMO and LUMO was obtained as 5.46eV in the gas phase calculations. For compound 5, the HOMO lying at
6.11eV whereas the LUMO lying at
0.55eV. The energy difference between the HOMO and LUMO was obtained as 5.53eV in the gas phase calculations. For compound 6, HOMO and LUMO were lying at
5.78 and
0.60eV respectively. The energy difference between the HOMO and LUMO was obtained as 5.18 eV in the gas phase calculations. Low charge separation in 6 explains eventual charge transfer interactions within the molecule and high chemical reactivity, which may influence the biological activity of the molecule. 4.5. Global reactivity descriptors The chemical reactivity and site selectivity of the molecular systems have been determined on the basis of Koopman’s theorem [29]. Global reactivity descriptors as electronegativity (c) ¼
1/2 (εLUMO þ εHOMO ), chemical potential (m) ¼ 1/2 (εLUMO þ εHOMO ), global hardness (h) ¼ 1/2 (εLUMO
εHOMO ), global softness (S) ¼ 1/2 h and electrophilicity index (u) ¼ m2/2 h are highly successful in

A. Sethi et al. / Journal of Molecular Structure 1201 (2020) 127136

7

Fig. 3. HOMO-LUMO molecular orbital diagram of compound 3, 4, 5, and 6.

predicting global reactivity trends [30e34]. Electrophilicity index (u) is a global reactivity index similar to the chemical hardness and chemical potential. This is positive and definite quantity. This new reactivity index measures the stabilization in energy when the system acquires an additional electronic charge (DN) from the environment. The energies of frontier molecular orbitals (εLUMO ; εHOMO ), energy gap (εLUMO
εHOMO ), electronegativity (c), chemical potential (m), global hardness (h), global softness (S), global electrophilicity index (u) for 2, 3, 4, 5 and 6 are listed in supporting information (Table S10). When two molecules react, which one will act as an electrophile or nucleophile will depend upon the value of electrophilicity index. Higher the value of the electrophilicity index better is the electrophilic character. Out of compound 2, 3, 4, 5 and 6, compound 3 and 4 acts as a good electrophile as the molecule shows high values for three global reactivity parameters, namely chemical potential (m) ¼
3.999, global electrophilicity index (u) ¼ 4.509, and softness (S) ¼ 0.283 along with the lowest HOMOLUMO energy gap (3.537 eV), as compared to compound 2, 5 and 6. Lower value of HOMO-LUMO energy gap of compounds 3 and 4, signifying lower excitation energy in comparison to other compounds, hence compounds 3 and 4 are softer and reactive in comparison to others (lower the HOMO-LUMO energy gap higher the softness).

4.6. Local reactivity descriptors In order to define a particular reactive site within the molecule, local reactivity descriptors such as local softness (Sk), Fukui Function (FF) and local electrophilicity index (uk) are used. In DFT theory of chemical reactivity, Fukui function f(r) is considered as one of the most fundamental indicator for defining the site selectivity in a given molecular species and for soft-soft type of interactions, the preferred reactive site in a molecule is the one with maximum values of (fk,sk,uk). Using Hirshfeld atomic charges of neutral, cation and anion state of initial reactant 2 and compounds 3 and 4 (other two compounds 5 and 6 have also been attached with sulphur
0 þ atom), the condensed Fukui functions (fþ k , fk , fk), local softness (sk ,
0 þ
0 Sk, Sk) and local electrophilicity indices (uk , uk , uk) [35]. Fukui functions are calculated by following equation.

fþ k ½qðN þ 1Þ
qðNÞ for nucleophilic attack f
k ½qðNÞ
qðN
1Þ for electrophilic attack f 0k 1 = 2½qðN þ 1Þ þ qðN
1Þ for radical attack where, q is the gross charge of atom k in the molecule and N, Nþ1, N-1 are electron systems containing neutral, anion, cation form of molecule respectively. Local softnesses and electrophilicity indices

8

A. Sethi et al. / Journal of Molecular Structure 1201 (2020) 127136

are calculated using following equation.
0 0
sþ ¼ Sf þ k ; sk ¼ Sf k ; sk ¼ Sf k for Local softnesses k
0
0 uþ ¼ uf þ k ; uk ¼ uf k ; uk ¼ uf k for electrophilicity indices k

Where þ,
, 0 signs show nucleophilic, electrophilic and radical attack respectively. Fukui functions, local softnesses and local electrophilicity indices for selected atomic sites in initial reactant 2 and compounds 3, 4, 5 and 6 are shown in supporting information (Table S11). þ þ In case of compound 2 the values of Gþ k , sk , uk for two atomic sites C-16 and C-17 are 0.161, 0.308, 0.459 and 0.062, 0.012, 0.179 respectively. Similarly for compound 3, the values of local reactivity þ þ descriptors Gþ k , sk , uk for atomic sites C-16 and C-17 are 0.009, 0.002, 0.044 and 0.036, 0.010, 0.163 respectively, for compound 4, þ þ the values of local reactivity descriptors Gþ k , sk , uk for atomic sites C-16 and C-17 are 0.009, 0.002, 0.040 and 0.037, 0.010, 0.167 respectively, for compound 5, the values of local reactivity deþ þ scriptors Gþ k , sk , uk for atomic sites C-16 and C-17 are 0.009, 0.001, 0.017 and 0.037, 0.006, 0.073 respectively and for compound 6, the þ þ values of local reactivity descriptors Gþ k , sk , uk for atomic sites C-16 and C-17 are 0.009, 0.001, 0.023 and 0.037, 0.074, 0.098 respectively. Maximum values of all the three local reactivity descriptors þ þ (fþ k , sk , uk ) in case of compound 2 indicate that C-16 site is more prone for nucleophilic attack in comparison to C-17 atomic site. Therefore, these local reactivity descriptors calculated in case of compounds 2, 3, 4, 5 and 6 confirms the favourable site of attack at C-16 position of compound 2 which further leads to the formation of the desired products. 4.7. Molecular electrostatic potential The Molecular Electrostatic Potential (MEP) is related to the electronic density and is a very useful descriptor in determining the sites for electrophilic and nucleophilic reactions. To predict reactive sites for electrophilic and nucleophilic attack for the investigated molecule, the MEP at the B3LYP/6-31G(d) optimized geometry was calculated for compound 2,3,4, 5 and 6. The negative (red and yellow) regions of the MEP are related to electrophilic reactivity and the positive (blue) regions to nucleophilic reactivity, as shown in supporting information (Fig. S24). In short in compound 2, red region at O4 indicate the possible site for electrophilic reactivity which undergoes nucleophilic attack and in compound 3, 4, 5 and 6, the red region at O3 indicate the possible site for electrophilic reactivity [36]. 4.8. Mathematical model In this section, we develop a mathematical model for reaction [37e39]. Physical parameters such as temperature, pressure, for

example, are ignored in this text and differential equations are constructed that are dependent only on the concentrations of the chemicals involved in the reaction. This is potentially a very difficult subject and some assumptions have to be made to make progress. Consider the simple chemical reaction.

Let R be the density of Enone, S be the density of Thiol and P be the density of Michael Product (MP). It is assumed that density of Enone and Thiol are increased by constant rate A1 and A2 respectively. In modelling process, the effect of catalyst (BF3$Et2O,AlCl3& FeCl3) in this reaction is represented by h1c, which increases the rate the reaction and density of product.Let a be the interaction rate between reacants and b be the growth rate of the product. We also assumed that density of reacants and product is decreased by different factors like oxidation etc, this effect is represented by m; m1 and b0 respectively. Thus keeping in view of these considerations, the non-linear model is proposed as follows

dR ¼ A1
a R S
m R
h1c ; dt dS ¼ A2
a R S
m1 S
h1c ; dt dP ¼ b R S þ h1c
b0 P: dt where Rð0Þ  0; Sð0Þ  0; Pð0Þ  0:

(4.8.1)

4.8.1. Numerical results The stability of the non-linear model system (4.8.1), in the positive octant, is investigated numerically by using the following set of parameters.

A1 ¼ 2; A2 ¼ 2; a ¼ 0:002; m ¼ 0:0002; h1c ¼ 0:001; m1 ¼ 0:0002; b ¼ 0:001; b0 ¼ 0:018: (4.8.1.1) The interior equilibrium point of the model system (4.8.1) corresponding to the above parameters values is Eð31:5649; 31:5649; 55:408Þ: The characteristic polynomial and characteristic roots of the model system corresponding to the interior equilibrium point are given as:

l3 þ 0:14466l2 þ 0:00230517l þ 4:55255  10
7 ¼ 0: (4.8.1.2)

l1 ¼
0:12646; l2 ¼
0:018; l3 ¼
0:0002:

(4.8.1.3)

From eq (4.8.1.3), it is clear that all characteristic roots of the characteristic polynomial (4.8.1.2) are negative. So, the interior equilibrium of the model system (4.8.1) is locally asymptotically

A. Sethi et al. / Journal of Molecular Structure 1201 (2020) 127136

stable. Supplementary Figs. 25 and 26 show that local and global stable behaviour of the system. Supplementary Fig. 27 shows the effect of catalyst on the production of product. If we use three different catalysts with different rates, for example catalyst BF3$Et2O (C), AlCl3(B) & FeCl3(A) with rates 0.8, 0.1 and 0.001 respectively then the production of product is highest for catalyst C and lowest for catalyst A. The 3D of stability behaviour of the system is shown in Supplementary Fig. 28. 5. Conclusions Novel sulphur derivative of 16-Dehydropregnenolone acetate (16-DPA) have been for the first time synthesized in one step by adopting thia-Michael addition. The structures of these compounds were characterized with the help of 1H, 13C NMR, FT-IR and mass spectrometry. On the basis of conformational analysis the most stable conformer was identified. From atom in molecule (AIM) approach, it was concluded that compound 3 and 4 possessed higher value of intramolecular interaction energy (these compounds are more stabilized in comparison to others). The local reactivity descriptors calculated in case of compound 2, confirmed that the favourable site of nucleophilic attack was C-16 position and þ þ not C-17 (because C16 possess maximum value of fþ k , sk , uk as compared to C17), which further leads to the formation of the compounds 3, 4, 5 and 6. The proposed mathematical model was analyzed by the stability theory of differential equations. The conditions of existence of equilibrium point and its stability in both local and global cases was obtained. The condition, under which the system persists, by using differential inequality, has been found. By using numerical simulation, the effects of different catalyst on the system has been shown graphically. Acknowledgements The authors are grateful to the SAIF division of the Central Drug Research Institute, Lucknow and Department of chemistry, IIT Kanpur for providing spectroscopic data and also thanks to Central Facility for Computational Research, Department of Chemistry, University of Lucknow. Appendix B. Supplementary data Supplementary data to this article can be found online at https://doi.org/10.1016/j.molstruc.2019.127136. References [1] A.V. Silva-Ortiz, E. Bratoeff, T. Ramírez-Apan, Y. Heuze, A. Sanchez, J. Soriano,

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