Exploration of Noncovalent Interactions, Chemical Reactivity, and Nonlinear Optical Properties of Piperidone Derivatives: A Concise Theoretical Approach.

The organic compounds with a π-bond system lead to electric charge delocalization which enables them to reveal fascinating nonlinear optical properties. Mono-carbonyl curcuminoids also have an appealing skeleton from the conjugation view point. Interesting chemical structures of the 3,5-bis(arylidene)-N-benzenesulfonyl-4-piperidone derivatives motivated us to perform density functional theory (DFT)-based studies. Therefore, computations using the B3LYP/6-311G(d,p) functional of DFT were executed to explore geometric parameters, highest occupied molecular orbital (HOMO)-lowest unoccupied molecular orbital (LUMO) energies, and natural bond orbital (NBO) analyses. Moreover, three different functionals such as HF, B3LYP, and M06 with the 6-311G(d,p) basis set were used to investigate the average polarizability ⟨α⟩ and first hyperpolarizability (βtot)-based properties of all compounds. A good concurrence among calculated and experimental parameters was obtained through root mean square error calculations. The molecular stability of piperidone derivatives was examined using the Hirshfeld surface and NBO analyses. Natural population analysis was also performed to obtain insights about atomic charges. Calculated HOMO-LUMO energies showed that charge transfer interactions take place within the molecules. Moreover, global reactivity parameters including electronegativity, chemical hardness, softness, ionization potential, and electrophilicity were calculated using the HOMO and LUMO energies. The average polarizability ⟨α⟩ and first hyperpolarizability (βtot) values of all compounds were observed to be larger in magnitude at the aforesaid functional than the standard compound.

Introduction

Synthetic organic chemistry is a promising field to generate numerous exciting molecules by applying various protocols, in quick time with complete structural investigation, high purity, and mostly with an attractive yield. The beauty of this chemistry is the generation of highly demanding functional groups from easily manageable precursors. Sometimes, a simple condensation reaction ends in a valuable functional group with stimulating structural features indispensable from the biological activity point of view.[1] Monocarbonyl curcuminoids are also among those functionalities that could be generated by the simple condensation reaction of aliphatic ketones and aromatic aldehydes. A curcuminoid is a linear diarylpentanoid having one carbonyl or a linear diarylheptanoid having two carbonyl groups.[2] Traditionally, monocarbonyl curcuminoids have been investigated for their assembly and molecular possessions.[3] Additionally, α,β-unsaturated carbonyl compounds like curcumin (Curcuma longa-based natural product) are vital from the medicinal standpoint with their potential to be antitumor, antioxidant, antibacterial, and anti-inflammatory agents. For instance, α,β-unsaturated ketone like functionalized 3,5-bis(arylidene)-4-piperidone have been reported to have promising antitumor and anti-inflammatory capabilities.[4] Moreover, further tuning through N-alkylation of the skeleton of 3,5-bis(arylidene)-4-piperidone by incorporation of various synthons with different electronic nature can generate chemical architectures with improved biological activities. The N-cyclopropyl monocarbonyl analogs of curcumin MAC 7a and N-benzoyl BAP c6 are the potential anti-inflammatory agents. The 3,5-bis(arylidene)-4-piperidone analog BAP 6d is the potential antitumor mediator, while BAP c6 and BAP d6 in combination are outstanding anti-tumors and anti-inflammatory agents.[4] Moreover, EF24 (3,5-bis(2-fluorobenzylidene)-4-piperidone) is also a potential antitumor agent and restrain the tumor expansion as well as the metastasis.[5] Anti-cancer 4-[3,5-bis(2-chlorobenzylidene)-4-oxo-piperidine-1-yl]-4-oxo-2-butenoic acid (CLEFMA) has the ability to induce apoptosis.[6] In addition to these, KalmanHideg and co-workers synthesized the N-substituted 3,5-bis(arylidene)-4-piperidone derivatives and explored their anti-cancer potential of cytotoxicity against cancer cells and linked it with molecular docking simulations.[7]

In this scenario, Li. et al.[4] reported the four 3,5-bis(arylidene)-N-benzenesulfonyl-4-piperidone derivatives. All the four compounds were crystallized by slow evaporation of dichloromethane/methanol solutions at room temperature, and the structures of the final compounds were confirmed by NMR, FT-IR, HRMS, as well as by the single-crystal analysis. The single-crystal analysis revealed that compound (a) is monoclinic with space group P21/n, while the remaining three compounds (i.e., b, c, and d) were found to be triclinic in nature with space group P1. Interestingly, all the four compounds presented similar stereochemistry that is mainly because of the linear olefinic double bond generated at either side of the 3,5-bis(arylidene)-4-piperidone ring where both the 4-(trifluoromethyl)phenyl rings adopted the E stereochemistry presenting the E,E isomer. Moreover, regarding the conformation, compound a and b, the arylsulfonyl group showed pseudo-axial conformation, while in the case of c and d, the arylsulfonyl group adopted a pseudo-equatorial conformation with respect to the 4-pyridone ring. Accordingly, the four compounds were tested for biological activity revealing that these compounds are of significant anti-inflammatory nature.

The starring role of density functional theory (DFT) in understanding the modern chemistry has gained enormous attention. These DFT-based calculations play a pivotal role in collecting key structural information as it helps in finding the insight of the reaction mechanism, stability, reacting sites, electronic properties, and so forth.[8] Moreover, nonlinear optical properties (NLOs) can also be accomplished using DFT.[9−13] NLO features can be explored at different ranges of wavelengths from the deep infrared to extreme UV region that provide valuable information which can be used in the field of information technology and telecommunication.[14] Currently, many of the valuable phenomena such as quantum computing, quantum optics, particle accelerators, and ultra-cold atoms, and so forth are associated with NLO.[15,16] NLO plays a key role in the diversification of lasers together with coherent light as the NLO practice may change the laser light. Interestingly, it might control the frequency and/or spatial features of the laser output. Material interaction is another important feature of NLO that has valuable applications in machining, spectroscopy, and in analysis tools.[17,18] Information technology is also based on NLO features in all areas like telecom, data storage, sensors, and signal processing.[19] Our research group is interested to find the NLO properties of the promising crystalline organic compounds (piperidone derivatives) reported by Li and co-workers.[4] According to the best of our knowledge, neither electronic, hyper, conjugative interactions nor NLO properties of 3,5-bis(arylidene)-N-benzenesulfonyl-4-piperidone derivatives have been reported so far. Herein, DFT calculations are used to provide insights into electronic and NLO properties and structural parameters, which have been compared to experimental data for better understanding of chemical structures.

Computational Methods and Materials

The inclusive quantum chemical calculations for piperidin-4-one derivatives: (3Z,5Z)-1-tosyl-3,5-bis (4-(trifluoromethyl)benzylidene)piperidin-4-one (TBTBP), (3Z,5Z)-1-((4-fluorophenyl)sulfonyl)-3,5-bis(4-(trifluoromethyl)benzylidene)piperidin-4-one (FSTBP), (3Z,5Z)-1-((4-nitrophenyl)sulfonyl)-3,5-bis(4-(trifluoromethyl)benzylidene)piperidin-4-one (NSTBP), 4-(((3Z,5Z)-4-oxo-3,5-bis(4-(trifluoromethyl)benzylidene)piperidin-1-yl)sulfonyl)-benzonitrile (OTBPS) were executed by utilizing Gaussian 09 program package[20] and making use of DFT approach with B3LYP which is abbreviated of the Becke, three-parameter, Lee–Yang–Parr exchange–correlation functional,[21] and 6-311G(d,p) basis set.[22,23]

Initial geometries of TBTBP, FSTBP, NSTBP, and OTBPS derivatives were attained through crystal structures using the Crystallographic Information File (CIF). Complete geometry optimization followed by vibrational analysis in the gas phase exclusive of symmetry restrictions was executed at the B3LYP/6-311G(d,p) functional. For estimation of FMO and NBO analyses, the B3LYP/6-311G(d,p) level of theory was utilized. Three levels of theory as HF, B3LYP, and M06 with the 6-311G(d,p) basis set were utilized to evaluate the NLO characteristics of BTBP, FSTBP, NSTBP, and OTBPS derivatives.

Lowest unoccupied molecular orbital (LUMO)/highest occupied molecular orbital (HOMO) energies and their energy gap values were utilized with the aid of following given eqs –6 to estimate the global reactivity parameters (GRP).[24−27] We found out the electronic affinity (A) and ionization potential (I) values using eqs and 2.

In above equations, “I” represents ionization potential, while “A” denoted the electron affinity.

Hardness and electronegativity values were accomplished using eqs and 4, respectively.

The electrophilicity value was calculated using eq .

The value of softness was calculated using eq .

Equation was used for estimating the average polarizability ⟨α⟩.[28]

First hyperpolarizability (βtot) was worked out from eq .[29]

All input as well as output files were treated with the assistance of Chemcraft,[30] GaussSum,[31] GaussView5.0,[32] and Avogadro[33] softwares.

Results and Discussion

Molecular Geometric Parameters

The geometries of the TBTBP, FSTBP, NSTBP, and OTBPS were optimized using the B3LYP/6-311G(d,p) functional. The structural parameters regarding experimental and theoretical study are organized in Tables S1–S4 (Supporting Information). The graphical illustration of bond lengths is shown in Figure , while graphical representation about bond angles is shown in Figure S1.

Figure 1

Comparison between experimental and simulated bond lengths (Å) of the entitled compounds.

Considering bond lengths, the identical DFT and XRD determined values were found to be 1.462 Å for C14–C15 in FSTBP and 1.502 and 1.222 Å for C2–C3 and N35–O40 in NSTBP, respectively. The least deviated DFT and XRD compared value were found to be 0.001 Å for C4–C14 in NSTBP and 0.001 Å for C1–N35, C6–C7, and C14–C15 in OTBPS. However, the most deviated DFT and XRD compared values were 0.072 Å for C22–F33 in TBTBP, 0.105 Å for C13–F39 in FSTBP, 0.046 Å for N34–S41 in NSTBP, and 0.052 Å for N35–S40 in OTBPS (Figure ).

While taking in account of bond angles, the identical DFT and XRD determined values were found to be 120.8° for C24–C23–C28 in TBTBP, 112.3° for C4–C5–N33 in FSTBP, 121.3° for C15–C16–C17 in NSTBP, and 117.9° for C8–C7–C12 in OTBPS. The least deviated DFT and XRD compared value was found to be 0.1° for C9–C10–C11 in TBTBP, C7–C8–C9 in FSTBP, C17–C18–C19 in NSTBP, and C4–C3–O37 in OTBPS. Nevertheless, the most deviated DFT and XRD compared values were 23.4° for F34–C22–F39 in TBTBP, 41.7° for F28–C13–F38 in FSTBP, 2.8° for C22–S41–O37 in NSTBP, and 2.6° for O38–S40–O39 in OTBPS (Figure S1). Overall, entitled compounds are diverged in the range of 0.0105–0.0 Å for bond lengths and 0.0–41.7° for bond angles.

The relative analysis exposed that DFT values of bond lengths (Figure ) and bond angles (Figure S1) were elevated as compared to XRD values. However, in a few cases, the opposite happened because of the medium effect.

To further strengthen the associated among DFT study and experimental findings, eqs –12 were utilized to calculate the error.

The mean absolute deviation (MAD), RMSE, and mean absolute percentage error (MAPE) can be estimated using eqs –12

In the above equations, DFT and EXP represent the bond angle and bond length values obtained through DFT and experimental calculations, respectively. “t” indicates the number of bond angle or bond length values, and “n” describes the total number of the considered bond angle or lengths values. The error calculation results obtained from eqs –12 had been collected in Table S5.

In structural calculations, the RMSE approach was frequently utilized. Therefore, our investigated systems were also processed using the RMSE approach. RMSE values were observed less in magnitude for bond lengths of the title compounds. However, for bond angles, the RMSE values in TBTBP and FSTBP were found to be larger because of higher deviation of the C–F values.

Hirshfeld Surface Analysis

Hirshfeld surface analysis for TBTBP, FSTBP, NSTBP, and OTBPS was performed to evaluate the intermolecular interactions.[34−36] The Hirshfeld surface configurations for molecules such as TBTBP, FSTBP, NSTBP, and OTBPS were shown in Figure . Red and white colors are used in the Hirshfeld surface plot to indicate the strongest and intermediate interactions, respectively, while the blue color demonstrates negligible intermolecular interactions.

Figure 2

(a–d) show Hirshfeld surfaces mapped over dnorm in the range from −0.200 to 1.307, −0.262 to 1.638, −0.291 to 1.265, and −0.185 to 1.453 au for TBTBP, FSTBP, NSTBP, and OTBPS, respectively. 1 au of electron density = 6.748 e Å–3.

Two-dimensional fingerprint plots were also used to explore the intermolecular interactions. Further disintegration of this plot enumerates the individual contributions of every intermolecular interaction involved in the molecular structure.[37−39]Figures S2–S5 were drawn to portray two-dimensional fingerprint plots of investigated compounds.

Various interatomic contacts in terms of percentage intermolecular contributions to the Hirshfeld surface for TBTBP, FSTBP, NSTBP, and OTBPS are shown in Tables S6–S9, respectively, and each atom percentage contributions in the Hirshfeld surface along with other atoms existing outside the Hirshfeld surface to identify its part in crystal packingare shown in Tables S10–S13 and Figure . In crystal packing of TBTBP, FSTBP, NSTBP, and OTBPS, Tables S6–S9 show that the F···H contact emerge to be the main contributor and its contribution for TBTBP, FSTBP, NSTBP, and OTBPS was 27.6, 35.2, 22.5, and 23.8%, correspondingly, as could be seen in Figure . The function of hydrogen atoms is extremely important in stabilization of TBTBP, FSTBP, NSTBP, and OTBPS structures, and its percentage involvement to intermolecular contact was observed in larger magnitude (Figure ). Tables S10–S13 shows that most interacted atoms are hydrogen atoms and play a prominent role in crystal packing, and the percentage contribution of intermolecular contacts of H-atoms with all other atoms existing outside the Hirshfeld surface are 49.4, 42.6, 47.2, and 41.2% for TBTBP, FSTBP, NSTBP, and OTBPS, respectively (Figure ). The smallest contribution to intermolecular interaction is of the sulphur atom; its role in crystal packing is found to be 0% in TBTBP, FSTBP, and OTBPS, while in NSTBP its contribution in packing is obtained to be 0.1% (Tables S10–S13). The voids in the unit of each compound were revealed in Figure :

Figure 3

Percentage contributions of all interatomic contacts for entitled compounds.

Figure 4

Show view of the voids (Wolff et al., 2012) in the crystal structure of TBTBP, FSTBP, NSTBP, and OTBPS.

These voids were calculated on the basis of sum of spherical atomic electron densities at suitable nuclear positions (pro-crystal electron density).[40] The crystal-void calculation (results under 0.002 au iso-value) shows the void volumes of TBTBP, FSTBP, NSTBP, and OTBPS are found to be 378.12, 164.27 160.11, and 202.04 Å3 respectively.

Natural Bond Orbital Analysis

Using NBO investigation, the significant explanation of orbital interaction, orbital hybridization, and atomic charge can be obtained.[41] NBO analysis offers elucidation regarding inter and intra-molecular interfaces which occur in empty and filled orbitals. The strong interactions between donors and acceptors produce large stabilization energy. The stabilization energy E(2) coupled with the delocalization for each donor (i) and acceptor (j) was evaluated using eq .where εj and εi are off-diagonal, and F(i,j) is the diagonal NBO Fock matrix elements; qi is the donor orbital occupancy and E(2) is stabilization energy.

The NBO analysis has been completed for compounds (TBTBP, FSTBP, NSTBP, and OTBPS). The NBO analysis for TBTBP, FSTBP, NSTBP, and OTBPS has been elaborated in Tables S6–S9. Some selected values are given in Table . The numbering scheme for entitled compounds was represented in Figures S6–S9.

Table 1

NBO Representative Values for TBTBP, FSTBP, NSTBP, and OTBPS

derivative	donor (i)	type	acceptor (j)	type	E(2)a	E(j) – E(i)b [au]	F(i;j)c [au]
TBTBP	C37–C45	π	C38–C40	π*	230.96	0.01	0.080
	C37–C43	π	C38–C40	π*	217.94	0.01	0.080
	C5–C11	π	C13–C21	π*	10.41	0.30	0.053
	C18–C19	σ	C16–C18	σ*	5.08	1.27	0.072
	C31–C32	σ	C29–C31	σ*	5.08	1.27	0.072
	F57	LP(2)	C42–C43	π*	20.05	0.43	0.089
	F47	LP(2)	C23–F49	σ*	5.03	0.66	0.052
FSTBP	C37–C45	π	C38–C40	π*	230.96	0.01	0.080
	C42–C43	π	C38–C40	π*	217.94	0.01	0.080
	C16–C18	π	C18–C19	π*	5.07	1.27	0.072
	C31–C32	σ	C36–F55	σ*	6.90	0.50	0.056
	C31–C32	σ	C36–F54	σ*	1.51	0.50	0.026
	F57	LP(2)	C42–C43	π*	20.05	0.43	0.089
	O54	LP(2)	C36–F55	σ*	5.12	0.66	0.053
	F56	LP(2)	C36–F55	σ*	5.12	0.65	0.053
NSTBP	C26–C34	π	C31–C32	π*	22.37	0.28	0.071
	C13–C21	π	C18–C19	π*	22.20	0.28	0.071
	C37–C45	π	C38–C40	π*	18.71	0.30	0.068
	N57–O58	π	N57–O58	π*	7.82	0.34	0.055
	C29–C31	σ	C31–C32	σ*	5.07	1.27	0.072
	C45–C46	σ	C37–C38	σ*	4.93	1.08	0.065
	O59	LP(3)	N57–O58	π*	175.14	0.15	0.147
	F47	LP(2)	C23–F49	σ*	5.03	0.66	0.052
OTBPS	C37–C45	π	C38–C40	π*	168.68	0.01	0.079
	C13–C21	π	C5–C11	π*	65.07	0.02	0.069
	C57–N58	π	C42–C43	π*	5.70	0.34	0.043
	C6–C7	σ	C24–C26	σ*	5.13	1.13	0.068
	O1	LP(2)	C6–C7	σ*	19.32	0.68	0.104
	F54	LP(2)	C36–F55	σ*	5.10	0.66	0.053
	F48	LP(2)	C23–F49	σ*	5.10	0.66	0.053

E(2)means energy of the hyper conjugative interaction (stabilization energy in kcal/mol).

Energy difference between the donor and acceptor i and j NBO orbitals.

F(i;j) is the Fock matrix element between i and j NBO orbitals.

The most probable transitions comprising gigantic stabilization energies such as π(C37–C45) → π*(C38–C40), π(C37–C45) → π*(C38–C40), π(C37–C45) → π*(C38–C40) and π(C37–C45) → π*(C38–C40) contained 230.96, 230.96, 18.71, and 168.68 kcal/mol for TBTBP, FSTBP, NSTBP, and OTBPS, respectively. The transitions indicating the conjugation in chemical structures as π(C37–C43) → π*(C38–C40) in TBTBP, π(C42–C43) → π*(C38–C40) and π(C16–C18) → π*(C18–C19) in FSTBP, π(C26–C34) → π*(C31–C32) and π(C13–C21) → π*(C18–C19) in NSTBP, and π(C13–C21) → π*(C5–C11) in OTBPS with stabilization energy values as 217.94 kcal/mol for TBTBP, 217.94 and 5.07 kcal/mol for FSTBP, 22.37 and 22.20 kcal/mol for NSTBP, and 65.07 kcal/mol for OTBPS, respectively. However, transitions such as π(C37–C45) → π*(C38–C40), π(C37–C45) → π*(C38–C40), π(C26–C34) → π*(C31–C32), and π(C37–C45) → π*(C38–C40) demonstrated highest stabilization energies of 230.96, 230.96, 22.37, and 168.68 kcal/mol, respectively, in all compounds: TBTBP, FSTBP, NSTBP, and OTBPS (see Tables S14–S17).

Moreover, transitions such as π(C5–C11) → π*(C13–C21), π(C16–C18) → π*(C18–C19), π(N57–O58) → π*(N57–O58), and π(C57–N58) → π*(C42–C43) consisting of 10.41,5.07, 7.82, and 5.70 kcal/mol stabilization energies with smallest magnitudes in TBTBP, FSTBP, NSTBP, and OTBPS, respectively. The σ → σ* transitions in contrast to π → π* transitions are originated owing to weak donor (σ), acceptor (σ*) interactions which are imperative for studying transitions with lesser stabilization energy values. Transitions such as σ(C18–C19) → σ*(C16–C18), σ(C31–C32) → σ*(C29–C31), σ(C31–C32) → σ*(C36–F55), σ(C29–C31) → σ*(C31–C32), and σ(C6–C7) → σ*(C24–C26) contained 5.08, 5.08, 6.90,5.07, and 5.13 kcal/mol energy values in TBTBP, FSTBP, NSTBP, and OTBPS, respectively, presenting larger energies amongst all σ → σ* interactions. While transitions σ(C18–C19) → σ*(C16–C18), σ(C31–C32) → σ*(C29–C31), σ(C31–C32) → σ*(C36–F54), σ(C45–C46) → σ*(C37–C38),and σ(C6–C7) → σ*(C24–C26) were having least stabilization energy values 5.08, 5.08, 1.51, 4.93, and 5.13 kcal/mol in TBTBP, FSTBP, NSTBP, and OTBPS, respectively (Table ).

Similar sort of interactions was noted in accordance to the resonance process. For example, LP2(F57) → π*(C42–C43), LP2(F57) → π*(C42–C43), LP3(O59) → π*(N57–O58), and LP2(O1) → π*(C6–C7) produced 20.05, 20.05, 175.14, and 19.32 kcal/mol in TBTBP, FSTBP, NSTBP, and OTBPS correspondingly. While interactions as LP2(F47) → σ*(C23–F49), LP2(O54) → π*(C36–F55), LP2(F56) → σ*(C36–F55), LP2(F47) → π*(C23–F49), LP2(F54) → π*(C36–F55), and LP2(F48) → π*(C23–F49) produced 5.03, 5.12, 5.12, 5.03, 5.10, and 5.10 kcal/mol stabilization energies in case of resonance for TBTBP, FSTBP, NSTBP, and OTBPS, respectively (Table ).

Vibrational Analysis

In order to have better perception of vibrational modes linked with TBTBP, FSTBP, NSTBP, and OTBPS, DFT studies were conducted at the B3LYP/6-311G(d,p) level of theory under solvent-free conditions (gas phase). The number of atoms in TBTBP, FSTBP, NSTBP, and OTBPS are 60, 57, 59, and 58 atoms correspondingly with the C1 point group symmetry.

The experimental vibrational bands observed at 1673–1675 cm–1, which are associated to the C=O functional group stretching vibration of TBTBP, FSTBP, NSTBP, and OTBPS, respectively, which are found in good correspondence with simulated values as 1627, 1627, 1633 and 1633 cm–1,[4] respectively. The experimental wave numbers in the range of 1615–1613 cm–1 existed because of strong bands of the C–C group in the α,β-unsaturated ketone of TBTBP, FSTBP, NSTBP, and OTBPS, which matched with simulated values as 1602, 1603, 1605, and 1605 cm–1, respectively. All the assignments were obtained in fine concurrence to the earlier reported similar structured piperidones values. The sulfonamide group (−SO2N−) in TBTBP, FSTBP, NSTBP, and OTBPS are attributed with the strong bands in the range of 1169–1161 cm–1 (Experimental Section), which are also found in correlation of simulated values as 1175, 1174, 1169, and 1168 cm–1, respectively. The simulated assignments are also observed in good harmony to the IR values of reported piperidones.[4] The stretching vibration of −CN is obtained at 2343 cm–1, which confirms the presence of a cyano group (−CN) in OTBPS.[4]

Natural Population Analysis

The natural charges of TBTBP, FSTBP, NSTBP, and OTBPS derivatives were measured by NBO analysis using the B3LYP/6-311G(d,p) functional, and results were presented in Figure . The natural charge examination was used frequently to evaluate the charge transformation process which originates in reactions, the phenomenon associating the electronegativity equalization and electrostatic potential on external surfaces of systems.[42] The electronic charges of atoms play a vital role in the bonding capability and molecular conformation.[43] Natural charges data of investigated molecules reveals that the electron density is unequally redistributed over the benzene rings in the attendance of extra electronegative atoms as N and O.[44]

Figure 5

Natural population analysis of the title compounds.

Our concern is to appraise the reactivity of figured charges and describe the distribution of electron density over investigated compounds.[45] Furthermore, no discrepancy in charge distribution was observed above all H-atoms indicated by natural population examination. Because of negative charge of carbon atoms, H-atoms bear positive charges. The high negative charges were contained by fluorine, nitrogen, and oxygen atoms in the entitled compounds. Because of the resonance process, some carbon atoms are enforced with large negative charges using oxygen and nitrogen atoms. However, the sulfur atoms in entitled compounds contained high positive charges.

Frontier Molecular Orbitals

The frontier molecular orbitals (FMOs) were not only used to describe the electric and optical properties, but chemical stability of investigated systems is also interpreted with this analysis.[46] The HOMO abbreviation is used for the highest occupied molecular orbital, the LUMO is used for the lowest unoccupied molecular orbital which happens to be the most substantial orbitals of FMOs. The HOMO exhibits the capability of donating an electron, whereas the LUMO shows capability of accepting an electron. The frontier orbital energy gap is an appreciated constraint in order to get knowledge concerning the dynamic stability and chemical reactivity of species (Table ).[47−55]

Table 2

Frontier Molecular Orbitals Energies for TBTBP, FSTBP, NSTBP, and OTBPSa

compounds	TBTBP		FSTBP		NSTBP		OTBPS
MO(s)	E (eV)	ΔE (eV)	E (eV)	ΔE (eV)	E (eV)	ΔE (eV)	E (eV)	ΔE (eV)
HOMO	–7.077	3.982	–7.163	3.988	–7.249	3.852	–7.238	4.021
LUMO	–3.095		–3.175		–3.397		–3.216
HOMO – 1	–7.077	5.074	–7.213	5.137	–7.336	4.140	–7.324	4.628
LUMO + 1	–2.003		–2.076		–3.196		–2.696
HOMO – 2	–7.223	5.859	–7.356	5.881	–7.638	5.526	–7.624	5.527
LUMO + 2	–1.364		–1.474		–2.112		–2.097
HOMO – 3	–7.482	6.312	–7.568	6.254	–7.968	6.083	–7.869	6.038
LUMO + 3	–1.170		–1.314		–1.886		–1.831

HOMO = highest occupied molecular orbital, LUMO = lowest unoccupied molecular orbital.

The HOMO–LUMO energy values were calculated to be −7.077/–3.095, 7.163/–3.175, −7.249/–3.397, and −7.238/–3.216 eV for TBTBP, FSTBP, NSTBP, and OTBPS, respectively. The band gaps of TBTBP, FSTBP, NSTBP, and OTBPS were obtained to be 3.982, 3.988, 3.852, and 4.021 eV, respectively. The band gap of NSTBP was obtained slightly lesser than its analogues because of the electron-withdrawing ability of −NO2.

The electron density in the HOMO of TBTBP, FSTBP, NSTBP, and OTBPS were dispersed on the 3-methylene-5-(4-(trifluoromethyl)benzylidene)piperidin-4-one fragment except for the 1-methyl-4-(methylsulfonyl)benzene, phenyl, and trifluoromethane groups. The electron density in the LUMO for TBTBP, FSTBP, NSTBP, and OTBPS concentrated on 3,5-bis((E)-benzylidene)piperidin-4-one except for 1-methyl-4-(methylsulfonyl)benzene and trifluoromethane groups (Figure ).

Figure 6

Frontier molecular orbitals of TBTBP, FSTBP, NSTBP, and OTBPS.

Global Reactivity Parameters

The global softness (σ), global electrophilicity (ω), global hardness (η),electronegativity (X), chemical potential (μ), electron affinity (A), and ionization potential (I) were also calculated using the HOMO and LUMO energies.[25,48,49,56−58] The findings of GRPs were obtained from eqs –6, which were tabulated in Table . These chemical quantities revealed the chemical reactivity of the former mentioned derivatives.

Table 3

Calculated Global Reactivity Parameters of Entitled Compounds, Units in eV

compounds	I	A	X	η	μ	ω	σ
TBTBP	7.077	3.096	5.086	1.991	–5.086	6.498	0.251
FSTBP	7.163	3.175	5.169	1.994	–5.169	6.699	0.251
NSTBP	7.249	3.397	5.323	1.926	–5.323	7.356	0.260
OTBPS	7.238	3.216	5.227	2.011	–5.227	6.795	0.249

In broad context, A and I values were used to describe the electron-accepting and donating aptitude of investigated molecules, respectively. The I values of TBTBP, FSTBP, NSTBP, and OTBPS were found to be larger in magnitude as compared to A values. The chemically hardness values were observed as 1.991, 1.994, 1.926, and 2.011 eV for TBTBP, FSTBP, NSTBP, and OTBPS, respectively. The chemically softness values were computed as 0.251, 0.251, 0.260, and 0.249 eV for TBTBP, FSTBP, NSTBP, and OTBPS, respectively (Table ). These results indicated that studied derivatives have enormous kinetic stability and exhibit fine concurrence with SC-XRD,[4] and NBO findings.

Nonlinear Optical Properties

The examination of NLO effects in organic compounds established a fascinating topic which was initiated by Champagne and Bishop.[59] The organic polymeric and heterocyclic compounds having large hyperpolarizability amplitudes have drawn attention owing to their applicability in the interest of NLO materials.[60,61] Recently, many researches are enthusiastic to establish the favorable synthetic procedures of organic chromophores for their distinct properties in the NLO field.[62] Furthermore, numerous researcher groups are doing extensive work on organic compounds because of their relative facile synthesis as well as greater efficacy in NLO response properties.[13] DFT-based studies have delivered an alluring type role in understanding of experimental findings, especially in NLO responses.[63] In this context, entitled compounds such as TBTBP, FSTBP, NSTBP, and OTBPS have not been investigated for their potential NLO characteristics by both computational and experimental researchers. The entitled compounds contain huge interest owing to their heterocyclic ring’s involvement in the electron-withdrawing groups. The electronic and optical properties might be expected significantly in magnitude because of their greater conjugated electronic systems.[64−69] Moreover, conjugated electronic systems could be the premeditated primary concept for the intramolecular charge transfer (ICT) process.[70] Indeed, the larger charge transfer may lead to larger amplitudes for mean polarizabilities ⟨α⟩ and first hyperpolarizabilities (βtot). Herein, we have the selected functional: HF, B3LYP, and M06 with the 6-311G(d,p) basis set for determination of average polarizabilities ⟨α⟩ and second-order polarizabilities for TBTBP, FSTBP, NSTBP, and OTBPS. Equations and 8 were utilized for the calculation of mean polarizabilities ⟨α⟩ and first-order hyperpolarizabilities (βtot) using x, y, and z components which are listed in Tables and 5, respectively.

Table 4

Dipole Polarizabilities and Major Contributing Tensors (au) of the Studied Compounds

func	comp.	αxx	αyy	αzz	⟨α⟩
M06	TBTBP	594.1	251.6	288.9	378.2
	FSTBP	581.1	237.7	275.3	364.7
	NSTBP	600.6	246.0	297.9	381.5
	OTBPS	283.6	155.2	678.1	372.3
B3LYP	TBTBP	598.0	251.3	287.1	378.8
	FSTBP	584.9	236.9	274.2	365.3
	NSTBP	604.0	250.3	292.27	382.2
	OTBPS	605.4	254.8	290.8	383.7
HF	TBTBP	512.9	233.6	273.4	339.9
	FSTBP	500.2	220.6	260.5	327.1
	NSTBP	517.6	226.3	282.7	342.2
	OTBPS	519.8	233.9	278.6	344.1

Table 5

Computed Second-Order Polarizabilities (βtot) and Major Contributing Tensors (au) of the Studied Compoundsa

func.	comp.	βxxx	βxxy	βxyy	βyyy	βxxz	βtot
M06	TBTBP	326.5	–505.4	89.5	–67.6	588.6	951.6
	FSTBP	280.6	–525.1	84.9	–76.4	583.7	914.2
	NSTBP	–383.1	–223.9	–310.5	147.1	–807.2	1170.3
	OTBPS	283.6	–400.2	155.2	10.2	678.1	904.9
B3LYP	TBTBP	–427.2	–538.8	–99.1	–92.9	–647.9	1102.6
	FSTBP	–369.7	–552.2	–94.2	–104.3	–646.5	1051.4
	NSTBP	–536.1	–349.6	–302.2	172.2	–837.3	1382.2
	OTBPS	–429.5	–470.7	–170.6	17.9	–717.7	1076.0
HF	TBTBP	115.1	–312.5	48.7	–22.4	–69.3	392.4
	FSTBP	77.1	–332.6	43.5	–46.3	297.5	502.3
	NSTBP	–72.6	–207.4	–144.1	19.5	–444.0	538.9
	OTBPS	79.4	–274.5	79.7	–28.6	359.7	500.2

Func = functionals; comp. = compounds.

The mean polarizabilities ⟨α⟩ are found to be larger at the exchange correlation functional B3LYP level as compared to magnitudes of ⟨α⟩ observed with the meta-hybrid GGA method M06 and HF method for TBTBP, FSTBP, NSTBP, and OTBPS. However, the mean polarizabilities ⟨α⟩ are obtained to be lesser at the HF level as compared to magnitudes of ⟨α⟩ at B3LYP and M06 levels for all investigated molecules. It can be concluded that mean polarizabilities ⟨α⟩ values of all studied compounds at the M06 level are found to be in between the values noted at B3LYP and HF levels. For TBTBP, FSTBP, NSTBP, and OTBPS, B3LYP and M06 methods exhibited almost similar mean polarizabilities ⟨α⟩ values (Figure ). The average polarizability values of investigated compounds are found to be in following order as B3LYP > M06 > HF. Moreover, average polarizability ⟨α⟩ values of TBTBP, FSTBP, NSTBP, and OTBPS were found to be larger than the standard urea molecule (⟨α⟩ =32.918 au at M06).

Figure 7

Calculated average polarizabilities at different levels of the studied compounds.

The literature discloses that HOMO–LUMO energy gap possess influence on the molecular polarizability.[71] The HOMO–LUMO energy gap has an inverse relationship with linear polarizability and nonlinear polarizability (Figures and 7). The compounds comprising small HOMO–LUMO energy gap supports large nonlinear and linear polarizabilities. In our investigation, NSTBP is observed with a narrow energy gap in contrast to TBTBP, FSTBP, and OTBPS energy gap values. Consequently, it exhibits larger linear and nonlinear polarizability values (Figures and 7).

The entitled compounds: TBTBP, FSTBP, NSTBP, and OTBPS contained substituents like −CH3, −F, −NO2, and −CN on the N-benzenesulfonyl moiety, respectively. The −CH3 substituent in TBTBP displayed electron-donating effect, while −F, −NO2, and −CN substituents of entitled compounds FSTBP, NSTBP, and OTBPS respectively, showed electron-withdrawing effects. The order of substitutes in terms of the electron-withdrawing effect can be NO2 > CN > F. Interestingly, NSTBP and OTBPS having strong electron-withdrawing substitutes, −NO2 and −CN, respectively, led to a remarkable effect on NLO as compared to TBTBP containing an electron-donating group (−CH3) and FSTBP with a weak electron-withdrawing substituent (−F). Therefore, first hyperpolarizability (βtot) values of NSTBP–NO2 were found to be larger as 1170.3, 1382.2, and 538.9 au at HF, B3LYP, and M06 levels, respectively, than TBTBP, FSTBP, and OTBPS.

The effect of electron-donating substituent −CH3 in TBTBP is evident with observed βtot values 951.6 (B3LYP) and 1102.6 (M06) which are found to be smaller than NSTBP–NO2 and larger than FSTBP and OTBPS βtot values at M06, B3LYP levels of theory. The first hyperpolarizability (βtot) values of OTBPS–CN were obtained to be lesser as 904.9, 1076.0, and 500.2 au than all studied compounds at the M06 level, smaller than NSTBP, TBTBP, and larger than FSTBP at the B3LYP level of theory. The substituents on TBTBP and FSTBP compounds do not play a significant role in first-order hyperpolarizability (βtot) value patterns. There might be an influence of conformation about second-order polarizabilities of TBTBP and FSTBP compounds. The literature revealed that TBTBP and FSTBP having pseudo-axial conformation for the arylsulfonyl group with the reference of the 4-pyridone ring, while NSTBP and OTBPS having pseudo-equatorial conformation for the arylsulfonyl group.[4] Furthermore, it has been observed that the HF method showed the least values of βtot for all compounds, while the B3LYP level was at the top one having the highest βtot for compounds as compared to other utilized levels HF and M06. The βtot values of studied compounds were found to be in the following order at different methods: B3LYP > M06 > HF (Figure ). The literature review revealed that urea is used as the standard molecule for a comparative study of NLO.[72−75] The calculated βtot values of TBTBP, FSTBP, NSTBP, and OTBPS at all aforementioned levels were obtained to be larger than urea (βtot = 66.847 au,) at the M06 level.

Figure 8

Computed first-order hyperpolarizabilities of different levels of the studied compounds.

Conclusions

The current study discloses that computed geometrical parameters (bond lengths and bond angles) are in excellent agreement with the SC-XRD data. The experimental FT-IR spectra results were found in line with simulated vibrational measurements. NBO analysis revealed that the intramolecular charge transfer exists in entitled compounds. Furthermore, NBO-based hyper conjugative interactions values were observed with larger values which endorse highest stability of investigated molecules. Moreover, Hirshfeld surface analysis also endorses the highest molecular stability. The energy gap of the HOMO and LUMO were found to be 3.982, 3.988, 3.852, and 4.021 eV for TBTBP, FSTBP, NSTBP, and OTBPS, respectively. The band gap of OTBPS was obtained slightly greater than its analogues because of the electron-withdrawing ability of −CN. The chemically hardness values for TBTBP, FSTBP, NSTBP, and OTBPS were observed larger in contrast to corresponding softness values which revealed that studied derivatives have enormous kinetic stability and exhibit fine concurrence with NBO findings. The entitled compounds have average polarizabilities ⟨α⟩ in the span of 365.3–383.7 (au) at B3LYP, 364.7–381.5 (au) at M06, and 327.1–344.1 (au) at the HF level. Furthermore, the entitled compounds have conspicuous large NLO response (βtot) in the span of 1051.45–1382.2 (au) at B3LYP, 904.9–1170.3 (au) at M06, and 392.4–538.9 (au) at the HF level. Among entitled compounds, NSTBP consists of highest ⟨α⟩ and βtot values. The βtot values of TBTBP, FSTBP, NSTBP, and OTBPS were 25.64, 24.45, 27.83, and 25.02, respectively, times larger as compared to the βtot value of the standard molecule (urea). It is anticipative that the quantum chemical-based investigation of the TBTBP, FSTBP, NSTBP, and OTBPS could be fruitful for granting a most favorable model for second-order NLO responses.