Synthesis, spectroscopic, SC-XRD/DFT and non-linear optical (NLO) properties of chromene derivatives

Abstract

In the present study, we reported the efficient synthesis of novel, heterocyclic, coumarin-based pyrano-chromene derivatives, 2-amino-8-methyl-5-oxo-4-[2-(2-oxo-2H-chromen-3-ylmethoxy)-phenyl]-4H,5H-pyrano[3,2-c]chromene-3-carbonitrile (4a) and 2-amino-8-methyl-5-oxo-4-[2-(2-oxo-2H-chromen-3-ylmethoxy)-phenyl]-4H,5H-pyrano[3,2-c]chromene-3-carboxylic acid methyl ester (4b). The chemical structures of synthesized compounds were resolved by employing various spectroscopic techniques like UV-Vis, FT-IR, ¹H & ¹³C NMR, and single crystal X-ray diffraction (SC-XRD) analysis. The compounds; 4a and 4b, with appealing π-bonded skeleton were further analyzed in terms of their electronic and structural aspects using an integral approach of density functional theory (DFT) and time-dependent DFT (TD/DFT). The methodology: M06-2X/6-31G(d,p) level of theory was applied to compare their experimental data with theoretical outcomes using quantum chemical analysis. The frontier molecular orbitals (FMOs) study revealed that, 4a possesses a low band gap (5.168 eV) as compared to 4b (6.308 eV). Global reactivity parameters were associated with E_gap values as 4a, with the lowest band gap showed the smaller value of hardness (0.094 eV) and a larger value of softness (5.266 eV). The non-linear optical (NLO) insight exhibited that, the average polarizability 〈α〉 and second hyperpolarizability (γ_tot) were observed in 4a as 6.77005 × 10⁻²³ and 0.145 × 10⁴ esu, respectively. Overall, the computational studies suggest that the investigated compounds have distinct NLO properties.

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1. Introduction

Diversity-oriented synthesis of heterocyclic frameworks has become indispensable in the construction of novel fused ring heterocyclic compounds and thus aims to design natural product ring systems with useful pharmacophores for drug development.¹ The structural and activity profiles of various coumarin derivatives have inspired pharmaceutical chemists to develop new drugs with safe activity and selectivity in their action for a variety of therapeutic disorders.^2–5 Coumarin derivatives are well known for their critical role in the prevention and treatment of pathogenic and infectious diseases.^6,7 Coumarin-based analogues are intended to show discrete valuable biological and clinical activities vulnerable to substitution patterns exhibited by the parent benzopyran core.^8,9 Amongst the highly studied pharmaceutical activities, it is noteworthy for antibacterial,^10,11 antiviral,¹² antifungal,¹³ anticancer,¹⁴ anti-inflammatory,¹⁵ antitubercular,¹⁶ antioxidant,¹⁷ antimutagenic,¹⁸ anticoagulant,¹⁹ scavenging of reactive oxygen species (ROS),²⁰ cyclooxygenase,²¹ lipoxygenase,²² cholinesterase (ChE), and monoamine oxidase (MAO) inhibitory activities, vasodilator,²³ CNS stimulant,²⁴ and cytotoxic²⁵ potential.

The analysis of supramolecular architecture has greatly revolutionized research in the field of crystal engineering, which accommodates non-covalent interactions where molecules accumulate in self-assembly, possessing various inter and intramolecular interactions.^26,27 The strong interactions like hydrogen bonding (inter and intramolecular) also play a pivotal role in molecular biology, supramolecular frameworks and crystal engineering.^28,29 There are various structural diversities found in the heterocyclic frameworks, like the presence of electronegative groups (such as –F), which influence the molecular stability as well as the molecular level interactions with the biological receptors. The various privileged biological compounds that undergo structural diversities are found with enhanced efficiencies. Moreover, the rapid synthesis of wide-ranged heterocyclic compounds with the help of multi-component reaction techniques has attracted the attention of researchers.^30,31

The heterocyclic chromene-based ring compounds are an important class of benzopyran family compounds that are efficiently being used in several pharmacological industries as anti-bacterial,^32–34 antiviral,³⁵ anti-malaria,³⁶ anti-inflammatory,³⁷ anti-cancer,³⁸ anti-HIV,³⁹ antifungal,⁴⁰ anti-anaphylactic, and anti-proliferative.⁴¹ Computational analysis, also known as density functional (DFT) analysis, is an important method for predicting structural parameters such as non-covalent interactions, electronic properties, stability, and chemical reactivity.⁴² The DFT and time-dependent DFT approaches envisage the bond distances, bond angles, FMOs, global reactivity descriptors (GRDs), natural population analysis (NPA), NBOs, molecular electrostatic potential (MEP), statistical average of molecular dipoles moment, linear and non-linear polarizabilities for various crystalline and non-crystalline compounds, including hydrazones, organic co-crystals,^43,44 pyrimidine rings⁴⁵ etc.

Non-linear optics (NLO) is one of the significant research areas which are being focused nowadays. In the present investigation, the chromene-based synthesized compounds are deliberated for their NLO parameters, i.e., 〈α〉, β_tot, and γ_tot, which were not evaluated so far, as evident from the literature review. Such organic compounds having a π-conjugated framework are efficiently utilized in wide bandwidth optical switching devices. The unique properties of such compounds as intramolecular charge transfer (ICT), electron delocalization, polarizability, and hyperpolarizability have paved the way for new research into efficient NLO devices.⁴⁶

The chromene-based synthesized crystalline compounds, i.e., 4a and 4b, were studied via the DFT approach. The NLO study of the entitled compounds might not be reported yet. Hence, to overcome the research gap, computational analysis is carried out to examine NLO properties. This research paper would be a new addition to the advancement of NLO compounds and surely serve as a synthesized non-fullerene (NF) based crystalline organic NLO materials in the research discipline for the future.

2. Experimental section

2.1 Synthesis of coumarin-based pyrano-chromene derivatives (4a and 4b)

An equimolar mixture of coumarin-based aldehyde (1) (1 mmol) and appropriate nitrile (2a–2b) (1 mmol) in EtOAc was initially stirred for half an hour at room temperature in the presence of 2–3 drops of Et₃N as a catalyst, and then 7-methyl-4-hydroxy coumarin (3) (1 mmol) was added. The course of the reaction was monitored by TLC. After completion of the reaction, the precipitates were formed, which were filtered and washed twice with hot ethyl acetate. Further purification was done by recrystallization using a mixture of CHCl₃ (4 parts) and MeOH (1 part) to furnish pure, newly synthesized heterocyclic coumarin-based pyrano-chromene compounds (4a and 4b) with excellent yield. Physical and spectroscopic data for compounds (4a and 4b) are shown below, while NMR and FT-IR spectra are shown in Fig. S1–S6.†

2.2 2-Amino-8-methyl-5-oxo-4-[2-(2-oxo-2H-chromen-3-ylmethoxy)-phenyl]-4H,5H-pyrano[3,2-c]chromene-3-carbonitrile (4a)

Colorless crystalline solid; m.p. 268–270 °C; yield: 97%; solubility: DMSO; FT-IR; KBr (cm⁻¹); 1681, 1718 ([double bond splayed left]C=O), 2180 (–CN), 3311, 3387 (NH₂-str.); ¹H NMR; (400 MHz, DMSO-d₆, δ, ppm) 2.37 (s, 3H, CH₃–H), 4.67 (s, 1H, CH, C₄–H), 4.80 (d, 1H, J = 10.2 Hz, OCH₂–H_a), 4.94 (d, 1H, J = 10.2 Hz, OCH₂–H_b), 6.89 (d, 1H, J = 6.4 Hz, Ar–H), 6.93 (t, 1H, J = 5.8 Hz, Ar–H), 7.07 (d, 1H, J = 6.5 Hz, Ar–H), 7.18–7.26 (m, 5H, NH₂–H, Ar–H), 7.34–7.37 (m, 3H, Ar–H), 7.51 (d, 1H, J = 6.2 Hz, Ar–H), 7.62 (td, 1H, J = 1.2 Hz, 7.3 Hz, Ar–H), 7.90 (s, 1H, CH, ); ¹³C NMR; (100 MHz, DMSO-d₆, δ, ppm) 21.71, 33.98, 49.06, 57.12, 65.32, 102.68, 110.69, 113.03, 116.60, 116.79, 119.07, 120.11, 121.42, 121.95, 123.98, 124.94, 125.77, 128.90, 129.07, 131.06, 132.27, 141.43, 143.85, 152.47, 153.46, 154.40, 156.44, 158.80, 159.90, 160.33; anal. calcd. for C₃₀H₂₀O₆N₂ (504): C = 71.42, H = 4.00, N = 5.55; found (%): C = 71.35, H = 4.03, N = 5.58.

2.3 2-Amino-8-methyl-5-oxo-4-[2-(2-oxo-2H-chromen-3-ylmethoxy)-phenyl]-4H,5H-pyrano[3,2-c]chromene-3-carboxylic acid methyl ester (4b)

Colorless crystalline solid; m.p. 230–232 °C; yield: 92%; solubility (DMSO, CHCl₃); FT-IR; KBr (cm⁻¹); 1687, 1717 ([double bond splayed left]C=O), 3324, 3420 (NH₂-str.); ¹H NMR; (300 MHz, DMSO-d₆, δ, ppm) 2.13 (s, 3H, CH₃–H), 3.52 (s, 3H, COOMe–CH₃–H), 4.73 (d, 1H, J = 12.6 Hz, OCH₂–H_a), 4.76 (s, 1H, CH, C₄–H), 4.82 (d, 1H, J = 12.8 Hz, OCH₂–H_b), 6.90 (t, 1H, J = 7.2 Hz, Ar–H), 6.99 (d, 1H, J = 8.1 Hz, Ar–H), 7.16 (t, 1H, J = 7.5 Hz, Ar–H), 7.24–7.30 (m, 3H, Ar–H), 7.34–7.41 (m, 3H, Ar–H), 7.48 (d, 1H, J = 7.5 Hz, Ar–H), 7.62–7.67 (m, 3H, NH₂–H, Ar–H), 7.81 (s, 1H, CH, ); ¹³C NMR, (75 MHz, DMSO-d₆, δ, ppm) 20.92, 34.02, 50.95, 65.50, 75.86, 105.11, 113.17, 113.29, 116.52, 116.64, 119.15, 120.78, 122.04, 124.17, 125.04, 128.43, 128.92, 131.81, 132.29, 132.59, 133.54, 134.02, 141.55, 150.60, 153.48, 153.90, 156.98, 159.36, 159.91, 160.52, 168.75; anal. calcd for C₃₁H₂₃O₈N (537.14): C = 69.27, H = 4.31, N = 2.61; found (%): C = 69.24, H = 4.33, N = 2.68.

2.4 Chemistry

In order to obtain o-ring heterocyclic (pyrano-chromenes), a multicomponent approach was designed to synthesize novel fused ring coumarin-based dihydropyranochromenes (4a and 4b) (Scheme 1). Coumarin-based aldehyde (1) was synthesized by utilizing the Baylis–Hillman reaction between salicylaldehyde and methyl acrylate.^47,48 The multi-component reaction of coumarin-based aromatic aldehyde (1), nitriles (2a–2b), and 7-methyl-4-hydroxy coumarin (3) in the presence of Et₃N through the Knoevenagel–Michael-cyclization path was utilized for the synthesis of these heterocyclic compounds with excellent yield. The optimization of various parameters like temperature, solvent, and catalyst, during the reaction was obtained to enhance the regioselectivity of the reaction as well as the yield of the product. Thus, ethyl acetate as solvent, Et₃N or Me₃N as a base, and 60 °C temperature were found to be the suitable parameters of choice for this reaction. The structures of synthesized compounds (4a and 4b) were elaborated via spectroscopic techniques like FT-IR, NMR, and CHN analysis. In FTIR spectroscopic analysis, the C=O functional group appeared in the range of 1671–1718 cm⁻¹, while the cyano group appeared at 2179 cm⁻¹, and NH₂ groups in the relevant products were identified by absorption bands in the range of 3387–3420 cm⁻¹.

Scheme 1 Synthesis of coumarin-based pyrano-chromenes (4a and 4b).

The ¹H NMR spectra of (4a and 4b) gave evidence for cyclized products as there is no downfield signal of CHO proton at δ 10.48–10.53 ppm. Instead, a singlet of two protons for the NH₂ group was observed at δ 7.18–7.68 ppm and this peak is merged into the aromatic range by shielding or deshielding. Furthermore, the disappearance of the signal for the singlet of the OH group in 4-hydroxylated coumarins confirmed the cyclization. The appearance of one signal for the singlet of 3H at δ 3.34 ppm illustrated the presence of methyl-ester in compounds (4b). Total proton counts in the aromatic region also fulfill the structural requirements of the compound. Their chemical shifts were allocated on behalf of spin-multiplicity as well as coupling constant.

The ¹³C NMR spectra of (4a and 4b) unveiled the accordance of chemical shifts of aliphatic, aromatic, and carbonyl moieties with the desired structures. Further confirmation of the representative compounds (4a and 4b) came from the absorption peaks of aliphatic carbons at 21.71, 33.98, and 49.06 ppm, aromatic carbons from 120 to 158 ppm, and carbonyl at 159.90 and 160.33 ppm. CHN analyses also favored the desired structures of pyrano-chromenes, as experimentally collected values were in accordance with calculated % ages. By utilizing the animation of Avogadro software, we calculated the results of vibrational analysis of fore-said compounds and compared with experimental results. The simulated stretching symmetrical and asymmetrical vibration band for –NH₂ groups in 4a and 4b are observed in the range of 3742–3509 and 3709–3538 cm⁻¹, respectively, which are in good harmony with experimental absorption bands (3466 and 3576 cm⁻¹, accordingly). Similarly, the experimentally determined stretching vibrational frequencies for –CN group in 4a are found as 2361 cm⁻¹ which showed good agreement with their DFT results (2376 cm⁻¹). The symmetrical stretching absorption bands for –CO are noted as 1886 and 1815 cm⁻¹ while their experimental bands are determined at 1719 and 1716 cm⁻¹, respectively. Many other kind of simulated vibrations frequencies in 4a and 4b are also studied which showed good agreement with their experimental absorption bands (see in Tables S10, S11 and Fig. S5, S6†). In this research paper, the non-fullerene-natured synthesized crystals, i.e., 4a and 4b, are evaluated in terms of their NLO characteristics. For this purpose, SC-XRD characterization is done and inspection of molecular configuration is carried out thoroughly via different parameters like bond lengths, bond angles, etc. The experimental data are compared with the theoretical results (DFT) to verify the chemical nature of the studied compounds.

2.5 Crystallization, data collection and structure solution

The crystals of compounds 4a and 4b were grown by slow evaporation in a methanol/chloroform solvent system in a 4 : 1. Colorless crystals appeared after a few days. Good quality single crystals were chosen for the diffraction experiment. The crystal was mounted on a goniometer head using grease. The data sets were collected on a Bruker D8 Venture with a PHOTON II detector and Mo microfocus source (λ = 0.71073 Å) (Bruker 2016) under ambient conditions using omega and phi scan methods. The diffracted intensities were processed using APEX3 tools. An analytical absorption correction was applied using the face indices of the crystal. Table 1 summarizes the crystallographic and refinement details.

Table 1 Crystallographic data of compounds 4a and 4b

Comp.	4a	4b
Crystal data
Chemical formula	C30H20N2O6·CH4O	C31H23NO8
Mr	536.55	537.50
Crystal system, space group	Triclinic, P1̄	Triclinic, P1̄
Temperature (K)	297(1)	297(1)
a, b, c (Å)	9.1201(7), 11.5487(7), 12.5810(8)	8.6139(15), 10.6283(16), 14.384(2)
α, β, γ (°)	93.498(2), 96.303(3), 100.317(3)	80.026(6), 80.436(7), 81.990(6)
V (Å^3)	1291.38(15)	1270.7(4)
Z	2	2
Radiation type	Mo Kα	Mo Kα
μ (mm^−1)	0.10	0.10
Crystal size (mm)	0.22 × 0.18 × 0.17	0.32 × 0.22 × 0.13
Data collection
Diffractometer	Bruker D8 Venture Photon II detector
Absorption correction	Analytical SADABS2016/2 (Bruker, 2016/2) was used for absorption correction. wR2(int) was 0.1247 before and 0.0684 after correction. The ratio of minimum to maximum transmission is 0.7828. The λ/2 correction factor is not present
Tmin, Tmax	0.667, 0.746	0.584, 0.745
No. of measured, independent and observed [I ≥ 2u(I)] reflections	35 003, 5884, 3085	33 043, 5205, 2618
Rint	0.064	0.083
(Sin θ/λ)max (Å^−1)	0.649	0.625
Refinement
R[F^2 > 2σ(F^2)], wR(F^2), S	0.064, 0.248, 1.22	0.056, 0.194, 1.07
No. of reflections	5884	5205
No. of parameters	365	371
H-atom treatment	H-atom parameters constrained	H atoms are treated by a mixture of independent and constrained refinement
Δ〉max, Δ〉min (e Å^−3)	0.35, −0.35	0.29, −0.25

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Both the crystal structures were solved by direct methods in the triclinic (P1̄) space group using Olex2 (ref. 49) (Fig. 1). All the hydrogen atoms could be located in different Fourier maps. However, they are fixed using a riding model.

Fig. 1 View of the atom-labeled structures of compounds 4a and 4b (thermal ellipsoids were drawn at 30% probability level for both molecules).

Both molecules crystallized with the P1̄ space group. The asymmetric unit of 4a contains one molecule of the organic compound along-with one molecule of methanol as solvent while the asymmetric unit of 4b contains only one molecule of the organic moiety Fig. 1. The angles between the planes of the fitted atoms of pyrano-chromene ring system (C17–C29/O4/O6) and the central phenyl ring (C11–C16) are 88° and 88.35° in 4a and 4b, respectively, while the angles between the phenyl (C11–C16) and the coumarin ring system(C1–C9/O1) are 78.38° and 72.35° in 4a and 4b, respectively. The molecular structures (ORTEP diagrams) of coumarin-based pyrano-chromenes 4a and 4b with their crystallographic numbering are shown in Fig. 1.

In the case of 4a, the molecular assembly is primarily built based on strong hydrogen bonds like N1–H1B⋯O2 and C14–H14⋯O5. Both interactions result in molecular dimerization. The interaction N1–H1B⋯O2, at a distance of 2.20(3) Å and N–H⋯O angle of 135.07(3)°, connects the molecules in dimers and generate twenty-four (24) membered ring motifs R₂²(24). Similarly, C14–H14⋯O5, connects the molecules to produce sixteen membered ring motifs R₂²(16), these two interactions go in a zigzag fashion at right angle. All these further extended into three-dimensional spaces through a large network of van der Waals's interactions. The amino group is involved in the formation of two hydrogen bonds. One we have discussed above while the other forms a hydrogen bond with N1–H1a⋯O7 at a distance of 2.171(3) Å and N–H⋯O angle of 155.1(3)° with the solvent molecule (methanol). The methanol molecule also forms another strong hydrogen bond with the reference molecule through the O7–H7A⋯O1 hydrogen bond (Fig. 2a). The hydroxyl group of methanol is bridging between the amino group and O1 of coumarin Fig. 2a. The interaction C3–H3⋯N2 connects the molecules along the diagonal of ab-plane. Other weak interactions from C5–H5⋯O5 and C3–H3⋯N2 generate fourteen membered ring motifs R₃²(14) Fig. 2a and Table 2.

Fig. 2 (a) A diagram showing the hydrogen bonding interactions. Formation of dimer in through a centrosymmetric network of reciprocal strong N–H⋯O and bridging via O–H⋯O hydrogen bonds of methanol. (b) A diagram showing the hydrogen bonding interactions. Chain formation running along a-axis.

Table 2 Hydrogen bonds for 4a and 4b

D	H	A	d(D–H)/Å	d(H–A)/Å	d(D–A)/Å	D–H–A/°
a 1 − X, 1 − Y, −Z.b 1 − X, 2 − Y, 1 − Z.c −1 + X, −1 + Y, +Z.d −X, 1 − Y, 1 − Z.e 1 + X, +Y, +Z.f −X, 1 − Y, 2 − Z.
4a
N1	H1A	O7	0.86	2.17	2.973(4)	154.6
O7	H7A	O1	0.82	2.40	2.997(4)	130.7
N1	H1B	O2^a	0.86	2.20	2.874(3)	135.4
C14	H14	O5^b	0.93	2.55	3.470(4)	168.8
C3	H3	N2^c	0.93	2.61	3.483(4)	156.3
C5	H5	O5^d	0.93	2.60	3.433(4)	150.0
4b
N1	H1A	O7	1.05(4)	1.84(4)	2.674(4)	133(3)
N1	H1B	O5^e	0.84(3)	2.32(3)	3.114(4)	158(3)
C13	H13	O2^f	0.93	2.55	3.221(4)	129.6

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Although the 4b has no solvent of crystallization but it is affording three different type of hydrogen bonding interactions. There is one classical hydrogen bond between N1–H1b⋯O5 at a distance of 2.321(3) Å holding the successive molecules together in Fig. 2b. In addition, there is a nonclassical weak interaction from C13–H13⋯O2 interaction that help in the expansion of the molecular assembly along a-axis, base vector (1 0 0). There is an intramolecular hydrogen bonding interaction via N1–H1⋯O7 (Table 2) forming the stable six membered (H1A/N1/C20/C21/C22/O7) ring motif S(6) with root mean square deviation of 0.0110(3) Å and this ring is fused with another ring (O6/C20/C21/C17/C18/C19). The presence of more hydrogen bonds in 4a than in 4b lends higher thermal stability to the former, which is evident from the relatively higher m.p. of 4a (268 °C) than in 4b (230 °C). The root mean square deviation for the ring (O6/C20/C21/C17/C18/C19) is 0.0588(16) Å and puckering parameters are Q = 0.144(3) Å, θ = 72.0(12)° and φ = 176.9(11)° which are indicating that the ring is slightly deviating from planer to chair shape conformation. Both the rings (H1A/N1/C20/C21/C22/O7) and (O6/C20/C21/C17/C18/C19) are twisted by 4.232(4)°.

2.6 Hirshfeld surface and fingerprint plot analysis

Hirshfeld surface analysis allows us to quantify the various intermolecular interactions contributing to the packing of a whole molecule in a crystal.^50,51 The Hirshfeld surface and fingerprint plot of 4a and 4b molecules were mapped with d_norm (Fig. 3 and 4) using Crystal Explorer.⁵⁸ The white colour shows the contacts, which are close to Vander Waal's radii; the blue colour indicates the longer contacts; and the red colour represents the stronger interactions present in the crystal of HA. In Fig. 3, the surface map for 4a represents the dark red region in the vicinity of O1, O2, and N1, showing the presence of strong O7–H7A⋯O1, N1–H1b⋯O2, and N1–H1a⋯O7, intermolecular interactions in the crystal. The rest of the surface does not show the presence of any strong interaction and appears neutral. These colour indications are very useful for the identification and relative strength of possible intermolecular interactions.

Fig. 3 A Hirshfeld surface of the 4a showing the regions of strong interactions along with fingerprint plots showing the contributions of various interactions.

Fig. 4 A Hirshfeld surface of the 4b showing the regions of strong interactions along with fingerprint plots showing the contributions of various interactions.

Similarly, in Fig. 4, the surface map for 4b represents a single dark red region only in the vicinity of N1–H1b, while the rest of the surface appears neutral. These colour indications are very useful for the identification and relative strength of possible intermolecular interactions.

Fingerprint plots analyse the intermolecular interactions and molecular packing in a crystal on the basis of the Hirshfeld surface.^56–58 The fingerprint plots of 4a and 4b molecules are shown in Fig. 3 and 4. In both molecules, the H⋯H interactions predominate on the surface, with 39% and 40.2% contributions, respectively. This is followed by the contributions of O⋯H contacts, which account for 28.1% and 21.3%, respectively. Contributions by C⋯H interactions are next in the hierarchy, with values of 20.8% and 25.3%, respectively. The N⋯H contribution in 4a is 11.6%, while in 4b this contribution is very negligible (0.3%). The Hirshfeld surface map enables us to understand the intermolecular interactions and the strength of above-mentioned strong and weak interactions that contribute to the surface of the molecules.

2.7 Computational procedure

For the computational analysis of synthesized crystalline compounds 4a and 4b, the Gaussian 09 program package⁵² was used. Primarily, the geometries of compounds were attained through SC-XRD by utilizing the crystallographic information file (CIF). Subsequently, DFT calculations for the entitled compounds were accomplished at M06-2X/6-31G(d,p) level of theory. Furthermore, NLO and FMOs analyses were performed for 4a and 4b at the aforementioned level of DFT, as well as NLO responses were calculated by using eqn (1)–(4).^53–55 However, natural bonding orbitals (NBOs) were investigated using the M06-2X/6-31G(d,p) level of theory,⁵⁶ because non-covalent interactions can be effectively studied at this level of theory. For interpretation of results from output files, Gauss View,⁵⁷ Avogadro,⁵⁸ Chemcraft,⁵⁹ PyMOlyze 2.0,⁶⁰ Origin 8.0,⁶¹ and Multiwfn 3.7 (ref. 62) were employed.

μ = (μ_x² + μ_y² + μ_z²)^1/2 (1)

〈α〉 = (a_xx + a_yy + a_zz)/3 (2)

β_tot = (β_x² + β_y² + β_z²)^1/2 (3)

where β_x = β_xxx + β_xyy + β_xzz, β_y = β_yxx + β_yyy + β_yzz and β_z = β_zxx + β_zyy + β_zzz.where

2.8 Result and discussions

In this research paper, the non-fullerene natured synthesized crystals, i.e., 4a and 4b are evaluated in terms of their NLO characteristics. For this purpose, SC-XRD characterization is done and inspection of molecular configuration is carried out thoroughly via different parameters like bond lengths, bond angles etc. The experimental data are compared with the theoretical results (DFT) in order to verify the chemical nature of the analyzed compounds. Moreover, the structural and optimized representation of entitled compounds is shown in Fig. 5.

Fig. 5 The optimized structures of 4a and 4b.

2.9 Geometrical parameters

The geometrical parameters of entitled compounds were optimized at the M06-2X/6-31G(d,p) level of theory, and their data is organized in ESI (Tables S1 and S2†). The results of SC-XRD and DFT are found in excellent agreement with a few variations.

The simulated C–C bond lengths in the benzene ring of compound 4a are found to be in the range of 1.162–1.507 Å, while in the range of 1.149–1.523 Å, as determined by XRD as shown in Table S1.† The bond lengths between carbon and oxygen atoms calculated through DFT are found to be 1.355, 1.366, 1.368, 1.364, 1.369, 1.415, 1.36, 1.385, 1.202, and 1.211 Å for O1–C10, O1–C15, O3–C20, O3–C22, O4–C9, O4–C31, O5–C17, O5–C18, O6–C18, and O7–C20, respectively, while through XRD the values were 1.366, 1.368, 1.373,1.375, 1.372, 1.431, 1.381, 1.387, 1.202, and 1.204 Å, respectively. Furthermore, the bond length for N2–C15 obtained by XRD is 1.342 Å, while the DFT calculated value for the above-mentioned bond length is examined to be 1.344 Å as given in Table S1.†

Similarly, for compound 4b, the aforesaid bond lengths are observed in the range of 1.345–1.526 Å, which have good agreement with experimental data as 1.336–1.534 Å (see Table S2†). Moreover, for O1–C10, O1–C32, O2–C15, O2–C16, O3–C19, O3–C27, O4–C22, O4–C24, O5–C26, O5–C40, O6–C24, O7–C19, and O8–C26 bond lengths in compound 4b, DFT values are noted to be 1.381, 1.418, 1.361, 1.364, 1.374, 1.362, 1.361, 1.38, 1.345, 1.425, 1.202, 1.205 and 1.224 Å, which are correspondingly matched with SC-XRD data at 1.381, 1.421, 1.364, 1.377, 1.376, 1.378, 1.376, 1.387, 1.338, 1.436, 1.215, 1.202, and 1.222 Å, respectively. For N9–C16 the bond length by both XRD and DFT calculation is found to be 1.355 Å and 1.336 Å, respectively.

In 4a, bond angle values in C10–O1–C15, O1–C15–N2, N2–C15–C14, C20–O3–C22, O3–C20–C26, C9–O4–C31, O4–C9–C8, O4–C31–C26, C17–O5–C18, O5–C17–C27, O5–C18–C11, and O7–C20–C26 were observed through DFT as 118.3°, 110.4°, 117.6°, 122.8°,117.6°, 117.2°, 116°, 108.8°, 122.6°, 117.6°, 117.2°, and 124.8°, respectively. Similarly, through XRD, prominent values are 118.5°, 109.8°, 128°, 122.6°,117.8°, 118.3°, 115°, 106.2°, 121.9°, 117.7°, 118.1°, and 125.9°, respectively, as shown in Table S1.†

Similarly, in 4b, the calculated bond angles between C10–O1–C32, O1–C10–C30, O1–C10–C35, O1–C32–C18, C15–O2–C16, O2–C15–C11, O2–C16–N9, O2–C16–C13, C19–O3–C27, O3–C19–O7, O3–C19–C18, O4–C22–C14, C26–O5–C40, O5–C26–O8, and N9–C16–C13 are observed through DFT as 114.7°, 120°, 118.9°, 107.9°,118.8°, 123.2°, 109.6°, 123°, 122.3°, 118.4°, 117°,114.7°, 121.6°, 115.1°, 121.6°, and 127.5 as well as 118.6°, 123.3°, 115.6°, 107.1°, 118.7°, 123.6°, 109.4°, 122.1°, 122.1°, 116.5°, 117.7°,114.7°, 121.2°, 117.6°, 121.7°, and 128.5° through XRD, respectively as shown in Table S2.† The torsion angles experimentally determined in the solid state are shown in Table S3.† The above-discussion explored that a good agreement is noted in computed and experimental findings, which confirms that M06-2X/6-31G(d,p) is suitable level of theory for DFT study. The geometrical structures are shown in Fig. S7.†

2.10 Frontier molecular orbitals (FMOs) analysis

The electronic characteristics of the studied molecules are investigated using the energies of HOMO/LUMO and their frontier molecular orbitals (FMOs) diagrams to calculate their chemical reactivity and stability.⁶³ The Lewis donor is commonly known HOMO (highest occupied molecular orbital) and the Lewis acceptor is called as LUMO (lowest unoccupied molecular orbital).^64,65 The electrons are transferred from the donor to the acceptor (HOMO to LUMO), which provides information about the intramolecular charge transfer (ICT) and NLO behavior.⁶⁶ An inverse relationship exists between the ΔE and ICT of a compound. Molecules with a greater ability to transfer charge between orbitals exhibit significant NLO properties with a lower ΔE value, and vice versa.⁶⁷ Herein, we calculated the orbital energies and band gaps of our entitled compounds as shown in Table 3.

Table 3 The energies of HOMO, LUMO and their energy gap for 4a and 4b

MOs	4a		4b
	E (eV)	ΔE (eV)	E (eV)	ΔE (eV)
LUMO	−1.540	5.168	−0.932	6.308
HOMO	−6.708		−7.240
LUMO+1	−0.700	6.669	−0.693	6.767
HOMO−1	−7.369		−7.460
LUMO+2	−0.055	7.445	−0.436	7.330
HOMO−2	−7.500		−7.766

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The data of energies obtained for 4a are found to be −6.708 eV for HOMO and −1.540 eV for LUMO, while those for 4b are noted to be −7.240 eV and −0.932 eV, respectively. The ΔE of 4a is examined to be 5.168 eV, which is abridged to 6.308 eV in 4b. Interestingly, a significant reduction in orbital energies and E_gap is observed for 4a as compared to 4b. This reduction of energies in 4a is due to the presence of the nitro (–NO₂) group, as it is known that the nitro group has a stronger electron-withdrawing effect and inductive effect than the –CN group.⁶⁴ In addition to the energies of orbitals, ICT has also been studied in the entitled compounds, as shown in Fig. S9.† The electronic charge density for HOMO is concentrated over the entire molecule in both compounds, while for LUMO the electronic cloud is distributed significantly all over the molecular region except the nitro and cyano groups in 4a and 4b, respectively.

2.11 Global reactivity descriptors

The stability and reactivity of 4a and 4b molecules can be excellently elaborated with various global reactivity parameters (GRPs) calculated by utilizing the LUMO–HOMO energy gap.⁶⁸ The results of these parameters, including electron affinity (EA), ionization potential (I),⁶⁹ global hardness (η),⁷⁰ global electrophilicity (ω),⁷¹ electronegativity (X),⁷² chemical potential (μ)⁷³ and global softness (σ), are estimated with the help of eqn (S5)–(S11)† and their outcomes are tabulated in Table S4.†

Ionization potential (IP) is the tendency to donate electrons, and electronegativity represents the ability to attract electrons.⁶⁸ Table 3 reveals that compound 4a showed a higher value of electron affinity, electronegativity, and electrophilicity than compound 4b. The reason for this enhanced value for 4a might be the presence of highly electron-withdrawing nitro groups in the 4a molecule. The parameters like chemical potential (μ) and hardness (η) are directly correlated with the energy gap. The compounds with the higher values of these parameters are considered as kinetically more stable and less reactive.⁷⁴ In our synthesized compounds, 4a had a lower global hardness (η = 0.094 eV) and chemical potential (μ = −0.151 eV) with a higher softness (σ = 5.266 eV) than 4b, indicating that 4a is more kinetically stable and less reactive than 4b. This GRPs investigation indicated that our prepared compounds are kinetically more stable and show excellent concurrence with NBO and SC-XRD data (Table 4).

Table 4 Ionization potential (IP), electron affinity (EA), electronegativity (X), chemical potential (μ), global hardness (η), global softness (σ) and global electrophilicity (ω)^a

GRPs	4a	4b
a Units are in eV.
IP	0.246	0.266
EA	0.056	0.034
X	0.151	0.150
η	0.094	0.116
μ	−0.151	−0.150
ω	0.121	0.097
σ	5.266	4.314

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2.12 Natural bond orbitals (NBOs) analysis

The NBOs are important for the investigation of bond interactions, the distribution of charges, and their delocalization among filled and vacant orbitals in a compound.⁷³ Moreover, the NBO analysis also facilitates the study of charge densities among various parts of a donor–π–acceptor molecule. It has been explored from the literature that most commonly the donor moiety holds a positive charge, while the acceptors are found with negatively charged values. Whereas, the π-spacer may have positive or negative charges due to its role as a facilitator in the studied donor–π–acceptor framework. Assuming the above facts, the second-order perturbation theory of the said molecules is accomplished, and the stabilization energy for these molecules is calculated using eqn (5), which is as follows:where, E⁽²⁾ is the stabilization energy, ε_i and ε_j are off-diagonal, respectively; q_i is the donor orbital occupancy and F_i,j is the diagonal NBO Fock matrix element. NBOs investigation is performed for entitled compounds, as elaborated in Table 5. However, some significant results are given in Tables S5 and S6.†

Table 5 Fock matrix investigation for the studied compounds (4a and 4b)

Comp.	Donor (i)	Type	Acceptor (j)	Type	E^(2)^a [kcal mol^−1]	E(j) − E(i)^b (a.u.)	F(i, j)^c (a.u.)
a E^(2) represents the energy of hyper conjugative interaction (stabilization energy in kcal mol^−1).b Energy difference between D and A NBO orbitals.c F(i, j) is the Fock matrix element between i and j NBO orbitals.
4a	C27–C33	π	C12–C17	π*	34.85	0.34	0.100
	C8–C24	π	C14–C15	π*	0.56	0.34	0.013
	C11–C18	σ	O1–C10	σ*	6.80	1.20	0.081
	C26–C31	σ	C31–H54	σ*	0.51	1.23	0.022
	N2	LP(1)	C14–C15	π*	77.62	0.36	0.153
	O4	LP(1)	C31–H55	σ*	0.66	1.15	0.025
4b	C16–C19	π	O8–C33	π*	34.95	0.37	0.106
	O7–C23	π	O7–C23	π*	0.78	0.51	0.019
	C13–C30	σ	O2–C18	σ*	6.82	1.19	0.080
	C22–C28	σ	C42–H43	σ*	0.51	1.34	0.023
	O5	LP(2)	O8–C33	π*	59.26	0.43	0.148
	O8	LP(1)	O5–C60	σ*	0.50	1.14	0.021

---

Four different forms of electronic transitions are frequently observed: π → π*, σ → σ*, LP → π*, and LP → σ*. The most dominant electronic transitions are found as π → π* among the above-mentioned transitions, while σ → σ* is examined as the least prominent, and LP → π* and LP → σ* are noticed as slightly dominant transitions.

In the case of compound 4a, the most prominent π → π* transitions are π(C27–C33) → π*(C12–C17) and π(C8–C24) → π*(C14–C15), which showed the highest and the least energies of stabilization as 34.85 and 0.56 kcal mol⁻¹, respectively. The weaker σ → σ* transitions are also examined with some prominent values as 6.80 and 0.51 kcal mol⁻¹ observed in transitions σ(C11–C18) → σ*(O1–C10) and σ(C26–C31) → σ*(C31–H54), respectively. Some resonance transitions that are also important for discussion include LP1(N2) → π*(C14–C15), which determined the highest stabilization energy of 77.62 kcal mol⁻¹, and LP1(O8) → σ*(C31–H55), which showed the lowest stabilization energy of 0.66 kcal mol⁻¹ (see Table 5).

In compound 4b, the highest stabilization energy obtained is 34.95 kcal mol⁻¹, which is exhibited during π(C16–C19) → π*(O8–C33) transitions, while, π(O7–C23) → π*(O7–C23) is noted with the smallest stabilization energy value as 0.78 kcal mol⁻¹. The other feeble electronic transitions that are significant to discuss for compound 4a are: σ(C13–C30) → σ*(O2–C18), σ(C22–C28) → σ*(C42–H43), LP2(O5) → π*(O8–C33), and LP1(O8) → σ*(O5–C60), which showed energies of 6.82, 0.51, 59.26, and 0.50 kcal mol⁻¹, respectively.

Overall, the results obtained from the above discussion validate the formation of charge separation states in the investigated molecules. Whereas, the stabilization energies also revealed comparable stability in both compounds, for which the ICT, conjugation, and hyper conjugative interactions might be the main reasons for their stabilities.

2.13 UV-vis analysis

The UV-Vis absorption spectra of the coumarin-based pyrano-chromene derivatives 4a and 4b in chloroform, dimethyl sulfoxide (DMSO), and 1,4-dioxane were recorded at room temperature. TDDFT UV-Vis absorption data were calculated in the gas phase. This study provides a reasonable apprehension of optoelectronic properties, probability of charge transfer, and molecular orbital configurations of electronic transitions for the studied compounds.^75–77 The TD-DFT methodology was employed using the above-mentioned level of theory to execute the UV-Vis absorption spectra. Table 6 presents the data obtained for 4a and 4b, including the maximum wavelength (λ_max), vertical excitation energies (eV), oscillator strength (f_os), and orbital transitions. The detailed results are recorded in Table S7,† and graphs of absorption maxima for both compounds are displayed in Fig. S8.†

Table 6 Computed transition energy (eV), maximum absorption wavelengths (λ_max), oscillator strengths (f_os), and transition natures of title compounds

Comp.	Exp. λmax (nm)	DFT λmax (nm)	E (eV)	fos	MO contributions
a Chloroform.b 1,4-Dioxane.c DMSO.d Gas phase.
4a	—	268.579^d	4.616	0.337	H−1 → L (68%), H → L (2%)
	335.5^a
	328.5^b
	337.5^c
4b	—	269.513^d	4.600	0.374	H → L+1 (36%), H−1 → L+2 (30%)
	339^a
	331.5^b
	317^c

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The data obtained from the analysis show the λ_max of 4a and 4b are 268.579 and 269.513 nm, respectively. Interestingly, the experimentally calculated values (in solvents i.e., chloroform, 1,4-dioxane, and DMSO) of λ_max are found bathochromically shifted as compared to the theoretical values (in the gas phase) of compounds (4a and 4b), which may occur due to change in environmental conditions as expressed in Table 6. 4a displayed a value of the absorbance at 268.579 nm with corresponding oscillation strength of 0.337 and 4.616 eV transition energy, which are associated with H−1 → L (68%) as a major contribution. Similarly, λ_max calculated in the case of 4b was 269.513 nm with two major transitions as H → L+1 (36%), and H−1 → L+2 (30%), possessing oscillation strengths of 0.374 and 4.600 eV transition energy.

2.14 Non-linear optical (NLO) properties

Non-linear optical materials have immense potential in photonics with striking applications in the optoelectronics and telecommunication sectors.^74,75 The NLO response varies with the variation of the position of diverse substituents on the compounds. Here, we compute the statistical average of molecular dipoles moment (u), linear and non-linear responses of 4a and 4b at the aforementioned level of theory, and the major results are tabulated in Table 7, whereas the detailed calculations are present in the ESI (Tables S8 and S9†).

Table 7 The statistical average of molecular dipoles, linear polarizability, and hyperpolarizabilities for compounds (4a and 4b)

Comp.	μtot	〈α〉 ×10^−23	γtot × 10^4
4a	6.236	6.770	0.145
4b	3.256	6.699	0.145

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Table S8† holds the linear polarizability with major contributing tensors along the x, y, and z-axes. The polarizability tensor along the x-direction (α_xx) shows the highest value and thus has more contribution towards linear polarizability in both 4a and 4b compounds. The total values of statistical average of molecular dipoles moment (μ_tot), average polarizability 〈α〉, and second order hyperpolarizability (γ_tot) are also shown in Table 7. The μ_tot is found to be 6.236 and 3.256 D, for compounds 4a and 4b, respectively. The highest computed value of statistical average of molecular dipoles moment exists for compound 4a as 6.236 D, while the smallest amplitude of 3.256 D is examined for compound 4b. All the entitled molecules showed significant statistical average of molecular dipoles moment values when compared with the standard urea molecule, which showed a value of 1.3732 D (ref. 78) (Table S8†). The average linear polarizability 〈α〉 values for compounds 4a and 4b are observed to be 6.770 × 10⁻²³ and 6.699 × 10⁻²³ esu, respectively. Hence, the greater 〈α〉 value is noticed in 4a as compared to 4b.

The second-order polarizability (γ_tot) values are observed in both the studied compounds as 0.145 × 10⁴ esu. It is also observed that the highest contributing value of γ_tot for 4a is shown along the z-axis (γ_zz = 2.324 × 10⁴ esu) and for 4b along the x-axis (8.907 × 10⁴ esu), which indicates the higher polarization along the z and x-directions for titled compounds (Table S8†). Interestingly, in our studied crystals, remarkable NLO results were obtained as their various parameters such as μ_tot, 〈α〉, and γ_tot when compared with urea molecule.^79,80 This comparative analysis of 4a and 4b with urea found to be many folds higher than urea. This urea-related examination implied that all considered molecules were appropriate to be NLO entities. This showed their effective structural tailoring using efficient donor and acceptor moieties to obtain significant NLO materials. The orientation of the 4a and 4b molecule along x, y and z axis are shown in Fig. S10 and S11.†

3. Conclusion

The current work indicates the quantum chemical investigation of two novel coumarin-based pyrano-chromene crystal chromophores, 4a and 4b. The compounds were synthesized in a good yield through the Knoevenagel–Michael-cyclization path using a one-pot multicomponent reaction. The structures of these o-ring heterocyclic compounds were ascertained by spectroscopic techniques like UV-Vis, FT-IR, ¹H & ¹³C NMR, and single crystal X-ray diffraction analysis. The SC-XRD analysis of 4a and 4b revealed the triclinic crystal lattice with space group P1̄. The spectroscopic results were found to be in good agreement with the SC-XRD data. The DFT and SC-XRD data were also perceived in good accordance, as shown by their computed bond lengths and bond angles. The NBO probe also confirmed the presence of charge separation, which showed that the entitled compounds are involved in the process of ICT, hence, endorsing their higher molecular stability. The higher energy band gap of 4b (6.308 eV) as compared to 4a (5.168 eV) was obtained due to the presence of highly electronegative cyano group in 4b. The GRPs were derived utilizing energies of HOMOs and LUMOs of said compounds. Fantastically, large 〈α〉 and γ_tot responses are computed for 4a than that of standard urea molecule. We infer that the present DFT-based study might be regarded as a remarkable achievement and may have prospective applications in developing new NLO materials.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

The authors would like to thank King Khalid University's Deanship of Scientific Research for funding this study under grant number (R.G.P.1/28/43). Dr Muhammad Khalid gratefully acknowledges the financial support of HEC Pakistan (project no. 20-14703/NRPU/R&D/HEC/2021). Authors are also thankful for cooperation and collaboration of A. A. C. B. from IQ-USP, Brazil especially for his continuous support and providing computational lab facilities.

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Footnote

† Electronic supplementary information (ESI) available. CCDC 2115636–2115638. For ESI and crystallographic data in CIF or other electronic format see DOI: https://doi.org/10.1039/d2ra07134g

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