Disentangling solvent effects on optical response via p-π and sp² lone-pair contributions in non-aromatic fused systems

Abstract

In this study, we disentangle solvent effects on optical responses in non-aromatic fused systems via p-π and sp² lone pair contributions. Donor-π-acceptor (D-π-A) molecules based on 5,7,9,14,16,18-hexahydroheptacene (6 H-Hep) were designed across three chalcogen series: oxygen (R1, IM1-IM3), sulfur (R2, IM4-IM6), and selenium (R3, IM7-IM9). DFT and TD-DFT studies on D3-B3LYP/6–31 + G(d) level of theory were used to explore electronic structure, absorption, and nonlinear optical (NLO) properties. HOMO-LUMO gaps ranged from 4.23 to 1.95 eV, with IM3 showing the smallest gap and strongest intramolecular charge transfer (ICT) due to enhanced p-π conjugation and sp² lone pair donation. Absorption maxima spanned 307–394 nm (π→π*), with IM6 red-shifted to 394 nm from solvent-polarity-amplified lone pair effects. First hyperpolarizability (β_x) increased dramatically from negligible values (< 0.02 a.u.) in parent compounds to 46.75 × 10⁶ a.u. for IM3 in water, far exceeding benchmarks. Solvent-dependent studies (water, benzene, ethanol) confirmed β_x dominates total hyperpolarizability, underscoring solvent polarity’s critical role in modulating p-π/lone pair-driven NLO responses. NICS(1)zz values and electrostatic potential mapping verified enhanced polarization in oxygen derivatives, while π-π stacking in IM3 stabilized charge delocalization. Radiative lifetimes (τ_r = 18–47 ns) support efficient optical activity. Collectively, IM3, IM6, and IM9 emerge as top candidates, with IM3 showing exceptional NLO performance. This work establishes heteroatom substitution, solvent-tuned electronic contributions, and donor-acceptor modulation as effective strategies for advanced electro-optical materials.

Introduction

The rapid advancement of photonic and optoelectronic technologies has intensified the global demand for materials with superior nonlinear optical properties^1,2. These materials play a vital role in modern applications such as frequency doubling^3,4, optical switching, optical data storage^5,6, laser protection^7,8, and signal modulation⁹. The interaction of high-intensity electromagnetic fields with matter underlies nonlinear optical processes, producing phenomena including second-harmonic generation (SHG), third-order nonlinearities, and electro-optic modulation^10,11. Among the different types of materials investigated for such applications, organic non-linear optical compounds have drawn have gained considerable attention owing to their high optical susceptibilities, ultrafast response times, low dielectric constants, and vast structural diversity^12,13. Unlike their inorganic counterparts, organic molecules can be synthetically tailored to optimize the spatial arrangement of functional groups and modulate their electronic behaviour. The efficiency of an organic nonlinear optical materials is primarily governed by its ability to promote ICT from push-pull donor-acceptor framework across a π-conjugated bridge^14,15,16. This D-π-A framework promotes efficient polarization in the presence of an applied external electric field, thereby enhancing polarizability (α), first-order hyperpolarizability (β_tot), and second-order hyperpolarizability (γ), which are fundamental descriptors of NLO activity. Accordingly, rational molecular design focusing on donor-acceptor engineering remains central to the development of high-performance nonlinear optical systems^17,18,19.

Heterocyclic systems offer a promising molecular scaffold for the advancement of nonlinear optical materials. These structures provide extended conjugation pathways, enable diverse substitution patterns, and support electronic delocalization features that are highly conducive to nonlinear optical response^20,21. Among various heterocyclic modifications, the incorporation of heteroatoms such as oxygen (O), sulphur (S), and selenium (Se) into the core structure markedly influences molecular electronic characteristics. These atoms differ in electronegativity, atomic size, and polarizability, which in turn affect aromaticity, HOMO-LUMO energy gaps, and ICT efficiency. For instance, oxygen tends to increase the electronegativity and reduce polarizability, while selenium contributes to enhanced delocalization and stronger electron cloud distortion under an external field. Moreover, heteroatom substitution alters the electronic nature of the conjugated backbone and introduces anisotropy in charge distribution, which is vital for enhancing the nonlinear optical response. The position and nature of substituents on these heterocycles further modulate their optical and electronic behaviour^22,23,24. Introducing electron-donating group (e.g., -NH₂) at one end and electron-withdrawing groups (e.g., -NO₂, -CN, -CHO) at the opposite end creates a push-pull system, encouraging efficient ICT and resulting in large dipole moments and reduced energy gaps. Such asymmetry in molecular architecture is a key factor in enhancing first-order hyperpolarizability, making these systems strong candidates for second-order NLO applications. Additionally, the incorporation of functional groups with varying electron affinities allows fine-tuning of molecular polarizability and transition energies, leading to improved absorption characteristics and better nonlinear efficiency^25,26,27,28.

Scheme 1

Newly designed π-conjugated organic systems (R1-IM3, R2-IM6 and R3-IM9).

In the continuation of our work²⁹, three series (Series 1–3) of newly designed π-conjugated organic systems (R1-R3, IM1-IM9) has been theoretically designed and explored for their nonlinear optical properties as depicted in Scheme 1. The molecules are based on seven-membered heterocyclic cores substituted individually with O (in series one), S (in series two), and Se atoms (in series three). These cores are systematically functionalized with strong electron donating -NH₂ at one end and electron accepting groups -NO₂, -CN, -CHO at other end, to create diverse D-π-A frameworks. The molecular modifications are strategically chosen to investigate how different heteroatoms (O, S and Se) and terminal substituents (-NH₂ at one end and -NO₂, -CN, -CHO at other end) influence the overall electronic, optical, and nonlinear optical behaviour. By evaluating parameters such as frontier molecular orbital energies, dipole moments, TD-DFT, fermi-level, NICS(1)_ZZ, polarizabilities, and hyperpolarizabilities, this study aims to provide a comprehensive understanding of structure property correlations in such systems. This investigation is significant not only for its systematic approach to heteroatom and substituent variation but also for its potential to uncover high-efficiency NLO candidates. The designed compounds are expected to demonstrate strong second-order nonlinear optical responses and favourable optical transparency, making them appropriate for practical applications in optical modulation, photonic circuitry, and telecommunications. Ultimately, this work contributes to the growing body of knowledge on molecular level design strategies for next generation NLO compounds, offering prospects for new synthetic targets and experimental validation.

Computational details

All parent and designed molecules were optimized at the DFT level without imposing geometric restrictions. Further computations were performed using D3-B3LYP in combination with the 6–31 + G(d) basis set, selected for its accuracy with heterocyclic compounds. This functional merges Becke’s three-parameter exchange with the Lee-Yang-Parr correlation to ensure reliable predictions^30,31 and schematic overview of the computational tools, methods, and basis sets employed in this work is illustrated in Scheme S1. The global reactivity descriptors were estimated by using equations S8-S14, while the fermi level (E_F) and hole/electron injection barriers were obtained by the equations S15-S17.

Because β_tot plays a crucial role in assessing nonlinear optical response, the molecular geometries of all compounds were fully optimized before performing static hyperpolarizability calculations. The dipole moment (µ), total polarizability (α_tot), and β_tot of each molecule were computed using four functionals D3-B3LYP, CAM-B3LYP³², ωB97XD³³ and M06-2X³⁴ with same basis set^35,36,37. The equations (S18-S20) were applied to evaluate the dipole moment, polarizability and hyperpolarizabilities^38,39. To analyse the main electronic transitions, TD-DFT calculations were conducted using the ωB97XD functional. At the optimized geometries, all tensor components were evaluated using Gaussian 16⁴⁰, and the resulting molecular structures were visualized with Multiwfn⁴¹ and GaussView 6.0⁴², DOS was performed by using the GaussSum software⁴³ based on the Gaussian output files.

To elucidate the origin of nonlinear optical responses in these compounds, the two-level model (TLM) was applied⁴⁴. Its arithmetic form is given by:

$${\beta}_{CT}=\varDelta{\upmu}\times\frac{{f}_{o}}{{\varDelta\text{E}}^{3}}$$

(1)

Where; ∆µ is difference in dipole moment between ground and excited states, f₀ represents the oscillator strength of the electronic transition, and ΔE corresponds to the transition energy between the electronic states.

To enhance the analysis of NLO behavior, frequency-dependent calculations were conducted for the designed systems. The first hyperpolarizabilities were computed at λ = 1460 nm and λ = 1907 nm to assess their wavelength-dependent response. The present investigation incorporated EFSHG and β_EOPE according to Eq. (2)⁴⁵. The method involves the application of perpendicular light polarizations, with β_HRS defined as:

$${\beta}_{HRS}\left(-2\omega;\omega,\omega\right)={\left[\right({\beta}_{zzz}^{2})+{(\beta}_{zxx}^{2})]}^{\frac{1}{2}}$$

(2)

Moreover, the chromophore geometry, essential for the compound’s NLO response, can be analysed via the depolarization ratio (DR), which is given by⁴⁶:

$$DR=\frac{{\beta}_{zzz}^{2}}{{\beta}_{zxx}^{2}}$$

(3)

The mathematical representation of the dipolar and octupolar tensor components, the anisotropy ratio, and their contributions to the first hyperpolarizability tensor is as follows:

$${\beta}_{HRS}=\frac{{\beta}_{HRS}^{2}}{{\beta}_{zxx}^{2}}$$

(4)

$${\beta}_{HRS}=\sqrt{{{(B}_{HRS})}^{2}}$$

(5)

$${\uprho}=\frac{{\beta}_{J=3}}{{\beta}_{J=1}}$$

(6)

$${{\Phi}}_{J=3}=\rho\frac{\rho}{1+\rho}$$

(7)

The first hyperpolarizability (β) is a third-rank tensor composed of individual tensor components (β_ijk), which describe the second-order nonlinear optical response along specific Cartesian directions. These tensor elements are combined to obtain the directional components (β_x, β_y, β_z), and the total first hyperpolarizability (β_total) is calculated from their vector combination, representing the overall molecular nonlinear response. In addition, the Hyper-Rayleigh Scattering hyperpolarizability (β_HRS) is derived from the orientational average of the tensor components and corresponds to the experimentally measurable second-harmonic scattering response of randomly oriented molecules. Thus, β_HRS provides a direct link between the calculated tensor components and experimentally observable nonlinear optical properties.

Results and discussion

Optimized quantum geometry

In computational investigations, geometry optimization is essential for determining the lowest-energy, most stable molecular structure⁴⁷. It allows for accurate prediction of electronic properties and ensures reliable evaluation of nonlinear optical responses^48,49. The cartesian co-ordinates’ of all the optimized structures are listed in Tables S1-S12, while optimized structures of parent molecules (R1, R2 and R3) are shown in Fig. 1 and their derivatives are depicted in Figure S1. The bond lengths and bond angles, optimized at the chosen level of theory, for oxygen (O), sulphur (S), and selenium (Se) substituted systems were evaluated using DFT to explore their structural effects on nonlinear optical behaviour as given in Table S13-S14.

For R1, R2, and R3 derivatives, the C-H bonds remain constant at 1.08 Å, while C-X bond lengths increase with heavier atoms: C-O (1.38 Å), C-S (1.78 Å), and C-Se (1.93 Å). Similarly, in donor-acceptor systems, the C-X-C bond angles decrease from O (116°) to S (107°) and Se (105°), indicating more bond bending with larger atoms. As shown in Section S2.1 of the Supporting Information, the optimized structures offer insight into how various substituents influence molecular geometry (Table S14-S15), and electron delocalization, which is essential for understanding reactivity and potential applications. The D3-B3LYP-D3/6–31 + G* optimization confirms that structural modifications in Series 1-Series 3 results in significant alterations in bond lengths, bond angles, and electron distribution. Such structural and electronic variations play a key role in evaluating reactivity, stability, and potential applications in materials science applications.

Fig. 1

Optimized structures of reference molecules R1, R2 and R3 at D3-B3LYP level of theory.

Nucleus independent chemical shift

The Fig. 2 provides a ring-resolved representation of NICS(1)⁵⁰ values, a well-established magnetic criterion for evaluating aromaticity. In this convention, negative values are diagnostic of diatropic ring currents that confer aromatic stabilization, whereas positive values reflect paratropic currents associated with antiaromatic destabilization. In the reference framework (6 H-Hep), the peripheral rings A and G display markedly negative NICS(1)⁵⁰ values (–11.28), confirming their strong aromatic character. By contrast, the adjacent rings B and F exhibit distinctly positive values (24.40), signaling pronounced antiaromaticity. Similarly, the central region, particularly ring D (24.63), sustains a strong antiaromatic contribution, while the flanking rings C and E (–7.98) retain modest aromatic character. This alternating pattern of stabilization and destabilization highlights the electronic non-uniformity of the conjugated system, where localized aromatic domains at the molecular termini are counterbalanced by antiaromatic centers toward the core.

Fig. 2

NICS (1) _ZZ values of chalcogen-containing heteroaromatic rings for all three reference compounds (R1, R2, and R3).

The NICS(1)zz⁵⁰ analysis provides deep insights into how heteroatom substitution modulates aromaticity within the fused π-framework. In the reference system (6 H-Hep), the terminal rings (A, G) display strongly negative values (–11.28), confirming pronounced aromatic stabilization, while adjacent rings (B, F) exhibit distinctly positive values (24.40), indicating antiaromaticity; the central ring D (24.63) is also strongly antiaromatic, whereas rings C and E (–7.98) retain modest aromaticity, thus revealing an alternating pattern of stabilization and destabilization across the scaffold. Upon oxygen substitution in R1, the electronic distribution is profoundly reorganized, with oxygen-adjacent rings exhibiting very large positive NICS values (44.26 and 41.97), highlighting localized antiaromaticity, while the terminal rings (–7.70, − 7.76) preserve aromatic character. In R2 (sulfur substitution), the NICS values (38.14 and 35.87) remain positive but are significantly reduced compared with oxygen, reflecting weaker perturbation of the π-framework, and the peripheral rings (–2.95) show diminished aromatic stabilization. In R3 (selenium substitution), the antiaromatic values decrease further (36.06 and 34.42), reflecting selenium’s poor orbital overlap with the π-system, and the outer rings (–3.49) sustain weak but recognizable aromatic contributions.

Overall, the degree of antiaromatic disruption follows the order O > S > Se. The strong antiaromatic perturbation in R1 enhances electronic polarization and intramolecular charge transfer (ICT), which directly boosts its first hyperpolarizability and makes it highly promising for applications in nonlinear optics, such as optical switching, frequency doubling, and high-speed telecommunications. R2 produces a moderate balance between aromatic stabilization and antiaromatic destabilization, giving rise to intermediate nonlinear performance that may be suitable for optoelectronic sensors, data storage, and bioimaging devices. R3, while minimizing antiaromaticity, also reduces charge delocalization due to weaker orbital overlap, which translates into the lowest NLO efficiency, restricting its potential to niche applications where stability is prioritized over strong optical response. Thus, R1 derivatives (IM3) is predicted to be the best candidate for advanced NLO technologies, followed by R2 and then R3 substituents.

Frontier molecular orbitals (FMO) analysis

To assess materials for use in nonlinear optics and photovoltaics, understanding their frontier orbital characteristics is fundamentally important for predicting electronic and chemical stability^51,52. Moreover, evaluating HOMO and LUMO energies is crucial to predict charge transfer mechanisms^53,54, as these frontier orbital energies serve as the foundation for calculating global reactivity descriptors such as chemical hardness, softness, electronegativity, and electrophilicity index (Section S2.2). The corresponding HOMO-LUMO energy values are illustrated in Figure S2 and Fig. 3. The FMO analysis of R1-IM3, R2-IM6, and R3-IM9 showed systematic changes in their electronic characteristics, with energy gaps (E_g) varying from 1.95 eV for IM3 to 4.23 eV for R1. The calculated Fermi levels (E_f), defined as the average of HOMO and LUMO energies, demonstrated that compounds with smaller energy gaps (IM3, IM6, IM9) have reduced charge injection barriers for φ_h and φ_e, indicating more efficient charge transport and stronger intramolecular charge transfer leads to nonlinear optical performance. This behavior is further supported by the TDOS and PDOS spectra presented in section S2.3, which reveal enhanced electronic state contributions near the Fermi level, facilitating charge transport.

In studied systems, HOMO is largely confined to the donor moiety with partial delocalization over the π-bridge, while the LUMO is mainly distributed over the acceptor units, extending slightly into the π-spacers. As illustrated in Section S2.4 of the supporting information, the orbital distribution illustrates effective electron transfer from the donor to the acceptor through the π-conjugated system and facilitating charge transfer. The results confirm that the π-conjugated linkers in the investigated compounds efficiently mediate ICT, supporting their potential use in nonlinear optical active materials.

Fig. 3

FMOs representation and their associated HOMO, LUMO, and energy gap of all the designed compounds from Series 1-Series 3. Units are in eV:

UV-Vis Analysis

The TD-DFT computational analysis of the studied molecules (R1-R3 and IM1-IM9) highlights a strong correlation between structural modifications specifically donor-acceptor groups and heteroatom substitutions and their photophysical properties, particularly radiative lifetime and light-harvesting efficiency, as discussed in section S2.5. All compounds display prominent π→π^* transitions in the 307–394 nm region, with TD-DFT data showing consistent agreement with HOMO-LUMO gaps and ESP distributions. The nature of the central heteroatom’s oxygen in R1-based structures, sulphur in R2-based, and selenium in R3-based directly influences the electronic delocalization and absorption behaviour. The designed derivatives IM1-IM9 introduce electron-donating -NH₂ group and electron-withdrawing -CN, -CHO, and -NO₂ groups, creating strong internal dipoles. These donor-acceptor combinations enhance charge transfer and significantly reduce the HOMO-LUMO gaps. In the 6 H-Hep, the absorption maximum is observed at 253.63nm with an excitation energy of 4.89 eV and a HOMO-LUMO gap of 5.57 eV while in the oxygen-containing reference compound R1, the electronic distribution remains relatively localized due to the higher electronegativity of oxygen. This results in an absorption maximum at 318.61 nm with an excitation energy of 3.89 eV and a HOMO-LUMO gap of 4.23 eV, the widest among the series. Upon donor-acceptor substitution, IM1 and IM2 absorb at 307.93 and 333.44 nm, respectively. These blue to mild red-shifts reflect the onset of ICT as a result of introducing electron-rich and electron-deficient terminals. IM3 (NH₂ as donor and NO₂ as acceptor), the most conjugated in the R1 series, shows a pronounced redshift at 343.58 nm with a reduced gap of 1.95 eV, revealing enhanced electronic delocalization due to the combined effect of donor-acceptor substitution and the polarizing influence of the oxygen atom in the core. Replacing oxygen with sulphur in the R2-based structures enhances conjugation due to sulphur’s lower electronegativity and larger atomic radius. This promotes greater orbital overlap, leading to deeper LUMO stabilization and stronger ICT. The reference R2 absorbs at 365.46 nm (E_x = 3.39 eV) and a corresponding E_g of 3.48 eV. Upon substitution, IM4 and IM5 exhibit absorptions at 336.26 and 370.28 nm, with further narrowing of energy gaps to 2.80 and 2.52 eV, respectively. IM6, bearing the most extended π-conjugated and polarized framework, shows a marked red-shift to 394.46 nm the highest among all compounds with a narrow gap of 2.18 eV and a HOMO-LUMO transition contributing 81%. The sulphur atom not only facilitates better delocalization of π-electrons but also stabilizes excited states more effectively than oxygen.

Table 1 Wavelength (λ_max in nm), oscillator strength (f_o) and Excitation energy of all the synthesized systems.

The selenium-based core in R3 introduces even more pronounced electronic effects due to selenium’s greater polarizability and larger size. These factors enhance intramolecular charge separation and orbital diffusion. R3 itself shows absorption at 365.98 nm (E_x = 3.38 eV) with a gap of 3.59 eV, close to that of R2 but with slightly more delocalized frontier orbitals. IM7-IM9, with varied donor-acceptor substitution on the Se-core, demonstrate red-shifted absorptions at 367.69, 354.32, and 378.81 nm, and corresponding energy gaps of 2.83, 2.58, and 2.21 eV, respectively. The compound IM9, in particular, shows strong ESP polarization, efficient orbital overlap, and a HOMO-LUMO excitation dominated by a 68% single transition, reflecting a balance between orbital delocalization and excitation stability. These observations are further supported by the TD-DFT results summarized in Table 1 and visually represented in the absorption spectra of Fig. 4, confirming the influence of donor-acceptor strength and heteroatom substitution on excitation energies and absorption behaviour.

Thus, the combined electronic effects of heteroatom substitution (O < S < Se) and strong push-pull substituents (-NH₂ as donor; -NO₂, -CN, -CHO as acceptors) contribute to modulating the optoelectronic properties of these compounds. Particularly, molecules like IM3, IM6, and IM9, which feature strong donor-acceptor (NH₂-NO₂) combinations and heavy heteroatoms, show the most favourable characteristics for applications in organic electronics, nonlinear optics, and photodynamic systems due to their small band gaps, visible-light absorption, and strong ICT behaviour.

Two level model

The TLM expression quantitatively relates the first hyperpolarizability to molecular parameters through the proportionality as shown in Eq. (1). Our TD-DFT results reveal that the reference molecules R1-R3, with the highest transition energies (3.39–3.89 eV) and negligible charge-transfer contributions (β_CT = 0.00), display vanishing β_tot values due to the absence of significant dipole moment variation (µ = 0.00 D for R1 and R3).

Fig. 4

The TD-DFT simulated absorption spectra of Series 1-Series 3 at the B3LYP-D3 level of theory.

Conversely, the substituted derivatives IM1-IM9 exhibit a pronounced enhancement in β_tot (ranging from 1164 a.u. in IM7 to 3315 a.u. in IM3), which arises from their lower transition energies, stronger charge transfer, and larger µ_tot values. Among these, IM3 demonstrates the highest β_tot (3315 a.u.), driven by a low transition energy (3.61 eV), moderate β_CT (0.04), high oscillator strength (f_o = 0.08), and the largest µ = 11.73 D. This enhancement trend is evident across the series: IM2 (β_tot = 2834 a.u., <µ> = 11.68 D, E = 3.72 eV) and IM1 (β_tot = 2729 a.u., <µ> = 9.18 D, E = 4.03 eV) also show strong NLO activity due to favorable f_o values (0.23 and 0.21). As the energy gap decreases from IM1 (4.03 eV) to IM9 (3.27 eV), λ_max shifts toward longer wavelengths (307.93–378.81 nm), confirming enhanced π-conjugation and charge-transfer characteristics. IM6 (β_tot = 1800 a.u., <µ> = 6.01 D) and IM5 (β_tot = 1654 a.u., <µ> = 5.91 D) exemplify the interplay of these parameters, whereas IM4 and IM8 exhibit moderate nonlinear optical responses due to smaller dipole moments.

Fig. 5

Relationship between β_tot and β_CT values for all the designed molecules.

The strong correlation between β_CT and β_tot is shown in Fig. 5 demonstrates that the TLM framework reliably explains the superior nonlinear optical performance of the IM-series by emphasizing the inverse cubic dependence on transition energy and the positive contributions of both µ_tot and f_o.

NLO parameters, including µ _tot, α _₀, and β _tot

The dipole moment (µ_tot) results further substantiate the interplay between heteroatom identity and donor-acceptor substitution in modulating molecular charge distribution. In Series 1 (oxygen heteroatom, R1-IM3), µ_tot increases markedly from 0.00 D in the reference compound to 11.79 D in the most strongly substituted derivative, reflecting pronounced intramolecular charge transfer in the presence of the NH₂ donor. Series 2 (sulphur heteroatom, R2-IM6) shows a rise from 0.00 D to 6.15 D, indicating moderate enhancement due to sulphur’s inherently higher polarizability but slightly reduced ICT amplification compared with oxygen analogues. In Series 3 (selenium heteroatom, R3-IM9), µ_tot increases more modestly, from 0.00 D to 5.53 D, consistent with selenium’s already highly delocalized electron density, which lessens the incremental effect of further electron-withdrawing substitution. Across all series, µ_tot follows the acceptor strength order -CHO < -CN < -NO₂, reaffirming the strategic role of donor-acceptor engineering in tailoring nonlinear optical relevant dipole characteristics. The calculated µ_tot values for each compound are summarised in Table 2.

Table 2 The calculated values of ground state dipole moment (µ_tot), linear polarizability (a₀) and β_tot (in a.u.) of all the designed molecules for all Series 1- Series 3 at M06-2X level of theory.

The mean polarizability (α₀) quantifies the electronic deformability of a molecular framework under an external electric field. In this study, three heteroatomic cores-oxygen, Sulphur, and selenium form the basis of Series 1 (R1-IM3), Series 2 (R2-IM6), and Series 3 (R3-IM9), respectively. In Series 1 (O-heteroatom), the reference R1 exhibits the lowest α₀ (305.29 a.u.), with gradual increases upon substitution by -CHO (369.95 a.u.), -CN (372.97 a.u.), and -NO₂ (374.95 a.u.) due to enhanced ICT. Series 2 (S-heteroatom) begins at a higher baseline (R2, 442.08 a.u.), with acceptor substitutions yielding more pronounced gains 469.53, 477.30, and 480.32 a.u. reflecting Sulphur’s greater polarizability and delocalization capacity. Series 3 (Se-heteroatom) achieves the highest values, from 491.22 a.u. (R3) to 524.41 a.u. (IM9), owing to selenium’s large, easily polarizable electron cloud. The calculated α₀ values are listed in Table 2, while their graphical trends at four functionals are shown in Figure S3. Notably, systems with higher α₀ also exhibit enhanced β_tot, confirming a direct structure-property relationship wherein greater electron cloud deformability promotes stronger NLO responses, particularly for selenium-based derivatives.

The nonlinear optical performance of the studied molecules was evaluated through the computation of first-order hyperpolarizability, a parameter that directly reflects the ability of the molecular electronic distribution to undergo distortion under an applied electric field. In the present work, the first hyperpolarizability values were calculated at the M06-2x level of theory and are summarized in Table 2, while Fig. 6 depicts graphical trends for all compounds under investigation at M06-2X, ωB97XD, and CAM-B3LYP level of theory. For Series 1, the x-axis component of the first hyperpolarizability (β_x) shows a pronounced enhancement upon substitution, while the reference molecule R1 exhibits a negligible β_x value (0.00 a.u.). Among the substituted derivatives, IM1 (7,447,529.14 a.u.) and IM2 (8,030,733.64 a.u.) display significantly increased β_x values, whereas IM3 shows the highest β_x value of 10,986,210.86 a.u. This dominant β_x contribution originates from the strong electron donating and withdrawing (-NO₂) group in IM3, which intensifies donor-acceptor interactions and promotes efficient intramolecular charge transfer along the molecular x-direction. The reference R1 exhibits a negligible β_tot (0.10 a.u.), consistent with its symmetric charge distribution. Upon substitution with electron-withdrawing groups, a substantial enhancement is observed-IM1 reaches 2729.02 a.u., IM2 increases to 2833.86 a.u., and IM3 attains the maximum value of 3314.55 a.u. in this series.

Fig. 6

The graphical representation of β_tot (in a.u.) at M06-2X, ωB97XD, CAM-B3LYP, and B3LYP level of theory for all the designed molecules.

The sharp rise in β_tot for IM3 indicates the strong charge-transfer capability imparted by the -NO₂ group, significantly exceeding the performance of well-known standards such as p-nitroaniline (β_tot = 908 a.u.). In Series 2 (Sulphur as heteroatom), the β_x component again dominates the nonlinear optical response. The reference compound R2 shows an almost zero β_x value (0.00 a.u.), whereas substitution leads to a marked increase. Among the derivatives, IM6 exhibits the highest β_x value of 2,964,874.22 a.u., surpassing the other compounds in this series. This enhancement is attributed to the combined electron-withdrawing nature of the substituent groups, which increase molecular asymmetry and facilitate charge delocalization predominantly along the x-axis. Similarly, R2 (0.10 a.u.) giving way to markedly higher β_tot values upon substitution 1466.84 a.u. for IM4, 1653.91 a.u. for IM5, and 1800.29 a.u. for IM6. Although the increases are substantial, they remain lower than those in the oxygen series, highlighting the interplay between heteroatom identity and the efficiency of intramolecular charge transfer.

For Series 3 in which Selenium heteroatom, a similar but comparatively weaker trend is observed. The reference molecule R3 exhibits negligible β_x (0.00 a.u.), while substitution increases the x-axis contribution. Among the derivatives, IM9 shows the highest β_x value of 2,790,639.43 a.u., indicating enhanced polarization along the molecular x-direction. This behavior arises from the synergistic effect of the selenium heteroatom and the electron-withdrawing substituent, which promotes charge separation and directional charge transfer.

Series 3 shows the lowest β_tot enhancement among the substituted derivatives, starting from R3 (0.01 a.u.) and increasing to 1163.98 a.u. (IM7), 1437.58 a.u. (IM8), and 1707.25 a.u. (IM9). The comparatively smaller gains can be attributed to selenium’s inherently high polarizability, which lessens the relative impact of electron-withdrawing group substitution. Overall, the β_tot values across all compounds are significantly larger than the frequently cited reference urea (14 a.u.), in some cases exceeding it by more than two orders of magnitude. Among all studied systems, IM3 emerges as the most efficient nonlinear optical candidate, with a β_tot value of 3314.55 a.u., reflecting its optimal combination of a highly polarizable oxygen-based core and a strongly electron-withdrawing -NO₂ group, which together maximize ICT. These results confirm that strategic incorporation of donor-acceptor substituents, combined with heteroatom variation, provides an effective route to enhance the NLO responses of organic molecular systems.

Solvent effect on dipole moment, polarizability and hyperpolarizability

The dipole moment and linear polarizability values reveal a pronounced interplay between solvent polarity and molecular substitution. In general, polar solvents (water, ethanol) enhanced the dipole stabilization of the donor-acceptor systems, while also increasing the overall polarizability compared to the nonpolar medium (benzene). The systematic variation across the IM series reflects the effect of heteroatom substitution. All calculations were carried out using the M06-2X functional, which is well-suited for predicting nonlinear optical properties for these systems. The reference compound 6 H-Hep, which contains no heteroatom (O, S, Se) bridging unit, shows µ_tot (1.50 in water, 1.03 in benzene, and 1.43 in ethanol) and α₀ values in all solvents (456.31 a.u. in water, 382.40 a.u. in benzene, and 448.99 a.u. in ethanol), thereby establishing a baseline against which all substituted systems can be compared. Also, R1, R2 and R3 shows lowers values which contains heteroatoms but not having any donor and acceptor groups. Relative to this minimal response, heteroatoms (O. S, Se), and donors and acceptors incorporation produces dramatic enhancements.

Table 3 The calculated values of ground state dipole moment (µ_tot in Debye) and linear polarizability (a₀ in a.u.) of all the designed molecules in solvents (water, benzene and ethanol) at M06-2X level of theory.

Among the O-substituted series (IM1-IM3), IM3 exhibited the highest dipole moment in water (13.36 D), closely followed by IM1 (13.30 D), emphasizing the strong influence of polar substituents in stabilizing charge-separated states. In ethanol, nearly identical values were obtained for IM3 (13.30 D) and IM1 (13.24 D), confirming the robustness of these O-bridged frameworks across polar solvents. The S-substituted molecules (IM4-IM6) showed intermediate dipole responses, with values around 5–6 D in water and ethanol, while the Se-substituted IM7-IM9 maintained slightly lower dipole values (4–5 D) but demonstrated consistent behavior across solvents. In benzene, dipole magnitudes were uniformly reduced, reflecting diminished solvation stabilization; nonetheless, IM3 (12.58 D) and IM1 (12.40 D) retained their dominant response. These results establish O-substituted derivatives (IM1-IM3) as the most solvent-sensitive dipolar systems in this series. The α₀ values showed a strong dependence on both substitution and solvent polarity. In all solvents, Se-substituted IM7-IM9 exhibited the largest polarizability values, reaching 748.23 a.u. (IM7) in water and 734.31 a.u. in ethanol, markedly higher than the O- and S-substituted counterparts. This trend can be rationalized by the increased delocalization and softer electron cloud associated with heavier chalcogen atoms, which amplify polarizability. S-substituted IM4-IM6 occupied an intermediate range (550–670 a.u.), while O-substituted IM1-IM3 remained comparatively lower (410–480 a.u.), despite their high dipole values. Solvent polarity further enhanced α₀: for example, IM7 in benzene (609.62 a.u.) increased to 748.23 a.u. in water. Collectively, these findings demonstrate that while O-substituted molecules maximize dipole response, Se-substituted molecules dominate in linear polarizability, highlighting a clear substitution-property correlation.

The computed µ_tot and α₀ values are summarized in Table 3. The results indicate that O-substituted derivatives (IM1-IM3) exhibit the largest dipole moments, while Se-substituted derivatives (IM7-IM9) display the highest polarizabilities. Figure S4 presents these trends graphically for α₀, highlighting the strong influence of solvent polarity and chalcogen substitution on electronic responses.

The solvent environment clearly influences β_tot, with polar solvents such as water and ethanol enhancing charge-transfer interactions by stabilizing high dipolar excited states, while the nonpolar solvent benzene provides comparatively lower β_tot values. This observation is in line with previous findings that dielectric stabilization strongly promotes intramolecular charge transfer in push-pull frameworks. All calculations were performed at the M06-2X functional, which is widely useful for predictions of nonlinear optical properties for these systems. The results are summarized in Table 3 and represented graphically in Fig. 7.

Fig. 7

Graphical representation of first hyperpolarizability (a.u.) in solvents (water, benzene and ethanol) at M06-2X level of theory.

The x-axis component of first hyperpolarizability (β_x) for the best-performing compounds IM3, IM6, and IM9 shows a pronounced solvent-dependent enhancement, with the highest values consistently observed in water, followed by ethanol and benzene. Among these, IM3 exhibits the largest β_x value, reaching 4.68 × 10⁷ a.u. in water, which decreases to 4.42 × 10⁷ a.u. in ethanol and 2.28 × 10⁷ a.u. in benzene. This strong enhancement arises from the presence of the highly electron-withdrawing -NO₂ group, which promotes efficient intramolecular charge transfer along the molecular x-axis, further amplified in polar solvents. Similarly, IM6 shows a maximum β_x value of 1.24 × 10⁷ a.u. in water, compared to 1.19 × 10⁷ a.u. in ethanol and 6.20 × 10⁶ a.u. in benzene, reflecting increased molecular polarization in a high-dielectric medium. In the same manner, IM9 attains its highest β_x value of 1.01 × 10⁷ a.u. in water, followed by 9.79 × 10⁶ a.u. in ethanol and 5.40 × 10⁶ a.u. in benzene. The overall trend confirms that polar solvents significantly enhance β_x by stabilizing charge-separated states, thereby intensifying x-axis-directed intramolecular charge transfer in these optimized nonlinear optical systems. The Fig. 8 while Table 4 demonstrates that higher solvent polarity enhances β_x by stabilizing polarized electronic states, thereby strengthening intramolecular charge transfer along the x-axis.

Fig. 8

Graphical representation of hyperpolarizability (a.u.) in solvents (water, benzene and ethanol) at M06-2X level of theory.

The 6 H-Hep compound, which contains no heteroatom bridging unit, shows hyperpolarizability values in all solvents (207.99 a.u. in water, 130.51 a.u. in benzene, and 196.43 a.u. in ethanol), thereby establishing a baseline against which all substituted systems can be compared. Also, R1, R2 and R3 shows lowers values which contains heteroatoms but not having any donor and acceptor group. Relative to this minimal response, heteroatoms (O. S, Se), and donors and acceptors incorporation produces dramatic enhancements. Like given in the Table 4, the oxygen-bridged compound IM3 exhibits β_tot value of 6.84 × 10³ a.u. in water. Similarly, sulphur-bridged IM6 (3.61 × 10³ a.u. in water) and selenium-bridged IM9 (3.23 × 10³ a.u. in water) also show strong enhancements, confirming the critical role of heteroatom bridges, and donors and acceptors at opposite ends in promoting charge delocalization and amplifying nonlinear optical responses.

Also, IM3 shows the strongest response among all compounds at the x-axis with values of 4.68 × 10⁷ a.u. in water, 2.28 × 10⁷ a.u. in benzene, and 4.42 × 10⁷ a.u. in ethanol, which are significantly higher than those of the other designed molecules. By comparison, the corresponding y- and z-axis components remain close to zero, indicating that the molecular response is highly anisotropic and dominated by the x-axis contribution.

Table 4 The calculated values of β_tot (in a.u.) of all the designed molecules in solvents (water, benzene and ethanol) at M06-2X level of theory.

Across the three-substitution series, oxygen-bridged IM1-IM3 molecules consistently deliver the highest hyperpolarizability, with IM3 outperforming all other candidates across solvents (6837.70 a.u. in water, 4773.40 a.u. in benzene, and 6649.93 a.u. in ethanol). Sulphur-bridged IM4-IM6 compounds yield moderate values ranging between 2500 and 3600 a.u., whereas selenium-bridged IM7-IM9 derivatives provide slightly lower but more stable values across solvents, ranging from approximately 2000 to 3200 a.u. The heavier selenium atoms enhance polarizability, but their reduced dipole stabilization compared to oxygen results in intermediate performance. The negligible β_tot values of the pristine 6 H-Hep, clearly illustrate the necessity of heteroatom incorporation, while the consistently superior performance of IM3 highlights the impact of oxygen substitution combined with donor-acceptor architecture. Figure 8 further emphasizes these differences, showing the minimal response of 6 H-Hep, R1, R2 and R3 and the markedly enhanced performance of IM1-IM3, IM4-IM6, and IM7-IM9, with IM3 emerging as the best-performing candidate for optoelectronics across all the solvents.

Electric field-induced SHG analysis

The application of dynamic perturbations is intended to explore how frequency dispersion corrections influence the nonlinear optical response. This study particularly emphasizes key indicators, including HRS (hyper-Rayleigh scattering) and the DR (depolarization ratio), along with additional parameters such as β_HRS, DR, β_J=1, β_J=3, ρ, φ_J=1, and φ_J=3, which can be evaluated using Eqs. (2–7)^55,56. Table 5 presents the β_HRS values of all the designed molecules evaluated at two key wavelengths, λ = 1907 nm and λ = 1460 nm. The results indicate that β_HRS increases under increased optical frequency, following the trend β_HRS (∞) < (1907 nm) < β_HRS (1460 nm) in Table 5.

Table 5 Calculated β_HRS, DR, β_j=1, β_j=3, ρ, Ф_j=1, and Ф_j=3 values (in a.u) of Series 1-Series 3 on two wavelengths (λ = 1460 nm, 1907 nm) at the M06-2X/6-311 + G(d) level.

Of all the derivatives studied, IM3 shows the most significant β_HRS, attaining 1699.69 a.u. at an excitation wavelength of 1460 nm, 1341.91 a.u. at ∞ and 1535.96 a.u. at λ = 1907 nm. Additionally, all structures exhibit DR values above 1.5, which confirms that the compounds are non-resonant in SHG processes. The observed ρ values (0.59–18.94) confirm that octupolar behaviour predominates in these molecules. An inverse dependence of DR on ρ values is evident throughout the wavelengths selected for frequency-dependent analysis. To better understand the mechanism underlying the second-order nonlinear optical response, Fig. 9 highlights how the harmonic generation strength of IM3 varies with polarization angle (Ψ bends) at λ = 1460 nm as compared to R1.

Fig. 9

Polar representation of harmonic intensities for Series 1-Series 3 at λ = 1460 nm.

The octupolar features evident at this wavelength not only validate their classification as octupolar but also highlight their potential as alternative nonlinear chromophores, where the synergy of symmetry and strong optical response is crucial for practical applications. The observed static and dynamic hyperpolarizabilities establish structure-property relationships that directly inform NLO design. In particular, IM3 achieves a strikingly high static β_tot value of 3314.55 a.u. This enhanced activity can be ascribed to the molecule’s tailored push-pull architecture, wherein the strong electron-donating -NH₂ and electron-withdrawing -NO₂ groups optimize ICT. The β_tot value of IM3 significantly outperforms established benchmarks para-nitroaniline derivatives, typically lie in the 10²-10³ a.u. range. This exceptional performance highlights its suitability for electro-optic modulators in telecommunications, where high β values are critical for efficient signal control at low operating voltages. The dynamic findings further strengthen this potential. At telecom-relevant wavelengths of 1460 nm and 1907 nm, IM3 retains high β_HRS values (1699.69-1535.96 a.u.), while the low depolarization ratio (DR = 5.54–5.48) confirms its non-resonant nature, favourable for frequency doubling. In addition, the octupolar feature (ρ = 0.71) observed in the polarization response Fig. 10 offers an advantage for polarization-independent devices such as optical switches, as it alleviates alignment constraints in thin-film fabrication.

The frequency-dependent behavior, with β_HRS being larger at 1460 nm than at 1907 nm, is in agreement with the two-level model, demonstrating the robustness of the computational methodology in assessing wavelength-dependent NLO responses. The outcomes directly guide application-specific material selection. IM3, among all the series with exceptional β_tot and octupolar characteristics, is a strong candidate for integrated photonic devices, while compounds with moderate β_tot values may serve effectively in sensor technologies.

Although this study provides valuable theoretical insights into the electronic and nonlinear optical properties of the designed compounds, experimental synthesis is necessary to validate these predictions. The computational approach offers a cost-effective alternative, eliminating the need for extensive wet-lab experiments. Some derivatives may be synthetically accessible at relatively low cost, making them promising candidates for further study. Additionally, factors such as long-term stability and real-world operational conditions were not considered. Overall, the theoretical results serve as a practical guide for identifying potential NLO materials before experimental work.

Phenomenon of Aromatic π-π Stacking

The analysis of stacked dimers was carried out to evaluate intermolecular interactions that can significantly influence charge transport, electronic coupling, and solid-state optical properties of conjugated donor-π-acceptor systems. In this study, π-π stacking is quantitatively defined based on the interplanar distance and centroid-centroid separation between adjacent aromatic rings, which fall within the characteristic range of π-π interactions (3.3–3.8 Å). In DFT studies, π-π stacking interactions result from the overlap of π-electron densities between neighbouring aromatic rings, with stabilization provided by van der Waals and electrostatic contributions. Conventional DFT often underestimates such weak forces; hence, dispersion-corrected methods like DFT-D3 or ωB97XD are essential for accurate predictions.

Fig. 10

π-π stacking interactions of IM3, IM6, and IM9 visualized at an isosurface value of 0.004.

The stacking geometry whether parallel, offset, or slipped directly influences electronic delocalization, charge transfer, and nonlinear optical behavior. The green iso-surfaces in the Fig. 10 mark the regions where π-π stacking is most dominant, reflecting stabilization through electron density overlap. This effect plays a vital role in tuning the electronic structure by narrowing the HOMO-LUMO energy gap, thereby facilitating more efficient charge transfer^57,58.

In the examined compounds (6 H-Hep, IM3, IM6, IM9), green contours highlight the spatial zones where π-π contacts dominate, reflecting stabilization through van der Waals interactions. The π-π overlap (Fig. 10) between neighboring rings stabilizes the geometry without the need for covalent bonding. Among the three models, IM3 exhibits the most efficient stacking, as its nearly planar orientation and favourable interplanar distance maximize orbital overlap. In contrast, IM6 and IM9 show partial distortions, which limit delocalization and weaken the stacking effect. The red-highlighted atoms in IM3 indicate center of enhanced electron density overlap, reinforcing the strength of its stacking arrangement. This optimized configuration enables more effective charge redistribution and a highly delocalized π-system. As a direct consequence, IM3 shows a reduced HOMO-LUMO energy gap (E_g= 1.95 eV), which facilitates efficient charge transfer. Owing to this feature, IM3 demonstrates the highest first hyperpolarizability (β_tot = 3314.55 a.u.) among the series, linking its structural stability with superior NLO performance. The enhanced delocalization provided by π–π stacking not only stabilizes the system but also amplifies its optical nonlinearity, making IM3 the most promising candidate for optoelectronic applications.

Character of π-electron delocalization

The π-delocalization characteristics of reference compounds R1, R2 and R3, analysed through the electron localization function for π-electrons (ELF-π) and the localized orbital locator for π-electrons (LOL-π), were examined to confirm their enhanced nonlinear optical response, as shown in Fig. 11(a) and (b) respectively. In general, π-delocalization results from interactions among π-orbitals. To explore how absorption correlates with nonlinear optical amplitudes, a detailed analysis was conducted using the ELF^55,59 and LOL. Within the conjugated structures, π-electron delocalization was characterized solely through π-molecular orbitals by means of widely applied spatial functions, namely ELF-π and LOL-π. Figure 11(a) presents the ELF values for R1, R2, and R3, reflecting different extents of electron localization. The reported numerical values (0.75, 0.80, and 0.95) in Fig. 11 represent the isosurface thresholds applied for generating the ELF-π and (0.50) for LOL-π graphical maps. Among them, compound R3 exhibits an ELF of 0.75, suggesting a moderate degree of delocalization typically observed in π-conjugated systems. Such delocalization generally increases a molecule’s polarizability, an essential parameter for NLO behaviour, since delocalized electrons are more susceptible to distortion under external electric fields. In contrast, R2 and R3 exhibit increased ELF values of 0.95 and 0.80, respectively, indicating strongly localized electrons. This localization, characteristic of covalent bonds or lone pairs, usually results in reduced polarizability and weaker nonlinear optical activity. In terms of NICS, ELF analysis provides further insight into the aromatic nature of the substituted benzene rings. Molecule R1, with oxygen substitution, exhibits the highest positive NICS value, indicating the lowest aromatic stabilization. This reduced aromaticity facilitates greater π-electron polarization, which explains the comparatively stronger nonlinear optical response observed for the R1 derivative. In contrast, R2 (sulphur) and R3 (selenium) show lower positive NICS values, reflecting relatively higher aromatic stabilization, which restricts electron delocalization and results in weaker nonlinear optical activity than R1 derivatives.

Fig. 11

The color-filled isosurface maps of ELF-π (a) and LOL-π (b) of R1, R2 and R3 with their values.

LOL visualizes the probable positions of electrons within a molecule and is useful for mapping their distribution across different bonds. The iso-surfaces displayed in Fig. 11(b) illustrate the regions where π-electrons are delocalized, extending over multiple molecular orbitals (MOs). These shapes highlight the regions where π-electrons are more mobile between atoms. The results show that π-electrons are more delocalized over shorter bonds than longer ones, implying that shorter bonds facilitate stronger electron sharing^36,60. In Fig. 11(b), the color-coded LOL isosurfaces reveal the π-electron distribution in the benzene rings of the substituted derivatives. For R1, the C-O bond exhibits stronger delocalization across the ring, enabling higher electron mobility. In comparison, the C-S bond in R2 shows reduced delocalization, while the C-Se bond in R3 presents the weakest distribution of π-electrons. This decreasing trend (O > S > Se) suggests that R1 facilitates greater electronic polarization, consistent with its enhanced NLO behaviour. Furthermore, the lower electron density observed in R2 and R3 indicates less freedom of electron movement and weaker delocalization. Consequently, R1, with its higher delocalization, is more effective in electron sharing, which influences its stability, reactivity, and electronic behaviour. Such enhanced density not only strengthens intermolecular interactions but also improves material properties, particularly conductivity and nonlinear optical response.

Conclusion

In this work, a systematic computational investigation was carried out on heteroatom-substituted π-conjugated donor-π-acceptor systems (R1-IM3, R2-IM6, R3-IM9) to assess their nonlinear optical behavior. Structural optimization and electronic analyses confirmed that replacing O, S, and Se in the heterocyclic core markedly influences bond lengths, aromaticity, and intramolecular charge transfer efficiency. FMO studies revealed energy gaps ranging from 1.95 to 4.23 eV, where IM3 exhibited the narrowest E_g, ensuring stronger ICT and enhanced polarizability. GRD and DOS analysis supported these trends, indicating higher reactivity and charge transport in IM3, IM6, and IM9 compared to their parent molecules. TD-DFT absorption spectra showed π→π* transitions within 307–394 nm, with IM6 demonstrating the most red-shifted absorption band, highlighting improved delocalization in sulfur-based frameworks. Electrostatic potential (ESP) mapping and NICS(1)zz values further validated enhanced polarization, particularly in oxygen-containing derivatives. Importantly, hyperpolarizability analysis demonstrated a dramatic rise in β_tot, from negligible values in reference compounds (0.01–0.10 a.u.) to outstanding values in substituted systems, with IM3 achieving 3314.55 a.u., far exceeding known NLO standards. Radiative lifetime calculations (18–47 ns) confirmed long-lived excited states and efficient optical activity, while π-π stacking interactions in IM3 provided additional stabilization and superior nonlinear optical performance. Collectively, the findings establish IM3, IM6, and IM9 as the most promising candidates for photonic and optoelectronic applications. This study underscores the effectiveness of heteroatom engineering and donor-acceptor modulation as powerful strategies for tailoring next-generation organic nonlinear optical materials.