Quantum Chemical Exploration of A−π₁–D₁–π₂–D₂-Type Compounds for the Exploration of Chemical Reactivity, Optoelectronic, and Third-order Nonlinear Optical Properties

Abstract

Organic compounds exhibit significant nonlinear optical (NLO) properties and can be utilized in various areas like optical parameters, fiber optics, and optical communication. Herein, a series of chromophores (DBTD1–DBTD6) with an A−π₁–D₁–π₂–D₂ framework was derived from a prepared compound (DBTR) by varying the structure of π-spacer and terminal acceptor. The DBTR and its investigated compounds were optimized at the M06/6-311G(d,p) level of theory. Frontier molecular orbitals (FMOs), nonlinear optical (NLO) properties, global reactivity parameters (GRPs), natural bonding orbital (NBO), transition density matrix (TDM), molecular electrostatic potential (MEP), and natural population analysis (NPA) were accomplished at the abovementioned level to describe the NLO findings. DBTD6 has the lowermost band gap (2.131 eV) among all of the derived compounds. The decreasing order of highest occupied molecular orbital–lowest unoccupied molecular orbital (HOMO–LUMO) energy gap values was DBTR > DBTD1 > DBTD2 > DBTD3 > DBTD4 > DBTD5 > DBTD6. The NBO analysis was carried out to describe noncovalent interactions such as conjugative interactions and electron delocalization. From all of the examined substances, DBTD5 showed the highest λ_max value at 593.425 nm (in the gaseous phase) and 630.578 nm (in chloroform solvent). Moreover, the β_tot and ⟨γ⟩ amplitudes of DBTD5 were noticed to be relatively greater at 1.140 × 10^–27 and 1.331 × 10^–32 esu, respectively. So, these outcomes disclosed that DBTD5 depicted the highest linear and nonlinear properties in comparison to the other designed compounds, which underlines that it could make a significant contribution to hi-tech NLO devices.

Introduction

The modification of the optical characteristics of a substance’s structure in the presence of photons or light exhibits a macroscopic phenomenon called nonlinear optics (NLO).¹ In recent decades, multiple enhancements regarding NLO have been made in the data transformation, electro-optics, fiber optics, photonic lasers, and data storage disciplines.² Moreover, the telecommunications sector has been extensively developed owing to the potential employment of second-order NLO materials, which exhibit ultrafast signal transmission via electro-optic modulation.³ The most prominent characteristics of NLO compounds are broadly categorized as their conjugated molecular framework, amplitude, optical frequency, phase, and polarizable nature.⁴ Researchers have put tremendous effort into both theoretical and experimental exploration of different classes of NLO materials, including NLO polymers, molecular dyes, organic as well as inorganic semiconductors, and nanomaterials.⁵⁻⁷

Following the development, organic NLO compounds have been extensively studied considering the presence of many proficient features like an extendable π-conjugated system,⁸ remarkable photothermal stability, flexibility in molecular structure, durability, novel optic, electronic spectra, large NLO susceptibility, quick response time, and ease in structural designing and modulation.⁹⁻¹¹ Conventionally, semimetal NLO materials, mainly silicon based, have been employed in quantum dots, batteries, and photosensitized solar cells.¹² While moving a step ahead in computational modulation, polymer-based NLO materials emerged as a very promising area of research contrary to their semimetal counterparts.¹³

It is well known that conducting-type polymers are used in the synthetic process of medical equipment such as inhalers,¹⁴ transistors,¹⁵ and most specifically field-effect transistors.^16,17 In accordance with the manufacturing domain, they are also potentially employed in electrochromic materials, smart windows, light-emitting diodes (LEDs), optical data storage, solar cells, and shielding materials.¹⁸⁻²⁰ Most of the recently developed NLO polymers have a guest–host configuration of chromophores immersed in the polymer matrix or covalently attached to the chains of the polymer. It is noted that the nonlinearity in the optical properties is associated with the chromophore substituent on the polymer chain, encompassing excellent NLO response.²¹

Furthermore, the NLO properties of these organic systems are strongly influenced by the delocalization of electric charge across the π-conjugated network. The configuration pattern of NLO chromophores involves the interaction of donor and acceptor through π-spacers. The electronic charge delocalization happens from donor to acceptor moieties via π-linker beyond hurdle, generating first- and second-order nonlinear responses as well as the dipole nonlinearity.²²⁻²⁴ Efficient assembly of donor, π-spacer, and acceptor moieties contributes solely to enhance the intramolecular charge transfer (ICT), which is also taken as an impactful strategy while tuning NLO response properties.²⁵⁻²⁸ Numerous studies successfully reported that the listed techniques, such as extended delocalization through π-linkage; metal–ligand structural framework; incorporation of an electronic charge network; assimilation of a suitable donor, π-spacer, and acceptor unit; and bond-length alteration, are employed to achieve better NLO properties.²⁹

The current computational investigation is expected to improve electronic charge delocalization by utilizing different lengths of π-spacers in the entitled derivatives. It is noticed from the literature that among all of the conducting polymers, polyanilines are of high interest owing to their remarkable stability and exceptional conduction process.^30,31 The functional groups attached to the polymer’s backbone are responsible for these intriguing properties along with their electrical properties. Thus, functionalized conduction polymers (polyanilines) are potentially endorsed by the scientific community and have been reported significantly in the literature as suitable NLO candidates.³²

Herein, Flu-RH is being taken as a parent compound that was recently synthesized via the Suzuki coupling mechanism, where rhodanine dye has been incorporated at both ends of the fluorine backbone.³³ In this work, Flu-RH is transformed into DBTR via side-chain modifications. The rhodanine moiety at one end is replaced by N,N-dimethylaniline and a varied number of aniline moieties are introduced in each new derivative. This series of derivatives is subjected to density functional theory (DFT) (NLO and NBO study) and time-dependent density functional theory (TD-DFT) (frontier molecular orbitals (FMOs), transition density matrices (TDMs), density of state (DOS), global reactivity parameters (GRPs), absorption spectrum (UV–vis), and hole–electron analyses) approaches at the M06 level of theory and 6-311G(d,p) basis set. Moreover, the NLO response of said chromophores is estimated in terms of hyperpolarizabilities, UV–visible spectra, and HOMO/LUMO diagrams with the utilization of corrected long-range hybrid DFT methods, and the computed results are displayed in their respective sections. Through structural modification with various efficient donor, spacer, and acceptor units, the efficacy of optoelectronic materials significantly improved. Therefore, it is expected that the current study will open ways to synthesize rhodanine-dye-based compounds having enhanced NLO behavior.

Results and Discussion

In this work, the NLO properties of DBTR and DBTD1–DBTD6 have been investigated to develop promising NLO materials. We utilized (5Z,5′Z)-5,5′-(((9,9-dimethyl-9H-fluorene-2,7-diyl)bis(thiophene-5,2-diyl))bis(methaneylylidene))bis(3-ethyl-2-thioxothiazolidin-4-one) abbreviated as DBTR as a reference compound with A−π–D−π–A configuration. A series of designed chromophores with A−π₁–D₁–π₂–D₂ architecture is made by the structural modulation of DBTR (Figure 1). First, DBTD1 is designed by changing one end-capped acceptor with N,N-dimethylaniline (donor moiety) and thiophene (π-spacer) with N1-methyl-N4-(p-tolyl) benzene-1,4-diamine. DBTD1–DBTD6 are designed by the addition of N1-methyl-N4-(p-tolyl) benzene-1,4-diamine (monomer) in each derivative. The ChemDraw structures of these studied chromophores are depicted in Figure 2 and their IUPAC names are presented in Table S34. Furthermore, Figure S3 presents the optimized structures of these molecules, while their Cartesian coordinates are tabulated in Tables S1–S7. It is estimated that this research will be very useful for the synthesis of high-efficacy NLO materials.

Figure 1.

Sketch map of designed compounds (DBTD1–DBTD6) from reference (DBTR).

Figure 2.

ChemDraw structures of investigated moieties (DBTR and DBTD1–DBTD6).

Frontier Molecular Orbitals (FMOs)

FMO analysis is an effective way to investigate electronic transitions, chemical stability, and reactivity of a molecule.³⁴⁻³⁷ The HOMO (highest occupied molecular orbital) and the LUMO (lowest unoccupied molecular orbital) of a system have a significant impact on the optical and electrical properties of molecules by using the HOMO–LUMO band gap.³⁸⁻⁴⁰ LUMO expresses the capacity to accept electrons, whereas HOMO depicts the potential to donate electrons.^41,42 Molecules showing large ICT usually offer the best NLO response.^43,44

The E_HOMO and E_LUMO of designed chromophores (DBTD1–DBTD6) are computed at the M06/6-311G(d,p) level, and the outcomes are presented in Table 1, while the energies of higher orbitals (E_HOMO–1, E_LUMO+1, E_HOMO–2, and E_LUMO+2) are tabulated in Table S8. All of the designed chromophores (DBTD1–DBTD6) display a lower energy gap (E_gap = E_LUMO – E_HOMO) in contrast to the reference chromophore (DBTR) (Figure S4). Theoretically calculated values of E_HOMO and E_LUMO of DBTR are −5.937 and −2.867 eV, respectively, with a 3.070 eV band gap.

Table 1. E_HOMO, E_LUMO, and Energy Gap (ΔE) of the Entitled Species^a.

compounds	EHOMO	ELUMO	band gaps
DBTR	–5.937	–2.867	3.070
DBTD1	–5.177	–2.680	2.497
DBTD2	–5.041	–2.682	2.359
DBTD3	–4.897	–2.675	2.222
DBTD4	–4.866	–2.670	2.196
DBTD5	–4.814	–2.676	2.138
DBTD6	–4.797	–2.666	2.131

^aUnits in eV.

For DBTD1–DBTD6, the observed E_HOMO/E_LUMO values are −5.177/–2.680, −5.041/–2.682, −4.897/–2.675, −4.866/–2.670, −4.814/–2.676, and −4.797/–2.666 eV, respectively. Moreover, the observed energy gaps for DBTD1–DBTD6 are 2.497, 2.359, 2.222, 2.196, 2.138, and 2.131 eV, respectively. A reduction in ΔE is noticed in all of the designed chromophores due to a higher level of HOMO and a lower level of LUMO, which deliver a high intramolecular charge transfer (ICT).

The reference compound has a higher energy gap value than all of the derivatives. This band gap is lowered to 2.497 eV in DBTD1 because of the development of a strong push–pull phenomenon that is accompanied by structural variation, i.e., by swapping the terminal acceptor by the N,N-dimethylaniline donor unit (D2) and the thiophene ring with N1-methyl-N4-(p-tolyl) benzene-1,4-diamine (π-spacer 2). The energy gap is further reduced in DBTD2 and DBTD3 (2.359 and 2.222 eV) due to the addition of three and five aniline monomers (which act as π-linkers), respectively. Thus, the conjugation of the system is improved by increasing π-linkers, which reduces the energy gap. Frontier molecular orbitals of DBTR and DBTD1–DBTD6 are depicted in Figure S1.

Due to the addition of six, seven, and eight aniline monomers in DBTD4–DBTD6, the band gap is further decreased (2.196–2.131 eV). DBTD6 has the lowest band gap among all of the studied species due to an increase in resonance and conjugation, which is attributed to the addition of eight aniline π-linkers. The ascending order of the HOMO–LUMO energy gap is as follows: DBTD6 > DBTD5 > DBTD4 > DBTD3 > DBTD2 > DBTD1 > DBTDR. This pattern shows that the continuous addition of aniline would be influential in achieving remarkable NLO behavior.

To support the above calculations, we also studied the FMO diagrams to realize the charge-transfer processes resulting from the density distribution among the ground and excited states. In DBTDR, the electronic cloud of HOMO and LUMO is primarily located throughout the molecule. However, in DBTD1–DBTD6, the majority of the charge density for HOMO is focused above the π-spacer (π₁) and donor (D₂); only a small amount of it lies on the donor (D₁), while for LUMO, a greater quantity of charge has existed on the π-spacer (π₂). The same phenomenon of ICT between higher orbitals is shown in Figure S1. This electronic charge reinforcement indicates that all of the designed molecules are competent NLO active compounds.

Absorption Analysis

To evaluate the optical properties, UV–vis absorption spectra of DBTR and DBTD1–DBTD6 are computed in the gaseous and solvent phases. The maximum absorption wavelength (λ_max), excitation energy (E), oscillator strength (f_os), and molecular orbital (MO) assistances of DBTR and DBTD1–DBTD6 are shown in Tables S9–S22, and their spectral details are depicted in Figure 3. Additionally, six-state transitions of DBTR and DBTD1–DBTD6 are shown in Tables S9–S22 in the solvent and gaseous phases. It is observed that enhanced conjugation in addition to an electron-withdrawing peripheral unit displays the greatest bathochromic shift in the UV–visible spectrum.^45,46 Our designed species having A−π₁–D₁–π₂–D₂ configuration and extended π-conjugation exhibit a wide range of absorption wavelengths.

Figure 3.

UV–vis absorption spectra of investigated molecules DBTR and DBTD1–DBTD6.

Tables S9–S22 display that the computed values of λ_max for DBTR and DBTD1–DBTD6 are found in the range of 485.641–593.425 nm in the gaseous phase and 508.945–630.578 nm in the solvent phase (chloroform). DBTD5 has the highest λ_max at 593.425 and 630.578 nm with excitation energies of 2.089 and 1.966 eV in the gaseous phase and chloroform, respectively. The highest λ_max is due to the presence of seven aniline π-linkers, which boost the conjugation as well as lower the band gap sandwiched between the ground and excited states and give rise to a bathochromic shift resulting in better optical properties. DBTR demonstrates the lowest λ_max values at 485.641 and 508.945 nm with 2.553 and 2.436 eV excitation energies in gas and chloroform, respectively. The decreasing order of λ_max values in the gas phase is DBTD5 > DBTD6 > DBTD4 > DBTD3 > DBTD2 > DBTD1 > DBTR, with values of 593.425 > 584.638 > 577.584 > 575.012 > 558.840 > 533.931 > 485.641 nm. Likewise, the declining trend of λ_max values in chloroform is DBTD5 > DBTD6 > DBTD3 > DBTD4 > DBTD2 > DBTD1 > DBTR with values of 630.578 > 626.246 > 616.745 > 615.642 > 591.274 > 569.990 > 508.945 nm. To summarize the entire discussion, these compounds are excellent NLO materials for use in optoelectronics due to their high absorption wavelength and high charge transferability.

Global Reactivity Parameters (GRPs)

Global reactivity parameters (GRPs) are used to accurately determine stability, chemical reactivity, and several other factors.^47,54−56 Using ΔE data, determined from FMOs, the GRPs envisage the chemical potential (μ), ionization potential (IP), electron affinity (EA), global softness (σ), electronegativity (X), global hardness (η), and electrophilicity index (ω) of the examined species. These values are calculated by using eqs 1–7⁴⁸⁻⁵² and results are tabulated in Table 2.

1

2

3

4

5

6

7

Table 2. Global Reactivity Descriptors of DBTR and DBTD1–DBTD6^a.

compounds	IP	EA	X	η	μ	ω	σ
DBTR	5.937	2.867	4.402	1.535	–4.402	6.311	0.325
DBTD1	5.177	2.680	3.929	1.249	–3.928	6.180	0.400
DBTD2	5.041	2.682	3.862	1.179	–3.861	6.328	0.423
DBTD3	4.897	2.675	3.786	1.111	–3.786	6.450	0.450
DBTD4	4.866	2.670	3.768	1.098	–3.768	6.465	0.455
DBTD5	4.814	2.676	3.745	1.069	–3.745	6.559	0.467
DBTD6	4.797	2.666	3.732	1.066	–3.731	6.534	0.469

^aUnits are in eV.

Ionization potential (IP) and electron affinity (EA) measurements can be used to quantify an object’s capacity to donate electrons. These characteristics, which are closely connected to the energies of HOMO and LUMO, are used to define the electron-accepting capacity of the molecule under investigation. The compounds with higher values of these parameters are considered kinetically more stable and less reactive.^53,54 The chemical (μ) and hardness (η) factors have a direct impact on the energy gap. The negative results of μ demonstrate that the species under investigation are stable enough. In the field of experimental study, particularly in the biological activity of chemicals, these encouraging results may be crucial.^55,56 According to Table 2, the reference chemical outperforms all of the derivatives in terms of electron affinity, electronegativity, and electrophilicity. The donor moiety effectively transfers the electronic charge density to the acceptor since DBTR has the maximum IP value (5.937 eV) among all of the described compounds, whereas DBTD1–DBTD6 have the lowest IP values. The descending order of IP of all of the examined species is DBTR > DBTD1 > DBTD2 > DBTD3 > DBTD4 > DBTD5 > DBTD6. Furthermore, the abovementioned electronegativity values are found to be higher as compared to the electron affinity values. The global hardness values of the derivatives are obtained at a higher level (1.535–1.066 eV) than global softness (0.325–0.469 eV). Interestingly, the highest value of softness is illustrated by DBTD6 (0.469 eV), and it is considered to be more polarizable than the other chromophores. Thus, all of the evidence designates that DBTD6 would depict substantial NLO properties.

Natural Bonding Orbital (NBO)

NBO analysis is one of the most precise methods for determining electronic charge transfer from the valence band to the conduction band as well as bond interaction and hyperconjugation interaction.^57,58 To study charge transmission in DBTR and DBTD1–DBTD6, NBO analysis is performed. The π-spacer is employed to transfer charge from a fully occupied donor to an acceptor. By using the second-order perturbation approach, the delocalization of electrons is determined; however, for every donor (i) to acceptor (j) transition, the stabilization energy E⁽²⁾ is accomplished by delocalization i → j and is calculated by using eq 8.

8

Equation 8 describes q_i as the donor occupancy, F(i, j) represents the off-diagonal NBO Fock matrix elements, and E_j and E_i denote the diagonal elements.⁵⁹ The higher the stabilization energy, the greater the interaction between donor and acceptor species.^60,61 The results of NBOs for DBTR and DBTD1–DBTD6 are shown in Tables S23–S29.

Overlapping of orbitals results in various hyperconjugative interactions such as σ → σ*, π → π*, LP → π*, and LP → σ* (Tables S23–S29). The most obvious transitions are from π → π* and the less significant are LP → π* and LP → σ* and the least dominant are σ → σ*. It is vindicated that the topmost values of π → π* transition of the DBTDR, DBTD1, and DBTD2 occur at 24.62, 40.33, and 28.63 kcal mol^–1 for π(C38–C40) → π*(C44–C45), π(C1–C2) → π*(C3–C4), and π(C5–C6) → π*(C3–C4), respectively. The bottommost values of stabilization energies are detected as 0.67, 0.77, and 0.52 kcal mol^–1 for reference (DBTDR) and computed compounds (DBTD1 and DBTD2) for π(C49–O63) → π*(C49–O63), π(C80–C82) → π*(C76–C78), and π(C5–C6) → π*(C5–C6), respectively.

The highest values of stabilization energies for σ → σ* occur as 10.8, 273.77, and 10.86 kcal mol^–1 of σ(C44–H46) → σ*(C45–S47), σ(C1–C2) → σ*(C1–C6), and σ(N97–C102) → σ*(C98–H99) for DBTR, DBTD1, and DBTD2, respectively, and the lowest values of the same kind of transition occur as 0.5, 0.7, and 0.51 kcal mol^–1 of σ(C44–H46) → σ*(C45–C48), σ(C90–H93) → σ*(C82–N85), and σ(N97–C102) → σ*(C98–H99), respectively. Furthermore, the highest values of LP → π* are calculated as 49.37, 0.69, and 77.15 kcal mol^–1 of LP(N51) → π*(C54–S65), LP(S30) → π*(C28–C29), and LP(N40) → π*(C41–S43), and the highest values for LP → σ* transition observed as 25.87, 0.7, and 30.86 kcal mol^–1 of LP(O63) → σ*(C49–N51), LP(S30) → σ*(C28–C29), and LP(O42) → σ*(C39–N40) for the reference and designed compounds (DBTD1 and DBTD2), respectively.

In the computed compounds DBTD3, DBTD4, DBTD5, and DBTD6, the topmost values of stabilization energies of π → π* interaction occur as 29.19, 29.26, 326.86, and 323.24 kcal mol^–1 of π(C5–C6) → π*(C3–C4), π(C5–C6) → π*(C3–C4), π(C125–C126) → π*(C128–C132), and π(C137–C138) → π*(C140–C144). Moreover, the bottommost values of the same transition are observed as 0.5, 0.51, 0.55, and 0.51 kcal mol^–1 of π(C3–C4) → π*(C3–C4), π(C3–C4) → π*(C3–C4), π(C135–C137) → π*(C135–C137), and π(C3–C4) → π*(C3–C4), respectively. Many other kinds of electronic transitions are defined in the supplementary data (Tables S23–S29).

For the least significant σ → σ* transition, the highest values of stabilization energies for DBTD3–DBTD6 are 10.88, 10.91, 8.32, and 10.89 kcal mol^–1 for σ(C35–H37) → σ*(C36–S38), σ(C35–H37) → σ*(C36–S38), σ(C35–H37) → σ*(S30–C33), and σ(C35–H37) → σ*(C36–S38), whereas the lowest values of the same kind of transition are detected as 0.51, 0.5, 0.51, and 0.52 kcal mol^–1 of σ(N121–C122) → σ*(C126–H127), σ(C19–C24) → σ*(C24–H26), σ(C113–C114) → σ*(C108–N113), and σ(C77–C79) → σ*(C72–N75), accordingly.

The maximum values of slightly significant transition LP → π* occur as 77.17, 77.16, 77.22, and 77.23 kcal mol^–1 of LP(N40) → π*(C41–S43), LP(N40) → π*(C41–S43), LP(N40) → π*(C41–S43), and LP(N40) → π*(C41–S43) for DBTD3–DBTD6, accordingly (Tables S23–S29). For LP → σ* transition, the observed values of energies are 30.88, 30.85, 30.86, and 30.86 kcal mol^–1 of LP(O42) → σ*(C39–N40), LP(O42) → σ*(C39–N40), LP(O42) → σ*(C39–N40), and LP(O42) → σ*(C39–N40) for DBTD3–DBTD6, correspondingly. NBO investigation predicts that strong charge transfer and hyperconjugation perform a significant role in stabilizing the designed chromophores in addition to enhancing NLO efficiency.

Natural Population Analysis (NPA) and Molecular Electrostatic Potential (MEP)

Mulliken charges are essential in the quantum chemical simulation of the entitled chromophores. The chemical reactivity, dipole moment, and electromagnetic spectra are directly linked to the atomic charges of compounds as mentioned in the literature.⁶² For a better understanding of chemical systems, it is essential to understand the atomic charge distribution over the whole chromophore. Moreover, MEP analysis also investigates the charge sites within the compound. The different colors on the MEP surface represent different electrostatic potential values; for example, the red color in the MEP map represents a negative charge area, whereas the green and blue colors represent a positive charge area. The escalating trend of potential is red < orange < yellow < green < blue. The electrophile mostly attacks on the maximum negative area, whereas the nucleophilic attack most likely occurs on the positive region. MEP epitomizes the complete electronic and nuclear charge dissemination of a molecule and is very helpful to analyze the reactive nature of the molecule. The Mulliken charge distribution of DBTR and DBTD1–DBTD6 is displayed in Figure S2. The Mulliken population analysis depicts the imbalanced distribution of atomic charges over the whole molecule because of sulfur and nitrogen atoms. The unequal distribution of charges also has a significant influence on intermolecular and intramolecular interactions. Furthermore, it is also observed that the positive charges are distributed above the hydrogen atoms and negative charges are primarily located on the carbon atoms in all of the examined molecules. Consequently, sulfur atoms have a positive charge, whereas nitrogen atoms have a negative charge. The MEP analysis of DBTR and DBTD1–DBTD6 is accomplished to elucidate the chemical reactivity of compounds (Figure S5). We noticed that the enormous negative potential is dispersed on the nitrogen, sulfur, and oxygen atoms in all of the moieties. The comprehensive delocalization of electrons over the structure is verified by the predominance of green color on the compounds. The nucleophilic and electrophilic positions deliver evidence about the zone from where the molecule has inter or intramolecular interactions. Hence, it is shown that the molecules have a higher shift in charge density, signifying that these designed moieties are more appropriate for promising charge transformation reactions.

Transition Density Matrix (TDM)

TDM analysis is considered an excellent tool for the measurement and transmission of electronic density in the excited state. In any molecular system, the TDM analysis presents 3-D heat maps that illustrate the scattering of charge carriers and permit one to detect their coherence as well as delocalization.⁶³ TDM heat maps for absorption and emission from S₀ to S₁ state of entitled compounds (DBTR–DBTD6) are evaluated in the vacuum and shown in Figure 4. It helps to study the donor–acceptor interaction in the excited state and localization of electron holes. The hydrogen atoms are excluded during computation because of their extremely small contribution to transition. The reference molecule is split into three parts, i.e., A, π-spacer, and D, while the derivatives are divided into five fragments, i.e., A₁, π₁, D₁, π₂, and D₂, to draw the TDM graphs. The π-linker serves as a path for charge transfer by providing interactions between donor and acceptor assemblies. The TDM pictographs illustrate that in all of the entitled molecules, there is a good diagonal transference of charge coherence from the donor to the acceptor via π-spacer.

Figure 4.

TDM heat maps of DBTR and DBTD1–DBTD6.

Binding Energy (E_b)

Binding energy (E_b) is the most accurate way to check out the optoelectronic features and exciton dissociation potential. It is the difference between the E_HOMO/E_LUMO band gap (E_L–H) and the minimum energy that is needed for the first excitation (E_opt).⁶⁴ The E_b of examined molecules is computed by utilizing eq 9.

9

In the above equation, E_b represents the binding energy, E_L–H is the energy difference, and E_opt describes the energy required for the first excitation, while the electron and hole pair is generated. Theoretically calculated binding energies of DBTR and DBTD1–DBTD6 are shown in Table 3.

Table 3. Calculated E_L–H, First Singlet Excitation Energy (E_opt), and Binding Energy (E_b)^a.

compounds	EL–H	Eopt	Eb
DBTR	3.070	2.436	0.634
DBTD1	2.497	2.175	0.322
DBTD2	2.359	2.097	0.262
DBTD3	2.222	2.010	0.212
DBTD4	2.196	2.014	0.182
DBTD5	2.138	1.966	0.172
DBTD6	2.131	1.980	0.151

^aUnits in eV.

The binding energy of DBTR is 0.634 eV, whereas the E_b values of designed compounds (DBTD1–DBTD6) are 0.322, 0.262, 0.212, 0.182, 0.172, and 0.151 eV, respectively, which are lower than the reference molecule. A gradual decrease in binding energy values is observed among all of the investigated molecules. The reducing order of E_b of the studied compounds is DBTR > DBTD1 > DBTD2 > DBTD3 > DBTD4 > DBTD5 > DBTD6. It has been discovered that compounds with an E_b value of 1.9 eV are the best candidates for optical activity. Amusingly, all of the designed derivatives have a lower value of E_b than 1.9 eV and were found to be suitable for the optical activity and various other NLO applications.

Nonlinear Optics (NLO)

Significant research is being carried out in nonlinear optics due to its broad range of applications in optoelectronics and telecommunications.⁶⁵⁻⁶⁷ Owing to their synthetic flexibility and large hyperpolarizability, organic molecules comprising donor and acceptor moieties with a π-conjugative system are widely investigated in comparison to inorganic materials.⁶⁸ The computational and experimental fields are granting multidisciplinary activities for the development of NLO active species owing to their optoelectronic modulation, optical signal processing, and superior data rates.⁶⁹ Optical analyses such as linear polarizability (α) and nonlinear response (second- and third-order polarizability (β and γ)) of the designed chromophores are determined through electronic characteristics to assess the impact of different π-linkers. The outcomes of μ, ⟨α⟩, β_tot, and γ_tot were computed at the aforesaid basis set and level of DFT, and the main results are shown in Table 4, while their contributing tensors are tabulated in Tables S30–S33.

Table 4. Average Polarizability ⟨α⟩, Dipole Moment (μ), First Hyperpolarizability (β_tot), Second-Order Hyperpolarizability (γ_tot), and Major Donating Tensors (esu) for (DBTR and DBTD1–DBTD6) Molecules in esu.

compounds	μtot	⟨α⟩ × 10–22	βtot × 10–29	γtot × 10–32
DBTR	7.5202	1.446	0.072	0.734
DBTD1	11.130	1.502	0.903	0.896
DBTD2	9.630	1.678	0.936	1.037
DBTD3	11.350	2.019	1.019	1.116
DBTD4	11.401	2.194	1.008	1.122
DBTD5	12.597	2.378	1.140	1.331
DBTD6	12.855	2.533	0.997	1.121

The dipole moment is observed due to the electronegativity (E.N) difference and is directly associated with it, i.e., the larger the E.N difference, the greater would be the dipole moment.⁷⁰ Moreover, the polarity of the molecule also influences dipole moment by escalating their nonlinear values.⁷¹ The data shown in Table S32 reveals that the dipole moment is more dominant along the x-axis in all of the computed molecules. The magnitude of μ_xx tensor is found to be the highest in DBTD6, which is 11.888 D (Table S32). The decreasing order of μ_tot for the studied molecules is DBTD6 > DBTD5 > DBTD4 > DBTD3 > DBTD1 > DBTD2 > DBTR. The values of ⟨α⟩ are used to describe the linear response. The observed ⟨α⟩ values of DBTR and DBTD1–DBTD6 are 1.446 × 10^–22, 1.502 × 10^–22, 1.678 × 10^–22, 2.019 × 10^–22, 2.194 × 10^–22, 2.378 × 10^–22, and 2.533 × 10^–22 esu, respectively (Tables S31 and 4). The declining order of ⟨α⟩ of all of the computed species is observed as DBTD6 > DBTD5 > DBTD4 > DBTD3 > DBTD2 > DBTD1 > DBTR. Like μ_tot, the highest value of α_tot is noticed in DBTD6, which is due to the increase in conjugation.

For second hyperpolarizability, the main contribution to β_tot is due to β_xxx tensor with a magnitude of 9.658 × 10^–28 esu in DBTD5, which indicates that a significant amount of charge transfer is observed from donor to acceptor via π-bridge along the x-axis (Table S30). The highest computed value of β_tot is noted in DBTD5, which is 1.140 × 10^–27 esu and is much greater than the urea molecule (β for urea is 0.3728 × 10^–30 esu). The remarkably higher value of β_tot of DBTD5 might be due to the good donor moiety, which enhances the push–pull mechanism and the seven aniline π-linkers, which have an eminent effect on conjugation. γ_tot is one of the main factors used to estimate the NLO response. Among all of the computed molecules, the largest value of γ_tot is noted in DBTD5, which is 1.331 × 10^–32 esu. γ_x tensor is prominent and depicts a larger value than all of the other tensor components (Table S33). From the above discussion, it can be summarized that the x-axis mainly contributes to intramolecular charge transfer more than other axes, and all of the investigated compounds exhibit greater potential for NLO applications with higher hyperpolarizability values.

Conclusions

In this study, we explored NLO characteristics of hypothetically designed compounds (DBTD1–DBTD6) from DBTR to discover highly competent NLO material. The effect of changing the π-linker and donor was noticed for NLO response, and the outcomes illustrated that it has a significant influence over A−π₁–D₁–π₂–D₂ architecture. Interestingly, a reduced energy difference was noticed in the range of 3.070–2.131 eV (DBTD1–DBTD6) with a wider absorption spectrum than the reference. The lowest value of the band gap was noted in DBTD6, which is 2.131 eV. The GRP data disclosed that increased conjugation in chromophores gives extraordinary stability to all of the studied compounds, whereas the highest softness value was seen in DBTD6. Furthermore, DBTD5 exhibits a bathochromic shift with the highest λ_max values of 593.425 and 630.578 nm along with 2.089 and 1.966 eV transition energy values in both gaseous and solvent phases, respectively. The lowest binding energy value of 0.151 eV in DBTD6 reveals that the molecule has the highest power conversion efficiency (PCE). Moreover, the NBO study exposes that the most prominent transition along with the largest value of stabilization energy (326.86 kcal mol^–1) was observed in DBTD5. All of the titled derivatives exhibit a greater dipole moment (μ = 11.130–12.855 D) than the reference compound, which shows their better polarizability and resulted in a fascinating NLO response. A remarkable β_tot and ⟨γ⟩ values of 1.140 × 10^–27 and 1.331 × 10^–32 esu, correspondingly, were noted in DBTD5, which demonstrated that it exhibits auspicious second- and third-order NLO properties. Thus, it can be summarized that our work would give valuable insight for experimentalists to discover these alluring NLO materials.

Computational Procedures

Density functional theory (DFT) and time-dependent density functional theory (TD-DFT) analyses were accomplished to acquire the absorption spectrum, electronic, and NLO characteristics of DBTR and DBTD1–DBTD6. Gaussian 09 program⁷² was utilized to perform the quantum chemical calculations at the M06/6-311G(d,p) level of theory,^73,74 and the results were visualized by utilizing the GaussView 6.0 program.⁷⁵ For UV–visible and FMO analyses, the TD-DFT approach was employed to evaluate the electronic transitions and compute the energy gap between HOMO and LUMO. The NBO, FMO, GRP, MEP, NPA, NLO, and TDM analyses were conducted at the aforementioned level of theory in solvent (chloroform) media. Moreover, for the elucidation of output results, ChemCraft,⁷⁶ Origin 8.0,⁷⁷ Avogadro,⁷⁸ and Multiwfn 3.7 program⁷⁹ packages were employed. The dipole moment was calculated from eq 10.⁸⁰

10

Average linear polarizability ⟨a⟩ was evaluated using eq 11.⁸¹

11

The magnitude of the first hyperpolarizability was measured by utilizing eq 12.⁸²

12

Moreover, the values of second hyperpolarizability ⟨γ⟩ were estimated by using eq 13.⁸³

13

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsomega.3c01472.

• Cartesian coordinates of DBTR and DBTD1–DBTD6; calculated energy (E) and energy gap (ΔE) of entitled compounds; NBO and UV–vis data (wavelength, excitation energies, and oscillator strengths) of investigated compounds; FMOs of DBTR and DBTD1–DBTD6; dipole moment, dipole polarizability, and IUPAC names of the studied compounds; and NLO of reported chromophores was calculated using the M06/6-31G (d,p) method. (PDF)

The authors declare no competing financial interest.