Effect of different end-capped donor moieties on non-fullerenes based non-covalently fused-ring derivatives for achieving high-performance NLO properties

A series of derivatives (DOCD2–DOCD6) with D–π–A configuration was designed by substituting various efficient donor moieties via the structural tailoring of o-DOC6-2F. Quantum-chemical approaches were used to analyze the optoelectronic properties of the designed chromophores. Particularly, M06/6-311G(d,p) functional was employed to investigate the non-linear optical (NLO) response (linear polarizability ⟨α⟩, first (βtot) and second (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\upgamma$$\end{document}γtot) order hyperpolarizabilities) of the designed derivatives. A variety of analyses such as frontier molecular orbital (FMO), absorption spectra, transition density matrix (TDMs), density of states (DOS), natural bond orbital (NBO) and global reactivity parameters (GRPs) were employed to explore the optoelectronic response of aforementioned chromophores. FMO investigation revealed that DOCD2 showed the least energy gap (1.657 eV) among all the compounds with an excellent transference of charge towards the acceptor from the donor. Further, DOS pictographs and TDMs heat maps also supported FMO results, corroborating the presence of charge separation states along with efficient charge transitions. NBO analysis showed that π-linker and donors possessed positive charges while acceptors retained negative charges confirming the D–π–A architecture of the studied compounds. The λmax values of designed chromophores (659.070–717.875 nm) were found to have broader spectra. The GRPs were also examined utilizing energy band gaps of EHOMO and ELUMO for the entitled compounds. Among all the derivatives, DOCD2 showed the highest values of βtot (7.184 × 10–27 esu) and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\upgamma$$\end{document}γtot (1.676 × 10–31 esu), in coherence with the reduced band gap (1.657 eV), indicating future potentiality for NLO materials.

Computational procedure. The molecular geometries were optimized at ground state S 0 without any symmetry restrictions using the M06 25 functional along with 6-311G(d,p) basis set to perform all the computational calculations. The software employed for this purpose was Gaussian 09 26 system from the lab facilities provided by Dr. Ataualpa Albert Carmo Braga. The FMOs diagrams were achieved using Avogadro software 27 which helped to show the highest occupied and the lowest unoccupied molecular orbitals along with their energies. Another important analysis was the NBO study for determining the stabilization pattern of the studied compounds which was performed with NBO software package 3.1 28,29 . The UV-Vis spectral analysis was performed using TD-DFT method at an aforesaid level employing the Gauss Sum 30 and Origin 31 software programs. NLO properties of entitled chromophores were also examined at the aforementioned functional. The Eq. (1) was used for β tot .
The other nonlinear parameters like linear polarizability < α > 32 and second-hyper polarizability γ tot were also calculated with the help of the following Eqs. (2) and (3).
Frontier molecular orbital (FMO) analysis. The study of the electronic structure of the chromophores provided by the FMOs analysis plays a significant role in determining their non-linear optical properties 36 . The quantum orbitals entitled as HOMO and LUMO unveil charge transfer efficiency from the higher to lower levels in a molecule 37 . The HOMO is known as the electron donor orbital while, the LUMO is at a lower energy level, regarded as the electron acceptor molecular orbital 38 . The FMO energy gap is considered as a useful tool in deducing the dynamic stability and chemical reactivity of a substance 1,39-45 . Table 1 manifests the energy band gap for all the studied compounds which is obtained as the difference between HOMO and LUMO energy values (E LUMO − E HOMO ).
In order to interpret the chemical nature of a molecule, it is important to comprehend the movement of electrons from HOMO towards LUMO. The data of Table 1 Figure 4 shows the pictorial demonstrations of HOMOs and LUMOs of the designed compounds. Here, the negative phase of molecular orbitals is indicated by the in red shade, while the positive phase is indicated by the blue color. The band gap can simply be used to assess the polarizable nature of compounds. In this case, a smaller band gap indicates more ICT from the electron donor towards the acceptor parts within a molecule, and such compounds have high chemical polarizability. The compound DOCD2 has shown the lowest value of the HOMO-LUMO energy gap i.e. 1.657 eV, as illustrated in Table 1. This might be due to a suitable engineered donor induced in the molecule named as; N,N-dialkylaniline and shows reasonable electron donating tendency within DOCD2 (Fig. 1).
The compound DOCD3 revealed slightly higher band gap than DOCD2 (1.787 eV) due to incorporated indoline as a donor part. Furthermore, the other compounds (DOCD4, DOCD5 and DOCD6) also demonstrate significantly higher energy band gaps than DOCD2 i.e. 2.065, 2.116 and 2.122 eV. The donor species accompanied by these derivatives are carbozole, phenothiazine and phenoxazine, respectively. The orbital energy gap in all the series of derivatives are arranged in ascending order as: DOCD2 ˂ DOCD3 ˂ DOCD4 ˂ DOCD5 ˂ DOC D6˂DOCR1 (see Table 1). Concluding the above discussion, the derivative coded DOCD2 is seemed to be the most polarizable designed molecule in the series.
Moreover, the overall results obtained are interesting meeting our expectations as all the designed derivatives have shown lower band gaps than the reference compound. It is inferred that these derivatives have a bathochromic shift as compared to the fused ring electron acceptor molecule (DOCR1). Further, from Fig. 4, excellent charge transference from donor to acceptor via π-bridge is done. Hence, our engineered molecules may be appealing to high-performance NLO material.
Density of states (DOS) analysis. The DOS plots are used for elucidating results obtained from FMO analysis upon examining the role of donor groups in the designed molecules (DOCR1 and DOCD2-DOCD6). For this purpose, we divided our compounds into acceptor, donor and π-spacer, demonstrated by red, blue and green colored line graph, respectively (Fig. 5). In DOS pictographs, the HOMO represents the valence band exhibiting negative values while the positive values are depicted by the conduction band (LUMO) 46,47 . Moreover, it also displays charge density on the acceptor, donor and π-spacer fragments 48 . In DOCR1, the electronic charge density at HOMO and LUMO is distributed across the core unit (π-spacer). Utilization of different donor motifs alter the arrangement of electronic charge on MO that are explained through DOS percentages on HOMO and LUMO 46 . For derivatives DOCD2-DOCD6, the charge density for HOMO is mainly distributed over donor and significantly on the π-linker. In LUMO, it is prominently present over the the π-spacer motif and slightly on the acceptor region. The percentages of electronic distribution on the HOMO for acceptor (A) are 10  Absorption analysis. TD-DFT computations were performed via M06/6-311G(d,p) combination to comprehend the absorption spectra for the excited states of DOCR1 and DOCD2-DOCD6. Data concerning charge transfer probability, configurations leading to transition and the nature of electronic transition are elucidated by the UV-Vis spectroscopy 41,49,50 . As reported by the Franck-condon principle, vertical excitation is associated with the highest absorption peak (λ max ) in the spectrum. From the aforementioned computations, permissible   51 . Besides, effects on molecular spectra of the computed compounds by donor and acceptor moieties are also evaluated. The λ max of our investigated compounds reveals their absorbance in the visible region of the electromagnetic spectrum as shown in Table 2. Figure 6 represents the simulated absorption spectra of the studied derivatives with an absorption range of 700.792 to 717.88 nm (DOCD4-DOCD6) higher than the λ max of DOCR1 i.e. 683.45 nm. The absorption spectrum of reference chromophore (λ max= 683.447 nm) exhibited good harmony with experimental results (λ max= 683 nm) that supports the suitable selection of DFT functional 23 . However, derivatives DOCD2 and DOCD3 reveal 1.023 and 1.036 times less absorption value than that of DOCR1 (667.730 and 659.070 nm, respectively). The λ max values ( Table 2) are greatly influenced by donor moieties in the structure owing to the push-pull configuration in the proposed NLO compounds. The highest absorption peak of reference (DOCR1) is 683.447 nm with 1.814 eV transition energy and f os of 3.394, revealing 92% contributions of molecular orbitals from HOMO to LUMO. On introducing the donor (N-(4-(dimethylamino)phenyl)-N,N-dimethyl-N-phenylbenzene-1,4-diamine) in DOCD2 has decreased its λ max at 667.730 nm with transition energy of 1.857 eV and 1.552 f os . In this case. the major molecular orbitals contributions in this case are recorded as 84% for HOMO-1 to LUMO. The λ max is further decreased in DOCD3 upon introducing (4-  Compound DOCD4 is remarkable and should be synthesized for use in optoelectronic devices.

Study of natural bond orbitals (NBOs).
To interpret the nucleophilic and electrophilic hyper-conjugative interactions, other bonding interactions and mode of electronic transitions, NBO analysis is the most precise technique 52 . It is an important tool to investigate intra-molecular charge delocalization and its transference from occupied orbitals (D) to unfilled orbitals (A) in D-π-A 53 framework. Table 3 shows combined data including all the possible electronic transitions, their types and the stabilization energies associated with these transitions for DOCR1 and DOCD2-DOCD6.
For evaluating the reactions involving delocalization, second-order perturbation approach is utilized. To measure the stabilization energy E (2) in every single donor (i) to acceptor (j) transition, leading i → j delocalization the formula employed is: where E (2) is the stabilization energy, E i and E j are diagonal element orbital energies, q i is the donor-orbital occupancy and F i,j is the Fock matrix element between the natural bonding orbitals of the entire structure 54 . Hyper-conjugation occurs due to the overlapping of the following orbitals: σ → σ*, π → π*, LP → σ* and LP → π. The π-conjugated systems like our designed D-π-A derivatives could be justified from their π → π* transitions credited as the most significant NLO materials. The other type of allowed transitions are feeble such as σ → σ* on account of weaker interactions between electron-rich donor and electron-deficient acceptor parts. The major values of these transitions are presented in Table 3 while, the detailed analysis is recorded in the supplementary information part (Tables S1-S6). In DOCR1, the highest value of stabilization energy in case of significant π → π* transitions is revealed at 48.87 kcal mol −1 exhibited by π (C23-C32) → π*(C21-S30). While, the slightest value is shown in π(C85-N86)→ π*(C87-N88) is 0.71 kcal mol −1 .
Global reactivity parameters (GRPs). The E HOMO and E LUMO together with the band gap can be utilized to depict the reactivity and stability of compounds to predict chemical reactivity parameters 54,55 . These include electronegativity (X) 33 , ionization potential (IP), global softness (σ), electron affinity (EA), global hardness (η) 34 , electrophilicity index (ω) 35 and chemical potential (μ). Ionization potential is the energy required to eliminate an electron from the highest occupied MO. While, the electron affinity is defined as the amount of energy liberated upon the addition of an electron to the lowest unoccupied MO 56 . The capability of an atom to attract the shared pair of electrons towards itself is its electronegativity 57 . Global reactivity parameters can be calculated using the Eqs. S1-S7 58,59 which are given in supplementary file.
It has been noticed that the stability of the compound is directly influenced by the hardness (η) while, the softness (σ) is directly related to its reactivity. Molecular stability corresponds with the µ negative integer 60

Hole-electron interaction analysis. Hole-electron interaction analysis offers a deeper understanding
of the nature of electron excitations in a molecule 61 . Multiwfn 3.8. was used to perform electron excitation analysis 62,63 . Figure S2 shows that in the reference molecule, a hole is produced at the C atom of the 5,5-dimethylcyclopenta-1,3-diene ring of the π-linker. At the same time, a significant electronic cloud can be observed over the thiophene ring (S atoms) of the π-bridge. The reason behind this could be the presence of the powerful  www.nature.com/scientificreports/ electron-withdrawing ability of the Sulphur group. Noticeably, it is observed that a hole is induced in various atoms of the π-spacer, consecutively moving towards the acceptor region, demonstrating proficient charge transference from the π-linker towards the acceptor group under the effect of the electron donating group in all the designed compounds. Further, Fig. S2 also reveals high-intensity holes at different atoms of the π-linker and charge is transferred at the acceptor region and studied maximum over the C atoms of the methylene group, which further linked with the strong electron-withdrawing cyano groups and resulted in an efficient ICT in all the derivatives (DOCD2-DOCD6). Overall, in investigated compounds (DOCR1 and DOCD2-DOCD4), the electron intensity is detected to be maximum at the electronic band compared to the hole; therefore, they seem to be electron rich materials (Fig. S2). However, DOCD5 and DOCD6 are hole-type materials because the hole intensity ratio is higher at the hole band gap in these compounds.
Transition density matrix (TDM) and binding energy (E b ) analysis. TDM is an essential tool for observing the charge transference in reference (DOCR1) and designed compounds (DOCD2-DOCD6) 51 . TDM aids in calculating the excitation of charge density, localization and delocalization of electron-hole pairs and the relation between electron-accepting and donating entities in the excited state [64][65][66] . In this work, the impact of the hydrogen (H) atom is neglected owing to its minute involvement in transitions. The TDM heat maps of every single designed entity manifest the nature of the electronic transition. The TDM outcomes of all the studied reference and derivatives are presented in Fig. 7.
To factor in the transfer of electronic charge, we distributed our studied compounds into three segments such as donor, π-spacer, and acceptor. TDM pictographs illustrate a reasonable proportion of diagonal electronic charge transference (CT) in all the designed chromophores. From comparative study of TDM heat maps of all the compounds (DOCR1 and DOCD2-DOCD6) it is observed that they exhibit almost similar behavior. TDM pictographs in S 0 -S 1 energy level (Fig. 7) confirm that electrons are significantly shifted from π-spacer to the acceptor counterparts which accelerate the transfer of electrons without any restriction. The results of TDM heat maps suggest schematic separation in the excited transition state that is significant for the production of NLO materials. The difference between electrical and optical band gap energies is called binding energy, which is a major tool to determine the optoelectronic characteristics of the designed compounds. Equation (5) is employed to estimate the binding energy of the reference and designed chromophores 67 .
In Eq. (5) E b shows the binding energy, E L−H indicates the band gap and E opt depicts the first excitation energy 6,9 . The calculated outcomes of binding energy are displayed in Table 6. Table 6 shows that all the investigated compounds show smaller binding energies (0.361-0.20 eV) than the reference DOCR1 (0.511 eV). These values could be due to the alteration in the configuration that establishes a strong push-pull alignment. Correspondingly, the exciton binding energy values of DOCD2-DOCD6 are smaller than that of DOCR1 with a comparable LUMO-HOMO energy gap sequence. This lower binding energy and smaller first excitation energy and E gap values assist the large exciton dissociation and remarkably greater charge movement with improved optoelectronic characteristics 10 . The overall descending trend of binding energies of reference and designed chromophores is: DOCR1 > DOCD5 > DOCD6 > DOCD4 > DOCD2 > DOCD3. Binding energy relates to polarizability, and those with less binding energy are considered ideal photonic compounds with outstanding NLO responses 10 . Interestingly, the lowest binding energy (− 0.20 eV) of DOCD2 owing to the high charge transport rate and ease of segregation into individual charges makes it an excellent NLO material.
Nonlinear optical (NLO) properties. Improved nonlinear optical (NLO) properties in many substances are useful for emerging applications in the growing areas of harmonic generation, electro-optic modulation, frequency blending and in communications 13,68,69 . Therefore, sufficient comprehension of NLO characteristics is necessary to design such materials. Magnitude of optical response is determined by material's electronic properties and influenced by polarizability (linear, α) and hyperpolarizability (nonlinear, β and γ , etc.) and the dipole moment (μ tot ) 52 , which is greatly influenced by the electronegativity of molecules. Computed data of dipole moment (μ tot ) for the studied compounds (DOCR1 and DOCD2-DOCD6) is available in Table S8 (calculated in Debye). The dipole moment tensor along the z-axis (μ z ) shows the major contribution towards μ tot values while, the values along the x and y-axis are small. The dipole moment values for these compounds are found in order DOCD2 > DOCD3 > DOCD4 > DOCD5 > DOCD6 > DOCR1. The derivative DOCD2 shows the highest value and is considered as the most polarized molecule.
Likewise, the linear polarizability <α> effectively describes the electronic properties of compounds along-with their polarity. The <α> values along with their major contributing factors are enlisted in Tables S7-S10 while, the major values are presented in Table 7 of the manuscript (all parameters in esu unit). The average polarizability tensor along x-axis (α x ) values are dominant among all other tensor components, indicating that <α> lie along this direction. The measurements for average polarizability confirms that average polarizability is dominant in the derivative DOCD5 (3.114 × 10 -22 esu) with α xx = 5.438 × 10 -22 esu, α yy = 2.552 × 10 -22 esu and α zz = 1.352 × 10 -22 esu as x, y and z-axis parameters, respectively. It has been noted that α xx is the major contributing factor in the overall value of <α>. It is known from literature that the energy gap between LUMO and HOMO influences the polarizability of a molecule. The molecules with small energy gap values possess significant linear polarizability.
Utilizing transfer of charge (CT) among electron-donating and extracting motifs so to reduce the band gap by designing new D-π-A framework that increases the first hyperpolarizability (β tot ) 70 . The NLO response of designed compounds is highlighted by determining their first hyperpolarizability (β tot ) values. The computed The second hyperpolarizability γ tot values for the investigated compounds were also calculated using M06 method with 6-311G (d,p) basis set are displayed in Table S10. According to the data obtained, the major contribution in γ tot values is done by the second hyperpolarizability tensor along x-axis ( γ x ) in all the entitled compounds. Compound DOCD2 (1.667 × 10 -31 esu) is found with highest γ tot value with dominant tensor γ x = 1.667 esu while the tensor along z-axis ( γ z ) displayed least contribution towards γ tot in the same compound (0.0001 × 10 -31 esu) 72 . A comparative analysis is made among the DOCR1 and DOCD2-DOCD6 and urea molecule which is used as a standard compound in order to examine the NLO response of photonic materials 73 . By comparing the NLO findings of DOCR1 and DOCD2-DOCD6 with standard, we came to know that β tot value of DOCD2 compound is found as 1.931 × 10 -56 times greater than that of urea which is equal to 0.372 × 10 -30 esu 74 . The computed statistics obtained from comparative analysis with urea highlighted that designed compounds possess appreciable NLO characteristics suggesting that they may prove to be suitable NLO materials. On attaining the maximum values of µ tot , β tot and γ tot , the compound DOCD2 is nominated as the potential NLO material in emerging NLO-related technology.

Conclusion
Herein, some unique non-fullerene ring compounds (DOCD2-DOCD6) have been designed with D-π-A architecture using the DOCR1. The central core acts as a π-spacer along with a terminal acceptor at one end, and the other end is modified with various donor moieties. Surprisingly, all the derivatives were found to have less HOMO-LUMO band gap than the reference (DOCR1) with the following increasing order: DOCD2 ˂ DOC D3 ˂ DOCD4 ˂ DOCD5 ˂ DOCD6 ˂ DOCR1. Their UV-Vis spectra also reported stronger absorption wavelengths (700.792-717.875 nm) with correspondingly lower transition energies. The binding energy (E b ) values indicated that donor moieties play a key role in decreasing these values. The compounds showed lower E b values (− 0.20 to 0.361 eV) than the reference DOCR1 (0.511 eV) which infer that less Columbic forces with enhanced coherence electron transmission were noticed in bridge and acceptor motifs. The values of <α>, β total and γ total are remarkable for designed derivatives compared to DOCR1. Interestingly, promising results are obtained in the case of DOCD2 (<α> = 2.767 × 10 -22 , β total = 7.184 × 10 -27 and γ total = 1.676 × 10 -31 esu). To conclude all our DFT computations, the effective strategies utilized in the designing lead to better entrants for NLO, which could have prospective applications in advancing the technology.

Data availability
All data generated and analyzed during this study are included in this published article and its supplementary information files.