Role of donors in triggering second order non-linear optical properties of non-fullerene FCO-2FR1 based derivatives: A theoretical perspective

Abstract

The organic compounds are known as an emerging class in the field of nonlinear optical (NLO) materials. In this paper, D–π–A configured oxygen containing organic chromophores (FD2-FD6) were designed by incorporating various donors in the chemical structure of FCO-2FR1. This work is also inspired by the feasibility of FCO-2FR1 as an efficient solar cell. Theoretical approach involving DFT functional i.e., B3LYP/6-311G(d,p) was utilized to achieve useful information regarding their electronic, structural, chemical and photonic properties. The structural modifications revealed significant electronic contribution in designing HOMOs and LUMOs for the derivatives with lowered energy gaps. The lowest HOMO-LUMO band gap obtained was 1.223 eV for FD2 compound in comparison to the reference molecule (FCO-2FR1) i.e., 2.053 eV. Moreover, the DFT findings revealed that the end-capped substituents play a key role in enhancing the NLO response of these push-pull chromophores. The UV–Vis spectra of tailored molecules revealed larger λ_max values than the reference compound. Furthermore, strong intramolecular interactions showed the highest stabilization energy (28.40 kcal mol^-1) for FD2 in the natural bond orbitals (NBOs) transitions, combined with the least binding energy (-0.432 eV). Successfully, the NLO results were favorable for the same chromophore (FD2) which showed the highest value for dipole moment (μ_tot = 20.049 D) and first hyper-polarizability (β_tot = 11.22 × 10^-27 esu). Similarly, the largest value for linear polarizability ⟨α⟩ was obtained as 2.936 × 10^-22 esu for FD3 compound. Overall, the designed compounds were calculated with greater NLO values as compared to FCO-2FR1. The current study may provoke the researchers towards designing of highly efficient NLO materials via using the suitable organic linking species.

1. Introduction

From the past few decades, the structural tailoring of advanced materials for obtaining unique non-linear optical (NLO) response has been the most interesting task in the modern research areas. The NLO materials have gained much importance in the advanced research regarding both theoretical and experimental viewpoints. These materials are extremely beneficial in the field of telecommunications [1], optical computing [2], laser technology [3], optoelectronics [4] and photonic devices [5]. Almost all NLO materials have possessed direct relation between optical properties and intensity of incident light [6]. Many schemes have been applied in designing new and improved materials that exhibit excellent NLO response [7]. These materials include; polymer framework; nanomaterials; organic and inorganic semiconductors; organometallic compounds andss molecular dyes [8,9]. Each class shows its own advantages and disadvantages regarding their practical applications for NLO response.

The development in the nonlinear optics focused on the solid inorganic materials such as LiNbO₃ and KH₂PO₄ which gradually shifted towards organic and organometallic systems due to various reasons [10]. The transition organometallic complexes also served as potential building blocks for second order NLO materials owing to their low energy and intense electronic charge transfer (CT) excitations [11]. Overtime, novel organic NLO materials have been known as valuable materials for simulation analysis due to their attractive structural features such as, fast reaction chemistry, high hyper-polarizability, low cost, higher band gap and tunable structural modulations to obtain high NLO response. Moreover, they are naturally soft, show high optical transparency and good stability in the visible region [12]. Furthermore, organic materials impart robust NLO response due to the versatility in their molecular structure owning to different functional groups and wide variety of synthetic methodologies. These diverse structural features are the reason that they are extensively being utilized in various optical applications [13] such as frequency doubling, electro-optic switching, modulation, and terahertz (THz) wave production [14].

The rapid intramolecular charge transfer (ICT) has underpinned the NLO properties in organic chromophores generated mainly due to interconnection of strong donor and acceptor moieties via the conjugated π-system [15]. A strong D–π–A chromophore can be developed by varying the length and composition of a push-pull system and evaluating the effect of donor-acceptor groups [16]. As NLO response is a property of the entire molecule, therefore the insight of molecular composition is an essential phenomenon. Among various NLO properties, linear polarizability and hyper-polarizabilities have been vital in the proper assessment of NLO response [17].

The non-fullerene based NLO materials have been developed in the recent years and are continuously gaining significant attention nowadays. The non-fullerene acceptors (NFAs) have shown several advantages over their fullerene counterparts such as; low production cost; fine tenability; easy purification; high molar extinction coefficient and strong absorption range in the visible and near infrared (NIR) regions [18]. They have possessed varying electron affinities and chemical structures over a wide range as well as efficient charge separation and small driving energies [19]. Due to these advanced features the efficiency of NFAs has increased dramatically in the recent years. Moreover, NFAs due to their π-conjugated structure provide strong charge transference at donor-acceptor interface in order to facilitate the electronic delocalization [20].

Several useful strategies have been applied in order to develop high performance NFAs such as; increasing extended conjugation; altering π-spacer and insertion of oxygen in the backbone. Among all these strategies, the insertion of oxygen has proved to be the most efficient and useful strategy [21,22]. Recently, some fascinating W-shaped molecules are developed (W1–W6) from the synthesized FCO molecule in order to gain efficient environment friendly solar materials. The toxic –CN group has been replaced with nature friendly electronegative groups (−CF₃, –SO₃H, –NO₂) in the designed chromophores. The materials have shown exceptional photo-physical and photovoltaic properties with lower band gaps as compared to the reference compound and could be efficiently utilized in the future organic solar cells (OSCs) [23].

Our present research work is greatly influenced by the above mentioned compounds and we have planned to design and present a comparative theoretical analysis regarding their electronic, photonic and nonlinear properties. In addition to this, we have also designed some unique molecular geometries from the attractive non-fullerene compound (FCO-2FR1) which have not been discussed in the past. It is noteworthy that we have also defined the role of donor species in determining the NLO response of D–π–A configuration in this research regime. FCO-2FR1 and its designed chromophores (FD2-FD6) are extensively analyzed using the most popular density functional methodology which is much better and cost effective technique than other conventional methods 24,25,26,27,28]. The DFT calculations have been used to answer many of the compelling scientific questions which could be impossible to determine via experimentation. Moreover, the method is well-suited to optimize the structures once at the initial approximation for the geometry [29].

2. Methodology

The computational calculations for all the designed derivatives were performed via Gaussian 09 program [30]. The structures were optimized without any geometrical constrain using the density functional theory (DFT) i.e., B3LYP (Becke, 3-parameter, Lee-Yang-Parr correlation functional) [31] with the basis set such as 6-311G(d,p) [32,33]. Further analysis of the optimized structures was done in order to confirm their real local minima i.e., assuring the absence of imaginary frequencies. For this benchmark study, several bulk-level electronic and optical properties were analyzed using the same DFT functional and basis set approach. These included density of states (DOS), HOMO-LUMO band gaps, natural bond orbitals (NBOs), global reactivity parameters (GRPs), UV–Visible (UV–Vis) spectroscopy, natural population analysis (NPA), transition density matrix (TDM) and one of the most significant non-linear optical study (NLO). The Gaussview 5.0 software program [34] was utilized to view the optimized geometries. The DOS investigation was performed using PyMOlyze software [35] and revealed the electronic nature of the compounds using energy band gap between HOMOs and LUMOs. Similarly, their stabilization energies were predicted from the NBOs data obtained using NBO program 5.0 [36]. Some other important software programs utilized to interpret the outcomes of various analyses were Avogadro [37], Chemcraft [38] and GaussSum [39]. The global reactivity descriptors (GRDs) included: electron affinity (EA), ionization potential (IP), electronegativity (X), global softness (σ), electrophilicity index (ω), global hardness (η) and chemical potential (μ) were calculated using Equations (1)–7). The crucial electronic assignments and oscillation frequencies of the studied compounds were examined with the help of UV–Vis spectral data using time dependent DFT (TDDFT). The dipole moment (μ_tot) [40], linear polarizability ⟨α⟩ [15] and first hyper-polarizability (β_tot) [41] values were calculated by using Equations (10)–12). The 3 × 3 tensors for the first hyper-polarizability were calculated through Gaussian suite programs.

3. Results and discussion

3.1. Chemistry of entitled chromophores

The present computational investigation is used to design and interpret promising non-fullerene organic NLO chromophores. For this purpose, we have selected a synthesized oxygen heterocyclic fused NF acceptor molecule as a parent compound (FCO–2F). It is based on the A-D-A configuration i.e., central donor moiety surrounded with similar acceptor species at both ends [42]. For the sake of convenience, we have replaced the bulky alkyl (-C₈H₁₇) groups with simple methyl (-CH₃) groups and created a new reference molecule (FCO-2FR1) as shown in Fig. 1. The acceptor part is the point of interest as it is having the highly toxic cyano (–CN) groups which must be replaced with some less toxic groups in order to achieve eco-friendly organic non-linear compounds. Moreover, from the literature survey it is cleared that fine tuning of electronic properties greatly depend upon the chemical strength of donors, acceptors and π–spacers incorporated into the structural framework [43]. Therefore, the A moiety at one end is replaced with efficient donors for acquiring D–π–A configuration. Here, the central oxygen containing core unit is playing the role of π–spacer (positively charged) and we have obtained a series of five NF-based eco-friendly NLO compounds (FD2-FD6). Fig. 2 shows the colored structures of FCO-2FR1 and FD2-FD6 to elaborate the structural differences and their optimized structures are also presented in Fig. S1. The donor moiety incorporated in FD2 compound is named as N-1-(4-(dimethylamino)phenyl)-N-4,N-4-dimethyl-N-1-phenylbenzene-1,4-diamine (DPB); in FD3 as N-phenyl-4-(1,3,3a,8b-tetrahydrocyclopenta[b]indol-4(2-H)-yl)-N-(4-(1,3,3a,8b-tetrahydrocyclopenta[b]indol-4(2-H)-yl)phenyl)aniline (TPA); in FD4 as N-(4-(9-H-carbazol-9-yl)phenyl)-4-(9-H-carbazol-9-yl)-N-phenylaniline (CPA); in FD5 as N-(4-(10-H-phenothiazin-10-yl)phenyl)-4-(10-H-phenothiazin-10-yl)-N-phenylaniline (PPA) and in FD6 as N-(4-(10-H-phenoxazin-10-yl)phenyl)-4-(10-H-phenoxazin-10-yl)-N-phenylaniline (PZA). A schematic representation of all the designed molecules is presented in Fig. 3a. Whereas, Fig. 3b represents the structure of donor species. In order to evaluate how the modification of various donors influence the NLO properties such as dipole moment (μ_tot), linear polarizability ⟨α⟩ and first-order hyper-polarizability (β_tot), the DFT/TDDFT investigation has been performed for the entitled chromophores (FCO-2FR1 and FD2-FD6).

Fig. 1.

Side-chain modification of parent molecule FCO–2F into a reference FCO-2FR1.

Fig. 2.

Structures of reference (FCO-2FR1) and designed compounds (FD2-FD6).

Fig. 3a.

Schematic representation of reference and various donors used in the designed chromophores.

Fig. 3b: The structures of various donor moieties used in the designed compounds (FD2-FD3).

3.2. Electronic properties

The frontier molecular orbitals (FMOs) examination is carried out for pristine reference (FCO-2FR1) and newly designed derivatives (FD2-FD6) along with their density of states (DOS) analysis. The FMOs are considered as remarkable method for studying the chemical stabilities, electronic transitions and molecular reactivity of organic molecules [44]. Further, the energies of the highest occupied molecular orbitals (HOMOs) and the lowest unoccupied molecular orbitals (LUMOs) of compounds are significant in determining their optical and electronic properties. Concurring to Koopman's hypothesis, HOMO energies with a negative sign explain the ionization potential, while, the LUMO energies demonstrate the electronic affinity of a system [45].

The B3LYP/6-311G(d,p) functional is utilized during FMOs energy calculations, providing a clear understanding of the E_HOMO/LUMO, representing the E_gap in electron volts (eV) for the studied compounds (see Table 1). The data obtained for higher energy levels (HOMO-1/LUMO+1 and HOMO-2/LUMO+2) are included in Table S1.

Table 1.

Calculated energy (E_HOMO/E_LUMO) and energy gap ($\Delta$E) of the entitled compounds in eV.

Compounds	EHOMO	ELUMO	Egap
FCO-2FR1	-5.688	-3.635	2.053
FD2	-4.659	-3.436	1.223
FD3	-4.754	-3.446	1.308
FD4	-5.189	-3.464	1.725
FD5	-5.239	-3.465	1.774
FD6	-5.069	-3.468	1.601

It has been known from the previous studies that compounds with lesser HOMO-LUMO energy gaps are thought to be more reactive, less stable and softer. Consequently, such compounds are considered as better NLO candidates [46]. The theoretically calculated energy values of FCO-2FR1 (E_HOMO = -5.688 and E_LUMO = -3.636 eV) are found in close agreement with the experimental results of parent compound, FCO–2F [42] (E_HOMO = -5.37 eV, E_LUMO = -3.78 eV with $\Delta$ E = 1.59 eV).

The HOMO-LUMO energy gap found in FCO-2FR1 is 2.053 eV and the doping of compound with donors increased the energy of HOMO orbitals in the derivatives (FD2-FD6). Excessive electronic flow due to structural modification caused the formation of new HOMOs and consequently, the electrons reside in them and efficiently travel towards new LUMOs.

The E_HOMO values observed for FD2-FD6 are -4.659, -4.754, -5.189, -5.239, and -5.069 eV, respectively. Similarly, E_LUMO calculated as -3.436, -3.446, -3.464, -3.465, and -3.468 eV, respectively. In comparison to FCO-2FR1, quite high HOMO energies are observed in the designed compound implying that HOMOs are formed at higher position than the reference molecule. The ultimate band gap is narrowed in all the designed molecules (FD2-FD6) allowing for a high charge transfer rate between their molecular orbitals.

The lowest energy gap value observed in the FD2 (1.223 eV) is most likely due to the efficient donor (DPB) end-capped group. In case of FD3, the energy gap is found to be smaller than FCO-2FR1, but greater than FD2 (1.308 > 1.223 eV) which might be due to the lesser resonance effect in its donor moiety (TPA). Furthermore, the lower HOMO-LUMO band gap are observed in FD6 (1.601 eV) due to the presence of heteroatom (O-atom) in its donor part (PZA) which enhances the electron transfer process and lowers the energy gap. The other compounds like FD4 and FD5 showed higher band gaps than FD6 (1.725 and 1.774 eV, respectively). The overall increasing order of HOMO-LUMO band gaps for the investigated molecules is as follows: FD2 < FD3 < FD6 < FD4 < FD5 < FCO-2FR1.

A comparative analysis of various donors determined that the most effective push-pull mechanism is found in FD2 and FD3 with DPB and TPA donors incorporated, respectively. Both the donor species are enriched in electrons for donation hence, create a strong intramolecular transfer of electrons with lesser HOMO-LUMO band gaps in D-π-A systems. On the other hand, the distinct chemical frameworks and less efficient push-pull mechanism exhibited larger band gaps in case of FD4, FD5 and FD6 having CPA, PPA and PZA donor groups, respectively.

The obtained results clearly demonstrate that the structural tailoring by introducing various electron-rich donor substituents is a suitable way to improve the NLO response. Moreover, the lesser energy gap values explained the sufficient intramolecular charge transfer (ICT) within these π-conjugated molecule which is an evidence of the NLO materials’ functionality [47].

3.3. Density of states (DOS)

The DOS outcomes corroborated the results shown in the FMOs diagrams and explain the electronic distribution in boundary molecular orbitals [48]. Fig. 4 demonstrates HOMOs and LUMOs of FCO-2FR1 and FD2-FD6 which clearly depict the electronic re-distribution pattern in the studied compounds by altering electron donors at their terminal portion. However, the HOMO-1/LUMO+1 and HOMO-2/LUMO+2 of the above mentioned compounds are also represented in Fig. S2. The electronic density in case of FCO-2FR1 at HOMO is present mostly in the central core of the molecule and minutely on the terminal acceptors (A-D-A). While, in case of LUMO, the entire molecule is covered with the electronic clouds. In FD2, FD3 and FD6 compounds, the donor region shows the clear electronic charge density at HOMO while, even distribution of charge is seen at the acceptor region and minutely at the central π–spacer in their LUMOs according to the trend (see Fig. 4). However, different distribution pattern is observed at HOMOs of other designed derivatives (FD4 and FD5). In this case, a great extent of electronic charge is also observed at central π–spacer region and minutely at the donor region, while, the same trend is followed in their LUMOs as described previously i.e., acceptor region is showing the electron density.

Fig. 4.

HOMOs and LUMOs of entitled compounds (FCO-2FR1 and FD2-FD6).

DOS pictographs are used to understand the participation of each molecular fragment in determining the electronic characteristics of the studied molecules. The interpretation was performed at the same DFT functional for FCO-2FR1 and FD2-FD6. For determining the total density of states (TDOS), we split our studied molecules into separate fragments. The FCO-2FR1 is divided into two fragments i.e., donor (D) and acceptor (A) while, the derivative compounds (FD2-FD6) are divided into three segments i.e., donor, π-spacer and acceptor. The pictographs of all the examined compounds are shown in Fig. 5.

Fig. 5.

Graphical representation of density of states for FCO-2FR1 and FD2-FD6.

Herein, the donor shows contribution as 76.7% to HOMO and 35.7% to LUMO, while contribution of acceptor is 23.3% to HOMO and 64.3% to LUMO for FCO-2FR1. However, for FD2-FD6 the participation of donor is 84.2, 86.9, 46.3, 32.8, 100% to HOMO and 0.4, 0.4, 0.3, 0.3 and 0.3% to LUMO, respectively. Similarly, π-spacer contributes 15.2, 11.9, 50.7, 63.1, 0.0% to HOMO and 33.8, 33.1, 33.4, 33.4, 33.4% to LUMO in FD2-FD6, correspondingly. Likewise, acceptor demonstrated the electronic distribution pattern as 0.7, 1.2, 3.0, 4.1, 0.0% to HOMO, while, 65.7, 66.5, 66.3, 66.3 and 66.4% to LUMO for FD2-FD6, respectively. The given data shows that in case of FCO-2FR1, FD2, FD3 and FD6 the HOMO is concentrated on donor, while, in case of FD4 and FD5, it is majorly resided over the π-spacer. Similarly, the relative density of LUMO is more intense over the acceptor region in all the studied compounds (see Fig. 5). The overall contribution pattern illustrates a considerable electronic charge variation in molecular systems which depicts that a significant amount of charge transfer takes place from the donor to acceptor region via the π-spacer.

3.4. The UV–vis analysis

In an attempt to interpret the probability of charge transfer, electronic excitation energy, maximum absorption and oscillation frequency within the studied compounds, UV–Vis spectral analysis is performed using time dependent DFT functional i.e., B3LYP/6-311G(d,p). The afore-mentioned parameters are calculated in both gas and solvent (chloroform) phases, as summarized in Table 2. While, the six lowest singlet-singlet transitions are recorded in Tables S2–S13.

Table 2.

Computed transition energies (eV), maximum absorption wavelengths (nm), oscillator strengths (f_os) and transition natures of designed compounds in solvent phase and gaseous phase.

	Systems	DFT λmax	EXP λmax	E	fos	MO contributions
Solvent Phase (Chloroform)	FCO-2FR1	711.408	703	1.743	2.176	H→L (98%)
	FD2	749.059	–	1.655	0.919	H-1→L (77%)
	FD3	752.697	–	1.647	0.904	H-1→L (68%)
	FD4	810.725	–	1.529	0.851	H→L (98%)
	FD5	792.738	–	1.564	0.974	H→L (99%)
	FD6	784.760	–	1.580	0.990	H-2→L (99%)
Gaseous Phase	FCO-2FR1	659.210	–	1.881	1.956	H→L (99%)
	FD2	542.672	–	2.285	1.029	H-3→L (69%)
	FD3	714.647	–	1.735	0.725	H-1→L (97%)
	FD4	751.738	–	1.649	0.685	H→L (99%)
	FD5	728.719	–	1.701	0.693	H-2→L (73%)
	FD6	718.749	–	1.725	0.882	H-2→L (99%)

The conductor like polarizable continuum model (CPCM) [49] is employed for calculating the absorption spectra in the chloroform solvent in order to achieve better comprehension of optical properties of systems. Moreover, the polar medium involved the π→π* and n→π* stabilization state at suitable energy level [50]. It has been mainly observed that the UV–Vis data obtained for a polar medium is highly influenced by the van der Waals interactions. More specifically, hydrogen bonding and dipole forces significantly enhance the stabilization of the first singlet transition level of systems under investigation. The greater polarity in the excited states as compared to ground level induces the electronic transitions towards longer wavelength (bathochromic shift) [51]. Table 2 clearly shows that all the compounds exhibited maximum absorption wavelengths in the visible region of electromagnetic spectrum.

The theoretical value of $\lambda$_max for FCO-2FR1 (in chloroform solvent) shows a great correspondence with experimental value of parent compound (FCO–2F) [42] i.e., 711.408 and 703 nm. Moreover, the corresponding energy of transition calculated for FCO-2FR1 is 1.743 eV, the oscillation frequency (f_os) is 2.176 and the major orbital assignment is H→L (98%). All the designed chromophores show a red-shift with higher $\lambda$_max values as compared to FCO-2FR1. The highest value is obtained for compound FD4 (810.725 nm) as compared to other derivatives. Therefore, it is regarded as a compound with the largest bathochromic shift which might be due to its unique chemical framework. The following order of UV–Vis wavelengths (nm) is seen in the compounds under analysis: FCO-2FR1 (711.408) < FD2 (749.05) < FD3 (752.697) < FD6 (784.760) < FD5 (792.738) < FD4 (810.725). Similarly, their corresponding transition energies (eV) are found in the reverse order of the wavelengths as: FCO-2FR1 (1.743) > FD2 (1.655) > FD3 (1.647) > FD6 (1.580) > FD5 (1.564) > FD4 (1.529). The oscillation frequencies are as follows: FCO-2FR1 = 2.176, FD2 = 0.919, FD3 = 0.904, FD4 = 0.851, FD5 = 0.974 and FD6 = 0.990. Among designed molecules, 99% molecular orbital transition is seen in first transition energy levels such as: H→L in case of FD5. While, in compounds FD2, FD3, FD4 and FD6, the major orbital transitions seen are: H-1→L (77%), H-1→L (68%), H→L (98%) and H-2→L (99%), accordingly.

In gaseous phase, the reference FCO-2FR1 showed the $\lambda$_max = 659.210 nm with major HOMO-LUMO contributions observed as H→L (99%) and an oscillation frequency (f_os) of 1.956. Except for FD2, all the designed compounds (FD3-FD6) exhibited higher $\lambda$_max values than FCO-2FR1 in the range of 714.647–751.738 nm. A blue-shift is seen in case of FD2 with 542.672 nm as $\lambda$_max and a higher transition energy of 2.285 eV (higher than FCO-2FR1) with an oscillation strength of 1.029. Whereas, in case of FD3, a significantly higher $\lambda$_max value is obtained as 714.647 nm and less transition energy of 1.735 eV. The frequency of oscillation in compound is calculated to be 0.725 showing major molecular orbital contributions from H-3→L as 69%. Similarly, the compound FD4 showed the highest absorption wavelength as 751.738 nm and lowest energy of transition as 1.649 eV with a least oscillation frequency of 0.685 (see Table 2). The other derivatives (FD5 and FD6) showed $\lambda$_max values as 728.719 and 718.749 nm with corresponding energies as 1.701 and 1.725 eV, respectively. The percentages of major molecular orbital contributions are observed as 73 and 99% for similar level (H-2→L) in both compounds with an oscillation frequency of 0.693 and 0.882, accordingly.

In gas phase, the maximum absorption wavelengths (λ_max) of all molecules are discovered to be in the following increasing order: FD2 < FCO-2FR1 < FD3 < FD6 < FD5 < FD4. Excitation energy is another method for measuring the efficiency of NLO material. In general, lower molecular excitation energy provides higher power conversion efficiency. The molecular transition energies are observed in the reverse order as: FD2 > FCO-2FR1 > FD3 > FD6 > FD5 > FD4. The oscillator strengths of the investigated compounds are found in the same order as the energy of transition. The UV–Vis plots in both solvent (chloroform) and gaseous phase are demonstrated in Fig. 6 (A and B, respectively).

Fig. 6.

UV–Vis plots for FCO-2FR1 and FD2-FD6 in chloroform solvent (A) and gas phase (B).

Concisely, the doping of reference compound with suitable donors resulted in clear red-shift in case of the designed compounds. The lower excitation energy and large charge transfer in molecular orbitals demonstrated that these molecules are promising candidates for best use in various NLO applications.

3.5. Global reactivity parameters (GRPs)

The malleability and stability of the studied compounds (FCO-2FR1 and FD2-FD6) are mainly predicted by working on their global reactivity parameters as defined by Koopmans’ theorem [52]. The electron donating and accepting properties of molecules in a chemical system are directly related to the ionization potential (IP) and electron affinity (EA), respectively. The other important parameter is electronegativity (X) [53] which determines the potential of a molecule to attract the electronic cloud towards itself. Moreover, parameters like IP and X play a significant role in determining the reactivity and stability patterns of the studied organic species. Furthermore, the negative values of chemical potential (μ) depict a clear picture of stability for the organic compounds which resist towards their decomposition. The electrophilicity index ($\omega$) [54] describes the energy variations in correlation with the maximum amount of electronic charge transferred. The other global reactivity descriptors including chemical hardness (η) [55,56] and softness (σ). Equations (1)–7) are used to estimate the GRPs which are mentioned here;

$$IP=-E_{\mathrm{H}\mathrm{O}\mathrm{M}\mathrm{O}}$$ (Equation 1)

$$EA=-E_{\mathrm{L}\mathrm{U}\mathrm{M}\mathrm{O}}$$ (Equation 2)

$$\mu =-\frac{\left(IP+EA\right)}{2}$$ (Equation 3)

$$X=\frac{\left[IP+EA\right]}{2}$$ (Equation 4)

$$\eta =\frac{\left(IP-EA\right)}{2}$$ (Equation 5)

$$\sigma =\frac{1}{\left(IP-EA\right)}$$ (Equation 6)

$$\omega =\frac{{\mu }^2}{2\eta }$$ (Equation 7)

The GRP values are depicted for FCO-2FR1 and FD2-FD6 and are shown in Table 3.

Table 3.

Global reactivity parameters for FCO-2FR1 and FD2-FD6 in eV.

Compounds	IP	EA	X	η	μ	ω	σ
FCO-2FR1	5.688	3.635	4.662	1.027	-4.662	10.584	0.487
FD2	4.659	3.436	4.048	0.612	-4.048	13.395	0.817
FD3	4.754	3.445	4.100	0.654	-4.100	12.851	0.765
FD4	5.189	3.464	4.327	0.863	-4.327	10.851	0.580
FD5	5.239	3.465	4.352	0.887	-4.352	10.676	0.563
FD6	5.069	3.468	4.269	0.801	-4.269	11.380	0.624

The results predict some very important facts about HOMO-LUMO band gaps and various global reactivity parameters. A close relationship is found between GRPs and energy gaps. Greater the energy band gap between HOMO and LUMO, the more is the kinetic stability of a molecule with resistance towards change in electronic configuration [57]. The enhanced stability results into harder molecules with the least reactivity. Contrarily, the compounds having small energy gaps are softer, having flexible character, greater reactivity and less kinetic and physical stability. Hence, the lesser energy gap marked suitable NLO materials with higher polarizabilities.

The stability and reactivity of investigated compounds are quantified by utilizing the energy values of their FMOs [58]. Overall, the ionization potential values for FCO-2FR1 and FD2-FD6 are observed to be larger as compared to their electron affinity values describing the better electron donating capability of molecules. Among the designed compounds, the maximum IP value is found as 5.239 eV in case of FD5, while, the minimum value is observed in FD2 compound as 4.659 eV. The decreasing order of ionization potential is observed to be: FCO-2FR1 > FD5 > FD4 > FD6 > FD3 > FD2. The highest electron affinity (EA) value is calculated as 3.468 eV in FD6, while, 3.436 eV is the least value observed in compound (FD2).

Chemical potential (μ) is another parameter to study the reactivity and stability of compounds under investigation. It varies inversely with reactivity of compounds and directly with the stability. The more negative μ values predict the more reactivity and less stability of a D-π-A system [59]. Table 3 shows the negative chemical potential for derivatives (FD2-FD6). Moreover, the calculated hardness values are presented in the following decreasing order: FCO-2FR1 > FD5 > FD4 > FD6 > FD3 > FD2, which follows exactly the same trend as followed by E_gap values. Nevertheless, the chemical hardness (η) values (in eV) are greater for FD5 (0.887) in comparison to FD2 (0.612), FD3 (0.654), FD4 (0.863) and FD6 (0.801), which certainly reflected more stability of FD5 compound as compared to the other derivatives. The order of increasing softness is as follows: FCO-2FR1 < FD5 < FD4 < FD6 < FD3 < FD2 which is the reverse of hardness order. The global electrophilicity (ω) of studied compounds are found in the following decreasing order: FD2 > FD3 > FD6 > FD4 > FD5 > FCO-2FR1.

Due to the existence of strong donor species, more electron donating tendency is found among the designed molecules. The statement is valid for the designed chromophores which have shown effective CT potential among their HOMOs and LUMOs. The compound (FD2) is predicted as the most favorable fabricated molecule among all, owing to its highest value of softness (0.817 eV) and the lowest hardness (0.612 eV) which coincide with its lowest energy gap (1.223 eV).

3.6. Natural bond orbitals (NBOs) study

NBOs investigation gives an extensive approach relating to charge density transference and intramolecular charge delocalization from filled donor (D) orbitals towards vacant acceptor (A) orbitals in the π-conjugated framework [60]. It is also efficient in elucidating local orbital interactions between bonds as well as hyper-conjugative interactions between the electrophile and nucleophile. Second order perturbation approach [61] helps in analyzing the delocalization reactions, utilizing the following Equation (8):

$$E^{\left(2\right)}=q_{\mathrm{i}}\frac{{\left(F_{\mathrm{i},\mathrm{j}}\right)}^2}{{\epsilon }_{\mathrm{j}}-{\epsilon }_{\mathrm{i}}}$$ (Equation 8)

Here, i and j corresponds to D and A motifs, respectively, E⁽²⁾ is stabilization energy following i $\to$ j delocalization. Moreover, q_i, F_i,j and ${\epsilon }_{\mathrm{j}}-{\epsilon }_{\mathrm{i}}$ are donor orbital occupancy, diagonal and off-diagonal NBO fock matrix elements [62].

Literature conveys the information about NBOs charges for individual D, π-spacer and A species that the positive charges are regarded to donor motif, negative charges to the acceptor while, π-linkers show both (positive and negative) charges based on their molecular framework. Positive charge of π-conjugated linker characterizes that they avoid electron trapping thus facilitating smooth transference of electrons. The calculation of NBO charges conveys information about the net charge transfer within the systems under investigation. Table 4 depicts the natural charges for entitled molecules (FCO-2FR1 and FD2-FD6). The calculations show that all the designed compounds including reference exhibit same trend of electronic charges. The D and π-linker possess positive charges while, the A species attain negative charges. The derivative FD2 is nominated with the most successful ICT because of the most positively charge donor (DPB) and 2-(5,6-difluoro-3-oxo-2,3-dihydro-1-H-inden-1-ylidene)malononitrile as acceptor species incorporated into its molecular structure (see Table 4). Similarly, after FD2, FD3 is nominated as a molecule with favorable CT, owing to the efficiency of utilized donor units. These results elucidate successful charge transfer from D towards A without any charge trapping in π-linker leaded to the formation of charge separation state.

Table 4.

Natural charges for donor (D), π-spacer and acceptor (A) moieties for the investigated systems.

Compounds	Donor	π-linker	Acceptor
FCO-2FR1	0.530098	–	-0.38537
FD2	0.13985	0.092451	-0.2323
FD3	0.120001	0.107683	-0.2277
FD4	0.090669	0.130653	-0.22132
FD5	0.087627	0.133047	-0.22068
FD6	0.084235	0.135728	-0.21996

Intramolecular transitions result in system's stabilization are σ $\to$ σ*, π $\to$ π*, LP $\to$ σ* and LP $\to$ π*. Moreover, the charge transference in π $\to$ π* are dominant than σ $\to$ σ* transitions. Table 5 predicts the most important selected transitions for the investigated compounds, while, the detailed NBOs values are recorded in Tables S14–S19. The interactions are among the local orbitals which included both occupied bonding and empty non-bonding orbitals.

Table 5.

Selective natural bond orbitals (NBOs) of investigated compounds (FCO-2FR1 and FD2-FD6).

Compounds	Donor(i)	Type	Acceptor(j)	Type	E(2)	F(i,j)c	E(J)E(i)b
FCO-2FR1	C21–C22	π	C24–C25	π*	27.31	0.30	0.081
	C68–N69	π	C70–N71	π*	0.79	0.45	0.017
	C24–H60	σ	S20–C22	σ*	9.82	0.71	0.075
	C74–C84	σ	C84–H85	σ*	0.57	1.03	0.022
	O2	LP(1)	C1–C6	π*	63.05	0.15	0.106
	O54	LP(2)	C26–C28	σ*	20.25	0.72	0.109
FD2	C27–C28	π	C30–C31	π*	28.40	0.29	0.082
	C32–O45	π	C30–C31	π*	3.90	0.41	0.038
	C30–H42	σ	S26–C28	σ*	9.99	0.71	0.075
	C9–C55	σ	C55–H57	σ*	0.58	1.01	0.022
	N110	LP(1)	C93–C97	π*	41.33	0.27	0.099
	O45	LP(2)	C32–C34	σ*	20.28	0.72	0.109
FD3	C27–C28	π	C30–C31	π*	28.27	0.29	0.082
	C47–N48	π	C49–N50	π*	0.80	0.45	0.017
	C30–H42	σ	S26–C28	σ*	9.97	0.71	0.075
	C124–C125	σ	C125–H132	σ*	0.50	1.01	0.02
	N110	LP(1)	C135–C136	π*	40.67	0.28	0.098
	O45	LP(2)	C32–C34	σ*	20.28	0.72	0.109
FD4	C27–C28	π	C30–C31	π*	28.08	0.29	0.082
	C49–N50	π	C47–N48	π*	0.81	0.44	0.017
	C30–H42	σ	S26–C28	σ*	9.93	0.71	0.075
	C54–C75	σ	C12–C13	σ*	0.50	1.16	0.022
	N110	LP(1)	C122–C123	π*	39.55	0.29	0.097
	O45	LP(2)	C32–C34	σ*	20.28	0.72	0.109
FD5	C27–C28	π	C30–C31	π*	28.06	0.29	0.082
	C32–O45	π	C34–C36	π*	4.40	0.40	0.041
	C30–H42	σ	S26–C28	σ*	9.92	0.71	0.075
	C143–S152	σ	C142–C143	σ*	0.50	1.21	0.022
	O52	LP(2)	C18–C19	π*	30.05	0.34	0.097
	O45	LP(2)	C32–C34	σ*	20.27	0.72	0.109
FD6	C27–C28	π	C30–C31	π*	28.05	0.29	0.081
	C49–N50	π	C47–N48	π*	0.81	0.44	0.017
	C30–H42	σ	S26–C28	σ*	9.92	0.71	0.075
	C54–C75	σ	C12–C13	σ*	0.50	1.16	0.022
	N110	LP(1)	C122–C123	π*	36.43	0.28	0.093
	O45	LP(2)	C32–C34	σ*	20.27	0.72	0.109

In FCO-2FR1, the significant values of stabilization energy (E²) obtained are 27.31, 9.82, 63.05 and 20.25 kcal mol^-1 correspond to transitions among π(C21–C22) $\to$ π*(C24–C25), σ(C24–H60) $\to$ σ*(S20–C22), LP2 (O54) $\to$ σ*(C26–C28) and LP(1)(O2) $\to$ π*(C1–C6), respectively. The lowest stabilization energies in π(C68–N69) $\to$ π*(C70–N71) and σ(C74–C84) $\to$ σ*(C84–H85) are recorded as 0.79 and 0.57 kcal mol^-1, respectively.

For derivative FD2, the highest π $\to$ π* transition energy is obtained among all the derived values for this transition i.e., 28.40 kcal mol^-1 obtained for π(C27–C28) $\to$ π*(C30–C31) transitions. The lowest value is 3.9 kcal mol^-1 for π(C32–O45) $\to$ π*(C30–C31). The feeble σ $\to$ σ* transitions also show significant values calculated as 9.99 and 0.58 kcal mol^-1 regarded as the highest and the lowest values, for σ(C30–H42) $\to$ σ*(S26–C28) and σ(C9–C55) $\to$ σ*(C55–H57), correspondingly. The transitions due to resonance involving lone pair of electrons also play an important role in determining the chemical nature and electronic transition patterns in compound. Among lone pair transitions LP1(N110) $\to$ π*(C93–C97) and LP2(O45) $\to$ σ*(C32–C34) are the most significant transitions recorded with energy values as 41.33 and 20.28 kcal mol^-1, respectively.

The stabilization energy values in case of FD3 are recorded as 28.27, 0.80, 9.97, 0.50, 40.67 and 20.28 kcal mol^-1 with relative transitions as π(C27–C28) $\to$ π*(C30–C31), π(C47–N48) $\to$ π*(C49–N50), σ(C30–H42) $\to$ σ*(S26–C28), σ(C124–C125) $\to$ σ*(C125–H132), LP1(N110) $\to$ π*(C135–C136), LP2(O45) $\to$ σ*(C32–C34), respectively. The compound FD3 is regarded as a significant chromophore and shows second highest values for π-conjugated transitions after FD2.

In FD4, the transitions like π(C27–C28) $\to$ π*(C30–C31), σ(C30–H42) $\to$ σ*(S26–C28) and LP(1)(N110) $\to$ π*(C122–C123) are obtained with the highest values as 28.08, 9.93 and 39.55 kcal mol^-1, respectively. Similarly, the smallest stabilization energy values for the above mentioned transitions in FD4 are found as 0.81, 0.50 and 20.28 kcal mol^-1 observed in due to the π(C49–N50) $\to$ π*(C47–N48), σ(C54–C75) $\to$ σ*(C12–C13) and LP(2)(O45) $\to$ σ*(C32–C34) transitions, correspondingly.

For FD5, the highest value of stabilization energy for π $\to$ π* transition energy is obtained for π(C27–C28) $\to$ π*(C30–C31) as 28.06 kcal mol^-1. Among weaker σ $\to$ σ* transitions, σ(C30–H42) $\to$ σ*(S26–C28) are the most prominent with largest value for compound i.e., 9.92 kcal mol^-1. Similarly, LP(2)(O52) $\to$ π*(C18–C19) are obtained with stabilization energy as 30.05 kcal mol^-1 is the highest lone pair transition for FD5. The lowest corresponding transitions are π(C32–O45) $\to$ π*(C34–C36), σ(C143–S152) $\to$ σ*(C142–C143) and LP(2)(O45) $\to$ σ*(C32–C34) with respective energy values as 4.4, 0.50 and 20.27 kcal mol^-1, respectively.

The FD6 is the last derivative in which, π(C27–C28) $\to$ π*(C30–C31), σ(C30–H42) $\to$ σ*(S26–C28) and LP(1)(N110) $\to$ π*(C122–C123) transitiond are recorded with highest value of E⁽²⁾ as 28.05, 9.92 and 36.43 kcal mol^-1, respectively. While, the lowest E⁽²⁾ value is recorded for the transitions like; π(C49–N50) $\to$ π*(C47–N48), σ(C54–C75) $\to$ σ*(C12–C13) and LP(2)(O45) $\to$ σ*(C32–C34) at 0.81, 0.5 and 20.27 kcal mol^-1, respectively.

It is evident from the above discussion that the NBOs results of all the studied compounds are closely related to each other. However, the highest stabilization energies are obtained for FD2 as compared to other designed compounds. This might be due to the presence of efficient end-capped donor moiety (DPB). The NBO charges also support the molecular stability of compound. Hence, it is proved that intramolecular charge transfer (ICT) and hyper-conjugation highly influence the stabilization of investigated molecules and are the main cause to their exclusive NLO properties.

3.7. Transition density matrices (TDMs)

The electronic excitation phenomena in the newly designed chromophores (FD2-FD6) are interpreted efficiently by TDM graphs and compared with the reference compound (FCO-2FR1) [63,64]. With use of the Multiwfn 3.8 program [65], we have interpreted the coherence of electronic excitations in the individual fragments of each molecule i.e., donor, π-linker and acceptor. We have neglected the effect of H-atoms due to their least contributions in the transitions of our interest. Fig. 7 displays the TDM heat maps which depict the pattern of flow of electrons in the form of colored spots. In reference compound (FCO-2FR1), an efficient diagonal electronic delocalization occurs from D towards A region. However, in the designed molecules (FD2-FD6), the charge density is most efficiently transferred in FD4 and FD5 compounds after FCO-2FR1. Whereas, the other derivatives showed minute spots of electronic charge shift in the acceptor part. Overall, most of the charge is localized in the π-spacer region in all compounds and is minutely transferred towards the acceptor region. Furthermore, a significant coherence of charge is seen in both diagonal and off-diagonal elements in the derivatives.

Fig. 7.

TDM heat maps for the entitled chromophores (FCO-2FR1 and FD2-FD6).

3.8. Exciton binding energies (E_b)

Binding energy (E_b) is a crucial factor in determining the rate of charge separation and optoelectronic properties of compound. It shows a direct relationship with energy gap and optimization energy values, while, shows an inverse relation with the exciton dissociation and charge mobilities. The lower E_b shows the higher exciton dissociation in compounds and vice-versa. It can be determined by subtracting the E_gap from the energy of optimization [66,67] and is represented by Equation (9).

$$E_{\mathrm{b}}=E_{\mathrm{L}-\mathrm{H}}-E_{\mathrm{o}\mathrm{p}\mathrm{t}}$$ (Equation 9)

Here, E_b is denoted as the binding energy, E_opt is the first excitation energy and E_L-H is energy band gap [68].

Interestingly, all the designed chromophores (FD2-FD6) exhibited lower E_b values than FCO-2FR1 (see Table 6). Moreover, they also showed lesser values than 1.9 eV and indicated higher exciton dissociation rate with larger rate of charge transfer which is essential for perfect photonic and nonlinear response [69]. The following decreasing trend of binding energy (in eV) is observed in the investigated series of compounds: FCO-2FR1 (0.309) > FD5 (0.210) > FD4 (0.196) > FD6 (0.031) > FD3 (-0.338) > FD2 (-0.432).

Table 6.

Computed binding energy (E_b) of entitled chromophores.

Compounds	EL-H	Eopt	Eb
FCO-2FR1	2.052	1.743	0.309
FD2	1.223	1.655	-0.432
FD3	1.309	1.647	-0.338
FD4	1.725	1.529	0.196
FD5	1.774	1.564	0.210
FD6	1.611	1.580	0.0310

Units in eV.

From the facts obtained via transition heat maps and associated E_b values for the series of compounds under discussion, we have come to the conclusion that proposed tailored compounds are better candidates for NLO as they showed efficient allocation of charges from donor towards acceptor moiety.

3.9. Natural population analysis (NPA)

The charge dissemination on an atom had a great impact on the dipole moment, chemical reactivity and electrostatic interaction between the atoms and molecules and many other properties of the chemical system. The natural population analysis determines the electronic charge transformation and electrostatic potential on the external surface of molecules under study [70]. The electronic charge plays a key role towards the substantial contribution in the molecular conformation and bonding patterns [71]. The effective calculation of atomic charge of the reference (FCO-2FR1) and the designed compounds (FD2-FD6) is significant for the better understanding of their molecular system [72,73].The dissemination of charges describe that the nitrogen atoms associated with oxygen in all compounds are negatively charged, while, the sulfur atoms are positively charged (see Fig. S15). Furthermore, all the hydrogen atoms are also positively charged in FCO-2FR1 and FD2-FD6 compounds. Natural population investigation shows that no inconsistency in charge distribution is found over all the hydrogen atoms. Some of the carbon atoms are negatively charged, while, some are positively charged due to its donating and accepting nature of electrons, respectively. The inclusive investigation of NBO charges revealed that the unequal distribution of charges on the designed compounds is due to the nitrogen and oxygen atoms.

3.10. Nonlinear optical properties

The nonlinear properties are associated with several high-tech applications such as telecommunication, laser frequency modulation and biomedicine for which their study is crucial both at molecular and bulk levels [74,75,76]. The electrical properties of compound determine their nonlinear characteristics such as polarizability (linear response) and hyper-polarizability (non-linear response). For this reason, both the polarizability and hyper-polarizability are assessed to estimate linear and NLO potential of materials. Generally, a linear polarizability is essential to obtain large hyperpolaizability [77]. It is also well known that NLO response is exhibited by non-centrosymmetric materials. Therefore, the electronic spatial extent is considered as a prototype of push-pull chromophores (Donor-π-Acceptor).

The organic compounds are the preferred candidates which possess substantial features which effectively deal with the light-matter interactions [78]. Moreover, the push-pull mechanisms of organic chromophores are influenced due to the presence of π–conjugation feature in compounds, generating higher magnitudes of NLO properties. The NLO properties are determined using quantum chemical methods via the parameters such as dipole moment (μ_tot) [79], linear polarizability ⟨α⟩ [80] and first hyper-polarizability (β_tot) [81]. The reported structural modifications enhanced not only the charge transference (due to lower band gaps) but also the linear and hyper-polarizability values, highly associated with NLO response properties. The μ_tot, ⟨α⟩ and β_tot are calculated for the investigated molecules (FCO-2FR1 and FD2-FD6) using Equations 10–15. Moreover, Equations (12a)-12c) shows the tensors of hyperpolarizability along three axis (x, y and z).

$$\mu ={\left({\mu }_x^2+{\mu }_y^2+{\mu }_z^2\right)}^{1/2}$$ (Equation 10)

$$⟨\alpha ⟩=1/3\left({\alpha }_{xx}+{\alpha }_{yy}+{\alpha }_{zz}\right)$$ (Equation 11)

$$\beta \_\left(\mathrm{t}\mathrm{o}\mathrm{t}\right)={({\beta }_x^2+{\beta }_y^2+{\beta }_z^2)}^1{/}^2$$ (Equation 12)

$${\beta }_x={\beta }_{xxx+}{\beta }_{xyy+}{\beta }_{xzz}$$ (Equation 12a)

$${\beta }_y={\beta }_{yxx+}{\beta }_{yyy+}{\beta }_{yzz}$$ (Equation 12b)

$${\beta }_z={\beta }_{zxx+}{\beta }_{zyy+}{\beta }_{zzz}$$ (Equation 12c)

Where, μ_tot is in Debye (D) and ⟨α⟩, β_tot are in esu.

3.10.1. Dipole polarizability

The dipole moment or dipole polarizability (u) is defined as the factor highly influenced by electronegativity difference and is obtained as a product of magnitude of charges and the distance between them. The larger electronegativity indicate the higher dipole moment values in a system [82]. Moreover, the polarity along with the dipole moment plays a key role in enhancing the nonlinear properties of a molecule [83]. The u_tot is called as the average dipole moment, while, u_x, u_y and u_z are known as the contributing tensors along x, y and z-orientations which determine the u_tot [84]. Their values are calculated in debye (D), recorded in Table S20, while, the major u_tot values are presented in the manuscript (Table 7). The extraordinary high u_tot are observed in designed derivatives (FD2-FD6) i.e., in the range of 11.175–20.049 D as compared to FCO-2FR1 with u_tot = 4.065 D. The following decreasing order is obtained in the entitled chromophores: FD2 > FD3 > FD5 > FD4 > FD6 > FCO-2FR1. The results showed that y-axis is majorly contributing in the average values of dipole moment more than x- and z-axes (see Table S20). The FD2 compound is found as the most polarizable molecule with highest u_tot = 20.049 D with contributing tensors calculated as u_x = −19.998 D, u_y = -1.393 and u_z = 0.346 D. The dipole moment of urea is considered as a standard value for comparison, recorded as 1.373 D in the literature [58]. Fortunately, our designed compounds showed much larger dipole moments than urea.

Table 7.

The computed NLO properties for FCO-2FR1 and FD2-FD6.

Systems	μtot	⟨α⟩ × 10-22	βtot × 10-27
FCO-2FR1	4.065	2.318	0.7724
FD2	20.049	2.618	11.22
FD3	19.055	2.936	8.223
FD4	12.138	2.850	4.661
FD5	12.420	2.879	4.384
FD6	11.175	2.811	4.215

3.10.2. Linear polarizability

The linear polarizability ⟨α⟩ (also known as first-order NLO response) is related with intramolecular charge transfer (ICT) which operates from D via π–linkers towards the A species. The external electrical field interacts with the excess electrons in such systems and enhance the dipole moments which in turn increase the linear polarizability and first-order hyper-polarizability [85]. Table S21 shows the ⟨α⟩ value for compounds under discussion (FCO-2FR1 and FD2-FD6) and also revealed the important 3-D tensors for polarizability. For FCO-2FR1, the ⟨α⟩ = 2.318 × 10^-22 esu which is known as the lowermost value in the recorded series of compounds. The FD3 has shown the most polarizable nature with significantly highest ⟨α⟩ = 2.936 × 10^-22 esu. The rest of the molecules (FD2, FD4, FD5 and FD6) have shown ⟨α⟩ values as 2.618 × 10^-22, 2.850 × 10^-22, 2.879 × 10^-22 and 2.811 × 10^-22 esu, respectively. Similarly, a detailed study of their related tensors (α_xx, α_yy and α_zz) predicts the ⟨α⟩ values which demonstrated that α_xx is the major contributing tensor for linear polarizability in compounds. All the entitled compounds have shown comparable values of ⟨α⟩ with the following decreasing trend: FD3 > FD5 > FD4 > FD6 > FD2 > FCO-2FR1.

3.10.3. First hyper-polarizability

The first hyper-polarizability (β_tot) is profoundly a contributing factor in calculating the NLO response of a compound [86]. It is increased in the presence of excessively strong push-pull models which take part in enhancing the molecular nonlinearity owing to the extended conjugation [87]. The values are determined which contain nine contributing tensors listed as β_xxx, β_xxy, β_xyy, β_yyy, β_xxz, β_yyz, β_xzz, β_yzz, β_zzz. The detailed hyper-polarizability results are tabulated in Table S22, whereas, the average values of β_tot are also recorded in Table 7. A linear decreasing trend is observed in the values among the investigated compounds (FD3-FD6) i.e., (FD3 = 8.223 × 10^-27, FD4 = 4.661 × 10^-27, FD5 = 4.384 × 10^-27, FD6 = 4.215 × 10^-27). Whereas, the compound (FD2) possesses the highest i.e., 11.22 × 10^-27 esu and FCO-2FR1 has shown the least β_tot value as 0.7724 × 10^-27 esu. Further, the results of β_tot are also compared with first hyper-polarizability of urea molecule (β_tot = 0.372 × 10^-30 esu) [88]. The comparison shows that FCO-2FR1 exhibited 2.076 × 10^-57 times higher β_tot than the standard urea molecule. Similarly, for FD2 (3.016 × 10^-56), FD3 (2.210 × 10^-56), FD4 (1.253 × 10^-56), FD5 (1.178 × 10^-56) and FD6 (1.133 × 10^-56) times higher values are observed.

The graphical representation further illustrates the correspondence of ⟨α⟩ and β_tot results with HOMO-LUMO energy gaps for the studied compounds (Fig. 8). The depicted NLO properties showed that the FD2 molecule possessed the highest dipole moment (20.049 D) and first hyper-polarizability values (8.223 × 10^-27 esu) and FD3 has shown the highest linear polarizability value (2.936 × 10^-22 esu). The reason might be their reduced energy gaps i.e.,1.223 and 1.308 eV, respectively. Furthermore, they possess the higher values of global softness (σ) as 0.817 and 0.765 eV, respectively which clearly depicts that the soft molecules are more polarizable than hard molecules. Thus, the investigated organic chromophores are regarded as the suitable materials with potential NLO amplitudes. Moreover, it has been observed in this study that suitable donor species could play a significant role in determining the NLO response among the π–conjugated systems.

Fig. 8.

A comparison of energy gaps with ⟨α⟩ and β_tot for entitled chromophores.

4. Conclusion

In summary, we have systematically designed new molecular entities (FD2-FD6) with D–π–A architecture from the non-fullerene acceptor molecule (FCO-2FR1). The DFT/TDDFT calculations have been performed to elucidate the relation among D, π–spacer and A moiety in the designed push-pull schemes. Surprisingly, all the compounds (FD2-FD6) exhibited a prominent decrease in their HOMO-LUMO energy gap as compared to the FCO-2FR1 molecule. The least band gap is obtained in case of FD2 compound as 1.223 eV. Similarly, their UV–Vis spectra were reported to have a prominent bathochromic shift with correspondingly smaller transition energies. Furthermore, the NBOs investigation depicts their stability due to intramolecular interactions and formation of charge separation states. Here also, the highest stabilization energy is exhibited by FD2 (28.40 kcal mol^-1). The tailored species showed lower binding energies (E_b) from the reference compound and offered less Coulombic force which also influenced their TDM heat maps. Overall, a significant charge transfer is observed from D towards A via the π–spacer among the designed molecules. Interestingly, an eye-catching NLO response is seen in FD2-FD6 as compared to FCO-2FR1. Among the designed species, the highest β_tot and u_tot are obtained for FD2 i.e., 11.22 × 10^-27 esu and 20.049 D, respectively, whereas, the largest ⟨α⟩ is 2.936 × 10^-22 esu observed in case of FD3. Also, their GRP studies proved them as the softest molecules with σ values as 0.817 and 0.765 eV, respectively. Expectedly, the two compounds (FD2 and FD3) also exhibited the least E_b values as -0.432 and -0.338 eV, respectively, which indicate the higher exciton dissociation rate and support their large NLO response properties. Consequently, FD2 and FD3 are preferred as better NLO entrants for the future. The present study also emphasizes the role of donor species in the fine-tuning of NLO attributes. Therefore, this research work would provide the experimentalists an enrich understanding of structure-property relationships of designed compounds and would also pave a pathway in their synthesis for reasonable NLO response.

Author contribution statement

Muhammad Khalid, Mashal Khan: Conceived and designed the experiments; Wrote the paper. Iqra Shafiq, Khalid Mahmood: Performed the experiments; Wrote the paper. Muhammad Nadeem Akhtar, Javed Iqbal: Analyzed and interpreted the data; Wrote the paper. Mohammad Khalid Al-Sadoon, Wajid Zaman, Ataualpa Albert Carmo Braga: Contributed reagents, materials, analysis tools or data; Wrote the paper.

Funding statement

The authors would like to extend their sincere appreciation to the Researchers Supporting Project Number (RSP2023R410), King Saud University, Riyadh, Saudi Arabia.

Data availability statement

Data included in article/supplementary material/referenced in article.

Declaration of competing interest

The authors declare no competing interests.

Appendix B. Supplementary data

The following is the supplementary data related to this article: