Linear and Nonlinear Optical Responses of Nitrobenzofurazan-Sulfide Derivatives: DFT-QTAIM Investigation on Twisted Intramolecular Charge Transfer

Abstract

In this study, we report on the green fluorescence exhibited by nitrobenzofurazan-sulfide derivatives (NBD-S_i, i = 1–4). The optical responses of these studied compounds in a polar methanol solvent were simulated by the use of time-dependent density functional theory (TD-DFT) employing the Becke-3-Parameter-Lee–Yang–Parr (B3LYP) functional along with the 6-31G(d,p) basis set. The computed energy and oscillator strength (f) results complement the experimental results. The band gap was calculated as the difference between the lowest unoccupied molecular orbital (LUMO) and the highest occupied molecular orbital (HOMO). Additionally, the density of states (DOS) was computed, providing a comprehensive understanding of the fundamental properties of these materials and further corroborating the experimental data. When the experimental data derived from ultraviolet/visible (UV/visible) and fluorescence spectroscopic techniques and those from simulated spectra are analyzed, the extracted values match up adequately. In addition, the NBD-sulfide compounds exhibit a large Stokes shift up to 85 nm in a polar methanol solvent. They are hypothesized to represent a novel paradigm of excited-state intramolecular charge transfer (ICT). To understand the intrinsic optical properties of NBD-S_i materials, an ICT was identified, and its direction within the molecule was evaluated using the ratio of β^vect and β_total, values extracted from the computed nonlinear optical (NLO) properties. Moreover, the reduced density gradient (RDG)-based noncovalent interactions (NCIs) were employed to characterize the strength and type of NBD-Si interactions. Furthermore, noncovalent interactions were identified and categorized using the Quantum Theory of Atoms in Molecules (QTAIM) analysis. Ultimately, the combination of Hirshfeld surface analysis and DFT calculations was utilized to enhance the characterization and rationalization of these NCIs.

1. Introduction

Since the first report on the intramolecular charge transfer (ICT)-based 4-(dimethylamino) benzonitrile (DMABN) molecule, as a groundbreaking example of electron donor/acceptor (D/A), by Lippert et al.,¹ there have been great efforts to obtain ICT-based aryl amine compounds. This has attracted considerable attention from the scientific publishing community owing to their potential ability to design new nonlinear optical (NLO) systems,² electro-optical switches,³ and organic light-emitting diodes.⁴⁻⁶ Furthermore, they find utility solar energy conversion⁷⁻¹¹ and as fluorescence sensors. However, quantifying the extent of ICT remains a challenge for the scientific community. First-order hyperpolarizability and therefore the second-order NLO responses are related to an ICT within the molecule.¹² Particularly, the investigation of π-conjugated systems with D/A moieties at opposite ends reveals a strong NLO response. Noncentrosymmetric D-π–A dipolar compounds are often used to achieve first- or second-order nonlinear polarizabilities. The electron capacity of the D and the electron-withdrawing capacity of the A groups play a key role in introducing the ICT extent.¹³⁻¹⁶ The design of NLO materials is a groundbreaking research area for both the theoretical and experimental communities, with numerous applications in optics, optoelectronics, photonics, and nanophotonics.^17,18 These NLO materials are greatly desirable due to their facile synthesis and superior flexibility. This offers the opportunity to fine-tune their structural and optoelectronic characteristics by designing chromophores with large first hyperpolarizability (β).^19,20

Methods of experimental and quantum chemistry have been widely used to evaluate the properties of NBD appended to morpholine,²¹ piperidine,²² pyrrolidine,²³ and other electrophilic systems involving NBD-Cl, NBD-OCH₃, and NBD-OC₆H₅²⁴

The present work reports the predicted optical (ultraviolet–visible (UV–vis) and photoluminescence (PL)) properties of four examples of NBD-sulfides.²⁵ The main objective was to understand the substituent effects on optical responses, validate the calculation method, and examine the extent of the ICT and NLO characteristics based on the findings. By the nucleophilic aromatic substitution (S_NAr) method, the electrophile NBD-Cl reacted with mercaptoderivatives 2a–2d acting as nucleophilic molecules (namely, 2a, 2-pyridinethiol; 2b, 4-pyridinethiol; 2c, N-acetylcysteamine; and 2d, N-acetylcysteine), affording the thioether derivatives 3a–3d (see Scheme 1).

Scheme 1. Applying the S_NAr Mechanism to Sulfides with an NBD-Cl Moiety to Convert Them into NBD-S_i, 3a–3d, Compounds²⁵.

The compounds will hereafter be referred to as NBD-S_i (i: 1–4), respectively. The structure of the designed molecules (3a–3d) was supported by ¹H and ¹³C NMR, Fourier-transform infrared (FTIR), and mass spectroscopy, and their optical responses are reported.²⁵ In this study, we employ density functional theory (DFT) and its time-dependent-DFT (TD-DFT) to calculate electronic characteristics, including highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) energy levels, UV–visible optical absorption and emission spectra, dipole moment variation (Δμ), average polarizability, and NLO properties.

2. Computational Details and Modeling Approach

The Gaussian 09 package²⁶ was employed to optimize the geometry of the NBD-S_i (i: 1–4) molecular structures. DFT calculations were performed in polar methanol (CH₃OH) using the IEFPCM solvent model²⁷ and the hybrid B3LYP functional^28,29 with the 6-31g(d,p) basis set.³⁰

Gauss View 5.0.8³¹ was utilized to visualize and analyze the output files. The stable molecular structure of each molecule was next employed to extract the energy levels of HOMO (ε_HOMO) and LUMO (ε_LUMO), dipole moment (μ), and DOS spectrum. Therefore, the TD-DFT method³² was employed to predict the electronic absorption spectra and the obtained results were subsequently compared with other DFT methods, including the Coulomb-attenuated hybrid exchange-correlation functional (CAM-B3LYP),³³ the Tamm-Dancoff approximation (TDA),³⁴ and the hybrid B3PW91 exchange-correlation functionals.³⁵ We performed QTAIM analysis to investigate the noncovalent interactions (NCIs). The Multiwfn_3.7 software³⁶ has been utilized to generate the electron localization function (ELF), the localized orbital locator (LOL), and the RDG analyses. We also used the Visual Molecular Dynamics (VMD) program³⁷ to display the iso-surfaces. The Hirshfeld (HS) surface was computed using the Crystal Explorer 17.5 program.³⁸ To explore the NLO NBD-S_i characteristics, electric dipole moment, polarizability (α), and static first and second hyperpolarizabilities (β and γ) were computed in methanol solvent.

3. Results and Discussion

3.1. Geometric and Energetic Parameters

First of all, the geometries of the NBD-S_i (i: 1–4) compounds in methanol were optimized in both their ground (GS) and excited (ES) states employing the B3LYP and CIS³⁹ approaches with the 6-31g(d,p) basis set, respectively. The geometry-optimized molecular structures are displayed in Figure 1, and the selected geometrical parameters, including bond lengths and dihedral angles, are listed in Table 1.

Figure 1.

Optimized geometric structures of investigated compounds revealing NCIs.

Table 1. Geometric Parameter Obtained in the Ground (S₀) State^a.

	bond length (Å)		dihedral angle (°)
structures	L1	L2	ϕ	dipole moment (μ, D)	Δμ (D)
NBD-S1	1.757 (1.695)	1.807 (1.780)	2.98 (27.35)	13.005 (14.779)	1.774
NBD-S2	1.760 (1.699)	1.799 (1.776)	1.41 (27.95)	8.083 (9.191)	1.108
NBD-S3	1.747 (1.695)	1.838 (1.821)	0.035 (0.237)	12.785 (14.905)	2.120
NBD-S4	1.750 (1.697)	1.840 (1.823)	4.56 (3.37)	12.034 (13.805)	1.771

^aThe values in parentheses correspond to excited (S1) state.

According to structural data, the optimized structures are found to mostly contain three forms of noncovalent contacts, namely, N---H, O---H, and N---O bond interactions, which are responsible for their stability. The computed dipole moment of the first excited state is also reported in Table 1. The geometrical parameters associated with these noncovalent contacts in GS and ES states are illustrated in Figure 1. All of these values are found to be shorter than the sum of van der Waals (VdW) radii [2.75 Å (N---H), 2.72 Å (O---H), and 3.07 Å (N--O)]. It is clear that the values of these short contacts decrease upon excitation.

Table 1 highlights that the variation in the dihedral angle ϕ and the electric dipole moment are the main differences between GS and ES. The value of dihedral angle ϕ, calculated between the NBD moiety and the sulfide group, in the ES is larger than that calculated in the GS for NBD-S_i (i: 1–3). Ultimately, all of the optimized structures show that the title compounds involve twisted geometry. As shown in Table 1, the dipole moment in each system was found to be higher in the S₁ state than that in the S₀ one, increasing by 1–3 D. Additionally, we have looked at the bridge length variations (L₁ and L₂) of the investigated compounds. As seen, the changes in electron delocalization in the molecular structure lead to only a small difference in bond lengths between the GS and ES states.

Using the hybrid functional B3LYP in conjunction with the empirical dispersion correction D3 (B3LYP-D3),⁴⁰ the structural parameters for all optimized molecular structures remained unchanged (see Table S1, Supporting Information).

3.2. FMOs and Quantum Theoretical Parameters

The frontier molecular orbitals (FMOs), formed mainly by the HOMO/LUMO iso-surfaces, are the significant orbitals in a molecule. The FMOs play an important role in judging optical and electrical performance, in addition to their chemical properties.⁴¹⁻⁴⁵ The ability to donate electrons is qualified by HOMOs acting as electron donors, and the aptitude to accept electrons is characterized by LUMOs acting as electron acceptors.⁴⁶Figure 2 depicts the HOMOs and LUMOs contour graphs, with the positive phase colored red and the negative phase colored green.

Figure 2.

HOMO–LUMO contour plots of the studied compounds with gap energy.

It appears that the FMOs distribution in the investigated compounds is almost the same. It is found that the electronic charge density distribution of HOMO is located all over the molecular structures, while the electronic charge density distribution of LUMO is mainly focused on the NBD moiety. This reveals the presence of an ICT inside the studied molecules from sulfide groups to the NBD acceptor moiety. The FMO’s molecular characteristics-based chemical descriptors, including ε_HOMO, ε_LUMO, energy gap (E_g), ionization potential (IP), electron affinity (EA), global hardness (η), chemical potential (μ), electronegativity (χ), and electrophilicity (ω), were extracted from calculations, and results are presented in Table 2. The energy gap (E_g) serves as a key indicator of a molecule’s stability and chemical reactivity.^47,48 According to our findings, the energy gaps of the investigated molecules ranged from 3.255 to 3.354 eV. The compounds NBD-S₂ and NBD-S₁ demonstrated the highest and lowest values, respectively. The compound NBD-S₂ is characterized by a lower reactivity and greater stability, indicating higher chemical hardness. On the other hand, the compound NBD-S₁ is identified as highly reactive, less stable, and soft. Band gap energy is recognized as a significant factor that offers valuable information regarding the photovoltaic efficiency of materials used in photovoltaic applications.^49,50

Table 2. Calculated Electronic Parameters and Derived Quantum Chemical Parameters for the Investigated Molecules (E_F Represents the Fermi Energy).

	energy levels				chemical reactivity descriptors
compounds	εHOMO (eV)	εLUMO (eV)	EF (eV)	Eg (eV)	μ (eV)	η (eV)	ω (eV)	χ = –μ (eV)	IP (eV)	EA (eV)
NBD-S1	–6.615	–3.359	–4.987	3.255	–4.987	1.628	7.638	4.987	6.343	3.679
NBD-S2	–6.742	–3.388	–5.065	3.354	–5.065	1.677	7.648	5.065	6.574	3.745
NBD-S3	–6.607	–3.332	–4.969	3.275	–4.969	1.637	7.540	4.969	6.473	3.511
NBD-S4	–6.638	–3.345	–4.991	3.293	–4.991	1.646	7.566	4.991	6.500	3.530

Additionally, the neutral, cation, and anion-optimized structures are used to compute EA and IP, which elucidate the barrier injection energies of holes and electrons. The readings of EA and IP are, respectively, in the ranges of 3.66–3.74 and 6.34–6.56 eV. The best electron donor is the molecule NBD-S₁, which has the lowest ionization value (IP = 6.342 eV). Although the best electron acceptor is NBD-S₂, which has the highest affinity (EA = 3.744 eV). Moreover, using ε_HOMO and ε_LUMO, chemical potential (μ), global hardness (η), and electronegativity (χ) can be determined as follows: ; ; χ = −μ. Besides this, the electrophilicity (ω)^51,52 has been computed using both chemical potential and global hardness . A molecule with a low electrophilicity is regarded as a strong nucleophile, whereas a molecule with a high electrophilicity is regarded as a strong electrophile. The results indicate that NBD-S₁ is a good nucleophile since it has lower values of (ω), whereas NBD-S₄ is a good electrophile.

Among the electronic properties of the materials under study, ε_HOMO and ε_LUMO are particularly crucial, as they facilitate the calculation of both E_g and E_F energies. The obtained values are listed in Table 2. The B3LYP-D3/6-31g(d,p) level of theory was also applied to extract electronic parameters for the investigated molecules (see Table S2, Supporting Information). As shown in Table S2, no appreciable changes have been detected.

3.3. Electronic Spectra Analysis of the Investigated NBD-S_i Molecules

The optical absorption (UV–vis) and the emission properties of NBD-S_i molecules, in methanol, are given in Tables 3 and 4, respectively, while their related electronic spectra are shown in Figure 3. The most intense absorption appears at 409–415 nm. A bathochromic shift of the absorption maxima is evident after functionalization with suitable sulfide groups, such as 2-pyridinethiol. In all cases, the maxima originate from HOMO–LUMO electronic transitions, with significant contributions of 98%. Based on FMO’s distribution analysis, these electronic transitions are associated with the π → π* type.

Table 3. Vertical Wavelength (λ, nm) and the Oscillator Strengths (f) Contributing to S₀ → S₁ Electronic Transitions for Investigated Molecules, Computed by the TD-B3LYP/6-31g(d,p) Method in Methanol Solvent.

compounds	λabs,expmax (nm)	fmax	major contribs (%)	minor contribs (%)
NBD-S1	271	0.0095	H – 5 → L (94%)	H → L + 4 (3%)
	306	0.1295	H → L + 1 (96%)
	426	0.3622	H → L (98%)
	λabs,expmax = 407 nm25
NBD-S2	265	0.0549	H – 6 → L (88%)	H → L + 4 (6%)
	300	0.1246	H → L + 1 (96%)
	409	0.3611	H → L (98%)
	λabs,expmax = 400 nm25
NBD-S3	265	0.0464	H – 5 → L (81%)	H – 1 → L + 1 (8%), H → L + 2 (7%)
	304	0.1288	H → L + 1 (97%)
	415	0.3635	H → L (98%)
	λabs,expmax = 414 nm25
NBD-S4	265	0.0474	H – 6 → L (86%)	H → L + 3 (6%)
	305	0.128	H → L + 1 (97%)
	415	0.3733	H → L (98%)
	λabs,expmax = 411 nm25

Table 4. Vertical Wavelength (λ, nm) and the Oscillator Strengths (f) Contributing to S₁ → S₀ Electronic Transitions of Investigated Molecules, Calculated by the TD-B3LYP/6-31g(d,p) Method in Methanol Solvent. The excitation wavelengths varied from 366 to 380 nm.

compounds	λPL,expmax (nm)	fmax	major contribs (%)	minor contribs (%)
NBD-S1	292	0.1476	L → H – 4 (54%), L → H – 2 (23%)	L + 4 → H (8%)
	366	0.0646	L + 1 → H (80%)	L + 1 → H – 1 (13%)
	515	0.5543	L → H (88%)	L → H – 1 (8%)
	λPL,expmax = 522 nm25
NBD-S2	287	0.0226	L + 2 → H – 3 (79%)	L → H – 4 (3%), L + 10 → H – 3 (8%)
	366	0.0625	L + 1 → H (90%)	L + 1 → H – 2 (4%)
	513	0.5486	L → H (95%)
	λPL,expmax = 521 nm25
NBD-S3	290	0.1458	L → H – 3 (73%)	L + 3 → H (12%) L → H – 4 (8%)
	367	0.059	H → L + 1 (95%)
	507	0.5614	L → H (97%)
	λPL,expmax = 516 nm25
NBD-S4	291	0.1482	L → H – 3 (73%),	L + 4 → H (12%), L → H – 5 (5%), L → H – 4 (3%)
	365	0.0558	L + 1 → H (95%)
	503	0.5636	L → H (97%)
	λPL,expmax = 542 nm25

Figure 3.

Electronic spectra (UV–vis and PL) achieved at the TD-B3LYP/6-31g(d,p) level of theory of materials.

In fluorescence spectroscopy, the difference in spectral position between the first absorption band’s maximum and the fluorescence emission’s maximum is identified as the Stokes shift (SS), which can be expressed in wavelength: SS = λ^max_PL λ^max_abs. In some cases, significant reabsorption effects due to the overlap of absorption and emission spectra limit practical applications. To address this, the development of D–A or D-π–A push–pull systems aims to minimize the overlap between absorption and emission spectra, effectively reducing reabsorption losses.^53,54 Herein, NBD-sulfide compounds exhibit a large SS up to 85 nm in polar methanol solvent (see Figure 3). The ICT phenomenon is an alternative reason for the large SS. In summary, the extracted values from the experimental data obtained through UV/visible and fluorescence spectroscopic techniques (Tables 3 and 4) align well with the values derived from simulated spectra. Furthermore, the change in dipole moment relaxes the polar solvent around the excited molecule, leading to the lowest energy state.⁵⁵ This is supported by assignments previously reported by Heberer et al.⁵⁶ for NBD derivatives, where the lower energy band is attributed to an ICT between the sulfide electron donor and the nitro electron-withdrawing groups of the NBD moiety.

To enhance the result validation, we employed three DFT methods (CAM-B3LYP, TDA, and B3PW91) to predict UV–vis properties for the studied molecules.

The computed results were compared with the available experimental data (see Table S3, Supporting Information). Overall, we consider that the TD-B3LYP/6-31g(d,p) level of theory can be proposed to obtain better results at a reasonable cost.

3.4. DOS Analysis

Nearby orbitals within the boundary area may have quasi-degenerate energy levels, so it may not be practical to use only HOMO and LUMO to define the FMOs.⁵⁷ Therefore, the DOS spectra for the investigated compounds were generated by the Gauss Sum 3.0 software (the full width at half-maximum (fwhm) is 0.3 eV).⁵⁸Figure 4 shows the obtained DOS spectra.

Figure 4.

DOS spectra obtained at the B3LYP/6-31g(d,p) level, labeled as (a–d), corresponding to NBD-S_i (i = 1–4).

Virtual orbitals, also known as acceptor orbitals, are unoccupied, while filled orbitals are termed donor orbitals. The DOS exhibits a positive value when indicating bonding interactions, a negative value for antibonding interactions, and zero when there are no bonding interactions present.^59,60 Furthermore, the DOS spectra directly provide the energy gap.

3.5. RDG Analysis

The molecular stability can be attributed to the presence of relatively weak intra- and intermolecular interactions that can be identified and studied by the NCI methodology. This method uses RDG to provide further evidence for NCIs. The RDG is a fundamental dimensionless parameter based on the relationship between the electron density (ρ) and its derivative,^61,62 expressed as

1

The result of the product of the electron density ρ(r) and the sign of the second-lowest eigenvalues of the electron density Hessian matrix (λ₂(r)) is highly significant in anticipating the nature of interaction. The attractive, repulsive, and intermediate interactions correspond to sign(λ₂) × ρ < 0 and sign(λ₂) × ρ > 0 and sign(λ₂) × ρ ≈ 0.⁶³ Two-dimensional (2D) scatter plots and the 3D-RDG isosurface densities of studied molecules in the GS are indicated in Figure 5. Correspondingly, as shown in the RDG plots, there are three kinds of spikes in the zone between −0.05 and 0.05 a.u. The blue regions represent attractive interactions like H-bonds, the red regions signify repulsive interactions, such as steric effects, and the green regions take place for very weak interactions, typically VdW ones.⁶⁴ Looking at the NCI-RDG graphs, the van der Waals interactions are clearly shown within our NBD molecules. As well, the detection of a blue surface highlights the existence of H-bond interactions. Moreover, red areas are positioned in the center of the rings, demonstrating the effect of steric repulsion.

Figure 5.

RDG scatter plots (left) and NCI plots (right) of the investigated materials in GS.

3.6. ELF and LOL Topological Analyses

ELF and LOL analyses, developed and explained by Silvi and Sain,⁶⁵ both conduct covalent bonds analysis, revealing areas in the molecular space with high electron pairing potential. ELF and LOL have comparable chemical maps since they depend on the kinetic energy density. Furthermore, ELF is rooted in the analysis of electron pair density, whereas LOL identifies and characterizes the gradients of localized orbitals.⁶⁶ The ELF and LOL color-filled maps generated by Multiwfn software for the S₀ and S₁ states of the investigated materials are shown in Figures 6 and 7, respectively. These maps range from 0 to 1. An ELF value greater than 0.5 corresponds to the area in which the bonding and nonbonding electrons are localized, whereas a value under 0.5 indicates a delocalized electronic region.⁶⁷ LOL values exceed 0.5 in areas where the electron density is controlled by electron localization. Several colors are shown in the ELF and LOL maps. High ELF or LOL values are visually represented by the red color, indicating the presence of localized electrons surrounding hydrogen atoms. The delocalized electron cloud surrounding C, N, S, and O atoms is visually represented by the blue. From the LOL maps, it is evident that the central region of the hydrogen atom appears white, indicating an electron density that surpasses the upper limit of the color scale (0.8). In addition, the red regions between C–C, C–N, C–S, and N–O atoms present covalent interactions with a high LOL value.

Figure 6.

Color-filled map of the ELF (top) and LOL (bottom) of studied molecules in their S₀ states.

Figure 7.

Color-filled map of (top) and LOL (bottom) of the studied molecules in their S₁ states.

3.7. MEP Analysis

The molecular electrostatic potential (MEP) describes the charge distribution around the molecular structure generated by its nuclei and electrons. The distribution of charge can be used to determine how molecules interact with each other.^68,69 It also serves as a tool for identifying reactive sites for nucleophilic and electrophilic reactions.⁷⁰ The nucleophilic sites assume a high attraction, while the electrophilic sites show a high repulsion. The MEP 3D plots of all structures in both S₀ and S₁ states were computed by employing the B3LYP/6-31(d,p) level, as illustrated in Figure 8. The figure presents the electrostatic potential values in false colors, progressing in order: red < orange < yellow < green < blue. The positive (blue) areas of the MEP are the preferred nucleophilic attack sites, whereas the negative (red-yellow) areas are the preferred electrophilic attack sites, and green colors are neutral regions. As shown in the MEP three-dimensional (3D) graphs, areas with negative potential are over the electronegative atoms (nitrogen and oxygen atoms) of NBD moieties and the sulfide groups, which support electrophilic attacks.

Figure 8.

MEP 3D plots of studied molecules.

The positive potential zones are over the hydrogen atoms, favoring nucleophilic attack. For all studied molecules, the NBD moieties are very evident in the red-yellow region, confirming the acceptor properties of this group. Consequently, the presence of electrophile and nucleophilic attacks in these molecules supports their push–pull (D–A) nature.

3.8. QTAIM Analysis

The QTAIM analysis, developed by Bader and co-workers,⁷¹ identifies the nature and type of intra- and intermolecular H-bonds, including NCIs,⁷² in a topological manner. According to QTAIM theory, the bond path (BP) is the link between an interacting atom and the saddle point where the gradient of the electron density is zero, also called the critical point (CP). The QTAIM graphs are obtained using Multiwfn software and are illustrated in Figure 9. As shown in the graph, three types of critical points can be identified: a large red spot (+3,–3) represents the nuclear critical point (NCP), a small orange spot (+3,–1) indicates the bond critical point (BCP), and a yellow spot (+3,+1) is the ring critical point (RCP). The BCPs offer an effective measure of the distance between atoms in a molecular system.⁷³⁻⁷⁵ Mainly, hydrogen bond interactions can be efficiently characterized and quantified by the use of a variety of topological parameters: electron density ρ (r) and its Laplacian ∇²ρ (r), kinetic energy G (r), potential energy V (r), kinetic energy of Hamiltonian H (r) = G (r) + V (r), and the binding energy BE, calculated by means of the expression provided by Espinosa et al.:⁷⁶ BE = V (r)/2. Among them, the most significant are the electron density ρ (r) and its Laplacian ∇²ρ (r), which are used to identify the nature of the bond or interaction. A large ρ (r), greater than 0.20 a.u. and negative ∇²ρ (r) values show a covalent bond, whereas small ρ (r), less than 0.10 a.u. and negative ∇²ρ (r) values signify a closed-shell interaction (ionic, H-bond, VdW). In Figure 9, solid lines indicate CBs, while NCIs are shown as dashed lines. Specifically, H-bond interactions can be classified into three categories.⁷⁷ First, when ∇²ρ (r) > 0 and H (r) > 0, it denotes weak H-bonds. Second, when ∇²ρ (r) > 0 and H (r) < 0, it signifies moderate H-bonds. Lastly, when ∇²ρ (r) < 0 and H (r) < 0, it indicates the strongest H-bonds.

Figure 9.

QTAIM molecular graphics with examples of BCPs for the investigated molecules.

Table 5 presents the topological parameter values at the CBs of various NCI examples. In the QTAIM molecular graphs, NBD-S₁ exhibits two BCPs representing N–O and N–H interactions, while NBD-S₂ has a single N–O interaction. NBD-S₃, in comparison to NBD-S₁, features both N–H and N–O interactions. Alternatively, there are four kinds of interactions obtained in the last compound: O–H, N–H, N–O, and C–H interactions. The ρ(r) values of bond critical points vary from 0.0079 au to 0.012 a.u., and their Laplacians range from 0.030 to 0.050 a.u., which are similar to the values offered by Koch and Popelier.⁷⁸ Also, the positive values of the energy density H (r) justify the weak H-bond. In addition, the band energy appears between −5.382 and −12.602 kJ/mol. The N–H and O–H interactions in NBD-S₃ and NBD-S₄, respectively, are considered the strongest ones, with BE = 12.602 kJ/mol.

Table 5. Topological Parameters Computed for Investigated Compounds at BCPs.

compound	interaction	ρ (r)	∇2ρ (r)	G (r)	V (r)	H (r)	BE (kJ/mol)
NBD-S1	1	0.010	0.036	0.0075	–0,0058	0.0016	–7.613
	2	0.012	0.050	0.0110	–0.0095	0.0015	–12.471
NBD-S2	1	0.012	0.050	0.0110	–0.0095	0.0015	–12.471
NBD-S3	1	0.010	0.038	0.0077	–0.0059	0.0018	–7.745
	2	0.012	0.050	0.0110	–0.0096	0.0014	–12.602
NBD-S4	1	0.0079	0.031	0.00603	–0.0041	0.0019	–5.382
	2	0.0083	0.030	0.0065	–0.0053	0.0012	–6.957
	3	0.010	0.038	0.0078	–0.0059	0.0018	–7.745
	4	0.012	0.049	0.0110	–0.0096	0.0014	–12.602

3.9. Hirshfeld Surface (HS) Analysis

The analysis of the Hirshfeld surface (HS)⁷⁹⁻⁸¹ offers insights into the characteristics of molecular surfaces and introduces a novel method to visualize intermolecular interactions. HS analysis is utilized to examine intermolecular interactions involved in the stabilization of crystal packing for the studied compounds.^82,83 This visualization is achieved through color coding, which distinguishes short- or long-term contacts.⁸⁴ HS may be mapped with various properties, such as d_norm, curvedness, and shape index. Figure 10(i–iii) displays the molecular HS (d_norm, curvedness, and shape index) of the studied molecules. The Hirshfeld molecular surfaces are produced using a standard (high) surface resolution. In the case of NBD-S₁, the 3D d_norm surfaces are mapped on a fixed color scale ranging from −1.1876 Å (red) to 5.9755 Å (blue). For NBD-S₂, the mapping ranges from −1.1858 Å (red) to 6.038 Å (blue). Similarly, for NBD-S₃, the range is from −1.2575 Å (red) to 6.4383 Å (blue), and for NBD-S₄, it is from −1.2364 Å (red) to 5.8931 Å (blue). Curvedness is mapped within the range of −4.0 to 4.0, while the shape index is mapped in the color range of −1.0 to 1.0. The d_norm attributed is a symmetric function that evaluates the surface distances (d_i and d_e) between nuclei inside and outside the HS area, respectively, in relation to their respective van der Waals (vdW) radii. The red and blue regions, corresponding to the negative and positive d_norm values, display shorter and longer contacts, respectively. However, the white color designates the contacts around the VdW radii (d_norm values near zero). On the d_norm surface, the deep red spots indicate intermediate contacts involved in H-bonds.⁸⁵ The red spots in Figure 10(i) are assigned to N–H···S, N–H···O, and C–H···O hydrogen bonds for compounds NBD-S₁ and NBD-S₂, C–H···S, C–H···N, N–H···O, and C–H···O H-bonds for compounds NBD-S₃ and NBD-S₄. Additionally, the presence of red/blue triangles and the expansive green region in the curvedness triangles within the shape index serve as indicators of C–H···π and π···π stacking interactions taking place among the molecules.

Figure 10.

Hirshfeld surfaces mapped over (i) d_norm, (ii) shape index, (iii) curvedness, and (iv) percentage contributions of the various intermolecular contacts and 2-D fingerprint plots of each studied compound.

The 2D depiction of the HS is commonly referred to as a fingerprint,⁸⁶ as it has the ability to unveil additional insights into the intermolecular contacts. The 2D fingerprint plots can be decomposed to highlight the interactions and the area corresponding to each of these interactions. The HS surfaces and the 2D fingerprint plots have been generated using the Crystal Explorer program.⁸⁷ The decomposed 2D fingerprint plots of all compounds and all major and minor intermolecular interactions with the percentage of contributions are shown in Figure 10(iv). In this study, the 2D fingerprint plots show various types of interactions that ensure the structure’s cohesion. The overall 2D fingerprint plot showed that the intermolecular interactions of the investigated compounds were dominated by H···O/O···H, H···H, C···N/N···C, C···H/H···C, O···O, and C···O/O···C. The major contribution of Hirschfeld’s total surface in all compounds is attributed to H···O/O···H interactions with 28.9, 26.1, 23.9, and 31.4% for NBD-S₁, NBD-S₂, NBD-S₃, and NBD-S₄, respectively. These interactions are characterized by one large spike in the middle of the scattered points. The interactions with the second contribution, however, vary depending on the molecule. NBD-S₁ and NBD-S₂ exhibit interactions such as H···H, C···N/N···C, C···O/O···C, and C···C. On the other hand, NBD-S₃ and NBD-S₄ involve interactions such as C···O/O···C, C···H/H···C, O···O, and H···H. The analysis of Hirshfeld surfaces also indicates the existence of additional weak intermolecular interactions that make modest contributions to the surface area (C···S/S···C, N···O/O···N. and H···/S···H).

3.10. NLO Responses for Investigated Compounds

Polarizability and hyperpolarizability measurements can be used to explore the NLO characteristics of the investigated molecules. The significance of these two parameters was crucial for defining ICT properties.^88,89 By means of the B3LYP/6-31g(d,p) level of theory, we evaluated the static dipole moment (μ), mean polarizability (α₀), polarizability anisotropy (Δα), and static first and second hyperpolarizabilities (β and γ) of the investigated molecules. The relevant expressions used for the calculation are as given below⁹⁰⁻⁹³

2

3

4

5

And,

6

where α_xx, α_yy, and α_zz are the polarizability tensor components, and β_xxx, β_xyy, β_xzz, β_xxy, β_yyy, β_yzz, β_xxz, β_zyy, β_zzz and γ_xxxx, γ_yyyy, γ_zzzz, γ_xxyy, γ_yyzz, and γ_zzxx are the first- and second-order hyperpolarizability tensor components along the x, y, and z axes, respectively. The calculated values are given in Table 6. These values have been converted into electrostatic units (for α, 1 a.u. = 0.1482 × 10^–24 esu; for β, 1 a.u. = 8.6391 × 10^–33 esu and for γ, 1 a.u. = 0.000504 × 10^–36 esu).

Table 6. Computed Electric Dipole Moment (μ), Polarizability (α), 1st- and 2nd-Order Hyperpolarizability (β) and (γ), Respectively, for the Studied Compounds.

polarizability, α × 10–24 esu					2nd-order hyperpolarizability, γ × 10–36 esu
	NBD-S1	NBD-S2	NBD-S3	NBD-S4		NBD-S1	NBD-S2	NBD-S3	NBD-S4
αXX	40.949	39.721	36.733	40.046	γXXXX	43.838	26.617	23.898	25.751
αYX	–2.097	–0.311	0.951	1.826	γXXYX	–0.994	–0.243	2.322	5.444
αYY	17.352	20.334	17.230	19.470	γXXYY	0.533	1. 497	1.619	3.658
αZX	7.718	6.817	40.661	3.9125	γYXYY	–0.627	–0.118	0.316	2.089
αZY	3.148	0.532	0.438	–1.159	γYYYY	1.725	2.974	1.530	2.927
αZZ	52.684	48.045	52.402	55.105	γXXZX	34.132	11.633	10.861	8.619
α0 = αISO	36.995	36.034	35.455	38.207	γXXZY	–1.043	–0.179	1.844	2.542
Δα = αANISO	34.541	27.333	31.375	31.936	γYXZY	–0.465	0.699	0.730	1.281
1st-order hyperpolarizability, β × 10–30 esu					γYYZY	0.806	0.177	0.098	0.368
βXXX	–1.230	–0.455	0.267	–0.040	γXXZZ	42.439	8.534	7.033	5.798
βXXY	–0.152	–0.035	0.206	0.462	γYXZZ	–2.468	–0.589	2.572	4.280
βYXY	–0.126	0.045	–0.991	–0.551	γYYZZ	–1.362	–1.004	–0.617	1.866
βYYY	–0.350	–0.014	0.611	–0.315	γZXZZ	111.977	49.662	42.508	42.218
βXXZ	–2.379	–2.923	–1.778	–1.865	γZYZZ	–5.407	–2.173	5.666	5.970
βYXZ	–0.339	–0.072	0.207	0.560	γZZZZ	520.226	382.615	365.442	391.169
βYYZ	–0.882	–0.622	–1.307	–0.909	γ0 = γ||	129.800	86.051	81.387	88.497
βZXZ	7.168	3.798	3.628	3.559	γ⊥	43.267	28.684	27.129	29.500
βZYZ	–0.853	–0.346	0.639	1.217	electric dipole moment (debye)
βZZZ	87.016	74.188	79.671	79.848	μx	8.396	–4.646	–7.934	–6.592
|| (Z)	50.252	42.386	45.951	46.245	μy	1.798	–0.004	4.362	2.787
⊥ (Z)	16.750	14.129	15.317	15.415	μz	9.767	–6.615	–9.027	–9.674
|βvect|	66.466	59.752	75.647	63.268	μtot	13.005	8.084	12.785	12.034
β0	83.967	70.725	76.654	77.143
|βvect|/β0	0.791	0.844	0.722	0.820	βvec = ∑iβiμi/μ [i = x,y,z]100
θ (deg)	37.74	32.45	43.80	34.93

The calculated electric dipole moments are found to be 13.005, 8.084, 12.784, and 12.034 D for NBD-S₁, NBD-S₂, NBD-S₃, and NBD-S₄, respectively. It is noteworthy that the greatest dipole moment value is observed for compound NBD-S₁. The static polarizability (α₀), values of the investigated molecules increase in the subsequent order NBD-S₃ < NBD-S₂ < NBD-S₁ < NBD-S₄. Similarly, we can see that the anisotropy of polarizability (α_aniso) increases in the order: NBD-S₂ < NBD-S₃ < NBD-S₄ < NBD-S₁. The hyperpolarizability is a key property of the NLO response, with β₀ ranging from 70.725 × 10^–30 to 83.967 × 10^–30 esu. Additionally, it is noteworthy that the NBD-S1 compound exhibits the highest values for both first- and second-order hyperpolarizabilities, whereas the NBD-S2 compound shows the lowest values in this regard. Notably, the first hyperpolarizability demonstrates a direct correlation with linear polarizability values and an inverse correlation with energy gap values.⁹⁴⁻⁹⁷ In this context, there is a strong correspondence between the β_tot values and the observed patterns in E_g values, with the compound having the smallest band gap (3.255 eV) demonstrating the highest β_tot value (83.967 × 10^–30 esu).

In this section, urea was chosen as a reference because there was no experimental standard for the NLO properties of the molecules of interest (μ_urea = 1.3732 D, α_urea = 5.0477 × 10^–24 esu, β_urea = 372.8 × 10^–33 esu, and γ_urea = 48 × 10^–36 esu).^98,99 The first-order hyperpolarizability of all investigated compounds is significantly greater (i.e., ≥70 times) than that of the standard urea, and NBD-S₁ exhibits the best NLO characteristics. These results thus confirm that the studied molecules possess good NLO parameters and may be a good candidate for applications in optical devices.

According to Table 6, β_tot mainly depends on the β_ZZZ tensor component, while also showing supplementary contributions from the β_ZXZ tensor component. Furthermore, based on the collective results presented in Tables 1 and 2, it is evident that compounds with a narrow energy gap and a lower difference in dipole moment between the S₀–S₁ states (Δμ) will exhibit higher first-order hyperpolarizability.

Conversely, the relationship between β^vect and β_total is acknowledged to provide significant information regarding the direction of the ICT, as the following relationship holds: ,¹⁰⁰ where θ characterizes the orientation between the vector formed by the components of β^vec and the dipole moment vector. Note that a ratio approaching unity means maximum charge delocalization.¹⁰¹ This phenomenon occurs due to the dominance of one of the first hyperpolarizability components, which significantly contributes to the overall first hyperpolarizability. As a result, a unidirectional alignment parallel to the molecular dipole moment of ICT takes place. Here, the calculated angle θ is in the range of 32 to 44°. This confirms the twisted ICT in all of the investigated NBD-S_i molecules.

4. Conclusions

In this study, we used the TD-B3LYP/6-31g(d,p) level of theory to explain and predict the optical responses of four examples of NBD derivatives in a polar methanol solvent. The studied compounds, labeled NBD-S_i (i = 1–4), consist of NBD and sulfide moieties. These molecules absorb within the wavelength range of 250–500 nm and all emit green fluorescence in the 503–515 nm range. They also exhibited large Stokes shifts, up to 500 meV, in polar methanol solvent. We concluded that DFT and its time-dependent extension (TD-DFT) can predict the optical properties of the studied molecules. Additionally, we demonstrate that the optical properties of these investigated systems can be systematically tuned through the choice of substituents; including their nature, extended conjugated systems, and strength.

Findings from QTAIM, ELF, and RDG analyses indicate that the bonding between sulfide and NBD moieties is of electrostatic or hydrogen bond type. The DFT approach is also reliable for determining the NLO properties of the NBD-Si compounds.

In our NLO analysis, we found that small nonplanar NBD-Si molecules with intramolecular charge transfer (ICT) characteristics are excellent candidates for designing NLO materials. Specifically, dipole moment (μ), polarizability (α), and first-order hyperpolarizability (β) were larger in the case of NBD-S₁ (μ_tot = 13.005 D, α₀ = 36.995 × 10^–24 esu, and β₀ = 83.967 × 10^–30 esu). The twisted intramolecular charge transfer (TICT) from the sulfide to the respective NBD was clearly elucidated in our NLO studies. Ultimately, we conducted Hirshfeld surface analysis and employed some topological approaches based on DFT, including NCI plots and QTAIM analysis, to further characterize and describe the NCIs.

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.jpca.3c04277.

• Geometric parameters at the ground (S₀) state for investigated compounds obtained with B3LYP-D3/6-31g(d,p) level of theory (Table S1); computed electronic parameters for investigated molecules at the B3LYP-D3/6-31g(d,p) level of theory, recorded in methanol solvent (Table S2), and selected DFT methods for calculation of vertical wavelength maxima (λ, nm) and their corresponding oscillator strengths (f) contributing to HOMO → LUMO electronic transitions for investigated molecules in methanol solvent (Table S3) (PDF)

The authors declare no competing financial interest.