Fluorescence quenching, DFT, NBO, and TD-DFT calculations on 1, 4-bis [2-benzothiazolyl vinyl] benzene (BVB) and meso-tetrakis (4-sulfonatophenyl) porphyrin (TPPS) in the presence of silver nanoparticles

Steady-state fluorescence measurements were used to examine the fluorescence quenching of 1, 4-bis [-(2-benzothiazolyl) vinyl benzene (BVB) by sodium salt of meso-tetrakis (4-sulfonatophenyl) porphyrin (TPPS) in the presence and absence of silver nanoparticles (Ag NPs). The energy transfer (ET) process’s emission intensities and Stern–Volmer constants (KSV) showed that Ag NP’s presence increased ET’s efficiency. The molecular structures of TPPS, TPPS, and BVB/TPPS were optimized using the DFT/B3LYP/6-311G (d) technique to elucidate the mechanism. The discovered optimized molecular structure proved that whereas TPPS and BVB/TPPS MSs are not planar because the porphyrin group in TPPS is rotated out by phenyl sodium sulphate, the BVB MS is planer. All of the theoretical BVB results and the acquired experimental optical results were very similar.

Due to their unique optical properties, porphyrin compounds have found usage in a wide range of applications, such as nonlinear photonic devices, optical limiters, optical switches, antimicrobial, and anti-HIV medicines [7][8][9]. Additionally, they were utilized in the production of singlet oxygen and photosensitizer [10][11][12]. The synthesized mesotetrakis (4-sulfonatophenyl) porphyrin is one of the most significant water-soluble porphyrin derivatives (TPPS) [13]. In clinical trials, TPPS was examined and experimented with as a promising sensitizer for PDT [14]. Additionally, TPPS exhibits aggregation features used in singlet oxygen synthesis [15] and nonlinear optical absorption [16], which can lead to its implementation in photonic devices as optical limiters [17]. Trinitrotoluene (TNT), when used to analyze ground state interactions, changed the electronic absorption and static quenching of TPPS fluorescence [18].
The current work focuses on the following experiments to reveal the impact of the molecular charge on the effectiveness of energy transfer: crucial contacts of BVB as donors with a negatively charged TPPS as an accepter. Additionally, this analysis shows that only 20 vol.% Ag NPs are required to increase FRET [19]. Additionally, it provides DFT, NBO, and TD-DFT quantum calculations for the target MS (BVB).

Spectroscopic studies and characterizations of nanoparticles
The Shimadzu UV-3101 PC spectrophotometer had been used to record the optical absorption spectra. Using matched quartz cuvettes and a Perkin-Elmer LS-50B scanning Spectrofluorometer, the fluorescence spectra were measured. With the use of a transmission electron microscope (TEM), JEOL JEM-100SX Electron Microscope with a field gun, and an accelerating voltage of 80 kV, the size of the nanoparticle was determined.

Forster resonance energy transfer (FRET)
In hosts containing 0% and 40% by volume of ethylene glycol (EG) in methanol (MeOH) at room temperature, the fluorescence spectra (FS) of BVB were examined in the presence of TPPS as an acceptor. As a result of illumination at 337 nm in MeOH, the FS of BVB displays an emission maximum of 455 nm. The emission intensity of BVB declines without changing the spectral pattern as the concentration of TPPS rises, Fig. 1a, b, shows that no excited state complex between BVB and TPPS has formed. Using the Stern-Volmer equation, one may (1) [26] where [TPPS] is the quencher concentration in mol. dm −3 , I o and I are the fluorescence intensities of BVB in the absence and presence of the quencher, K SV is the Stern-Volmer quenching rate constant, and based on the slope of Fig. 1c, the values of K SV in MeOH and 40% EG/MeOH was determined as 4.67 104 M −1 in MeOH and 5.18 104 M −1 in 40% EG, respectively (R 2 = 0.974 and 0.981). As the medium viscosity rises, the quenching efficiencies marginally rise, demonstrating that the process is not diffusion-controlled and is compatible with the diffusionless energy transfer mechanism. The excited state BVB* is schematically quenched by the TPPS molecule in Fig. 1(d). The lifetime (τ o = 0.9 ns) of the BVB in MeOH has been used to compute the energy transfer rate constant (k ET ) [5]. The value discovered was k ET = 5.188 × 10 13 M −1 s −1 . This number suggests a diffusionless energy transfer mechanism because it is substantially greater than the diffusion rate constant in MeOH (k d = 1.8 × 10 9 M −1 s −1 ) at ambient temperature.
The critical transfer distance (R o ) of the (BVB/TPPS) pair was determined utilizing the interference between the experimental electronic optical absorption spectra of TPPS and the emission spectrum of BVB as shown in Fig. 2a. This interference was computed using the well-known Förster equation [27,28]: where Ro is the Förster critical transfer distance (50% transfer efficiency), (n) is the solvent refractive index, (k 2 ) = 2/3, is the BVB fluorescence quantum yield, and J (λ) is the "overlap area," which expresses the amount of spectral overlap between the BVB emission and TPPS absorption and is given by: where ε A (λ) is in M −1 cm −1 , (λ) in nm and unit of J( ) is in M −1 cm −1 (nm) 4 , F D is the peak-normalized fluorescence spectrum for the BVB (donor), and ( ε A ) is the molar absorption coefficient for the(TPPS) acceptor. The critical transfer distance R o was calculated as 25 Å. This value is higher than that for the collisional energy transfer mechanism in which R o is less than 10 Å [29]. The high value of R o , as well as the energy transfer rate constant, indicates that the expected mechanism of energy transfer in the BVB * /TPPS system is a resonance energy transfer due to long-range dipole-dipole interaction between the excited BVB and the ground state TPPS. (1) (2) 4.38 × 10 −17 cm 3 . The quenching sphere radius "r" was found to be 21.8 nm.

Quenching in presence of Ag NPs
Because BVB dye is difficult to dissolve in water, a 2% by volume water/MeOH ratio was necessary. So, to a total volume of 10 ml MeOH solutions, 0.2 ml of Ag NPs stock solution was added. The fluorescence spectra of BVB were recorded at room temperature with TPPS as an acceptor, plasmonic Ag NPs in MeOH (2% of the total volume), and 40% EG/MeOH by volume. The synthesized Ag NPs' TEM picture, shown in Fig. 3b, validates the particles' nanoscale dimensions and reveals that their average diameter is roughly 16 nm. Figure 3a displays the electronic absorption spectrum of the produced Ag NPs employed in our study. As seen in Fig. 4, the fluorescence intensity of BVB diminishes as TPPS concentration is increased (a and b). According to the Stern-Volmer plot (Fig. 4c), EG has lower quenching effectiveness (K SV ) than MeOH. This can be explained by the fact that when viscosity increases, the diffusion rates of both donor and acceptor toward Ag NPs decrease. This highlights how Ag NPs help strengthen the relationships between donors and recipients. We noticed that in Fig. 4d, the quenching's Stern-Volmer constant (K SV ) in the presence of Ag NPs is higher than it is in the absence of Ag NPs. The K SV value in the presence of Ag NPs is K SV = 0.692 × 10 5 M −1 is larger than K SV = 0.467 × 10 5 M −1 in the absence of Ag NPs. This may be taken to mean that the metallic Ag NPs are strengthening the contacts between the donors and acceptors [31,32].

DFT examinations
The electronic molecular structures (MSs) for the ground states (GSs) of the following compounds-BVB, TPPS, and BVB/TPPS-were calculated using the DFT method. The DFT/B3LYP/6-311G (d) approach was used to examine the electronic MSs optimizations in a gaseous state; the findings are shown in Fig. 5. Figure 5 shows the labeled optimized MSs for the chemicals BVB, TPPS, and BVB/TPPS. The BVB MS is planer while TPPS and BVB/TPPS MSs are not planar where the phenyl sodium sulfate rotates out the porphyrin group in TPPS and BVB/TPPS MSs via 61° and 63° respectively to prevent the steric hindrance as shown in Fig. 5. Hydrogen bonds are created between the BVB and TPPS MSs to bind them together. According to Fig. 5, the hydrogen bonds (C95-H…..O81) and (C96-H…..O80) are 2.20 and 3.26°A long, respectively. The DFT/B3LYP/6-311G(d) approach is used in the gaseous state to determine selected optimum structural parameters (bond length in °A, bond angle, and dihedral angle in degree) for BVB MS in the ground and excited states as shown in Table 1. The GS MS of BVB in the gaseous state was obtained using DFT. To obtain an electrically excited state (ES) for BVB MS in a gaseous phase, TD-DFT was also used. Table 1 for BVB MS can be used to draw several conclusions, including the following; (1) The two benzo thiazolyl and vinyl groups are  Table 1 and Fig. 5. (5) According to Table 1, the bond lengths of BVB in both the gaseous and electronic states are lengthened in MeOH relative to the gaseous state by a value of (0.001-0.005) due to particular solute/solvent interactions, while the dihedral angles are left unchanged.
The relative energies of the three molecular configurations under study-BVB, TPPS, and BVB/TPPS-in the gaseous state are, respectively, −1830.346 Hartree, −5056.802, and −6888.449 Hartree. Therefore, the higher stability of BVB/TPPS compared to the other examined compounds is caused by the lower energy of BVB/TPPS compared to BVB and TPPS. It is appropriate to mention that the adsorption energy (E a ) has been calculated using the following equation; E a = E BVP/TPPS -(E BVB + E TPPS ), where E BVB and E TPPS represent the total energy of the isolated BVB and TPPS, respectively, and E BVP/TPPS is the total energy for the adsorbed dye onto the TPPS molecular structure. The calculated adsorption energy (E ads ) value of BVB dye is −35.401 eV. This negative value indicates that the BVB dye undergoes chemisorption or physisorption on the TPPS compound [33].  Also, upon adsorption of BVB dye on TPPS, the change in thermodynamic parameters like change in Gibb's free energy (ΔG), change in entropy (ΔS), and change in enthalpy (ΔH) were obtained whose values are −366.583, −368.561 kcal/ mol and 6.635 cal mol −1 k −1 respectively. The ΔG value was negative, verifying that the adsorption of direct dyes onto TPPS was spontaneous and thermodynamically favorable [34]. The negative ΔH value indicates that the adsorption of direct dyes onto TPPS is an exothermic process [34]. Furthermore, the positive ΔS indicates that the degrees of freedom increased at the solid-liquid interface during the adsorption of direct dyes onto TPPS [34].
It is well acknowledged that understanding the MOs compositions and energy levels of the molecule is essential to understanding how molecular systems behave electronically [35]. E HOMO energy refers to the ability to donate electrons, whereas E LUMO energy relates to the ability to withdraw electrons [35]. Whereas the difference between E HOMO and E LUMO , energy gap (E g ), depicts the molecular chemical stability and electron conductivity it is vital to think about crucial molecular electrical transport [35]. The graphical presentation of HOMO-2 (H-2), HOMO-1(H-1), HOMO (H), LUMO-2 (L-2), LUMO-1 (L-1), and LUMO (L) MOs for BVB and BVB/TPPS MSs are presented in Fig. 6. Over the whole backbone MS, the electron density (ED) in the H and L MOs of the BVB is delocalized. The ED in H and L+2 MOs for BVB/TPPS MS, on the other hand, is localized to BVB MS as depicted in Fig. 6. In contrast, as illustrated in  [35]. According to the E g values, the highest reactive MS is BVB/TPPS in contrast to the other studied BVB MS. The distribution of electrons in different sub-shells of their atomic orbits is described by the natural population analysis [36] applied to the BVB, TPPS, and BVB/TPPS MSs [36].  Table 2 displays the accumulating electrical charges on a single atom. The most electronegative atoms in BVB, TPPS, and BVB/TPPS MSs are N43, O81, and O81, respectively. These negative atoms are prone to contribute an electron from the molecule's electrostatic perspective [37]. These negative atoms are prone to contribute an electron from the molecule's electrostatic perspective. Those findings suggest that, as illustrated in Fig. 5, the BVB MS connects to the TPPS MS by a hydrogen bond. The charges on the atoms (O81, O80, N28, C39, and C35) in BVB/TPPS are lower compared to the same atoms in TPPS MS, as shown in Table 2. On the other hand, as compared to the same atoms (C1 and C2) in BVB MS, the charges on the atoms (C95 and C96) in BVB/TPPS MS are higher. As a result, the charge was transferred from TPPS to BVB MS. This suggests that BVB functions as an electron-withdrawing MS and TPPS as an electron-donating MS.
Using the wrong E L and E H values, it was possible to determine some crucial quantum chemical characteristics, such as the dipole moment (μ), chemical potential (ρ), electronegativity ( χ ), and chemical hardness (η). The following formulae are used to calculate these quantum parameters' area units: [38,40].
Due to the change in chemical structure and electronic characteristics by an external electric field, a chemical structure with a high dipole moment would have a significant asymmetry in the electric charge distribution. Therefore, as indicated in Table 3, the compound BVB/TPPS has a higher μ value than the BVB compound, making it more active than BVB MS. As seen in Table 3, BVB/TPPS MS has a lower μ value than the other BVB compound. As seen in Table 3, BVB/TPPS MS has a lower ρ value than the other BVB compound. This suggests that fewer electrons are leaking from BVB/TPPS MS than from the BVB molecule. Additionally, the BVB MS molecule's strong ability to attract electrons from other compounds is due to its high ( χ ) value when compared to the BVB/TPPS compound (as seen in Table 3) [41]. In many ways, BVB MS has a higher η value than BVB. This indicates that while the BVB compound is a great option to allow electrons to a different acceptor molecule, the BVB/TPPS MS is exceedingly difficult to liberate electrons.

NBO examination
An effective tool for examining inter-and intramolecular bonding, as well as a useful foundation for examining charge transfer or conjugative interactions in molecular systems, is provided by the NBO analysis of the examined BVB and BVB/TPPS MSs [37]. Delocalization of electron density between occupied bond or lone pair NBO orbitals and unoccupied antibonding orbitals correspond to a stabling donor-acceptor interaction. Furthermore, the larger the E 2 value, the more intensive the interaction between the donor and acceptor. It is a well known fact that the oxygen atom has two lone electron pairs (LPs), each of which can be involved in donor-acceptor interactions, whereas the N nitrogen atom has only one lone pair [42]. Thus, for the systems where oxygen involves in the bonding, we observed in most cases two hyper conjugative interactions between two oxygen lone pairs (LP(1) and LP(2)) and the antibonding orbital of the donor group suggesting substantial charge transfer during bonding. In the cases, where C-H…..O are involved, the donor is the oxygen lone pair. The stabilization energy E 2 for the LP/oxygen interacting with the acceptor ligand for the investigated complexes ranges from 0.80 to 1.85 kcal mol −1 . Using NBO analysis at the B3LYP/6-311G (d) level of theory, the second-order perturbation energies (Stabilization or interaction energies) (E 2 (Kcal/mol)) and the most significant interaction between Lewis's type NBOs (donor) and non-Lewis NBOs (acceptor) for TPP complexes are calculated; the gathered data are summarised in Table 4. NBO analysis results for BVB and BVB/TPPS provide the following evidence of a potent hyper conjugative interaction: (1) πC19-C20 → LP*(2) S43, πC25-N30 → LP (2) S43, LP(1) C32 → π*C31-S44, π*C31-S44 → π*C37-N42, π*C31-S44 → π*C35-C36, LP(1)C32 → *C37-N42, LP(2)S43 → π*C25-N30, LP(2)S43 → π*C25-N30 and πC25-N30 → π*C19-C20 for BVB are 100.  Table 4.

AIM analysis
The optimized BVP/TPPS molecular structure is depicted in Fig. 7 along with bond and ring critical sites (a), and a topography map for BVB/TPPS (b). Bond critical points are represented by blue balls, while ring critical points are represented by green balls (RCP). Using the Mulitwfn 3.7 program, the topographical map and optimized molecular  [43]. Boyd and Choi have shown in two key contributions that it is possible to characterize hydrogen bonding purely from the (total) charge density for a broad collection of acceptor molecules, refuting the "atoms in molecules" theory (AIM) [42]. In light of these discoveries, we independently theoretically calculate using AIM to corroborate these hydrogen bonds. Topology: A first necessary condition to confirm the presence of a hydrogen bond is a correct topology of the gradient vector field. As is clear from Fig. 7, bond critical points do indeed appear where they are expected, i.e. between the hydrogen atom and the oxygen atom (O81…H110). Furthermore, the characteristic flat hydrogen bond interatomic surface appears as a pattern that has been observed.

TD-DFT investigations
Previous research has been done on the experimental UV-Vis absorption spectra of the BVB chemical under investigation [5]. Consequently, as shown in Fig. 8b, the actual maximum absorption wavelength in MeOH was 392 nm. The π-π* electronic transition was the cause of these electronic absorption spectra [2]. In this article, we define the most precise functional and basis set to use in computing computational absorption spectra and contrast them with actual ones. To calculate the absorption spectrum for BVB at various functionals, we first fixed the basis set at 6-311G. The resulting absorption spectra are displayed in Fig. 8a and Table 5. These functionals are B3LYP [44], CAM-B3LYP [45], M06-2X [46], and mPW1PW91 [47] to determine the best functional which is B3LYP. The resultant UV--is absorption spectra for BVB in MeOH are presented in Fig. 8b and Table 5. In contrast, the functional was fixed at B3LYP, and then the basis set was adjusted to produce the optimal basis set utilized to calculate the absorption spectra for BVB and its based structures. From all this, the computational electronic UV-Vis absorption spectra for BVB were calculated using the TD/B3LYP/6-311G++(2d, 2p) method. So, the diffuse functions are significant to obtain accurate UV-Vis absorption spectra compared to the experimental one. The calculated maximum UV-Vis absorption wavelength for BVB in MeOH is at 374 nm (f = 1.823) using B3LYP/6-311G++(2d, 2p) due to HOMO → LUMO electronic transition as shown in Table 6. Hence, the calculated