Introduction

High photo-stability hetero-atom-containing compounds with the general formula (Ar/-CH = CH-Ar--CH-Ar/) make effective laser dyes [1,2,3,4,5] and have potential uses in a variety of fields, including electroluminescent devices [6], optical imaging devices and electrochromic display [5] as well as electroluminescent devices [5]. One of the many benzothiazole derivatives, l, 4 bis [-(benzothiazolyl) vinyl] benzene (BVB), is a significant candidate in the domain of diolefinic compounds containing hetero-atoms. BVB was first mentioned as a potential member of the diolefinic laser dye family in 1999 [5]. Additionally, it has been reported that BVB’s photophysical properties, photoreactivity, laser parameters, and electronic energy transfer to N, N/-bis (2, 6-dimethyl phenyl) - 3, 4, 9, 10-perylene-bis (dicarboximide) [5].

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 meso-tetrakis (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).

Experimental

Materials

According to the general condensation method previously described [20], 1,4-bis[-(2-benzoxazoly1)vinyl] benzene (BVB) was created. Silver nanoparticles (Ag NPs) were created by citrate-reducing AgNO3 [21]. A typical solution of Ag NPs measuring 16 to 20 nm in diameter and displaying a distinctive surface plasmon band at 420 nm was developed [21]. Meso-tetrakis (4-sulfonatophenyl) porphyrin sodium salt (TPPS), methanol, and ethylene glycol were bought from Sigma-Aldrich. Fluka provided the silver nitrate AgNO3 and citrate trisodium salt (95%, C6H5O7Na3.2H2O).

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.

DFT and TD-DFT calculations

Using the DFT/B3LYP/6-311G (d) technique [22,23,24,25], the optimal MSs for BVB, TPPS, and BVB/TPPS in a gaseous state are obtained. Utilizing TD/B3LYP/6-311G++(2d, 2p), the UV-Vis absorption spectra for BVB in methanol are computed. In addition to the NBO analysis, the B3LYP/6-311G(d) level of theory was used to compute the MS for BVB and BVB/TPPS.

Results and discussion

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]

$$\frac{{I}_{o}}{\mathrm{I}}=1+{\mathrm{K}}_{\mathrm{sv}}\,[\mathrm{TPPS}]$$
(1)

where [TPPS] is the quencher concentration in mol. dm−3, Io and I are the fluorescence intensities of BVB in the absence and presence of the quencher, KSV is the Stern–Volmer quenching rate constant, and based on the slope of Fig. 1c, the values of KSV 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 (R2 = 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 (τo = 0.9 ns) of the BVB in MeOH has been used to compute the energy transfer rate constant (kET) [5]. The value discovered was kET = 5.188 × 1013 M−1 s−1. This number suggests a diffusionless energy transfer mechanism because it is substantially greater than the diffusion rate constant in MeOH (kd = 1.8 × 109 M−1 s−1) at ambient temperature.

Fig. 1
figure 1

a Emission spectra (λex = 337 nm) of 1 × 10−6 M BVB in MeOH recorded in the presence of TPPS of concentrations (at decreasing intensities) as 0.0, 0.5 1, 1.5, 2, 3, 4 and 5 × 10−5 M at room temperature. b Emission spectra (λex = 337 nm) of 1 × 10−6 M BVB in 40 vol.% EG/MeOH recorded in the presence of TPPS of concentrations (at decreasing intensities) as 0.0, 0.5 1, 1.5, 2, 3, 4 and 5 × 10−5 M. c S-V plots of the quenching of 1 × 10−6 M BVB by TPPS in (●) MeOH and in (▲) 40% EG by volume in MeOH. The fluorescence intensities were monitored at 450 nm, (λex. = 3 37 nm). d Schematic illustration simplifies the quenching of excited BVB* by TPPS

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The critical transfer distance (Ro) 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]:

$${\text{R}}_{\text{o}}^{6}=8.79\times {10}^{-5} \left({\text{k}}^{2}{\text{n}}^{-4}{\Phi}_{f}\;\text{J}\left(\lambda\right) \right)\quad\text{in}\;\;\mathring{\mathrm{A}}^{6}$$
(2)

where Ro is the Förster critical transfer distance (50% transfer efficiency), (n) is the solvent refractive index, (k2) = 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:

$$\mathrm{J}\left(\uplambda \right)={\int }_{\mathrm{o}}^{\infty }{\mathrm{F}}_{\mathrm{D }}\left(\uplambda \right) {\upvarepsilon }_{\mathrm{A}}\left(\uplambda \right) {\uplambda }^{4 }\mathrm{d\lambda }$$
(3)

where \({\upvarepsilon }_{\mathrm{A}}\left(\uplambda \right)\) is in M−1 cm−1, \(\left(\uplambda \right)\) in nm and unit of \(J\left(\lambda \right)\) is in M−1 cm−1 (nm)4, FD is the peak-normalized fluorescence spectrum for the BVB (donor), and (\({\upvarepsilon }_{\mathrm{A}}\)) is the molar absorption coefficient for the(TPPS) acceptor. The critical transfer distance Ro was calculated as 25 Å. This value is higher than that for the collisional energy transfer mechanism in which Ro is less than 10 Å [29]. The high value of Ro, 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.

Fig. 2
figure 2

a Spectral overlap between the electronic absorption spectrum of TPPS and emission spectrum of BVB. b Plot of Ln (Io/If) versus concentration of TPPS for the energy transfer from 1 × 10−6 M BVB to TPPS in MeOH. The fluorescence intensities were monitored at 450 nm, (λex. = 337 nm); all measurements were done in MeOH

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For energy transfer between donor–acceptor and radiative energy transfer, the Perrin model was helpful, where the following equations provide the Perrin relationships [30]:

$$\mathit{ln} \frac{{I}_{o}}{I}=\mathbf{V}\,{{\boldsymbol{N}}}_{\mathbf{o}}\left[{\boldsymbol{Q}}\right]\quad \boldsymbol{;}\quad \mathbf{V}=\frac{4}{3}{\boldsymbol{\pi}}\,{\mathbf{r}}^{3}$$
(4)

where Io and I are emission intensities in the absence and presence of a quencher, V is the volume of the quenching sphere in cm3, No is the Avogadro’s number, and [Q] is the molar concentration of the (TPPS) quencher. A plot of ln (Io/I) versus [Q] demonstrated linear behavior as shown in Fig. 2b and the slope = VNo. “V” value was found to be 4.38 × 10−17 cm3. 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.

Fig. 3
figure 3

a The SPR absorption spectrum of AgNPs aqueous solution, b TEM micrograph of Ag NPs

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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 (KSV) 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 (KSV) in the presence of Ag NPs is higher than it is in the absence of Ag NPs. The KSV value in the presence of Ag NPs is KSV = 0.692 × 105 M−1 is larger than KSV = 0.467 × 105 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].

Fig. 4
figure 4

a Emission spectra (λex = 337 nm) of 1 × 10−6 M BVB in presence of 2% silver NPs by volume in MeOH recorded in the presence of TPPS of concentrations (at decreasing intensities) as 0.0, 0.5, 1, 2, 3, 4 and 5 × 10−5 M, b Emission spectra (λex = 337 nm) of 1 × 10−6 M BVB in presence of 2% silver NPs by volume in 40% by volume in MeOH recorded in the presence of TPPS of concentrations (at decreasing intensities) as 0.0, 0.5, 1, 2, 3 and 4 × 10−5 M. c S-V plots for the quenching of 1 × 10−6 M BVB by TPPS in the presence of 2% silver NPs by volume in (▲) MeOH and in (●) 40% EGin MeOH by volume. The fluorescence intensities were monitored at 450 nm, (λex. = 337 nm) d S-V plots for the quenching of 1 × 10.−6 M BVB by TPPS in (■) presence of 2% Ag NPs by volume in MeOH and (●) absence of Ag NPs in MeOH. All the fluorescence intensities were monitored at 450 nm, (λex. = 337 nm)

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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 located in the same plane due to a 180° dihedral angle that spans the entire BVB backbone of the molecule. (2) Due to high conjugations, the difference between C-C single bonds and C=C double bonds is quite minor. (3) The sp2 hybridization over the whole BVB backbone MS is referenced by the obtained bond angles. (4) The All-bond lengths, bond angles, and dihedral angles for BVB MS in the gaseous state and MeOH are unaffected by excitation from GS to ES, as shown in 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.

Fig. 5
figure 5

Optimized MSs for BVB, TPPs, and BVB/TPPS via applying the DFT/B3LYP/6-311G(d) method in the gaseous state

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Table 1 Selected optimized structural parameters (bond length in ˚A, bond angle, and dihedral angle in degree) computed for BVB MS via applying the DFT/B3LYP/6-311G(d) method in a gaseous state. For labeling, belong to Fig. 5
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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 (Ea) has been calculated using the following equation; Ea = EBVP/TPPS – (EBVB + ETPPS), where EBVB and ETPPS represent the total energy of the isolated BVB and TPPS, respectively, and EBVP/TPPS is the total energy for the adsorbed dye onto the TPPS molecular structure. The calculated adsorption energy (Eads) 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]. EHOMO energy refers to the ability to donate electrons, whereas ELUMO energy relates to the ability to withdraw electrons [35]. Whereas the difference between EHOMO and ELUMO, energy gap (Eg), 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 Fig. 6, the ED in L MOs for BVB/TPPS MS is confined to the TTPS terminal groups. The entire BVB MS is localized for the H-1 and L+1 MOs. In contrast, H-2 MOs are localized on the left benzothiazole group of the BVB MS, while L+2 MOs are localised on the phenyl group. For the BVB/TPPS MS, the H-1 and L+1 MOs are localised on the TPPS compound. The energy levels of H-2(EH-2), H-1(EH-1), H(EH), L-2(EL-2), L-1 (EL-1), and L (EL) MOs as well as, the energy gaps between the following; H-2 and L-2 (Eg2), H-1 and L-1 (Eg1) and H and L (Eg) in the gaseous state for BVB and BVB/TPPS MSs are calculated; the obtained results utilizing B3LYP/6-311G(d) level of theory are represented in Fig. 6. The calculated values of EH and EL for the studied MSs were within the range (−5.75 → − 6.054 eV) and (−2.08 → −3.53 eV) respectively. Since the EH value for BVB and BVB/TPPS MSs is −5.75 and −6.054 eV respectively, BVB/TPPS MS has the most stable HOMO compared to BVB MS. On the other hand, within contrasting the EL values for BVB and BVB/TPPS as presented in Fig. 6, the high stable LUMO is BVB/TPPS MS while the lowest one is BVB MS. The Eg values for BVB and BVB/TPPS MSs are listed in the following order: BVB/TPPS < BVB. Those results indicate that the BVB MS is the most stable comparing with the other BVB/TPPS MS[35]. According to the Eg 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].

Fig. 6
figure 6

Graphical presentation of HOMO-2 (H-2), HOMO-1(H-1), HOMO (H), LUMO-2 (L-2), LUMO-1 (L-1), and LUMO (L) molecular orbitals (MOs) for BVB and BVB/TPPS MS’s victimization DFT/B3LYP/6-311G (d) method

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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.

Table 2 Natural charge for BVB, TPPS, and BVB/TPPS compounds in gaseous state victimization DFT/B3LYP/6-311G (d) method
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Using the wrong EL and EH 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:

\(\uprho =\frac{{E}_{H}+ {E}_{L}}{2}\) [38, 39], \((\upchi )= -\frac{{E}_{H}+{E}_{L}}{2}\;\;\mathrm{and}\;\;\eta =\frac{{E}_{L}-{E}_{H}}{2}\) [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.

Table 3 Calculated EH, EL, energy gap (Eg1), dipole moment (μ), and other quantum chemical parameters as electronegativity (χ), chemical potential (ρ), chemical hardness (η) of the BVB and BVB/TPPS MSs in gas obtained by B3LYP/6–311(d) level of theory
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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 E2 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 E2 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) (E2(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 100.99, 44.74, 233.44, 162.93, 39.35, 52.28, 50.43 75.89 and 57.92 kcal/mol respectively. (2) πC1-N5 → LP (1)C4, πC24-C32 → LP (1)C4, πC2-C3 → LP (1)C4 for BVB/TPPS are 41.68, 50.04, and 36.40 kcal/mol respectively as presented in Table 4.

Table 4 Second-order perturbation interaction energy values computed in the NBO basis for the BVB and BVB/TPPS MSs at DFT/B3LYP/6-311G (d) method
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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 structures for BVP/TPPS were carried out [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.

Fig. 7
figure 7

Optimized BVP/TPPS molecular structure with bond critical points and ring critical points (a). Topography map for BVB/TPPS. blue balls represent the bond critical points (BCP) and green balls the ring critical points (RCP) (b)

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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 UV-Vis absorption for BVB in MeOH is in agreement with the experimental one (392 nm) (see Fig. 8b) using the B3LYP/6-311G++(2d, 2p) level of theory.

Fig. 8
figure 8

Calculated absorption spectra of BVB MS obtained with the use of different functionals, B3LYP, CAM-B3LYP, M06–2X, and mPW1PW91 (a). Calculated absorption spectra of BVB MS obtained with the use of different basis sets, 6-311G, 6-311G (d, p), 6-311G + + (d, p), and 6-311G + + (2d,2p) (b). The solvent used was MeOH

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Table 5 The basis set was used 6-311G. Calculated maximum absorption spectra of BVB MS obtained using different functionals, B3LYP, CAM-B3LYP, M06–2X, and mPW1PW91 (A). Calculated absorption spectra of BVB MS using different basis sets, 6-311G, 6-311G (d, p), 6-311G++(d, p) and 6-311G++(2d,2p) (B). The functional was used B3LYP. The solvent used was MeOH
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Table 6 Calculated electronic absorption of BBVB and BBVB MSs in MeOH obtained with the use of TD/B3LYP/6-311G++(2d,2p) and the experimental maximum absorption wavelength (Exp. λmax nm)
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Conclusion

Through spectroscopic and computational analyses, this study aims to reveal the photophysical interaction and Fluorescence Resonance Energy Transfer (FRET) from BVB MS as donors to TPPS as an acceptor, exploring the impact of Ag NPs on FRET in addition. The energy transfer between D-A pairings was of the long-range Förster Resonance Energy transfer type (Ro > 10 nm), which entails an electrostatic interaction between D and A as well as coupling between the two dipoles, according to the spectrum overlap. The energy transfer was significantly impacted by the chemical structure, binding, electrostatic potential, and alignment of the donor and acceptor, according to the spectral analysis and DFT calculations for the current system. The immobilisation of (BVB*-TPPS) D*-A pairs on the surface of Ag NPs promotes coupling exchange, which improves energy transfer when Ag NPs are added to these interacting elements. These findings highlight the use of metal-improved FRET in energy-movement-based analyses, photodynamic therapy applications, and assessing the proximity of large biomolecules. By applying TD-DFT, the estimated optical characteristics for BVB MS are achieved. Also, the estimated UV-Vis absorption for BVB in MeOH coincides with the experimental one. The BVB/TPPS molecular structure’s hydrogen bond was validated by AIM analysis. In addition, the BVB adsorption on the TPPS compound was validated by the thermodynamic characteristics.