1 Introduction

The plant-derived biomolecules are being used as natural medicine right from the ancient times and have become important due to their costless synthesis and noble properties. The quantum mechanical calculations on such molecules for tracing the molecular path way of their activity are possible at this time because the computational and theoretical chemistry methods are now available [1]. Vincosamide-N-Oxide having molecular formula C26H30N2O9 comprising of 67 atoms has already been reported to isolated from the fruits of Anthocephalus cadamba plant and its anti-lung cancer activity against cell lines H1299 have already been reported [2], however the high level quantum chemical analysis for elaborating the electronic structure properties to trace the molecular pathway towards its bioactivity and exploring its other novel applications are yet to be performed to the best of our knowledge. Due to the relatively large number of constituent atoms in the title molecule, the quantum chemical computation of all the properties implementing high level theory required for the accuracy of the results becomes less practical in terms of cost and computing time via general model chemistry. That is why depending upon the less computing time requirement, such properties have been computed by adopting DFT approach [3, 4] popular for the consistency of outcomes with the experimental results in the recent reports on the bio molecules [5,6,7]. The IR active vibrations, (1H &13C NMR) chemical shifts and UV–visible spectra have been computed using DFT and compared with their reported experimental counterparts in order to validate the adopted model chemistry at the optimized structure of the heading molecule. In order to decide the reactivity of this molecule, we have calculated the global and local reactivity descriptors both, using the same theory. Since NLO properties have been calculated at the same theoretical level because of its reported importance in various optoelectronics applications [8, 9]. The NBO analysis has been performed at the same level of density functional theory to predict the Lewis type NBO (donor)- Non-Lewis type NBO (acceptor) interaction associated with the largest delocalization. The biological activity of this natural molecule has been theoretically examined by using molecular docking approach which has been reported to be an important theoretical mode for the evaluation of the biological activity [10]. Since, the 1GCN [11], 1HSG [12] and (1X2J, 5C5S) [13, 14] protein receptors have been reported to be a target for an anti-diabetic, anti-immunodeficiency virus and anti-lung cancer agent along with G Protein-Coupled receptors are the novel structures for anti diabetic drug agent [15, 16] hence the binding of the titled molecule as drug agent with these protein receptors has been examined via the same molecular docking reported to be useful tool in computer-aided drug design due to the importance of shape-matching in drug-macromolecule interactions [17]. Docking of this molecule with the human insulin protein receptor (3I40) [18] and pancreatic cancer receptor (2NMO) [19] has also been performed to ascertain its anti diabetic mellitus activity and the nucleic acid residue at the binding sites have been located with the objective of visualizing its active layer.

The layer containing residue sites of binding in ligand–protein complex generated after completion of docking process has been viewed in the light of its MESP, chemical reactivity descriptors and NBO analysis. An attempt has been made to form the theoretical basis for studying its bioactivity using these quantum chemical analyses. The reports of the present study may be a good contribution in the area of computational chemistry of large natural biomolecule and applicable for evolving the principle of the spontaneous bioactivity contained in such molecules and developing the multifunctional natural drug agent.

2 Theoretical methods

The ground state structure of the title molecule was obtained first by applying B3LYP hybrid functional- 6–31 + G (d, p) basis set combination in DFT method [20, 21] and its frequency calculation at the same level of theory has been performed to ascertain the existence of true minimum at the potential surface visualized via gauss-view 05 program [22]. The 1H and 13C NMR chemical shifts have been calculated by using the most popular GIAO approach at the same level of theory. The UV–visible absorption spectrum and electronic transitions involved in it were analyzed using the known TD-DFT method at the same theoretical level. The effect of solvent (ethanol) is accounted by the reported polarizable continuum model of Tomasi and coworkers [23]. Theoretical calculations of HOMO, LUMO and MESP have been performed by using same DFT approach. Gaussian 09 program package [24] has been used for implementing the DFT model quantum chemistry calculations on the title molecule. In order to screen the biological activity of the title molecule, the protein receptors retrieved from Protein Data Bank (PDB) [25,26,27,28,29,30] has been allowed to interact with the title molecule as ligand using molecular docking approach implemented through the Auto dock 4.2 program package [31, 32].

3 Results and discussions

3.1 Geometry optimization, active modes of vibrations, IR spectra and single point energy

The optimized geometry of the titled molecule consisting of 67 atoms has been displayed in Fig. 1 and the total energy calculated at the single point of the potential surface named as the single point energy is ≈ −1,126,473.87 kcal/mol. The frequency calculation reveals 195 active fundamental modes of vibration which is in agreement with the reported formula of maximum (3 N-6) numbers of such modes of vibrations in a nonlinear molecule containing N atoms [33]. None of these frequencies are imaginary indicating the existence of true minimum at potential surface. The vibrational frequencies corresponding to these fundamental modes are assigned via gauss-view program. The calculated frequency of each fundamental mode has been scaled with a factor of 0.9648 because the hybrid functional B3LYP in DFT approach tends to overestimate the fundamental modes as reported by Merrick et al. [34]. The calculated and scaled frequencies along with their detailed vibrational assignments for each active mode of vibrations have been attached as supplementary material-1. The vibrations in the region 3094–3029 cm−1 occurring at the active modes of vibrations 188–181, are observed to be C-H stretching which in agreement with reported characteristic region 3100–3000 cm−1 [35] appeared due to the aromatic ring. The vibrational modes 132–95 shows the frequency range 1294–1003 cm−1 which correspond to C–H in plane bending frequencies appearing in line with the reported range 1300–1000 cm−1 [36]. The C–H out of plane bending vibrations have been reported to be appearing in the region 1000–750 cm−1[37] which are aligned with the theoretical vibrations occurred at the active modes 94–70 in the region 997–750 cm−1. The C–C stretching vibrations in titled compound are found in the region 1573–1305 cm−1 corresponding to the vibrational mode 161–133. Theoretically obtained C-H stretching due to the aromatic ring, O–H stretching due to the hydroxyl group and C = O vibrations due to the carbonyl group occurring at the region 3094–3029 cm−1, 3700–3649 cm−1 and 1730 cm−1 respectively in this molecule are in fairly good agreement with the corresponding experimental values at 3075–2851 cm−1, at 3424 cm−1 and 1612 cm−1 respectively reported in reference [2] which indicates the compatibility of the DFT optimization and frequency calculations within the theoretical constraints. The low region frequencies of other modes have also been obtained and the variation of the IR intensity with the calculated scaled frequency has been shown in Fig. 2.

Fig. 1
figure 1

Optimized geometry of vincosamide-N-Oxide

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Fig. 2
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IR Spectra of vincosamide-N-Oxide

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3.2 NMR analysis

The theoretical 13C and 1H chemical shifts in NMR spectra are compared with the corresponding experimental values in order to get insight for the conformational changes large bio molecules [38]. The optimized structure of this molecule is used to calculate the 1H and 13C chemical shifts using B3LYP/6–31 + G (d, p) level of computation in DFT via GIAO approach depicted in Table 1. The GIAO approach is most popular formalism which shows a reasonable correlation with the experimental data within the theoretical constraints for fairly large systems as per the available literature [38,39,40,41,42,43]. The 1H chemical shift for 6H, 45H, 48H atoms are observed at triplet degeneracy, 5H, 13H, 14H, 35H, 65H, 39H atoms at double degeneracy and rest H-atoms at singlet degeneracy. 13C chemical shift of all the C-atoms are observed at singlet degeneracy. The chemical structure including the computationally assigned serial number of the atoms in the optimized geometry of the title molecule obtained via Gauss View 05 program, used for NMR chemical shift calculation has been displayed in Fig. 3.The good conformity between theoretical and experimental values of 13C and 1H NMR chemical shifts are observed which indicates that the conformation of the theoretically optimized geometry of the title molecule is congruent to that used in experimental characterization and is in line with our earlier report on other such molecules [44, 45].

Table 1 Comparison of calculated and experimental 1H and 13C NMR chemical shift (δ, ppm) in Vincosamide-N-Oxide with solvent DMSO-d6 at room temperature
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Fig. 3
figure 3

Sketch diagram of the optimized geometry of Vincosamide-N-Oxide

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3.3 UV–Visible spectrum analysis

The UV–Visible spectra incorporating the effect of solvent (ethanol) has been obtained using TD-DFT method because Briquet and Vercauteren reported that this is compatible for getting consistent theoretical results with the experiments [46] and shown in Fig. 4. We have analyzed the excited states by specifying the excitation energies, wavelengths and oscillator strengths listed in Table 2. The oscillator strength is the measure of how strongly the particular electronic transition is allowed in absorption. The maximum peak occurs at 324.27 nm at excitation energy 3.8235 eV corresponding to the orbital transitions H-5 → LUMO, H-4 → LUMO with oscillator strength 0.2244 which is largest amongst all and hence these transitions would be strongly allowed. The UV–Visible analysis predicts four electronic transitions involved in producing UV–visible absorption band out of which the maximum peak occurs at 324.27 nm leading to a good agreement with its experimental vale of 324 nm reported in reference [2]. The prediction of the electronic transitions, oscillator strengths and excitation energies corresponding to the absorption peak in UV spectrum, is an important advantage of the present study.

Fig. 4
figure 4

UV–Visible spectra of Vincosamide-N-Oxide

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Table 2 UV–visible spectrum of Vincosamide-N-Oxide
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3.4 Nonlinear optical properties (NLO)

The energy of a nonlinear molecule (ξ) subjected by an weak and homogeneous electric field (E) is given by

$$\xi = \xi^{0} - \, \mu_{{\text{l}}} {\text{E}}_{{\text{l}}} {\frac{1}{2}} - \alpha_{{{\text{lm}}}} {\text{E}}_{{\text{l}}} {\text{E}}_{{\text{m}}} {\frac{1}{6}} - \beta_{{{\text{lmn}}}} {\text{E}}_{{\text{l}}} {\text{E}}_{{\text{m}}} {\text{E}}_{{\text{n}}} + \cdots$$
(1)

where ξ0 is the energy of the unperturbed molecules, El is the field at the origin, μl, αlm and βlmn are the components of dipole moment, polarizability and first hyperpolarizability, respectively. The total static dipole moment μ, the mean polarizability α0, the anisotropy of the polarizability Δα and the mean first order hyperpolarizability β0, are defined as:

$$\mu=(\mu_{x }^{2} + \mu_{y }^{2} + \mu_{z }^{2})^{{{1}/{2}}},$$
(2)
$$\alpha_{0 }= \left( {\alpha_{{{\text{xx}}}} + \, \alpha_{{{\text{yy}}}} + \, \alpha_{{{\text{zz}}}} } \right)/{3}$$
(3)
$$\Delta \alpha \, = { 2}^{{ - {1}/{2}}} \left[ {\left( {\alpha_{{{\text{xx}}}} - \, \alpha_{{{\text{yy}}}} } \right)^{{2}} + \, \left( {\alpha_{{{\text{yy}}}} {-} \, \alpha_{{{\text{zz}}}} } \right)^{{2}} + \, \left( {\alpha_{{{\text{zz}}}} {-} \, \alpha_{{{\text{xx}}}} } \right)^{{2}} + { 6}\alpha^{{2}} {\text{xz}}} \right]^{{{1}/{2}}}$$
(4)
$${\upbeta }_{0}=({\upbeta }_{x }^{2} + {\upbeta }_{y }^{2} + {\upbeta }_{z }^{2})^{{{1}/{2}}}$$
(5)

where,

$$\begin{gathered} \beta_{{\text{x}}} = \left( {\beta_{{{\text{xxx}}}} + \, \beta_{{{\text{yyy}}}} + \, \beta_{{{\text{zzz}}}} } \right), \, \beta_{{\text{y}}} = \left( {\beta_{{{\text{yyy}}}} + \, \beta_{{{\text{yzz}}}} + \, \beta_{{{\text{yxx}}}} } \right), \, \beta_{{\text{z}}} = \left( {\beta_{{{\text{zzz}}}} + \, \beta_{{{\text{zxx}}}} + \, \beta_{{{\text{zyy}}}} } \right), \hfill \\ \beta_{0} = \left[ {\left( {\beta_{{{\text{xxx}}}} + \, \beta_{{{\text{yyy}}}} + \, \beta_{{{\text{zzz}}}} } \right)^{{2}} + \left( {\beta_{{{\text{yyy}}}} + \, \beta_{{{\text{yzz}}}} + \, \beta_{{{\text{yxx}}}} } \right)^{{2}} + \left( {\beta_{{{\text{zzz}}}} + \, \beta_{{{\text{zxx}}}} + \, \beta_{{{\text{zyy}}}} } \right)^{{2}} } \right]^{{{1}/{2}}} \hfill \\ \hfill \\ \end{gathered}$$

The first order hyperpolarizability is a third rank tensor whose 27 components of the 3D matrix can be reduced to 10 components because of the Kleinman symmetry [47]. The calculated values of μ, α and β are listed in Table 3. Since the values of the polarizabilities (∆α) and the hyperpolarizabilities (βtot) of the GAUSSIAN 09 output are obtained in atomic units (a.u.), the calculated values have been converted into electrostatic units (e.s.u.) (for α; 1 a.u = 0.1482 × 10–24 e.s.u., for β; 1 a.u = 8.6393 × 10–33 e.s.u.). The calculated values of dipole moment (D) for the title compounds were found to be 8.8450D respectively, which are approximately 6.22 times than those of urea (D = 1.3732 D). Urea is one of the prototypical molecules used in the study of the NLO properties of molecular systems. The first hyperpolarizability of title molecules is approximately 9.26 times than those of urea (β of urea is 343.272 × 10–33 esu). This result indicates that Vincosamide-N-Oxide is also suited for nonlinear optical applications.

Table 3 Calculated values of polarizability (α0), anisotropy of the polarizability (Δα) and the first order hyperpolarizability (β0) of Vincosamide-N-Oxide
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3.5 Chemical reactivity analysis

3.5.1 Global reactivity descriptors and thermodynamic parameters

In case of our molecule, HOMO = − 0.243a.u and LUMO = − 0.097.a.u. The band gap is −0.097–(−0.243) = 0.146a.u which is reasonably small indicating that this natural biomolecule is soft molecule as per Pearson who proposed the HOMO–LUMO energy band gap to be the measure of softness of molecule for chemical reaction [48] which explains the eventual charge transfer within the molecule. The ionization potential (I), electronic affinity (A), electronegativity (χ), chemical potential (µ), global hardness (η), global softness (S) and global electrophilicity index(ω) are the global reactivity descriptor explained in term of HOMO–LUMO energy band gap [49, 50] which are listed as supplementary material-2. The ability of electron transportation and excitation properties is qualitatively predicted through HOMO and LUMO [51, 52] wherein HOMO primarily acts as an electron donor and LUMO acts as an electron acceptor and tends to create chemical reactivity through electronic transition [53]. The HOMO and LUMO plots of the title compound have been shown in Fig. 5. The low HOMO–LUMO energy gap favors the high value of polarizability and hyper polarizbilty which are measure of NLO property [54].

Fig. 5
figure 5

HOMO–LUMO plots for Vincosamide-N-Oxide

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MESP surface is very useful to understand the potential sites for electrophilic (negative region) and nucleophilic (positive region) reactions [55, 56] which is well suited for recognition of one molecule by another through this potential, as in the case of drug- receptor interactions [57, 58] shown in Fig. 6.The values of the electrostatic potential at the surface are displayed by different colors in the order of red < orange < yellow < green < blue. The color code of these maps is in the range between −9.481 a.u. (deepest red) and 9.481 a.u. (deepest blue) in the titled compound, where blue indicates the most electropositive i.e. electron poor region and red indicates the most electronegative region, i.e. electron rich region. It is evident that the most electronegative region is located around 23O- atom which effectively acts as electron donor in molecule.

Fig. 6
figure 6

MESP surface for Vincosamide-N-Oxide l

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By default, the program package used in the present study carries out thermo chemical analysis at 298.15 K temperature and 1 atmosphere of pressure. The thermodynamic parameters namely zero-point energy (ZPE), zero-point corrected vibrational energy (E), heat capacity at constant volume (CV), entropy (S), Gibb’s free energy (G) and enthalpy (H) have been obtained and given in supplementary material-2. The total energy of this molecular system is given by Etotal = E0 + Evibrational + Erotational + Etranslational, where E0 = Eelectronic + ZPE where zero-point energy correction (ZPE) to the electronic energy accounts for the effect of vibrations persisting even at 0 K in the molecule which has been estimated to be 342.11 kcal/Mol in case of title molecule. The final vibrational energy E, Enthalpy H = E + RT and Gibbs free energy G = H-TS are subject to the thermal correction which have been accounted in the results.

3.5.2 Local reactivity descriptors

The relative site selectivity of the atoms belonging to the active region (high layer) within the title molecule is determined by Fukui function \(\left( {f_{k}^{ \pm } } \right)\), local softness \((s_{k}^{ \pm }\)), and local electrophilicity \(\left( {\omega_{k}^{ \pm } } \right)\) which have been calculated as per reported equations [59,60,61,62] given below:

$${f_{k}^{ + } } = \left[ {{\text{q}}\left( {{\text{N }} + { 1}} \right) - {\text{q}}\left( {\text{N}} \right)} \right]$$
(6)
$${f_{k}^{ - } } = \left[ {{\text{q}}\left( {\text{N}} \right) - {\text{q}}\left( {{\text{N}} - {1}} \right)} \right]$$
(7)
$$s_{k}^{ \pm } = Sf_{k}^{ \pm }$$
(8)
$$\omega_{k}^{ \pm } = \omega f_{k}^{ \pm }$$
(9)

where q(N) is the charge on nth atom for neutral molecule while q(N + 1) and q(N − 1) are the same for its anionic and cationic chemical species, respectively. S and \(\omega\) are global softness and electrophilicity index respectively. The values of these descriptors are presented in Supplementary Maerial-3. If molecule is attacked by a soft reagent, it has tendency to react at the site where the value of local reactivity descriptor is largest and when attacked by hard reagent it tends to react at the site where the value of the same is smallest [63]. It is observed that the largest value of all local reactivity descriptors corresponds to 11C connected to the ring. Therefore, this site is favorable to the nucleophilic as well as electrophilic attack although, 11C site is more prone to the nucleophilic attack than electrophilic attack due to \(f_{k}^{ + }\) > \(f_{k}^{ - }\) as per the report of Morell et al. [64].

3.6 NBO analysis

NBO analysis helps in identifying individual bonds and the energies associated with loan -pair electrons which play an important role in the chemical process [65,66,67]. It provides the second order perturbative estimates of filled ‘donor’- ‘acceptor’ empty orbital (bond-antibond) interaction in NBO basis which leads to the loss of occupancy from the localized NBOs of idealized Lewis structure into Non-Lewis empty orbitals known as ‘delocalization correction to the zeroth-order natural Lewis structure’. For each donor NBO (i) and acceptor NBO (j), the stabilization energy E(2) associated with electron delocalization is computed [68, 69]. Second order perturbation theory analysis of the Fock matrix in NBO basis is listed in Table 4.

Table 4 Second Order Perturbation theory analysis of Fock matrix for various lone pair’s interaction in the NBO basis
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We observe that greatest stabilization energy of delocalization = 29.12 kcal/mol, is associated with the donor LP (O23) π → π *(C18-N22) acceptor interactions. We note that the atoms O23 has already been identified to be the sites of electrophilic attack in MESP also. The same atoms have been observed to be formed residue sites of interaction in ligand (title molecule)-protein complex.

3.7 Screening of bioactivity

Vincosamide-N-Oxide biomolecule as ligand binds with 1GCN, 1HSG, 1X2J, 2NMO, 3I40 and 5C5S protein receptors screened through molecular docking approach. The calculated free energy of binding and intermolecular energy of each protein–ligand interaction has been depicted in Table 5. The free energy of binding of each protein–ligand interaction is significantly negative which reveals that the labeled molecule can be explored as potential inhibitor against the diabetic mellitus, HIV, Lung Cancer and Pancreatic Cancer. The nucleic acid residue site of binding is ASP-9 in 1GCN binding complex located around 67O atom of the heading molecule. The same are LYS-20, APS-25 & GLY-27 in 1HSG complex located around O23, O53 & O67-atoms respectively, APS-389 & GLU-449 in 1X2J complex located around O23 & O67-atoms, GLU-184 & BGC-501 in 2NMO complex located around O23 & O67-atoms, TYR-14 & LEU-13 in 3I40 complex located around O23 & O67-atom and ASN-3 located around N22-atom, HIS-232 & LEU-233 in 5C5S complex located around O23 & O67-atoms. In this way, the binding has been observed to be mediated through the O-atoms of the title molecule at all the residue sites. The molecular surface of the complex in each protein–ligand interaction has been show in Figs. 7, 8, 9, 10, 11 and 12. On the basis of the biological activity evaluated in the present study, the labeled molecule may be explored as multifunctional drug candidate.

Table 5 Intermolecular Energy and the Free energy of binding at a particular inhibition constant calculated by molecular docking
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Fig. 7
figure 7

Molecular surface of the complex produced in Vincosamide-N-Oxide -1GCN binding

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Fig. 8
figure 8

Molecular surface of the complex produced in Vincosamide-N-Oxide -1HSG binding

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Fig. 9
figure 9

Molecular surface of the complex produced in Vincosamide-N-Oxide -1X2J binding

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Fig. 10
figure 10

Molecular surface of the complex produced in Vincosamide-N-Oxide -2NMO binding

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Fig. 11
figure 11

Molecular surface of the complex produced in Vincosamide-N-Oxide -3I40 binding

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Fig. 12
figure 12

Molecular surface of the complex produced in Vincosamide-N-Oxide -5C5S binding

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4 Conclusion

The density functional theory at DFT-B3LYP/6–31 + G (d,p) level is compatible for geometry optimization without introducing the conformational changes evident from the fair agreement between theoretical and experimental spectral characteristics (IR, NMR and UV–Visible). HOMO, LUMO, MESP, NLO properties, local reactivity descriptors and NBO properties computed applying the same level of theory on the title molecule are significant characteristics for structural description of this molecule. Reasonably low HOMO–LUMO energy band gap makes this biomolecule soft for the chemical reaction which may be one of the reasons of its inherent bioactivity. The MESP surface of the title molecule is suited for the drug activity wherein electrophilic sites are located around the 23O atom which is the epicenter of its biological activity. The first order hyperpolarizability of title molecules is approximately 9.26 times greater than that of the prototype molecule Urea indicates that this biomlecule can be explored for nonlinear optical applications. The reactive sites identified through local reactivity descriptors match well with those identified through molecular docking of the title molecule with protein receptor’s 1GCN, 1HSG, 1X2J, 2NMO, 3I40 and 5C5S. The NBO analysis also predicts the largest electron delocalization is associated with donor (O23) π → π *(C18-N22) acceptor interaction which indicates that these atoms are the suitable active sites at surface of the title molecule and that is why the nucleic acid residue sites of ligand–protein complex are located around these atoms. The present study finds the title molecule not only biologically active for drug applications but also optically active for nonlinear optical applications. The findings of the present investigations infer that apart from its reported activity against the lung Cancer Cell Line H1299; it possesses the biological activity against the several types of lung cancer, HIV and diabetic mellitus.