A density functional theory insight into the structure and reactivity of diphenyltin(IV) derivative of glycylphenylalanine

Geometry optimization and structural analysis

The ground-state optimized geometry in the gas phase of Ph₂SnL calculated at the B3LYP/6-31G(d,p)/LANL2DZ(Sn) computational level of theory is presented in Figure 1B (cf. Figure 1A for atom number notation). The frequency analysis indicates that the optimized geometric configuration is the local minima on the potential energy surface (PES) of Ph₂SnL. The selected bond lengths and bond angles in Ph₂SnL are presented in Table S1 (Supplementary Material).

As presented in Figure 1B, the calculated geometric environment around the central Sn atom in Ph₂SnL is considerably distorted with terminal carboxylate oxygen O17 (Sn-O17=2.019 Å) and terminal amino nitrogen N1 (Sn-N1=2.430 Å) in the axial positions, and deprotonated peptide nitrogen N9 (Sn-N9=2.058 Å) and two phenyl carbons C30 and C41 (Sn-C30=2.126 Å and Sn-C41=2.124 Å) in the equatorial plane. The calculated equatorial angle C30-Sn-C41 in Ph₂SnL is 118.6°, which is close to that in experimentally reported penta-coordinated diorganotin(IV) dipeptides [e.g. Ph₂Sn(Gly-Gly), 117.5° (Huber et al., 1977); n-Bu₂Sn(Gly-Val), 125.3° (Mundus-Glowacki et al., 1992)] but smaller to that experimentally reported in n-Bu₂Sn(Trp-Gly), 151.6° (Nath et al., 2009), and Me₂Sn(Tyr-Phe)·MeOH, 136.4° (Nath et al., 2008). The distortion in the molecule is evident from the calculated axial angle N1-Sn-O17 of 153.4°, which is close to the experimentally reported values for n-Bu₂Sn(Trp-Gly), 147.9° (Nath et al., 2009), and Me₂Sn(Tyr-Phe)·MeOH, 149.6° (Nath et al., 2008). Further, various bond angles involving the central Sn atom suggest a distorted trigonal bipyramidal arrangement. Also, there seems to be a change in bond length of various bonds involving N1, N9, and O17 in Ph₂SnL relative to H₂L, indicating the electron redistribution around the central Sn atom through these coordinating atoms. The calculated distorted trigonal bipyramidal arrangement is consistent with previously reported geometry of diorganotin(IV) derivatives of dipeptides (Huber et al., 1977; Mundus-Glowacki et al., 1992; Katsoulakou et al., 2008; Nath et al., 2008, 2009; Girasolo et al., 2010).

The various energetic and thermochemical parameters for Ph₂SnL in the gas phase have been calculated at 1 atm and 298.15 K at the B3LYP/6-31G(d,p)/LANL2DZ(Sn) level of theory, and the results are presented in Table S2. The total energy of Ph₂SnL calculated after zero-point correction and the thermal correction to energy, enthalpy, and Gibbs free energy have been estimated; for instance, its calculated total energy after thermal correction to Gibbs free energy, which is the sum of electronic and thermal free energies (G=H-TS) (Foresman and Frisch, 1996), is -1227.9881 a.u. The contribution to internal thermal energy (E_tot), entropy (S_tot), and constant volume molar heat capacity (CV_tot) has the value for Ph₂SnL as 271.22 kcal/mol, 189.48 cal/mol-K, and 101.48 cal/mol-K, respectively.

Atomic charges and molecular electrostatic potential (MEP) map

The MEP is created in the space around a molecule by its nuclei and electrons and is related to the electron density. It holds significance because it provides substantial insight into the sites within the molecule where the electron distribution effect is dominant, for example, for the intermolecular association and molecular properties of small molecules, predicting molecular reactive behavior, and analyzing processes based on the ‘recognition’ of one molecule by another, such as between a drug and its cellular receptor, because it is through their potentials that the two species first ‘see’ each other (Politzer et al., 1985). The MEP surface of Ph₂SnL calculated on the ground-state optimized geometry in gas phase at the B3LYP/6-31G(d,p)/LANL2DZ(Sn) level of theory is presented in Figure 2A. The different values of the electrostatic potential at the surface are represented by different colors and potential increases in the order red<orange<yellow<green<blue. As evident from the MEP map (Figure 2A), the greater regions of the complex are of intermediary potential (green coded regions), but because the green color is toward the increasing range of the potential (toward the blue color), the complex possesses smaller electronegativity with electron-deficient regions having preference for an approach by nucleophiles.

Figure 2:

Molecular electrostatic potential (MEP) map and atomic charges for diphenyltin(IV) derivative of glycylphenylalanine.

(A) Molecular electrostatic potential (MEP) map. (B) Plot of atomic charges at the selected atoms based on MPA, HPA, and NPA for the ground-state optimized geometry (in the gas phase) for Ph₂SnL calculated at the B3LYP/6-31G(d,p)/LANL2DZ(Sn) level of theory.

The calculation of effective atomic charges is significant whenever quantum-chemical calculations are applied to molecular systems because they affect dipole moment, molecular polarizability, and electronic structure. In such systems, the atomic charges are attributed through population analysis. To study electrostatic arguments that would explain the probable structure and reactivity of Ph₂SnL, an electron density distribution analysis has been performed on the basis of atomic charges determined by the Mulliken population analysis (MPA), the Hirshfeld population analysis (HPA), and the natural population analysis (NPA) charge schemes in the gas phase within Ph₂SnL, at the B3LYP/6-31G(d,p)/LANL2DZ(Sn) level of theory, and the results based on these schemes for the selected atoms in Ph₂SnL are presented in Figure 2B and Table S3.

The population of the atomic orbitals suggest that in Ph₂SnL, the natural electron configuration of the central Sn atom is [core]5s^0.785p^0.926p^0.01, which differs significantly from Ph₂Sn(IV)²⁺ cation configuration [core]5s². The absolute value of the natural charge of the central Sn atom in Ph₂SnL on the basis of NPA is 2.299. Further, the natural electron configuration of coordinating oxygen atom (O17) is [core]2s^1.702p^5.163d^0.01, amino nitrogen (N1) is [core]2s^1.432p^4.523p^0.01, and deprotonated peptide nitrogen (N9) is [core]2s^1.352p^4.523p^0.01. The absolute values of the natural charge of N1, N9, and O17 on the basis of NPA are approximately -0.960, -0.884, and -0.872, respectively. Moreover, the natural electron configuration of two carbon atoms (covalently bonded to the central Sn atom), viz., C30 and C41, is [core]2s^1.052p^3.503p^0.02. The absolute values of the natural charge of C30 and C41 on the basis of NPA are approximately -0.576 and -0.578, respectively. The existence of the high positive value of charge at the central Sn atom and such oppositely charged centers around it further confirms the ionic interaction in the Sn-O and Sn-N bonds, resulting in the formation of coordinate/dative bonds between the ONN system of deprotonated H₂L and Ph₂Sn(IV) moiety. The results, as presented in Figure 2B, indicate that the most negative atomic charges are attributed to oxygen, nitrogen, and organotin(IV) carbon atoms in the Ph₂SnL derivative. Similarly, results are reported for tin systems with ligands having heterodonor atoms (Girichev et al., 2012; Latrous et al., 2013; Matczak, 2015). The population analysis based on MPA, HPA, and NPA also indicates an ionic interaction in these bonds (Table S3). The presence of such an ionic interaction in Ph₂SnL is significant as it may lead to a slow hydrolytic decomposition of Sn-O/N bonds, suggesting that the complex can exhibit potential activity, such as antiproliferative activity owing to the existence of R₂Sn(IV)²⁺ (R=Ph) moiety in the biological medium.

Conceptual DFT-based global reactivity descriptors

The molecular properties and the conceptual DFT-based global reactivity descriptors for the ground-state optimized geometries in the gas phase of H₂L and Ph₂SnL, calculated using finite difference approximation, are presented in Table 1. The results indicate that the dipole moment that accounts for the existence of charged separated regions within the system is greater for Ph₂SnL (10.35 Debye) in comparison with H₂L (3.31 Debye). The ionization potential (IP) and the electron affinity (EA) for Ph₂SnL are lower than that for H₂L. As a result, the band gap (ΔE) for Ph₂SnL (7.89 eV) is lower than H₂L (9.50 eV).

The FMO analysis is significant from the perspective of understanding the distribution of charge density within a system as it helps in estimating the energies and the type of frontier molecular orbitals because these orbitals are the sites of exchange of charge density, which leads to the interaction between molecules. The FMO analysis for Ph₂SnL has been performed through the Koopman’s approximation within the molecular orbital theory (Geerlings et al., 2003), and the E_HOMO and the E_LUMO energies are presented in Table 1. The E_HOMO and the E_LUMO plots along with the band gap (ΔE) in the gas phase, as presented in Figure 3, indicate that, in Ph₂SnL, the highest occupied molecular orbital (HOMO) is concentrated over the dipeptide, whereas the lowest unoccupied molecular orbital (LUMO) is concentrated around the central Sn atom and organic residues in organotin(IV) moiety, indicative of the interaction of H₂L with Ph₂Sn(IV) moiety through deprotonated oxygen (O17) and peptide nitrogen (N9) atoms, as reported previously for other diorganotin(IV)-dipeptide systems (Huber et al., 1977; Mundus-Glowacki et al., 1992; Nath et al., 2008, 2009; Girasolo et al., 2010). Further, the FMO analysis suggests that upon interaction with an electron donor/acceptor, in Ph₂SnL, the region around the central Sn atom will behave as an acceptor of charge density, whereas the dipeptide region (L²-) will behave as a donor of charge density. Moreover, the studied complex interacts with macromolecular receptors through the central Sn atom upon the slow hydrolysis (owing to ionic interaction) of Sn-O/N bonds.

Figure 3:

Highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) plots along with band gap (ΔE) in the gas phase for Ph₂SnL calculated at the B3LYP/6-31G(d,p)/LANL2DZ(Sn) level of theory.

The global reactivity descriptors calculated based on FMO analysis are tabulated in Table 1. The electronic chemical potential (μ), which measures the sensitiveness of the system’s energy to a change in the number of electrons at fixed external potential [μ=(∂E∂N)v(r→)] (Geerlings et al., 2003), is greater for Ph₂SnL in comparison with H₂L, indicating that the energy of the complex is more sensitive toward the change in the number of electrons. Further, because electronegativity (χ) is negative of μ, it increases on complex formation. The global hardness (η), which is the resistance of the electronic chemical potential to changes in the number of electrons [η=(∂2E∂N2)v(r→)=(∂μ∂N)v(r→)] (Parr and Pearson, 1983), can be regarded as a resistance to charge transfer, whereas global softness (S), which is the inverse of the global hardness [S=1η=(∂N∂μ)v(r→)] (Yang and Parr, 1985), is a measure of the ease of charge transfer and is associated with high polarizability. The value of η for H₂L is greater than Ph₂SnL, whereas that of S is smaller than Ph₂SnL. Because finite difference approximation to global hardness equates it to band gap, these results indicate that Ph₂SnL with small band gap is more soft and polarizable in comparison with H₂L. Moreover, the electrophilicity index [ω=-ΔE≡μ22η], which measures the electrophilic power of a system (Chattaraj et al., 2006) and which can be described as the maximum ability of a molecule to accept electrons in the neighborhood of an electron reservoir (Parr et al., 1999), has a value of 0.76 eV for Ph₂SnL. Because ω is positive for Ph₂SnL and also higher than H₂L, the complex possesses electrophilic power, and assuming the system as electron donor/acceptor, the process will be an energetically favorable process during partial charge transfer. The calculated global reactivity descriptors further suggest that Ph₂SnL can exhibit potential biological activity on its probable interaction with macromolecular receptors because it is soft and polarizable, and charge transfer during such an interaction will be an energetically favorable process.

Conceptual DFT-based local reactivity descriptors

The conceptual DFT-based local reactivity descriptors, such as Fukui function index [f^±(k)] (Parr and Yang, 1984; Geerlings et al., 2003; Roy and Saha, 2010), local softness [s^±(k)] (Geerlings et al., 2003; Roy and Saha, 2010), local electrophilicity [ω^±(k)] (Geerlings et al., 2003; Chattaraj et al., 2006; Roy and Saha, 2010), and hardness potential [Δ^±h(k)] (Geerlings et al., 2003; Saha et al., 2013), considered to predict the regioselectivity of the atoms in Ph₂SnL, have been calculated at all the atoms with three different population analysis schemes, viz., MPA, HPA, and NPA, and the results based on the NPA, HPA, and MPA schemes at the selected atoms of Ph₂SnL are presented in Tables S4, S5, and S6, respectively. The variation of f⁺(k) and s⁺(k), f^-(k) and s^-(k), ω⁺(k) and ω^-(k), and Δ⁺h(k) and Δ^-h(k) at the selected atoms of Ph₂SnL calculated on the basis of MPA, HPA, and NPA charge schemes is presented in Figure 4A–D, respectively.

Figure 4:

Variation of (A) f⁺(k) and s⁺(k), (B) f^-(k) and s^-(k), (C) ω⁺(k) and ω^-(k), and (D) Δ⁺h(k) and Δ^-h(k) at the selected atoms of Ph₂SnL based on MPA, HPA, and NPA charges, calculated at the B3LYP/6-31G(d,p)/LANL2DZ(Sn) level of theory (all values are given in eV).

Because there are some differences between the atomic charges obtained from MPA and NPA schemes (Reed et al., 1985), Fukui indices will be highly dependent on the population analysis method, and the results should therefore be analyzed with greater restraint. The Fukui function f+(r→) easures the reactivity toward the nucleophilic attack on the system, and its large value at a particular site indicates that the site is capable of accepting electron density. Similarly, the Fukui function f-(r→) measures the reactivity toward an electrophilic attack on the system, and its large value at a particular site indicates that the site is an electron-donating site (Geerlings et al., 2003). Further, it had been proposed that a larger value of the Fukui function indicates more reactivity (Parr and Yang, 1984), and hence, for a particular atomic center in the molecule, the greater the value of the condensed Fukui function, the more reactive it will be (Roy and Saha, 2010). Moreover, for a nucleophilic attack due to an addition of an electron to the molecule, a positive value for the Fukui function f+(r→) at a particular atom emphasizes an increase of atomic population on that position, whereas a negative value means that the electron density is reduced. Similarly, for an electrophilic attack, when an electron is removed from the molecule, a positive value for the Fukui function f-(r→) at a particular atom emphasizes a decrease of atomic population on that position, whereas a negative value means that the electron density grows larger (Roy and Saha, 2010).

As evident from the results (cf. Figure 4), in Ph₂SnL, the trends based on the values of f⁺(k), s⁺(k), and ω⁺(k) with all the population scheme suggest that the central Sn atom is an electrophilic site and is more reactive toward a nucleophile and that such an attack increases the atomic population at this center. Similarly, the trends based on the values of f^-(k), s^-(k), and ω^-(k) with all the population schemes suggest that O18 is the most reactive site toward an electrophilic attack. The results obtained are in accordance with the FMO analysis, which indicates that in Ph₂SnL, the HOMO is concentrated over the dipeptide unit and the LUMO is concentrated around the central Sn atom encompassing the phenyl residues covalently bonded to the central Sn atom. These results outline the general behavior of the central Sn atom in the organotin(IV) complexes in accordance with the previously reported experimental observations, that R₂Sn(IV)²⁺ is an active species in the biological medium (Pellerito and Nagy, 2002). The two variants of the hardness potential, viz., the electrophilic hardness potential [Δ⁺h(k)] and the nucleophilic hardness potential [Δ^-h(k)], which measures the reactivity toward an approaching nucleophilic and electrophilic reagent, respectively, have also been calculated at all the atoms of Ph₂SnL. The higher the value of Δ⁺h(k) at an atom, the higher the reactivity (i.e. electrophilicity) of that atom toward an approaching nucleophile (Saha et al., 2013). Likewise, the higher the positive value of Δ^-h(k) for an atom, the higher the reactivity (i.e. nucleophilicity) of that atom toward an approaching electrophile. As evident from the results (cf. Table S4 and Figure 4D), in Ph₂SnL, the trends based on the values of Δ⁺h(k) suggest that C30/C41 (carbon bonded covalently to the Sn atom) is the most reactive site toward an approaching nucleophilic reagent, and the trends based on the values of Δ^-h(k) suggest that O18 is among the most reactive site toward an approaching electrophilic reagent. Further, in the coordination sphere around the central Sn atom, the higher value of Δ⁺h(k) at the central Sn atom, N1_(amino), and C30/C41 indicates that these sites are more reactive toward a nucleophilic reagent. However, the higher value of Δ^-h(k) at N9_(peptidic) and O17/O18_{(carboxylate)} indicates that these sites are more reactive toward an electrophilic reagent.

The variation of relative electrophilicity [(s+(k)s-(k))] and relative nucleophilicity [(s-(k)s+(k))] (Roy et al., 1998; Geerlings et al., 2003) and dual reactivity descriptor [f²(k)] (Morell et al., 2005) at the selected atoms of Ph₂SnL based on MPA, HPA, and NPA charges is presented in Figure 5A–C, respectively. Because the MPA and the NPA schemes gave negative Fukui index values for some of the atomic sites, a comparative analysis of relative electrophilicity and relative nucleophilicity is presented based on the HPA scheme. The relative electrophilicity helps to locate the preferable site (or atom) in a molecule for a nucleophilic attack on it and it is the electrophilicity of any site as compared with its own nucleophilicity, whereas the relative nucleophilicity helps to locate the preferable site (or atom) in a molecule for an electrophilic attack on it and it is the nucleophilicity of any site as compared with its own electrophilicity (Roy et al., 1998). As evident from the results (cf. Figure 5A and B) based on the HPA scheme, C41 has maximum relative electrophilicity (62.1964), whereas O17 has maximum relative nucleophilicity (135.3333). Further, based on the HPA scheme (cf. Table S5 and Figure 5A), in the coordination sphere around the central Sn atom in Ph₂SnL, the central Sn (13.0191) and the N1_(amino) (1.0922) are also potential electrophilic sites and, thus, are the highly preferred sites for a nucleophilic attack, owing to the higher value of relative electrophilicity as compared with relative nucleophilicity. By contrast, C13 (4.9503) and O18_(carboxylic) (3.3902) are potential nucleophilic sites (cf. Figure 5B) and, thus, are the highly preferred sites for an electrophilic attack, owing to the higher value of relative nucleophilicity as compared with relative electrophilicity. These results further indicate that in the Ph₂SnL derivative, greater charge density is concentrated over the dipeptide unit. In the dual reactivity descriptor [f²(k)], a selectivity index is able to characterize both the nucleophilic and the electrophilic behaviors. As evident from the results (cf. Tables S4, S5, and S6), in Ph₂SnL, among the selected atoms, the central Sn atom has the most positive f²(k) value based on both NPA (3.3729 eV) and HPA (1.9185 eV) schemes (cf. Figure 5C), indicating it to be most susceptible for a nucleophilic attack, whereas O18_{(carboxylate)} has the most negative f²(k) value based on HPA (-1.9067 eV) and C16 based on NPA (-3.0420 eV) (cf. Figure 5C), indicating these sites to be most susceptible for an electrophilic attack. Furthermore, as evident from the results based on the HPA scheme (cf. Figure 5C), in the coordination sphere around the central Sn atom, the positive value of f²(k) at the central Sn atom, the carbon atoms in the organic residues (covalently bonded to the central Sn atom), and N1_(amino) indicates that these sites are favored for the nucleophilic attack, whereas the negative value of f²(k) at N9_(peptidic) and O17_{(carboxylate)} indicates that these sites are favored for an electrophilic attack.

Figure 5:

Variation of (A) relative electrophilicity, (B) relative nucleophilicity, and (C) dual reactivity descriptor at the selected atoms of Ph₂SnL based on MPA, HPA, and NPA charges, calculated at the B3LYP/6-31G(d,p)/LANL2DZ(Sn) level of theory (all values in panel C are in eV).

Computational details

All the quantum-chemical calculations have been performed using the Gaussian 09 program package (Frisch et al., 2010). The molecular geometries of glycylphenylalanine (H₂L) and Ph₂SnL were fully optimized in the gas phase at the DFT level using the B3LYP functional, which is a combination of Becke’s three parameter (B3) gradient corrected hybrid exchange functional (Becke, 1993), with the dynamical correlation functional of Lee et al. (1988) (LYP). All the atoms except Sn were described by the 6-31G(d,p) basis set, which contains a reasonable number of basis set functions that are able to reproduce the experimental observations. The Sn atom in Ph₂SnL was described by the LANL2DZ basis set in which Sn inner shells are described by effective core potential ECP46MWB (1s²2s²2p⁶3s²3p⁶3d¹⁰4s²4p⁶4d¹⁰) along with the basis set (3s3p)/[2s2p] (Hay and Wadt, 1985). The geometry optimization was conducted through an algorithm of iterative steps to locate true global minima on the PES with default parameters for convergence is met. The absence of an imaginary frequency in a harmonic frequency calculation conducted at the same level of theory indicates that the calculated geometry is a true global minimum on the PES. The atomic charges at all the atoms in the studied systems were calculated using MPA, HPA, and NPA at the same level of theory. The energies of FMOs and the conceptual DFT-based global and local reactivity descriptors based on MPA, HPA, and NPA have been calculated for the studied systems using finite difference approximation (Geerlings et al., 2003). The MEP maps and the visualization of all results have been performed using Gauss View 5.0 (Dennington et al., 2009).