Introduction

Schiff-base ligands are characterized by their ability to coordinate readily with various transition metal ions to form stable complexes that are easy to synthesize [1,2,3]. Often, the Schiff-base ligand has two or more electron-donating functional groups and can be coordinated with metal ions in different modes (monodentate, bidentate, tridentate, etc) via donor–acceptor interactions between the functional groups of the ligand and the metal [4]. Because of these remarkable properties, Schiff bases have become popular in a number of scientific fields, such as biological science and medicine [5]; indeed, metal–Schiff base complexes have been widely used as anti-inflammatory and antibacterial agents [6,7,8]. To improve their biological activities, several studies aimed at synthesizing new allylamine-derived Schiff-base ligands and their respective complexes (usually with first-row metal ions) have been carried out [9,10,11]. Recently, a new class of such complexes has been synthesized: Ni\( {\mathrm{L}}_2^2 \) (1), Pd\( {\mathrm{L}}_2^1 \) (2), and Zn\( {\mathrm{L}}_2^2 \) (3) (Fig. 1), where L1 and L2 are Schiff bases (L1 = 2-allyliminomethyl phenolate and L2 = 2-allyliminomethyl-4-methyl phenolate) synthesized from salicylaldehyde and 2-hydroxy-5-methylbenzaldehyde, respectively, as well as allylamine [12]. These three complexes have been fully characterized using different techniques and various spectroscopic methods of analysis. X-ray data show that complexes 1 and 2 adopt a square-planar geometry around the metallic ion and that complex 3 is nonplanar. In the UV-visible region, the three complexes are characterized by a weak band in the visible region and intense absorptions in the UV-C region. However, the geometric structures of the three complexes have not been well studied, particularly the first coordination sphere of the metal ion (or more precisely, how the metal ion coordinates with oxygen and nitrogen). In order to assign the main absorptions observed experimentally, the electronic absorption spectrum must be simulated. Numerous theoretical studies have been carried out to study the geometric and electronic properties of Schiff base ligands and Schiff base–transition metal complexes [13,14,15]. Those works provide additional and indispensable support to experimental investigations, allowing more detailed study.

The objective of the work reported in the present paper was to theoretically study the structural, electronic, and optical properties of the three complexes 1, 2, and 3 via density functional theory (DFT) and time-dependent density functional theory (TD-DFT) calculations. We also studied the optical properties of the complex Ni\( {\mathrm{L}}_2^1 \) (4) in order to examine how dimethylation of the phenolate rings in the ligands affects the optical properties of the nickel complex.

Fig. 1
figure 1

The geometries of Ni\( {\mathrm{L}}_2^2 \) (1), Pd\( {\mathrm{L}}_2^1 \) (2), and Zn\( {\mathrm{L}}_2^2 \) (3)

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Computational details

Geometry optimization calculations for complexes 1–3 were performed using density functional theory (DFT). This was achieved using the two hybrid functionals B3LYP [16,17,18] and mPW1PW91 [19] as well as the basis set 6-31++G(d,p) [20,21,22] to describe all nonmetal atoms and the combined basis set–pseudopotential Lanl2DZ [23, 24] to describe the metal atoms. The effects of the solvent (methanol, ε  = 32.613) were introduced implicitly in terms of the polarizable continuum model (PCM) [25, 26]. These methods were used because they performed well in our previous studies [27, 28]. Geometry optimizations were followed by vibrational frequency calculations to confirm that the optimized structures were real minima. The ground-state geometries obtained were used to perform natural bond analysis [29,30,31,32,33] using the NBO program [34] implemented in Gaussian [35]. The NBO interactions were visualized with Jmol [36] using the Jmol NBO Visualization Helper [37]. The lowest-lying excited singlet states in methanol (CH3OH) were studied using the TD-DFT method at the same level of theory used to perform the optimizations. All calculations were carried out using the Gaussian program.

Results and discussion

Structural investigations

The main structural parameters of the three complexes Ni\( {\mathrm{L}}_2^2 \) (1), Pd\( {\mathrm{L}}_2^1 \) (2), and Zn\( {\mathrm{L}}_2^2 \) (3) (Fig. 1) in methanol, as computed with mPW1PW91 and B3LYP, are reported in Table 1, together with the corresponding experimental values. Geometry optimization was performed at Ci symmetry for complexes 1 and 2 and without any constraint for complex 3. Therefore, the two complexes 1 and 2 present a square-planar ligand configuration around the metal ions Pd(II) and Ni(II), and the geometric parameters of the two ligands are equal in 1 and 2. The geometric parameters computed with B3LYP and mPW1PW91 were found to be in good agreement with the corresponding experimental values. The mPW1PW91 results agree better with the X-ray data than the B3LYP results do. All calculated M–O bond lengths in the three complexes are shorter than the M–N bond lengths, which shows that oxygen and nitrogen do not bind in a similar manner to the metal ion (see below). The four bond angles N–M–O in complexes 1 and 2 are slightly different from 90° (the usual angle seen for a square-planar complex), and the intra-ring bond angles O1–M–N1 and O2–M–N2 (91.9°) are clearly larger than the inter-ligand bond angles O1–M–N2 and O2–M–N1 (88.0°) due to the rigidity of the aromatic ring system. In contrast to complexes 1 and 2, complex 3 tends to adopt a deformed tetrahedral geometry in which the aromatic rings of the two phenolates are non-coplanar (see the dihedral angle values in Table 1).

Table 1 Selected optimized and experimental bond lengths (in Å) and bond angles (in degrees) of the complexes Ni\( {\mathrm{L}}_2^2 \) (1), Pd\( {\mathrm{L}}_2^1 \) (2), and Zn\( {\mathrm{L}}_2^2 \) (3)
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Wiberg bond indices (WBIs) were calculated to probe the nature of the metal–O and metal–N bonds in the three complexes (Table 2). The WBI of the metal–O bond is bigger than that of the metal–N one, indicating that the former is stronger than the latter, which explains why the M–O bond is shorter than the M–N bond. B3LYP and mPW1PW91 gave very similar WBIs, with both levels of theory indicating that the metal–N and metal–O bonds are only weakly covalent. Weakly covalent metal–O and metal–N bonds have also been observed for other similar complexes [38]. The natural atomic charges (NACs), natural electron configurations (NECs), and total natural populations (core + valence + Rydberg) of the oxygen, nitrogen, and metal atoms/ions in the complexes, as obtained from NBO calculations, are reported in Table 2. The NECs of the Ni and Pd ions in the corresponding complexes are 4s0.313d8.63 and 5s0.334d8.75, respectively (note that we omitted the small contribution from the 4p and 5d6p orbitals), while the NEC of the free metal ion is 4s3d8 for Ni2+ and 5s4d8 for Pd2+. Thus, upon complexation, electron density is donated from each ligand to a metal d orbital (significant donation) and from each ligand to a metal s orbital (low donation). Moreover, in complex 1, the natural charges on Ni, O, and N are +1.039e, −0.760e, and − 0.766e instead of the expected +2.0e, −2.0e, and − 1.0e, respectively. This result shows that electron transfer occurs from O and N orbitals to Ni orbitals. For the palladium complex, a similar interpretation of the NAC results shows that electron transfer occurs from O and N orbitals to Pd orbitals (Table 2). For complex 3, the difference between the d-orbital occupancy of the zinc ion after complexation (3d9.89) and that in the free ion (3d10) is negligible. The s-orbital occupancy of Zn increases slightly when going from the free ion to the complex. Moreover, the natural charge on the Zn ion (+2.0e) does not change dramatically after complexation (+1.707e). Therefore, in complex 3, electron transfer is weaker than in complexes 1 and 2. The computed occupancies of the natural bond orbitals and their compositions in terms of natural atomic orbitals (NAOs) are given in Table S1 of the “Electronic supplementary material” (ESM). We focused on Lewis and non-Lewis NBOs that were associated with significant interaction energies. The calculated second-order interaction energy (E2) of the strongest interactions between donor and acceptor orbitals are given in Table 3. Selected NBO–NBO* interactions are presented in Fig. 2 (complexes 1 and 3) and Figure S1 of the ESM (complex 2). As the two functionals give similar results in NBO analysis, we only provide the mPW1PW91 results here. Due to the symmetry (Ci) of complexes 1 and 2, the two ligands in each complex have the same NBO properties. The two lone pairs on the metal, LP*(1) and LP*(2) (non-Lewis NBOs), relate to the dx²−y² and 4s NAOs, respectively.

Table 2 The Wiberg bond indices (WBIs), natural atomic charges (NACs), total natural populations (TNPs, in parentheses), and natural electron configurations (NECs) of selected atoms/ions in complexes 1–3, as calculated at the B3LYP and mPW1PW91 levels of theory
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Table 3 Second-order perturbation energies E2 (kcal/mol), off-diagonal NBO Fock matrix elements F(i,j) (a.u.), and acceptor − donor NBO energies (Ej − Ei) (a.u.) of selected donor–acceptor NBO interactions in complexes 1–3, as calculated at the B3LYP and mPW1PW91 levels of theory
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Fig. 2a–b
figure 2

Visualization of selected NBO–NBO* interactions in the complexes Ni\( {\mathrm{L}}_2^2 \) (a) and Zn\( {\mathrm{L}}_2^2 \) (b), as calculated using B3LYP

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In complexes 1 and 2, the metal ion coordinates to the nitrogen and oxygen atoms through electron donation from the lone pairs (LPs) on the nitrogen and oxygen atoms to the non-Lewis orbitals LP*(1) and LP*(2) of the metal ions (Table 3). The LP(1) of nitrogen and the LPs(1,2) of oxygen relate to the valence NAOs 2s and 2p, whereas the LP*(1) and LP*(2) of the metal ions relate to n(dx²−y²) and n(s), respectively. The energies (E2) of the interactions (2s2p)N → (dx²−y²)M and (2s2p)N → (s)M were estimated to be 43.12 and 45.47 kcal/mol for the nickel complex and 72.37 and 38.93 kcal/mol for the palladium complex, respectively. The strongest interaction between the metal ion and oxygen occurs through LP(3)O → (dx²−y²)M and LP(3)O → (s)M electron donation, which present significant energy values. The interactions πC=C → π*C=C and LP(2,3)O → π*C–C are needed to form the aromatic rings of the ligands. In contrast to the Ni and Pd complexes, the d orbitals of the metal ion are not involved in the bonding of the Zn ion to N and O in complex 3, because this complex adopts a tetrahedral symmetry (sp3 hybridization). Instead, the Zn–N and Zn–O bonds result from charge transfer from LP(1)N and LP(1,2)O to an s orbital of Zn. The same donor → acceptor interaction has different energies for the three complexes due to differences between the complexes in the values of F(i,j) (the Fock matrix element) and Ej − Ei (acceptor − donor NBO energies).

Frontier molecular orbitals

The calculated frontier molecular orbital (FMO) energies and their compositions in terms of fragment orbitals in complexes 1 and 2 are given in Table 4 and Figure S2 of the ESM (the results obtained for complex 3 are given in Table S2 of the ESM). As reported in Table 4, the results obtained with the two functionals B3LYP and mPW1PW1 agree well in terms of the contributors to each molecular orbital, but their contributions differ depending on the functional used. The HOMOs of 1 and 2 are delocalized on the π* orbital of the phenolate and include only a small contribution from metal d orbitals. The LUMOs of 1 and 2 are delocalized principally on the phenolate ring. The almost degenerate molecular orbitals H-2 and H-3 of Ag symmetry are mainly composed of πphenolate and metal d orbitals. The H-1, H-4, and H-5 molecular orbitals are mainly delocalized on the imine group and the phenolate ring of the ligand. The unoccupied molecular orbitals L+1 and L+2 are mixed orbitals (πphenolate + dM) with a considerable contribution from metal d orbitals, which leads to the possibility of d–d transitions. For complex 3, the occupied d orbitals are lower in energy (H-7 to H-10 molecular orbitals). Indeed, the highest occupied molecular orbitals (HOMO to H-5) and lowest unoccupied molecular orbitals (LUMO to L+10) are delocalized in the ligand orbitals. The computed energy gaps for complexes 1 and 2 are very similar and do not differ much from that of complex 3. To study the effect of dimethylation of the phenolate rings in the ligands on the optical properties of the studied complexes, we studied the FMOs of the nickel complex without the two methyl groups on the phenolate rings (Ni\( {\mathrm{L}}_2^1 \); see Fig. S4 in the ESM). The calculated energies and compositions of the FMOs are given in Table S4 of the ESM. As shown in Tables 4 and S4 of the ESM, the dimethylation changes the FMO compositions slightly. Also note that the B3LYP-calculated energy gaps for Ni\( {\mathrm{L}}_2^1 \) (3.745 eV) and Ni\( {\mathrm{L}}_2^2 \) (3.679 eV) barely differ (the difference is only ~0.066 eV). We studied the effect of dimethylation only on the nickel complex, but we confidently predict that dimethylation of the zinc and palladium complexes will have the same effect.

Table 4 Energies, symmetries, and character of the FMOs of the complexes Ni\( {\mathrm{L}}_2^2 \) (1) and Pd\( {\mathrm{L}}_2^1 \) (2)
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TD-DFT study

The energies, oscillator strengths, and character of vertical transitions to low-lying singlet excited states of the complexes Ni\( {\mathrm{L}}_2^2 \) and Pd\( {\mathrm{L}}_2^1 \) in methanol, computed using B3LYP and mPW1PW91, are reported in Tables 5 and 6. For the complexes Zn\( {\mathrm{L}}_2^2 \) and Ni\( {\mathrm{L}}_2^1 \), the results are reported in Tables S3 and S5 of the ESM. Simulated and observed electronic spectra of the studied complexes are depicted in Figs. 3, 4, and 5. The simulated absorption spectra of 1–3 reproduce the main characteristics of the corresponding experimental spectra. B3LYP redshifts the mPW1PW1 spectra of the three complexes, leading to better agreement with the observed absorptions in the blue region. Complexes 1 and 2 start to absorb at ~465 nm (B3LYP), ~440 nm (mPW1PW91), and ~465 nm (observed), whereas complex 3 starts to absorb at ~424 nm (B3LYP), ~411 nm (mPW1PW91), and ~427 nm (observed). This difference occurs because the energy gaps of the three complexes are different sizes. As shown in the Fig. 3, the complexes Ni\( {\mathrm{L}}_2^2 \) and Ni\( {\mathrm{L}}_2^1 \) present similar spectra. The complex Ni\( {\mathrm{L}}_2^1 \) starts to absorb at ~440 nm (B3LYP), which shows that dimethylation redshifts the spectrum in the visible region.

Table 5 Energies, oscillator strengths, and character of the main absorptions of the complex Ni\( {\mathrm{L}}_2^2 \) (1), as computed with mPW1PW91 and B3LYP
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Table 6 Energies, oscillator strengths, and character of the main absorptions of the complex Pd\( {\mathrm{L}}_2^1 \) (2), as computed with mPW1PW91 and B3LYP
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Fig. 3
figure 3

Simulated absorption spectra (solid lines) and calculated absorptions (bars) of the complex Ni\( {\mathrm{L}}_2^2 \) (1), as obtained using B3LYP (blue) and mPW1PW91 (red). Also shown is the simulated absorption spectrum of the complex Ni\( {\mathrm{L}}_2^1 \) (4), obtained using B3LYP (green line), and the digitized experimental spectrum from [12] (black line)

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Fig. 4
figure 4

Simulated absorption spectra (solid lines) and calculated absorptions (bars) of the complex Pd\( {\mathrm{L}}_2^1 \) (2), as obtained using B3LYP (blue) and mPW1PW91 (red). Also shown is the digitized experimental spectrum from [12] (black line)

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Fig. 5
figure 5

Simulated absorption spectra (solid lines) and calculated absorptions (bars) of the complex Zn\( {\mathrm{L}}_2^2 \) (3), as obtained using B3LYP (blue) and mPW1PW91 (red). Also shown is the digitized experimental spectrum from [12] (black line)

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All transitions from S0 to any singlet excited state with Ag symmetry are forbidden (f = 0) and were therefore omitted. To determine the character of the absorptions S0 → Sn, we analyzed the natural orbital transitions of the main excited singlet states of the three studied complexes (Fig. 6). The NTOs of the complexes 1, 2, and 3 are given in Fig. 6 and Fig. S3 of the ESM. This analysis is very useful for visualizing and identifying the nature of the electronic excitation associated with each absorption. The low-lying singlet excited states of the nickel and palladium complexes are mainly characterized by mixed charge transfer (LLCT, MLCT, and LMCT). In the zinc complex, pure LLCT is dominant. The transition S0 → S5 in complex 1, calculated using B3LYP to lead to absorption at 400 nm (f = 0.078), can be assigned to the weak band observed experimentally at around ~380 nm. The hole NTOs of this absorption are mainly composed of dNi and πphenolate orbitals, while the electron NTOs are delocalized over the \( {\uppi}_{\mathrm{phenolate}}^{\star } \) orbital. The weak band and shoulder observed at ~330 nm and ~268 nm, respectively, in the spectrum of complex 1 can be assigned to the two absorptions S0 → S10 (f = 0.104) and S0 → S19 (f = 0.214), which are calculated to occur at 330 nm and 264 nm, respectively, using B3LYP. In the ultraviolet C region, the intense band observed at ~245 nm is assigned to a set of excited states calculated to occur in the interval 264–231 nm, in particular the S29 state, which is calculated to occur at 244 nm with a strong oscillator strength f = 0.345. NTO analyzes show that this absorption (S0 → S29) corresponds to two donor–acceptor pairs: the predominant donation occurs from dPd and πphenolate orbitals to the \( {\uppi}_{\mathrm{phenolate}}^{\star } \) orbital, while the other donation mainly occurs via the πphenolate → \( {\uppi}_{\mathrm{phenolate}}^{\star } \) transition. For complex 2, the two absorptions S0 → S3 (404 nm, f = 0.069) and S0 → S9 (319 nm, f = 0.089) computed using B3LYP are assigned to two weak bands observed at 396 nm and 324 nm, respectively. The shoulder observed at ~280 nm can be assigned to the absorption S0 → S19, which corresponds to a transition from dPd and πphenolate orbitals (the hole) to \( {\uppi}_{\mathrm{phenolate}}^{\star } \) orbitals (the electron). At the highest energies, the most intense of the observed bands can be assigned to the intense B3LYP-calculated absorption S0 → S29 (f = 0.657) at 243 nm, which mostly corresponds to the transition πphenolate → \( {\uppi}_{\mathrm{phenolate}}^{\star } \), although the transition dPd → \( {\uppi}_{\mathrm{phenolate}}^{\star } \) also plays a role according to the NTO analysis (Fig. 6). For complex 3, the weak band observed at 370 nm is assigned to the four absorptions calculated to occur in the interval 365–352 nm (0.043 < f < 0.101), which correspond to πphenolate → \( {\uppi}_{\mathrm{phenolate}}^{\star } \) transitions. In the UV region, the two bands observed at ~275 nm (moderately intense) and ~212 nm (intense) are mainly assigned to the two absorptions S0 → S9 (258 nm, f = 0.233) and S0 → S28 (211 nm, f = 0.663), which correspond to pure ligand-to-ligand charge transfer. In the same region, the band observed at ~243 nm can be assigned to the S0 → S20 transition, computed to occur at 232 nm, which has mixed (LLCT/MLCT) character.

Fig. 6
figure 6

Natural orbital transitions and their eigenvalues for the main excited singlet states of the complexes Ni\( {\mathrm{L}}_2^2 \) (1) and Pd\( {\mathrm{L}}_2^1 \) (2), as calculated with B3LYP

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Conclusions

In this study, the geometric parameters, natural bond orbitals, frontier molecular orbitals, and electronic absorption spectra of complexes 1–3 were calculated using DFT and TD-DFT methods. The geometric parameters computed using B3LYP and mPW1PW91 were found to be in good agreement with the corresponding experimental data. Wiberg bond indices indicated that the metal–N and metal–O bonds in these complexes are only weakly covalent. NBO analysis showed that in complexes 1 and 2, the metal ion coordinates to nitrogen and oxygen atoms through electron donation from lone pairs on the nitrogen and oxygen atoms to s and d orbitals on the metal ion; the energy (E2) associated with this coordination is significant. In complex 3, the coordination occurs through electron donation from nitrogen and oxygen orbitals to s orbitals on the metal ion. FMO analysis showed that the occupied and unoccupied orbitals of complexes 1, 2, and 4 are globally delocalized in the πphenolate orbitals, with a significant proportion of the metal d orbitals contributing to some of the frontier molecular orbitals. For complex 3, the frontier molecular orbitals are generally delocalizied in the ligand orbitals. The simulated absorption spectra of 1–3 presented similar shapes to the corresponding observed spectra. The B3LYP-calculated spectra of the three complexes showed better agreement with the observed absorptions in the blue region than the mPW1PW91-calculated spectra did. Dimethylation of the two phenolate ligands was calculated to redshift the spectrum of the nickel complex; the same behavior is probably exhibited by the other complexes. The low-lying singlet excited states of complexes 1 and 2 have mixed (LLCT/MLCT/LMCT) charge-transfer character, while those of complex 3 have pure LLCT character. Intense bands observed in the absorption spectra for complexes 1 and 2 were assigned to the transitions πphenolate → \( {\uppi}_{\mathrm{phenolate}}^{\star } \) and dMetal → \( {\uppi}_{\mathrm{phenolate}}^{\star } \). For complex 3, an intense band observed in the UV region was assigned to pure ligand-to-ligand charge transfer.