Metal-interacted histidine dimer: an ETS-NOCV and XANES study

Abstract

We have analyzed the metal coordination in a histidine dimer, hydrated with a water molecule, based on the extended transition state scheme with the theory of natural orbitals for chemical valence (ETS-NOCV). Metal interaction weakens and strengthens the C=O and C–N bonds respectively, which indicates σ bond formation between the metal and the ligand. Frequency analysis reveals C=O bond exhibits a red shift, which confirms that the π-back donation of electrons takes place through this bond. From the ETS-NOCV analysis, the electrostatic term is dominant over the orbital term. NOCV analysis indicates that the switching of bond strength between C–N bond and C=O bond in neutral and zwitterionic systems respectively is due to the amount of back donation in TM²⁺–N and TM²⁺–O bonds (TM²⁺ = Cu, Zn, Ca, Mg). K-edge XANES spectra for the metal indicates that oxidation state of Zn and Ca increases while for Cu and Mg it decreases. Oxygen K-edge spectra indicate that metals like zinc and copper back-donate the electrons largely to ligands.

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1. Introduction

In bioinorganic chemistry, the interaction of metal ions with biological molecules is an important area of research as it provides model compounds, the understanding of whose physical and chemical properties has strong implications in research fields such as biochemical reactions, biomedical implants, sensors, and catalysis.^1–4 The metalation of amino acids, peptides, nucleic acids and other biologically relevant molecules plays a crucial role in a variety of specialized functions^5–7 like control of structural and regulating properties,^7,8 transport processes through transmembrane channels,^9,10 energy storage, electron transfer and catalysis. In the above-mentioned list of functions the role of metal ions is truly critical, however often unknown as being dominant at the molecular level.

Generally bonding between metals and biomolecules obeys the Dewar–Chatt–Duncanson (DCD) model, which was originally developed for complexes of unsaturated carbon ligands. The model deals with two processes: the first is the σ-type bonding, wherein electron transfer occurs in the direction of ligand to metal, and the second involves back bonding, which involves a π-type bond where the electron flow occurs in the direction of metal to ligand. According to the DCD model, the bond strength depends on the degree of π-back-donation.¹¹ To analyze in detail the metal–ligand bond, tools like extended transition state-natural orbital chemical valence (ETS-NOCV) and X-ray absorption spectroscopy (XAS)^12–16 are highly valuable.

In our previous study¹⁷ on metal ion interaction with histidine dimer, it was observed that TM²⁺–N (TM²⁺ = Zn, Cu, Mg and Ca) bond is stronger in a neutral system whereas TM²⁺–O bond is stronger in a zwitterionic system. This switchover in the binding mode between neutral and zwitterion is interesting and needs to be explained. For this, ETS-NOCV calculations were performed for the atom which is bonded to oxygen and nitrogen (i.e. C=O and C–N bonds) to characterize these bonds quantitatively and qualitatively. Electron channels were visualized and qualitatively assigned (i.e., σ, π donation or back donation character), and the energy decomposition analysis provides their energetic weight in the bonding. In essence, this work will provide an understanding of the binding modes of metal cations with neutral and zwitterion forms of histidine. The information obtained will be useful in the field of metal–protein and metal–ligand chemistry.

2. Computational details

All the initial geometries were taken from the previous paper,¹⁷ where the complexes were optimized without symmetry constraints using B3LYP^18,19 functional and the 6-311G** basis set. ETS-NOCV analyses were performed^20–23 using B3LYP^18,19,24,25 functional and a standard triple-ζ STO basis with two sets of polarization (TZ2P)²⁶ implemented in the Amsterdam Density Functional (ADF 2013.01)^20,21 program. XANES studies for the K-edge of the metal and oxygen atoms were performed using time dependent density functional theory (TDDFT) calculation with BHLYP^24,27 functional. For the oxygen and metal atoms present in the structure, the Stuttgart RLC ECP basis set is used, and for the core excitation the 6-311G** basis set using NWChem 6.5 package.²⁸

2.1 Extended transition state (ETS)

Bonding analysis presented in this study is based on the ETS-NOCV approach,²⁹ which is a combination of both ETS^30–32 and NOCV schemes.^33,34 In our analysis, each system is divided into two individual fragments, as depicted in Fig. 3, to study the interaction between them. Thus, the bonding analysis focuses on the simultaneous interaction between the fragments, and the interaction energy is divided into three main components:

ΔE_int = ΔE_elstat + ΔE_Pauli + ΔE_orb.

The term ΔE_elstat corresponds to the classical electrostatic interaction between individual fragments as they are brought together to form the complex and is a stabilizing term. Further, ΔE_Pauli is the repulsive interaction between the occupied orbitals of the fragments in the complex comprising electrons with the same spin, resulting in a destabilizing interaction between electrons of the same spin on either fragment. Finally, ΔE_orb represents the interaction between the occupied molecular orbitals of one fragment and the unoccupied molecular orbitals of the other fragment. The orbital interaction accounts for charge transfer and polarization effects. Participation of the virtual orbitals gives rise to a change in density³⁰ expressed as

where the sum is over all occupied and virtual orbitals of the two fragments A and B, orthogonalized on each other.²⁹ The energy associated with the orbital interactions is
here F^TS_λμ is a Kohn–Sham–Fock matrix element that is defined in terms of a transition state potential at the midpoint between the combined fragments and the final molecule, hence the term extended transition state (ETS).^29,34

The total interaction energy between the fragments is given by adding the preparation energy. The bond distortion energy is calculated using the equation

−D_e = ΔE_int + ΔE_prep.

2.2 Natural orbitals for chemical valence (NOCV)

In the NOCV approach, the deformation density matrix ΔP is diagonalized^29,34 and mathematically represented as

ΔPC_i = v_iC_i, i = 1, M

where M denotes the total number of fragment molecular orbitals and C_i is a column vector containing the eigenvectors to ΔP. These eigenvectors are called the natural orbitals for chemical valency,^34–36 given as

In the NOCV representation, the deformation density can be written as the sum of the pairs of complementary eigenfunctions (φ_k,φ_−k) corresponding to the eigenvalues ν_k and ν_−k with the same absolute value but opposite signs:^29,34

Finally, the orbital interaction energy (ΔE_orb) is expressed in terms of the NOCV as

where F^TS_−k,−k and F^TS_k,k are diagonal Kohn–Sham matrix elements defined over NOCV with respect to the transition state (TS) (intermediate between the final molecule (AB) density and the superimposed fragment densities A′ and B′).²⁹ From the deformation density plots, contributions of orbitals can usually be interpreted in terms of interactions that correspond to σ, π, δ bonding or σ-donation and π-back donation, even when a system lacks symmetry.

3. Results and discussion

3.1 Bond length

The pictorial representations of the structure and optimized geometries of the histidine dimer monohydrated with a water molecule are shown in Fig. 1 and 2. The metal is coordinated with the oxygen atom of C=O, and nitrogen atom of C–N bonds in the imidazole ring of the histidine and with the oxygen atom of the water molecule.

Fig. 1 Pictorial representation of the atoms and labeling.

Fig. 2 Optimized geometry of the neutral and zwitterionic histidine dimer with monohydrated water using B3LYP/6-311G** basis set.

First the bond length of the C=O and C–N bonds at the metal coordination site is investigated in order to find out the back-bonding nature. For this the X–C (X = O, N) bond lengths in the neutral and zwitterionic complexes along with their corresponding monomer as well as the metal-to-ligand TM²⁺–X (TM²⁺ = Zn, Cu, Ca, Mg and X = O, N) bond lengths are listed in Table 1. The C=O bond lengths of neutral complexes are in the range from 1.22 to 1.23 Å which is higher than that of the monomer (1.20 Å). After interaction with the metal, weakening/elongation of the C=O bond in histidine is observed in the range 0.028–0.032 Å. This indicates that there is a possibility of π-back donation from the metal. Concomitantly, the C–N bond is shortened in the range 0.049–0.045 Å and therefore strengthened after the metal interaction. This shows that the ligand donates electrons to the metal through C–N bonds and the metal can back-donate the electrons from C=O bonds. The order of the degree of back bonding for C=O and C–N bonds is Cu²⁺ > Zn²⁺ > Mg²⁺ > Ca²⁺ and Zn²⁺ > Cu²⁺ ≈ Mg²⁺ > Ca²⁺ respectively. It is important to mention here that the histidine zwitterionic structure is yet to be synthesized in the gas phase and therefore, for comparison purposes, the bond length value for C=O and C–N is taken from the literature.³⁷ Unlike the neutral system, the bond length of C=O bond does not show the marginal variation except for a couple (Cu²⁺, Ca²⁺) of complexes. The C=O bond length of Cu²⁺ and Ca²⁺ complexes is longer than that of the monomer which indicates the back donation of electrons from metals. Zn²⁺ and Mg²⁺ complexes have no change in the bond length indicating the lack of back donation. In line with the C=O bonds, the C–N bonds in zwitterionic complexes are also strengthened and the charge is transferred from ligand to metal through σ bonds. The nature of the TM²⁺–X bond which depends on the radii of the metal cation is not sufficiently ascertained through the C=O and C–N bond lengths alone. Therefore, frequency calculations were performed in order to confirm the back bonding nature of the title complex.

Table 1 Optimized bond lengths (Å) of metals with histidine dimer

Bond	TM^n+ = Zn^2+		TM^n+ = Cu^2+		TM^n+ = Ca^2+		TM^n+ = Mg^2+
	Neu	ZW	Neu	ZW	Neu	ZW	Neu	ZW
a The value in parentheses indicates monomer values.b Not available.
N1–TM^n+	2.02	2.09	1.98	2.01	2.47	2.52	2.16	2.19
N2–TM^n+	2.02	2.09	1.98	2.01	2.45	2.48	2.16	2.19
O1–TM^n+	2.12	2.01	2.01	1.95	2.26	2.21	2.01	1.96
O2–TM^n+	2.12	2.01	2.01	1.95	2.29	2.28	2.01	1.96
O3–TM^n+	2.13	2.13	2.34	2.38	2.37	2.34	2.08	2.09
C=O1	1.22 (1.20)^a	1.25^b	1.23	1.26	1.23	1.25	1.23	1.25
C1–N1	1.33 (1.37)	1.32	1.32	1.32	1.32	1.32	1.33	1.32
C2–N1	1.39 (1.31)	1.39	1.39	1.39	1.39	1.38	1.39	1.39

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3.2 Frequency calculation

Often π-back-bonding weakens a bond, which is visible from the measurement of stretching frequency.³⁸ In the previous section it was observed that the C=O bonds in neutral complexes are weakened (increase in bond lengths) due to the presence of the metals. Affirmatively the C=O stretching frequency (given in Table 2) is decreased compared with the corresponding monomer. This red shift in frequency is observed for the C=O bond in all the neutral structures and is in the range of 93.82–107.85 cm⁻¹. Based on the bond lengths, expectedly the frequency analysis of the C–N bond shows a blue shift of 385.66–390.71 cm⁻¹. Hence, the back-bonding occurrence is minimal through the C–N bond in the neutral structures. In the case of the zwitterionic complex, C=O and C–N are optimized separately and the frequency is compared with the monomer as well from available results.^37,39 The frequency of the C=O and C–N bonds in the complex is smaller than that in the monomer. Here both the C=O and C–N stretching frequencies are red shifted when compared with the free C=O and C–N frequencies. The frequency shifts are in the range of 382.38–427.37 cm⁻¹ and 338.93–340.15 cm⁻¹ for the C=O and C–N bonds respectively. The frequency of ν(CO) bond is below the reference value of 2143 cm⁻¹, due to the strong electrostatic and σ-bonding effects.⁴⁰ Overall, the frequency decrease indicates that the electron densities flow out from the filled valence orbitals of a metal atom back to the π* orbitals of C=O and C–N ligands. Further, to characterize the back bonding nature, both quantitative and qualitative analyses have been performed as presented in the forthcoming sections.

Table 2 Frequency (cm⁻¹) analysis of the C=O1 and C–N1 bonds

Structure	Neutral			Zwitterionic
	C=O1	C1–N1	C2–N1	C=O1	C1–N1	C2–N1
a Obtained from ref. 30 and 32. Parentheses indicate the monomer value.
Zn^2+	1758.55 (1852.37)	1531.33 (1142.57)	1289.66 (1389.27)	1757.65 (2143)^a	1526.87 (1867.18)^a	1291.20
Cu^2+	1730.83	1533.28	1293.62	1746.47	1528.96	1294.89
Ca^2+	1755.15	1528.01	1288.39/1295.45	1715.63/1760.01	1527.03/1560.67	1259.09
Mg^2+	1744.52	1528.23	1289.06	1760.62	1528.25	1289.90

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3.3 Distortion energy

The electronic energy (without any zero-point vibrational energy correction) for a studied complex with three different types of fragments chosen (Fig. 3) is compared with free histidine and water. All the calculations were performed at the same level of theory in G09 software⁴¹ and the results are shown in Table 3. The order of distortion for type 1 and type 2 complexes is Cu²⁺ > Zn²⁺ > Mg²⁺ > Ca²⁺ and the maximum distortion appears in the Cu²⁺ substituted structure. The minimum distortion is noticed in the Ca²⁺ substituted structure, which indicates that the structure undergoes minimum strain during complex formation. The distortion energy is calculated for the type 3 fragment and the order is different from the two discussed above. The order of distortion is Mg²⁺ > Ca²⁺ > Cu²⁺ > Zn²⁺ and Ca²⁺ > Mg²⁺ >Zn²⁺ >Cu²⁺ for the neutral and zwitterionic complexes respectively. For the type 3 complexes, fragment 2 is water and has more affinity towards calcium. From this study, the electronic structure has strong influence on the bond formation quantitatively rather than the qualitative.

Fig. 3 Schematic representation for the fragments selected in ETS-NOCV calculation. The marked portion represents fragment 2 in each case.

Table 3 Energy (kcal mol⁻¹) decomposition analysis and distortion energy D_e (kcal mol⁻¹) for the studied complexes with three different types of fragments

Structure	Type	Neutral					Zwitterionic
		ΔEint	ΔEPauli	ΔEOrbit	ΔEElast	De	ΔEint	ΔEPauli	ΔEOrbit	ΔEElast	De
Zn^2+	Type 1	−436.91	111.12	−234.87	−313.16	−19.17	−472.59	109.00	−238.24	−343.35	−20.71
Cu^2+		−465.83	158.97	−291.44	−333.35	−20.38	−502.49	159.46	−297.27	−364.68	−21.99
Ca^2+		−303.11	84.38	−151.04	−236.45	−13.75	−341.74	87.89	−155.05	−274.58	−15.46
Mg^2+		−399.16	57.08	−193.49	−262.75	−17.82	−435.93	59.34	−198.74	−296.53	−19.47
Zn^2+	Type 2	−119.76	90.47	−74.47	−135.76	−5.83	−133.17	99.52	−79.04	−153.66	−6.48
Cu^2+		−107.18	127.86	−90.69	−144.36	−6.03	−126.30	133.05	−99.05	−160.31	−6.63
Ca^2+		−99.65	44.66	−49.53	−94.78	−4.57	−112.83	48.79	−51.59	−110.03	−5.18
Mg^2+		−120.71	47.60	−59.36	−108.95	−5.47	−135.49	51.65	−61.55	−125.58	−6.15
Zn^2+	Type 3	−18.31	28.02	−13.43	−32.90	−0.52	−16.95	34.78	−14.90	−36.83	−1.12
Cu^2+		−10.48	24.30	−9.26	−25.53	−0.85	−7.91	20.93	−7.11	−21.72	−0.73
Ca^2+		−24.97	18.25	−12.44	−30.78	−1.42	−27.76	29.51	−18.42	−38.85	−1.54
Mg^2+		−27.01	21.01	−13.75	−34.27	−1.47	−24.42	20.03	−12.52	−31.93	−1.3

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3.4 ETS-NOCV calculation

3.4.1 Type 1 (histidine dimer + water as fragment 1 and metal as fragment 2). The energy decomposition analysis (EDA) results for the histidine dimer with water molecule as fragment 1 and metal as fragment 2 are shown in Table 3 as type 1. Here ΔE_Orbit and ΔE_Elast are stabilizing terms, while ΔE_Pauli is the destabilizing term. The interaction energies are in the range of −498.74 to −303.11 kcal mol⁻¹ for neutral complexes. Further, the interaction energy decreases in the order Cu²⁺ > Zn²⁺ > Mg²⁺ > Ca²⁺, which indicates that substantial amount of electron is donated to Cu²⁺ cation due to its lone unpaired electron present in the valence shell. The Ca²⁺ cation-interacted structures have the minimum interaction energy, due to the filled valence orbital. It is worth mentioning here that the distortion energy and interaction energy follow the same trend and the electrostatic effect is dominant over the electronic (ΔE_Orbit) effect. ΔE_Pauli is maximum for the Cu²⁺ substituted complex, due to the shorter bond length observed for N–Cu²⁺ bond. In the zwitterionic structure, the same trend as for neutral complexes is followed for the interaction energy, although variations are observed quantitatively. Here again, the electrostatic term is dominant over the orbital term, and the interaction energy and distortion energy order is also same. Comparing both neutral and zwitterionic structures, the two stabilizing terms (ΔE_Orbit and ΔE_Elast) are larger in zwitterionic structures except for that containing Zn. Nevertheless, its stability is overwhelmed by the Pauli repulsion term, which is higher for zwitterionic structure, an important factor in destabilizing the zwitterionic structure compared to the neutral. From the above results, it is evident that the metal cation bonds with the histidine ligand electrostatically. Conclusively, the stability of the complexes increases with the cation charge, evident from ΔE values of Zn²⁺ and Cu²⁺ (transition metal) complexes which are more stable than the Mg²⁺ and Ca²⁺ substituted complexes.

3.4.2 Type 2 and type 3 (histidine 1 as fragment 1 and remaining part as fragment 2). The EDA results for type 2 system where histidine 1 is taken as fragment 1 and the remaining part as fragment 2 (Fig. 3) are shown in Table 3. The calculated interaction energies ΔE_int indicate that the strength of the intrinsic two fragments has the common order Mg²⁺ > Zn²⁺ > Cu²⁺ > Ca²⁺ in both neutral and zwitterionic complexes and the values are in the range −120.71 to −99.65 and −135.49 to −112.83 kcal mol⁻¹ respectively. Subsequently, for the type 3 system considering the water molecule as fragment 1 and the rest as fragment 2, as shown in Fig. 3, ETS-NOCV calculations were performed. Here for both neutral and zwitterionic complexes, the interaction energies are generally smaller owing to weak interaction.

The interaction energies for neutral and zwitterionic systems with water molecule are in the range −27.01 to −10.48 and −38.85 to −21.72 kcal mol⁻¹ respectively. The ordering for the interaction energy is dissimilar for neutral and zwitterionic complexes and is Mg²⁺ > Ca²⁺ > Zn²⁺ > Cu²⁺ and Zn²⁺ > Ca²⁺ > Mg²⁺ > Cu²⁺ respectively. From this trend it is noticed that there is a switching in metal affinity for water from Mg²⁺ in neutral to Zn²⁺ in zwitterionic complexes. Interestingly, calcium occupies the second and copper the last position in both complexes. Similar to the type 1 analysis, the interaction energy is electrostatically dominant over the electronic effect in the two types of system (type 2 and type 3).

Further, to characterize the metal back bonding, the frontier molecular orbital plots for the both forms were analyzed (shown in Fig. 4 and 5). The frontier molecular orbital distributions in the neutral and zwitterionic forms of the ligands are alike, and hence the discussion is common to both forms. In Fig. 4, the highest occupied molecular orbital (HOMO) of the Zn substituted histidine ligand complex shows that the π orbital distribution is localized on the imidazole of the histidine. Fig. 4a and c show the lowest unoccupied molecular orbital (LUMO) π orbital of the Zn- and Mg-coordinated systems is delocalized on the three-centre bond (O–TM²⁺–O (TM = Zn, Mg)) and oriented out of plane. From Fig. 4b, the presence of the d_x²−y² orbital for the Cu cation indicates that the Cu can back-donate its electron to the histidine ligands, which is backed up by the bond length and frequency calculation results. In the case of LUMO + 1 in the Cu-coordinated system, the σ orbital is distributed in the C=O bonds and can accept the electrons from the metal. Peculiarly, HOMO and HOMO − 1 orbital distribution is observed in either of the ligands in the Ca-coordinated complex. This may be due to the structural deformation observed in the complex. In contrast to the above, LUMO and LUMO + 1 orbitals are localized in the tri-center bond (O–TM²⁺–O), which indicates it can act as a good sigma acceptor. Similar trend is observed for the zwitterionic forms (Fig. 5) of the histidine ligands.

Fig. 4 HOMO–LUMO plot for the metal-interacted neutral histidine dimer.

Fig. 5 HOMO–LUMO plot for the metal-interacted zwitterionic histidine dimer.

3.5 Natural orbitals for chemical valence

To further characterize the metal coordination with ligand, ETS-NOCV analysis was performed. Introduced by Rauk and Ziegler, this has proven to be a very useful tool for discussing the bonding in a number of systems.^{29,34,38,42–64} From the deformation densities shown in Fig. 6 and 7, the charge flow is from green to violet region.

Fig. 6 Deformation densities for the type 1 ETS-NOCV calculation performed at B3lyp/TZ2P for neutral complexes. The charge flow of the electronic charge is green → violet. The orbital interaction energies ΔE are given in kcal mol⁻¹ and the eigenvalues υ indicate the size of the charge flow. The complexes are labeled as a, b, c and d for Zn²⁺, Cu²⁺, Ca²⁺, and Mg²⁺ respectively. * denotes σ-donation; $ and @ denote π-back donation in oxygen and nitrogen atoms respectively.

Fig. 7 Deformation densities for the type 1 ETS-NOCV calculation performed at B3lyp/TZ2P for zwitterionic complexes. The charge flow of the electronic charge is green → violet. The orbital interaction energies ΔE are given in kcal mol⁻¹ and the eigenvalues υ indicate the size of the charge flow. The complexes are labeled as a, b, c and d for Zn²⁺, Cu²⁺, Ca²⁺, and Mg²⁺ respectively. * denotes σ-donation; $ and @ denote π-back donation in oxygen and nitrogen atoms respectively.

3.5.1 Neutral complex. Fig. 6 and 7 show the deformation densities (Δρ) that are linked to the three most dominant deformation density channels and the color code used to characterize these densities are green (depletion) and violet (accumulation) and the direction of the charge flow is from green → violet. In each figure, orbital interaction (ΔE) strength and eigenvalue υ are given, which gives quantitative information of the amount of charge that is displaced. In general, both C=O and C–N are σ donors and π acceptors and this can be visualized in all the complexes. In Fig. 6, row (a) shows the deformation density plot for the zinc cation-interacted complex, wherein the coordination between the Zn²⁺ and histidine is through σ bonds. The dominant deformation density (Δρ₁) of Zn²⁺ substituted structure indicates that charge flows from the lone pair of nitrogen and oxygen atoms of the ligand to the metal with the highest orbital energy of about ΔE_k = −49.62 kcal mol⁻¹. This indicates that the σ donation from the ligand to the metal with the highest eigenvalue in this channel is about 0.490. The next notable contribution is observed from Δρ₃ with an orbital energy of about −19.54 kcal mol⁻¹. From the figure, it is clear that the metal can back-donate the electrons to the nitrogen atom that is present in the imidazole ring of the ligand. Besides, the back donation of electrons is from zinc d orbital to the antibonding π* orbital of C–N bond. The Zn²⁺ back-donates the electrons to the nitrogen of the imidazole and carbonyl oxygen atom in the ligand, which is visible in the deformation density (Δρ₆) with an orbital contribution of about −11.80 kcal mol⁻¹.

In the case of the Cu²⁺ site, the three dominant channels of the charge density transfers follow differential density decomposition, since their shares in orbital interaction energy are strongly modified by the environment. The dominant deformation density channel for Cu²⁺ substituted structure has an orbital energy of −78.89 kcal mol⁻¹ and σ and back donation is observed in N–TM²⁺–N and O–TM²⁺–O tri-centers respectively. The second most dominant channel has an eigenvalue of about 0.251 with orbital energy of about −15.56 kcal mol⁻¹. Back donation is observed through the O–TM²⁺–O bond in the deformation density (Δρ₄). Expectedly, back donation of electrons from the metal is observed through N–TM²⁺–N with the lowest orbital energy (−13.17 kcal mol⁻¹) in the deformation density (Δρ₇). This indicates that the O–TM²⁺–O bond is more favorable for the back donation than its competitor. Comparing the π-back bonding with the Zn²⁺ substituted complex, back bonding is dominant in the Cu²⁺ metal, endorsed by the large red-shift of C=O stretching frequency in the latter (shown in Table 2).

Generally, calcium has empty d-orbitals; hence, during bonding with the ligand donation occurs from metal to ligand from the s orbital of Ca. However, during this interaction with the ligand, the empty d orbitals are split into degenerate levels under the strong ligand field. Consequently, there occurs a large probability for the ligand to back-donate electrons to the low-lying d orbitals of calcium. This phenomenon has been reported previously.^65,66 Here, in the Ca substituted complex, electron flow is dominant through N–TM²⁺–N, and its contribution is more than its rival O–TM²⁺–O bond. In contrast, the second most dominant channel is favored for O–TM²⁺–O bond with orbital energy of −16.94 kcal mol⁻¹. The metal back donation is observed in both Δρ₂ and Δρ₅.

For the Mg atom, similar to zinc, the electrons are transferred from the lone pair of the nitrogen atom, with the orbital energy (−24.59 kcal mol⁻¹) indicating sigma donation. The back donation is observed in deformation density (Δρ₄) with orbital energy of −14.42 kcal mol⁻¹. The sixth deformation density clearly shows that the π orbital distribution is scattered along the N–TM²⁺–N bond. As is clear from the deformation density plots, the TM²⁺–N bond is stronger in the neutral system due to the dominant back donation occurring through tri-centre N–TM²⁺–N bond. It is known that the bond strength depends on the degree of π-back donation.¹¹ To summarize from the plot, the energy associated with the σ interaction between the metal and the binding site is stronger than the corresponding π interaction.

3.5.2 Zwitterionic complex. Similar to neutral complexes, the dominant electron transfer channel is through N–TM²⁺–N tri-center bond in all four zwitterionic complexes. In the zinc substituted complex, π back donation is observed through the O–TM²⁺–O bond centre in the fifth deformation density with orbital energy value of −13.28 kcal mol⁻¹. Back donation can also occur through the N–TM²⁺–N tri-center bond with marginally low orbital energy (−12.29 kcal mol⁻¹). Back donation of electrons in the Cu²⁺ substituted complex is transferred through the O–Cu²⁺–O bond with −161.97 kcal mol⁻¹ and −36.0 kcal mol⁻¹ for N–Cu²⁺–N bond. Here the second dominant contribution (−161.97 kcal mol⁻¹) corresponding to back donation of electrons is from copper d_π orbitals to the antibonding π* orbitals of C=O bond. Likewise, the Ca substituted complex also has a density distribution similar to that of the above discussed metals; however they vary only quantitatively (due to the size of the cation). In line with the above, O–TM²⁺–O tri-center bond is preferable for the Mg²⁺-interacted system with orbital energy of −17.20 kcal mol⁻¹. The back donation is observed in the N–Mg²⁺–N tri-center bond with orbital energy value of −11.05 kcal mol⁻¹ which is smaller than the previously discussed one. To conclude, the ligands can donate the electron through the N–TM²⁺–N bond and the metal can back-donate the electron through the O–TM²⁺–O bond. In general the dominant channel for the back donation in zwitterionic complexes is through the O–TM²⁺–O bond and hence the TM²⁺–O bond is stronger. This is largely due to 2p orbitals of oxygen atoms, which take part in back donation from cation to ligand. Overall, σ-charge-transfer channel dominates orbital energy for all four complexes studied in the present work.

3.6 K-edge XAS

3.6.1 Metal XAS. The X-ray absorption spectra for the metal K-edge involved in neutral and zwitterionic complexes are depicted in Fig. 8. In the K-edge spectra for the zinc substituted complex, 1s → 3d transition is forbidden in the dipole selection rule, which results in the minor pre-edge peak observed at 9513 and 9514 eV for zwitterionic and neutral complex respectively. These minor peaks are due to the bound states of Zn²⁺, which has a completely filled d¹⁰ electronic configuration, as well as the mixing of 3d (zinc) and 2p (oxygen) orbitals. The atomic eigenstates of these two orbitals are energetically close, which induces the strong interaction between the zinc 3d and oxygen 2p orbitals (i.e. Zn 3d t₂ like states coupled with O p states). The pre-edge or white line is due to the contribution from 1s → 4p orbitals. Comparing with neutral complex, the pre-edge in zwitterionic complex is blue shifted in nature, which indicates the shift in the oxidation state of Zn²⁺. In general, a higher oxidation state implies shorter bond length, which is observed in the neutral complex (N–Zn²⁺) which has shorter bond length than in the zwitterionic complex. The intensity of the zwitterionic complex is low when compared to the neutral complex, which may be due to the presence of the strong hydrogen^17,67,68 and M–X (X = O, N) bonds.

Fig. 8 K-edge spectra for the metal-interacted histidine dimer.

The pre-edge for the Cu²⁺-interacted complex is observed at 8849 and 8850 eV for the zwitterionic and neutral complex respectively. As for the Zn²⁺-interacted complex, here the small peak is due to the forbidden electronic transition from 1s → 3d orbital and the pre-edge is due to the 1s → 4p orbital transition. Cu²⁺ exhibits a d⁹ electronic configuration, and consists of one unpaired electron in the e_g state in square pyramidal geometry. This lone electron in the e_g state of the d-orbital forms strong σ-antibonding through anisotropic interaction with the ligands. Because of this bond, a non-spherical charge distribution prevails and consequently lowers the Jahn–Teller distortion of the metal environment. Lowering of Jahn–Teller distortion results in the orbital degeneracy and lowers the overall energy of the site. Further for the Cu complex in contrast to the Zn²⁺ complex, a red shift is observed for the zwitterionic complex, which indicates a shift in the oxidation state of the copper towards lower value. Furthermore, the pre-edge difference between the zwitterionic and neutral complex is about 1 eV. Moreover, the above results reflect the ligand field splitting of the 4p orbitals and sensitivity of the pre-edge to geometry.

For the magnesium metal cation, the pre-edge is observed at 1284 and 1286 eV for the zwitterionic and neutral complex respectively and there is a 2 eV difference in the rising edge. The pre-edge transition occurs in the form of 1s → 3p, because the valence 2p orbital of magnesium is completely filled. Obviously, here the role is due to the empty 3d state, which is not as significant as for other 3d elements. On comparing the intensities of both (zwitterionic and neutral) Mg²⁺ substituted complexes, no variation in pre-edge is observed, but the pre-energy is red shifted by about 2 eV.

In contrast with the three metal cations mentioned above, the pre-edge feature of the Ca²⁺ metal is blue shifted in the neutral complex which indicates a lowering of the oxidation state for Ca. The red shift (in zwitterionic complex) is due to the d⁰ electronic configuration of Ca²⁺ metal cation, and the allowed transition is 1s → 3p state, which consist of 3s core hole state along with the dipole allowed transitions 1s → 3d and 1s → 4s state. The peak shift may be due to the distortion in the coordination environment. Overall, the intensity of the peak depends on the hydrogen bonding present in the system.

3.6.2 Oxygen K-edge spectra. The oxygen K-edge spectra for all four complexes are shown in Fig. 9. The pre-edge feature of oxygen in the zinc substituted complex is observed at 530.20 and 536.79 eV for the neutral and zwitterionic complexes respectively. This indicates that the pre-edge contribution is mainly due to the hybridization of O 2p with the Zn 4s states.⁶⁹ The energy above 539 eV in the spectrum is mainly attributed to the hybridization of O 2p with the Zn 4p states. The zwitterionic complex has higher intensity than the neutral complex, due to the coordination and presence of N⋯H–O hydrogen bonds. On the contrary, for the Cu²⁺ substituted complex, intensity is higher for the neutral complex. The pre-edge (1s → 2p states) is observed at 535.67 and 534.67 eV for neutral and zwitterionic complexes respectively. Thus the pre-edge energy shift indicates that the oxidation state of the oxygen varies due to the strong coordination with Cu²⁺.

Fig. 9 Oxygen K-edge spectra for the metal-interacted histidine dimer.

In the oxygen K-edge spectra for the magnesium substituted complex, the pre-edge peak is observed 530.23 and 529.54 eV for neutral and zwitterionic complexes respectively. The K-edge spectrum of the neutral complex indicates that the pre-edge energy is blue shifted and the major contribution is from the mixing of 2p of oxygen with 3s of the magnesium. For the calcium-coordinated complex, the pre-edge energy is 534.48 and 535.28 eV for neutral and zwitterionic complexes respectively. The pre-edge feature is due to 1s → 2p transitions and the decrease in pre-edge intensity is due to the distortion in the coordination. Thus from the oxygen K-edge spectra, metals like zinc and copper are able to back-donate the electrons to the oxygen atom and for the d⁰ configuration, the receiving back of electrons is small due to the coordination of metals with oxygen.

4. Conclusion

The interactions of metal cations with monohydrated, neutral and zwitterionic dimer complexes are studied using ETS-NOCV and XANES plots to characterize the charge transfer between the C=O and C–N bonds. The bonds formed between the histidine and metal is through σ bonds and the order of the degree of back bonding for C=O and C–N bonds is Cu²⁺ > Zn²⁺ > Mg²⁺ > Ca²⁺ and Zn²⁺ > Cu²⁺ ≈ Mg²⁺ > Ca²⁺ respectively. The C=O bond length of the Cu²⁺ and Ca²⁺ complexes is longer than that of the monomer which indicates the back donation of the electrons from metals. Zn²⁺ and Mg²⁺ complexes have no change in the bond length indicating a lack of back donation. Frequency shifts for the C=O and C–N bonds are red and blue shifts respectively, which indicates the occurrence of π-back donation through C=O bonds. Interaction energy and distortion energy of the complexes show the same trend and is Cu²⁺ > Zn²⁺ > Mg²⁺ > Ca²⁺. EDA indicates the bond formation between metal and ligand is predominantly electrostatic. From the HOMO–LUMO plots, the Cu²⁺-interacted complex consists of the d_x²−y² orbital which indicates that the Cu can back-donate its electron to the histidine ligands which is backed up by the bond length and frequency calculation. NOCV calculations show that back donation is dominant over the O–TM²⁺–O tri-center bond compared to the N–TM²⁺–N bond. Overall, from the ETS-NOCV results and frontier molecular orbitals, neutral and zwitterionic forms of the ligand do not play a significant role in transferring the electrons. K-edge spectra for the metal indicate the intensity of the complex depends on the hydrogen bonding. Oxygen K-edge spectra indicate that the oxygen 2p orbital is mixed with the valence electron present in the metal, in which the back donation can occur.

Acknowledgements

Authors Dr L. Senthilkumar and P. Umadevi gratefully acknowledge the DST-SERB, New Delhi, India, for granting the project and fellowship under the Fast-Track Scheme.

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