The 28th element in the periodic table is nickel, a hard, ductile, silvery-white transition metal. It can be found in a range of oxidation states, from -1 to +4. Nonetheless, the most prevalent oxidation state in the environment and biological systems is +2 (Ni²⁺) (Muñoz & Costa, 2012). Protons are transferred within the molecule more easily when metal ions and water molecules connect to the adenine base. Various metal ions can attach to the adenine base at different locations, including Na⁺, K⁺, Ca²⁺, Mg²⁺, Zn²⁺, and Ni²⁺ (Ahamed M. Sabid, 2024; Gorb et al., 2004; Yousuf et al., 2023).

Nickel is necessary for certain microbes, plants, and animals, but there is no proof that it is good for human nutrition (Song et al., 2017). Nickel-based enzymes or cofactors are well-known in archaea, bacteria, algae, primitive eukaryotes, and plants, but they have not been found in higher organisms (Boer et al., 2014a, 2014b; Ragsdale, 2009). However, high nickel levels can damage plants by interfering with metabolic processes such as the synthesis of chlorophyll, photosynthetic electron transport, and enzyme activity (Sreekanth et al., 2013). Urease, methyl-coenzyme M reductase, CO-dehydrogenase, Ni-superoxide dismutase, glyoxalase, iridectome dioxygenase, lactate racemase, prolyl cis-trans isomerase, and [NiFe] hydrogenase are among the few enzymes that have been shown to include nickel (Macomber & Hausinger, 2011). There are other known nickel-dependent enzymes, including quercetins from Streptomyces sp. and glycerol-1-phosphate dehydrogenase from Bacillus subtilis (Guldan et al., 2008; Merkens et al., 2008). These enzymes play crucial roles in the global carbon, nitrogen, and oxygen cycles by being involved in processes that use or create gases such as CO, CO₂, CH₄, H₂, NH₃, and O₂ (Ragsdale, 2007).

Histidine and cysteine residues typically coordinate the catalytic sites of nickel-dependent enzymes, with aspartate and glutamate also playing a role (Ragsdale, 2009). Ni2+ ions have the ability to react with volatile organic compounds (VOCs), changing in the environment and influencing the chemistry of air pollution (Alam et al., 2024; Morales et al., 2007). According to studies, antioxidant compounds that increase the activity of antioxidant enzymes, such as taurine, melatonin, and L-carnitine, may be able to stop nickel-induced neurotoxicity and carcinogenicity (Amado & Jacob, 2007; Kalia & Lang, 2015).

Many enzymes that dont need metal ions to function can be inhibited by nickel, while the precise methods of inhibition are unclear. Analyzing the electronic and structural characteristics of Ni2+ interactions with oxygen (O) and nitrogen (N) is necessary to comprehend the behavior of these enzymes. Ni2+ ions can form a variety of coordination structures in water, including square, tetrahedral, and octahedral configurations. According to research, Ni2+ usually forms octahedral interactions with six water molecules. Vibrational frequencies fluctuate noticeably as a result of this coordination, which alters the angles and distances between O-H bonds. As the water cluster gets bigger, these changes get smaller. The strength of hydrogen bonding is enhanced, forming stable six- and eight-membered rings that are important for the growth of Ni²⁺-water clusters. This research is significant for understanding human health. By calculating the binding energies of Ni²⁺-water complexes, we can better understand how nickel interacts with water and compare these findings to experimental data.

Experimental Methods 

Although theoretical chemistry and quantum mechanics are intimately related, molecular modeling links them to other branches of chemistry. Like other areas of chemistry, computational chemistry makes use of tools to investigate chemical reactions and processes. Understanding and forecasting chemical systems, estimating energy differences across states, and elucidating reaction paths and processes are all major challenges in computational chemistry. AMBER and OPLS are two examples of tools.

Computational approaches frequently employ empirical parameters to account for a variety of impacts. For example, to simplify calculations, certain details, such as two-electron integrals, are occasionally approximated or disregarded in Hartree-Fock calculations. These computations are quicker and yield more precise predictions than semi-empirical methods.

All calculations discussed were performed using the B3PW91 gradient-corrected correlation functional (Wang & Perdew, 1991) with the 6-31G(d) basis set. Density Functional Theory (DFT) was used because it provides better results than many other computational methods. Calculations were carried out in both the gas phase and in a solvent (water) using the Gaussian 09 program, and Gauss View 5.0.8 was used for visualizing structures and simulated vibrational spectra (Ahamed M. Sabid et al., 2024). Geometry optimization was performed for individual reactants, transition states, and products of the reaction.

Binding energy was calculated using the formula:

Binding Energy = Energy of Complex - (Energy of Ligand + Energy of Receptor)

A lower binding energy indicates a more stable complex, while a higher binding energy indicates less stability. Reactions typically occur at the frontier molecular orbitals. The HOMO (highest occupied molecular orbital) represents the molecules electron-donating ability, while the LUMO (lowest unoccupied molecular orbital) represents its electron-accepting ability. A higher HOMO energy suggests stronger electron donation and a lower LUMO energy indicates greater ease in accepting electrons. The energies of HOMO and LUMO are used as indicators of chemical reactivity, such as electron affinity and ionization potential.

Insights of basis sets

We will consider the 6–31G*, 6–311G*, 6–311G (d,p), 6–311+G (d,p), and 6–311++G (d,p) basis sets, which are commonly used. These sets include variations with polarization () and diffuse (+) functions. Polarization functions () are applied to "heavy atoms," which are atoms beyond helium.

For hydrogen (H) and helium (He), the 1s orbital is represented by an inner and outer 1s basis function, resulting in two basic functions. Carbon includes a 1s function (six Gaussians), inner 2s, 2p x, 2p y, and 2p z functions (three Gaussians each), outer 2s, 2p x, 2p y, and 2p z functions (one Gaussian each), and six 3d functions, for a total of 15 basis functions. A 6–31G* calculation for CH₂ uses 19 basis functions, producing 19 molecular orbitals (MOs).

The 6–311G* basis includes polarization functions for heavy atoms. Adding polarization functions to H and He results in the 6-311G** (or 6–31G (d,p)) basis. The 6-311G* and 6-311G** differ in that H and He have five functions in the latter, compared to two in the former. The 6–311G** basis is only advantageous for cases like hydrogen bonding.

Diffuse functions, typically of the s and p-type, are denoted with "+" (for heavy atoms) or "++" (for all atoms, including H and He). For example, 6-311+G adds diffuse functions to 6-311G. Polarization functions are higher angular momentum functions (d or f type) and are indicated after the "G."

The 6-311+G(d) basis includes diffuse s and p functions and d polarization functions. The 6-311+G (d,p) basis has d polarization for the main group elements and p polarization for H atoms. Asterisks are sometimes used as shorthand, where 6-311G* is equivalent to 6-311G (d), and 6-31G** is equivalent to 6-311G (d,p).

Structure Optimization and Thermodynamic parameters

This research studied the electronic structure and geometry of ground states (GSs) of Ni²⁺(H₂O)ₙ complexes, where n ≤ 6. The BPW91 functional with 6-311G(d,p) and 6-311+G(d,p) basis sets was used for all-electron calculations of hydrogen, nitrogen, oxygen, and nickel atoms. All computations were performed using the Gaussian 09 quantum chemistry program.

At the BPW91/6-311G(d,p) level, the [Ni(H₂O)]²⁺ complex has a triplet spin ground state (GS) with a spin multiplicity of 3 (M = 2S + 1). The H-O-Ni-H dihedral angle of 180° indicates a planar structure. The [Ni(H₂O)₂]²⁺ complex also has a planar GS, with the oxygen atoms of the water molecules aligned along the molecular axis.

The GS of [Ni(H₂O)₃]²⁺ has a triangular pyramidal geometry, with the Ni atom slightly above the oxygen plane. For [Ni(H₂O)₄]²⁺, the GS shows a tetrahedral geometry. Accurate basis sets are critical for studying clusters like [Ni(H₂O)₄]²⁺.

The GS of [Ni(H₂O)₅]²⁺ has a square pyramidal structure with longer Ni-O bond lengths. For [Ni(H₂O)₆]²⁺, the GS has an octahedral geometry with Ni-O bond lengths of 2.103 Å, slightly longer than experimental values (2.003, 2.060, and 2.056 Å) observed for Ni²⁺ coordinated with six water molecules in the liquid phase (Table S4, S5, S6).

An analysis of 108 crystal structures containing the [Ni(H₂O)₆]²⁺ cation from the CSD and ICSD databases shows variation in bond lengths and angles, typical in condensed phase data (Basile et al., 2009). Our comparison with gas-phase calculations found Ni-O bond lengths overestimated by 0.035 Å, but this was reduced to 0.004 Å using the CPCM model, aligning closely with experimental values. While caution is needed when comparing computational and experimental data due to variability, the chosen level of theory and basis set in this study accurately describes the structural properties (Table 1).

In the supplementary table S3, summarizes the thermal enthalpy (∆H) and Gibbs free energy (∆G) for various [Ni(H₂O)]²⁺ complexes calculated using the B3PW91 functional in gas and solvent (water) phases with different basis sets. For [Ni(H₂O)]²⁺, ∆H values are -1.526 kcal/mol (gas phase) and -0.198 kcal/mol (solvent), while ∆G values are -1.520 kcal/mol (gas) and -0.188 kcal/mol (solvent) (Supplementary table S2). As the number of water molecules increases, both ∆H and ∆G become more negative in the gas phase, indicating greater stability, while in the solvent phase, the values decrease but remain less negative, reflecting a loss of stability due to solvation effects (Baranowski & Bocheńska, 1965; Trachtman et al., 2001).

Fig. 1: Evolution of the binding energies for [Ni(H2O)n]2+, n ≤ 6 at various phases and basis set.

Table 1: Three exothermic reactions involving the [Ni(H₂O)₆]²⁺ complex and chloride ions, with associated reaction energies.

The trans isomer of [Ni(H₂O)₆]²⁺ with two chloride ions is thermodynamically more stable, showing a reaction energy of -289.22 kcal, in contrast to the less exothermic cis isomer at -287.69 kcal Fig. 1.

Table 2: Bond length (Å) and Binding energy (kcal/mol) of [NiCln(H2O)m]2-n complexes for B3P91/6-311G(d,p) in gas phase.

Table 3: Enthalpy (∆H), Gibbs free energies (∆G) for Ni2+ complex reaction with chloride ion in gas phase at 298.15 K.

In Table 3, Reactions 2 and 3 are closely related, but Reaction 2 is slightly more favorable. It has a Gibbs free energy of 2.313 kcal/mol compared to 2.316 kcal/mol for Reaction 3. Additionally, in reaction 2 thermal enthalpy is 2.322 kcal/mol, while Reaction 3 is 2.324 kcal/mol. Overall, the lower Gibbs free energy and enthalpy of Reaction 2 indicate a greater likelihood of spontaneity compared to Reaction 3 (Fig. 2).

Table 4: Three exothermic reactions involving the [Ni(H₂O)₆]²⁺ complex and OH ions, with associated reaction energies. 

With a reaction energy of -61.18 kcal/mol, the cis isomer of [Ni(OH)₂(H₂O)₄] is more stable and exothermic than the trans isomer (-59.12 kcal/mol), showing stronger thermodynamic favorability.

Table 5: Bond length (Å) and Binding energy (kcal/mol) of [Ni(OH)n(H2O)m]2-n complexes for B3P91/6-311G (d,p) in gas phase.

The cis isomer has a greater binding energy (212.19 kJ/mol) than the trans isomer (209.66 kJ/mol), resulting in enhanced stability with a difference of 2.53 kJ/mol.

Table 6: Enthalpy (∆H), Gibbs free energies (∆G) for deprotonation in [Ni(H2O)n]2+ complex in gas phase at 298.15 K.

Natural Bond Orbital (NBO) analysis for cis and Trans isomer

The significance of atomic charges on the cis and trans isomers of Ni complexes was investigated using Natural Bonding Orbital (NBO) analysis (Uddin et al., 2023). As seen in Table 10, variations in the charge of the Ni, Cl, and O atoms correlate with the changes in geometry and the NBO charge of atoms such as Ni and Cl is higher in atoms than in complexes. Therefore, charge transfer takes place as a result. While the charge of nickel as atom is 2.000, it is less in complexes, such as [Ni(H2O)]2+, [Ni(Cl)(H2O)5)]+, trans isomer of [Ni(Cl)(H2O)5)] and cis isomer of [Ni(Cl)(H2O)5)], respectively, at 1.390, 1.227, and 1.193 (Fig. 2). On the other hand, the NBO charge of [Ni(OH)(H2O)5]+, trans isomer of [Ni(OH)2(H2O)4] and cis isomer of [Ni(OH)2(H2O)4] is 1.291, 1.169 and 1.181 respectively. NBO charges are comparatively less in Ni-OH complex than in Ni-Cl complex. Ni atom charge of Cis isomer of Ni-OH complexes is more than trans isomer and in the case of Ni-Cl complexes, Ni atom charge of trans isomer is more than cis isomer. The discrepancy of NBO charges of two isomers for both complexes arises for two atoms Cl and OH. Chlorine (Cl) is a deactivating group (electron withdrawing), and Hydroxyl (OH) is an activating group (electron donating). (Supplementary table S7, S8)

Electrostatic potential (ESP) map

The electrostatic potential (ESP) limit varies depending on the compound, with units ranging from -0.043 to +0.284 in the color hierarchy of red, yellow, green, and blue. 

Fig. 2: ESP maps for successive complexes of [Ni(OH)2(H2O)4] and [Ni(OH)n(H2O)m]2-n. All maps used consistent surface potential ranges (0.043 au (red) to 0.284 au (blue)).

Fig. 2 illustrates this and serves as a tool for comprehending and forecasting molecular interactions. Attack sites that are electrophilic (negative ESP regions) are indicated in red, and nucleophilic (positive ESP regions) attack sites are marked in blue (Uddin et al., 2023). Regions that are neutral are indicated by green (Fig. 2). The Ni-Cl and Ni-OH complex of the cis and trans isomers electrostatic potential (ESP) maps reveal significant electron-rich and electron-deficient regions for the Cl and OH ions responsibilities. It was found that Cl has a higher electron density than OH, which could be explained by Cls higher electronegativity.

This study provides important insights into the stability and electronic properties of nickel-aqua and nickel-chloride complexes using Density Functional Theory (DFT). The trans isomer of [Ni(Cl)₂(H₂O)₄] is more stable by 2.16 kJ/mol compared to the cis isomer, while the cis isomer of [Ni(OH)₂(H₂O)₄] is more stable by 2.53 kJ/mol than the trans form. In addition, the cis isomer of [Ni(OH)₂(H₂O)₄] is more stable and exothermic by 2.06 kcal/mol, whereas the trans isomer of [Ni(H₂O)₆]²⁺ with two chloride ions is more thermodynamically stable than the cis isomer by 1.53 kcal/mol. Natural Bond Orbital (NBO) analysis showed that the charge on the nickel atom in [Ni(H₂O)]²⁺ was 1.390, while it was 1.227 for the trans isomer of [Ni(Cl)(H₂O)₅]⁺ and 1.193 for the cis isomer. This indicates a change in electronic distribution between different complexes. Moreover, Electrostatic Potential (ESP) maps showed distinct regions of electron density in the Ni-Cl and Ni-OH complexes. These results provide a clearer understanding of the stability and charge distribution in nickel complexes. The nickel charge decreases from 1.291 in the formation of [Ni(OH)(H₂O)₅]⁺ to 1.181 in the trans isomer of [Ni(OH)₂(H₂O)₄] and 1.169 in the cis isomer. This shows a change in electronic distribution between the different complexes. Additionally, Electrostatic Potential (ESP) maps revealed specific regions of electron density in the Ni-Cl and Ni-OH complexes. These findings help improve the understanding of stability and charge distribution in nickel complexes.

M.J.A.: Conceptualization, Methodology, Formal analysis, Gaussian 09 program, Gauss View 5.0.8 software, Writing - original draft. M.S.A.: Methodology, Formal analysis, Gaussian 09 program, Gauss View 5.0.8 software, Writing - original draft. M.S.I.: Methodology, Formal analysis, Gaussian 09 program, Gauss View 5.0.8 software, Writing - original draft. M.E.H.: Methodology, Formal analysis, Investigation, Writing - review & editing. K.M.U.: Methodology, Formal analysis, Investigation, Writing - review & editing

The authors declare no conflicts of interest.

There is no acknowledgment to the any peoples or institutions.