The Effects of Oxidation States and Spin States of Chromium Interaction with Sargassum Sp .: A Spectroscopic and Density Functional Theoretical Study

The study of various oxidation states of chromium with Sargassum sp. is of particular interest since hexavalent chromium is reduced to trivalent chromium in an aqueous solution. In this study, a systematic density functional theory (DFT) calculations were performed to study the interactions of transition metal chromium ion with different oxidation states and spin states with the Sargassum sp. decorated with carboxylate (acetate) at the wB97XD/6-311++ G(d,p) level of theory. The structures and binding energies of chromium met-al-carboxylate complexes at various oxidation states and spin states in gas phase were examined. The coordination strength of Cr(VI) with the acetate ligand was predominantly the strongest compared to the other oxidation states. Vibrational frequency analysis, for the homoleptic monomers of tris [Cr III (AC) 3 ] 0 and [Cr VI (AC) 3 ] 3+ complexes, illustrate good harmony with the experimental and theoretical calculated frequencies. Using the time-dependent DFT (TD-DFT) at the level of CAM-B3LYP/6-311++G(d,p), the vertical excitation energies were obtained. The stabilization energies derived using the second order perturbation


Introduction
The toxic heavy metal chromium subsists in aqueous waste streams has the oxidation states of −2 to +6 [1]. The particular oxidation state of a metal is reliant on many factors comprising pH, redox potentials and kinetics. For chromium metal, thermodynamically, +3 and +2 are the most stable states, while in the environment, +3 and +6 oxidation states are the most common ones. The electronic configuration of the element chromium in the ground state is 3d 5 4s 1 , whereas the most prevalent states +3 and +6, it is 3d 3 4s 0 and 3d˚4s˚, respectively [1].
Pourbaix diagram [2] (pH plotted against EB) shows the existence of predominant or stable species of +3 state, ( ( ) 3 2 6 Cr H O + ) and +6 state ( 2 4 CrO − ) at low and high pH respectively. At pH < 1, the H 2 CrO 4 is predominant, while at the pH 2 to 6, the 4 HCrO − and 2 2 7 Cr O − anions prevail. The yellow ion 2 4 CrO − exists at a pH > 8 only. The oxidation state of +4 is the most stable at high pH. Especially in acid solution, the +4 oxidation state disproportionates easily to chromium (III) and chromium (VI) [3]. The Chromium species predominantly occurs in the environment at the trivalent and hexavalent state [4]. Sargassum sp., a brown seaweed which was decorated with electron donor groups carboxylates studied for the biosorption of Cr(VI) to reduce less toxic Cr(III) under acidic condition at pH 2 [5]. Above a certain pH level, the carboxylic acid groups usually dissociate, which makes them very reactive [6].
Cr(III) carboxylates show a ridiculous structural diversity like simple dimers as well as high nuclearity clusters [7] [8] [9]. In catalytic and materials applications, Cr(III) carboxylates are utilized commercially [10]. In different manufacturing industries, patented commercial products containing Cr(III) are used. The carboxylates, oxides and hydroxyl moieties usually bridged with metal centres via the presence of water in the reaction system [11]. Alfred Werner as early as 1908, synthesized the chromium metal triangular complex, Cr 3 O(RCO 2 ) 6 (H 2 O) 3+ and its derivatives were used theoretically for molecular magnetic interactions [12] [13]. These trimeric species are usually known as "basic chromium carboxylates" [14]. Chromium (V) is also found in organic matter for example humus.
In studies with various cell systems, starting with chromate (CrO 4 ) 3− , chromium (V) has been shown to be present as an intermediate. Previously reported that Cr(O 2 C 3 H 7 ) 3 was produced by the reaction of chromium (VI) oxide with carboxylic acid anhydrides [15]. The compound however soluble in methanol and consists of non-equivalent carboxylate groups in the infrared (IR) spectra inconsistent with monomeric structure. A homoleptic, monomeric, neutral Cr(III) car- We calculated the energy gap between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) and was used to calculate the chemical indices, for example chemical hardness, η [20] electronic chemical potential, µ [21] and global electrophilicity index, ω [22]. These outcomes support us to know the thermodynamic behavior of such systems as a function of the quantum chemistry chemical descriptors.

Computational Methods
We studied the tris acetate complexes of chromium [Cr (AC) 3 ] n at different oxidation states (n = −3 to +3) and spin states ( Figure 1). The carboxylic acid group was considered as the deprotonated carboxylic acid. The geometries of the complexes were optimized using density functional theory (DFT) with the hybrid exchange correlation functional DFT/wB97XD [23] and a triple-ζ basis set (6-311++G(d,p)) [24] [25] [26] in gas phase. DFT with the wB97XD hybrid functional as implemented in Gaussian16 [27] and Gauss View 6.0.8 was used for visualization of the optimized minimum energy structures and simulated the vibrational spectra. We checked the binding energies of Cr(III) at different spin states and high spin state(HS) was found to be the minimum energy state. Thus acetate was considered as a weak-field ligand and hence all the metal coordinated complexes were supposed to have high spin multiplicity. We also checked different oxidation states and spin states of these complexes. Normal mode coordinate analysis and no imaginary frequency confirmed the structure to be a minimum energy structure. The complexes were optimized without imposing any symmetry. After optimized the molecular geometry, the binding energies of the metal-ligand coordinated complexes were calculated as, [28] ( )  Figure 1 shows the monomeric, homoleptic optimized structure of tris-chromium    [5], b Ref. [9], c Ref. [40]. FT-IR is one of the well-established diagnostic probes of carboxylate coordination in metal complexes. The difference in wavenumbers between the antisymmetric and symmetric CO 2 stretches (Δ) distinguishes between monodentate and free ion (>200 cm −1 ), bridging (200 -100 cm −1 ) and bidentate (<100 cm −1 ) carboxylate bonding geometries [31].
These data demonstrates the antisymmetric ( COO asym ν ) stretch at 1526 cm −1 and the symmetric ( COO sym ν ) stretch in the ~1494 cm −1 region yielding a respective separation ( The presence of more than one band which may be assigned to (COO~) vibrations suggests that the three carboxylate groups are non-equivalent. These two leading infrared (IR) peaks are close in frequency to those previously calculated and experimental data observed for tris-chromium carboxylates complex Cr III (EH) 3 at 1515 and 1455 cm −1 respectively [16]. These data support carboxylate as bidentate coordination with the chromium centre [16]. This suggests the hexacoordination [15] of chromium provided one of the acetate groups is asymmetric with one Cr-O bond is normal and other significantly longer. All the υ CO 2 stretches was assigned supported by the computational modeling. The IR peaks with high intensities arose from the large charge polarization since the positive Cr(III) ion being en-closed by three negatively charged acetate ligands. Due to charge polarization, the vibrations that result in unsymmetrical distortions convince large dipole moment deviations and large IR intensities. Table 2 reports the vibrational normal modes allied with the bidentate carboxylate groups and their distinctive absorptions reflect the dissimilarities in molecular structure of Cr-acetate complex. The assignment of the theoretically calculated frequencies is based on the experimentally observed band frequencies and intensities in the IR spectra [15]. The monomer bidentate structure [Cr III (AC) 3 ] 0 demonstrates good harmony with the experimental infrared spectra.

Binding Energy Analysis
The In case of Cr (III) complexes, the relative energy of low-spin state is higher than high-spin state by 385.79 kcal·mol −1 (see Table 3  in water solvent, only fluctuating by less than 0.008%. Due to the presence of the solvent, the structural change of each complex was not considered in this calculation. We however guess that the near-octahedron geometry around the central metal of each compound rests approximately unbroken with the introduction of the solvent. Thus, the binding energies of metal-ligand apparently will not fluctuate far from those in the solvent. Due to the upturn of the amount of the precise interchange energy, high spin state with higher number of unpaired electrons is strongly stabilized compared to the low spin states. Thus energy investigation displays that the smaller ionic radius with more charge like Cr(VI), and the shorter bond distances M-O(Cr-O, 1.85 Å) allows the metal ion to withdraw more electron density from the carboxylates. These outcomes lead to the increase the charge transfer among the acetate (AC) and chromium metal ions. Furthermore, binding enthalpy (ΔH bind ) of coordination shows that the interactions between carboxylate and chromium ions are affected by the thermal correction in water. It is noticed that complexes with the same ligand acetate, Cr(VI) is more stable compare to the Cr(III). Thus a correlation is noticed between the complexation capacity and size of the metal ions, because the metal-ligand fascination proves to be the opposite of the ionic radius. Therefore, these results are reliable with the difference in size among the ions, 0.76 [38] and 0.44˚A [39] for Cr(III) and Cr(VI), respectively.

Spectroscopic Data
The theoretical absorption spectrum of tris [Cr III (AC) 3    HOMO orbital is primarily owing to 62% contribution from the chromium iron.
In the LUMO presented in Figure 4, however, the electron density is mostly moved out of the acetates into the chromium ion. Thus, the strongest peak of the tris acetate complex in the UV-vis spectrum created obviously from ligand-to-metal (L→M) charge transfer. The peak at 420 nm mainly (66%) involved the transition from HOMO to LUMO+1. The orbital illustration of LUMO+1 has likewise the similar type of configuration leading the major involvement of oxygen has 62.89 % contribution for the construction of LUMO+1 orbital. Again, this peak originated from the ligand-to-metal charge transfer; the electron density in HOMO is dispersed mostly over acetate ligands. The contribution of electron density from metal ion has only 7.1%. The peaks located at 420 and 528 nm arose mostly from the HOMO to LUMO+1 and HOMO to LUMO transitions correspondingly. The HOMO-1 is alike to the HOMO-2 in that the electron density is extended over acetate ligands. The LUMO+1 is alike to the LUMO in that electron density is contained round the metal−oxygen interaction area. Another is that LUMO+1 does not have π character of the LUMO orbital.

Atomic Charges
The atomic charges on the metal ions were checked and reported in Table 5. Six different schemes were applied to estimate the charges: the schemes are natural population analysis (NPA), [41] Merz-Singh-Kollman(MK), [42] CHelpG, [43] CHelp [44] methods to fit the electrostatic potential, and the charge fitting method, HLYGAt [45] and NBO [18] [19]. The atomic charges varied from different charge schemes. Such as, the charge at NPA is 1.203

Natural Bond Orbitals Analysis (NBO)
The natural bond orbital (NBO) analysis [18] [19] was carried out using NBO and (j) acceptor in the complexes, the stabilization energy or second order perturbation energy, associated with the delocalization from was estimated as fol- where q refers to the donor orbital occupancy, i ε and j ε are diagonal elements (orbital energies) and ˆi j F is the off-diagonal NBO Fock-matrix element. The higher the value of ( )    Table 3 and in Table 6 shows a correlation. In additional, an increase in values is followed by the increment of ΔE bind values.

Quantum Chemistry Reactivity Indices
To know the chemical stability of a complex, it needs the information of quan- The calculated quantum chemistry reactivity indices are reported in Table 7. In

Conclusion
In the present study, DFT calculations were conducted to illustrate the complex-