Characterizing Ni(II) hydration in aqueous solution using

ORIGINAL PAPERCharacterizing Ni(II)hydration in aqueous solution using DFT and EXAFSH.Y.Liu 1,2&C.H.Fang 1&Y.Fang 1&Y.Q.Zhou 1&H.W.Ge 1&F.Y.Zhu 1&P.C.Sun 1,2&J.T.Miao 1,2Received:18August 2015/Accepted:18November 2015#Springer-Verlag Berlin Heidelberg 2015Abstract In the present work,a detailed investigation of Ni(II)hydration in water solutions was carried out using den-sity functional theory (DFT)and extended X-ray absorption fine structure (EXAFS)spectroscopy.The hydrated character-istics of [Ni(H 2O)n ]2+clusters,such as energy parameters,atomic charge distributions,and bond parameters,were ex-plored using DFT with Becke ’s three-parameter exchange po-tential and the Lee –Yang –Parr correlation functional (B3LYP).DFT calculations indicated that the preferred struc-ture of the first hydration shell of Ni(II)generally has a coor-dination number of six and is almost unaffected by the water molecules in the outer solvation shell,whereas the structure of the second solvation shell varies as the hydration proceeds.EXAFS measurements are reported for aqueous NiSO 4and Ni(NO 3)2solutions and the Ni(NO 3)2·6H 2O crystal.Analysis of the EXAFS spectra of these three systems using a multipa-rameter fitting procedure showed that,in each case,the first coordination shell consists of six water molecules with a Ni –O coordination distance of 2.04Å,and that there is no Ni –S or Ni –N coordination in the first shell.There was no evidence of outer-shell SO 42−or NO 3−ions substituting inner-sphere wa-ter molecules in NiSO 4and Ni(NO 3)2.The characteristics ofNi(II)hydration obtained from DFT calculations agreed well with those obtained experimentally using EXAFS.Keywords Nickel ion .Coordination number .Hydration shell .DFT .EXAFSIntroductionMetal ion hydration is a very important aspect of electrochem-istry,solution chemistry,and homogeneous catalysis.In order to be able to describe the hydration of a metal ion accurately,and thus to be able to interpret many properties of solvated species correctly,an in-depth understanding of how the solvation shells are structured around the ion is needed.Many investigations of metal ions in solution have been carried out,and a great deal of important information about the structural parameters of the first hydration shells around various ions has been obtained [1–3].Knowledge of the hydrated structure of Ni(II)in aqueous solution is of paramount importance since it is required to un-derstand the roles of Ni 2+in chemical and biological processes [4].In recent years,the structural properties of the first solva-tion shell of Ni 2+have been the focus of much discussion [5–7].However,there are also many unanswered questions about the coordination of water molecules in the second hydration shell of Ni 2+.It is much more difficult to get information on solva-tion shell structure at long distances from the metal ion.Some neutron diffraction studies have indicated that the second sol-vation shell is coordinated only weakly to Ni 2+[3].Lots of methods have been used to study the hydration of metal ions theoretically,and DFT is among the most powerful of them.For example,researchers have investigated the hy-dration of Ca 2+,Mg 2+[2,8],Li +[9],Fe 2+,Fe 3+[10],K +[11],Ni 2+[5],and other metal ions [12],a cluster [13],and anions [14]using DFT.The results of these studies agree well withElectronic supplementary material The online version of this article (doi:10.1007/s00894-015-2871-2)contains supplementary material,which is available to authorized users.* C.H.Fangfangch@ *Y .Q.Zhouyongqzhou@1Institute of Salt Lakes,Chinese Academy of Sciences,Xining,Qinghai 810008,China2University of Chinese Academy of Sciences,Beijing 100049,ChinaJ Mol Model (2016) 22:2DOI 10.1007/s00894-015-2871-2those obtained using EXAFS spectroscopy,X-ray scattering, Raman spectroscopy,and so on.In particular,EXAFS spec-troscopy has recently become an effective method of researching nickel compounds,include those in aqueous so-lutions[5,15,16]and in the solid phase[17–19].Some DFT and EXAFS studies of Ni2+in aqueous solution have been reported previously[5,6,16].In the work reported in the present paper,hydrated clusters of formula [Ni(H2O)n]2+(n=1–18)were calculated using DFT with B3LYP/gen,and the minimum-energy configurations were obtained.Furthermore,EXAFS measurements at the Ni Kαedges of Ni(NO3)2and NiSO4were performed.The effect of the second solvation layer on the structure of the first hydra-tion shell around Ni2+was also briefly explored. Calculation and experimental methodsDFT calculationsThe local minimum-energy structures were calculated with the Gaussian09program package using the B3LYP functional [20]in a gradient-corrected hybrid density DFT[21]analysis of[Ni(H2O)n]2+(n=1–18)hydrated clusters.Two types of basis set were used in this work.Dunning’s aug-cc-pVDZ correlation-consistent basis sets[22],generally abbreviated to B aVDZ,^were used for the oxygen and hydrogen atoms, while the relativistic effective core potentials(RECPs)basis set Lanl2DZ was used for the nickel atom[23–25].We de-fined the basis sets B3LYP/aVDZ and B3LYP/Lanl2DZ col-lectively as B3LYP/gen,i.e.,a custom basis set.In order to account for the long-range electrostatic effects of the solvent on the[Ni(H2O)n]2+(n=1–18)clusters in the aque-ous phase,a single-point polarized continuum model(PCM) [26,27]was employed to calculate the hydration energies for the geometries when n≥6.The default radius model was con-sidered in PCM calculations.All possible initial configurations of the[Ni(H2O)n]2+(n=1–18)clusters were considered and optimized at the B3LYP/gen level.The basis set superposition error(BSSE)corrections must be taken into account in the study of complex formation energetics by ab initio using the standard Boys–Bernardi counterpoise method[28].All of the geometry optimizations,PCM calculations,and BSSE corrections were performed with the Gaussian09software package[29]. EXAFS spectroscopy of Ni(NO3)2and NiSO4EXAFS measurementsThe EXAFS experiments(the energy of the Ni Kαedge is 8333.0eV)were performed with the1W1B beamline in trans-mission mode at the Beijing Synchrotron Radiation Facility (BSRF)using a Si(111)double-crystal monochromator and a 50.0%harmonic rejection system.The storage ring was run at an energy of between1.5and2.2GeV with positron currents of80mA.In addition,Ni foil was used to calibrate the mono-chromator.The solution was kept in a cell with Kapton film windows,and all data were collected at room temperature. EXAFS analysisThe data obtained in the EXAFS experiments were analyzed with the IFEFFIT software[30,31],and the oscillation func-tion of EXAFS data,χ(k),can generally be represented as χkðÞ¼S20ΣN jkR jF j kðÞe−2σ2j k2−2R j−ΔðÞλj sin2kR jþΦj kðÞÂÃð1ÞThis equation represents the superposition of the contributions of the various coordination layers.All possible single scattering paths and significant multiple scattering paths are summed in Eq.1.The atoms surrounding the central atom(i.e.,Ni)are divided into j shells,where the atoms in a shell all have the same coordination number N j and are at the same coordination distance R j from the Ni atom.k is the photoelectron wave vector expressed as k=[2m(E−E0)/(ℏ2)]1/2,where m,E0,andℏare the mass of an electron,a threshold energy associated with the ejection of a photoelectron,and Planck’s constant divided by2π,respectively.F j(k)andФj(k)are the backscattering amplitude and phase func-tion of the j neighbors,whileλj(k)is a phenomenological mean-free-path term that accounts for inelastic losses.Moreover,Δis a correction factor(Δ=ΔR)in the mean-free-path concept,σj2is the Debye–Waller factor,and S02is the core hole or amplitude reduction factor resulting from shake-up/shake-off processes at the central atom Ni;its value was fixed at1.0[32,33].The EXAFS experimental data were fitted with Eq.1.The parameters R,N,Δσ2,andΔE0(the edge shift)of each shell were acquired by fitting the experimental data.In this article, theχ(k)data were generally multiplied by k2using a Hanning window with d k=1Å.The accuracies of the values of R and N areΔR≤0.02ÅandΔN/N≤15%,respectively.Results and discussionStructures and energetics of the[Ni(H2O)n]2+clustersA variety of Ni2+hydrated clusters with first and second hy-dration shells were investigated,and the hydration character-istics of those clusters are discussed below.In order to deter-mine the stabilities of the[Ni(H2O)n]2+clusters,four-,five-, and six-coordinate clusters were considered during the pro-cess of geometry optimization.A series of stable structures for the[Ni(H2O)n]2+(n=1–18) clusters in the gaseous phase were optimized at the B3LYP/ gen level of theory.These optimized geometries are shown in2 Page2of9J Mol Model (2016) 22:2Fig.1,and their energy and bond parameters are listed in Table 1.The energy parameters of the clusters in the aqueous phase were obtained using PCM calculations at the B3LYP/gen level.Such calculations are not accurate when n ≤5,so the values of ΔE solv for those clusters are not listed in Table 1.The energy and bond parameters of the lowest-lying six-coor-dinate conformers of [Ni(H 2O)n ]2+(n =12–18)clusters are presented in the B Electronic supplementary material ^(ESM).For the conformers of the stable [Ni(H 2O)n ]2+(n =1–18)clusters,the lowest hydration energy decreases with the number of water molecules present (see Fig.2).As the number of water molecules in the gas-phase cluster increases from one to five,Table 1shows that the hydration energy increases substantially.For each cluster,conformers with coordination numbers of five are clearly more stable than four-coordinate conformers.By comparison,if we study the values of ΔE and ΔE solv for n ≥6in Table 1and Fig.2,we can see that the most stable conformers are those with coordina-tion numbers of six.The hydration energy of the six-coordinate [Ni(H 2O)6]2+cluster is 640kcal/mol in the aque-ous phase,indicating that Ni 2+prefers to be surrounded by six water molecules in the first hydration shell,which is consis-tent with the results of other studies [5,6,15,16].Clusters with n >6include water molecules that are not directly coordinated with the Ni atom;instead,they link to the water molecules that are directly coordinated with the Ni atom.These water molecules comprise the second hydration shell.Looking at Table 1,it is clear that the lowest-energy [Ni(H 2O)n ]2+(n =1–18)cluster is that with 6water molecules in its first hydration shell and 12in its second.In this case,theW1W2W3W4W5-4L W5-5L W6-4L W6-5LW6-6L W7-4L W7-5L W7-6L W8-4L W8-5L W8-6LW9-4L W9-5L W9-6L W10-4L W10-5L W10-6L W11-4LW11-5L W11-6L W12-4L W12-5L W12-6L W13-4L W13-5LW13-6L W14-4L W14-5L W14-6L W15-4L W15-5LW15-6L W16-4L W16-5L W16-6L W17-4L W17-5LW17-6L W18-4L W18-5L W18-6LFig.1Selected optimized geometries of the [Ni(H 2O)n ]2+(n =1–18)clusters as calculated at the B3LYP/aVDZ level.The numbers next to W and L are,respectively,the number of water molecules in the cluster and the number of those water molecules that are directly coordinated to the metal ion.Hydrogen bonds are shown as dashed linesJ Mol Model (2016) 22:2 Page 3of 9 2water molecules in the first hydration shell act as proton do-nors and form hydrogen bonds with the water molecules in thesecond solvation shell,which act as proton acceptors,so the second hydration shell is only weakly associated with Ni 2+.ΔE (k c a l /m o l )n /H 2OΔE s o l v (k c a l /m o l )n /H 2OFig.2Plots showing how the calculated hydration energies of the stable clusters [Ni(H 2O)n ]2+(n =1–18,and with various numbers of water molecules directly coordinated to the metal ion:4L ,5L ,6L )vary as thenumber of water molecules in the cluster (n )increases.Calculations were performed for clusters in the gaseous (ΔE ;left panel )and aqueous (ΔE solv ;right panel )phasesTable 1Energy and bond parameters of the optimized structures of the [Ni(H 2O)n ]2+(n =1–18)clusters,as calculated at the B3LYP/aVDZ level in the gaseous and aqueous phasesGeometries aBondparameters b Energy parameters c Geometries aBondparameters b Energy parameters c R Ni –Oq Ni ΔE ΔE solvR Ni –Oq Ni ΔE ΔE solv W1 1.915 1.72−127.6W12-4L 1.969 1.32−454.9−781.3W2 1.876 1.58−224.9W12-5L 2.029 1.24−469.9−800.3W3 1.938 1.51−243.0W12-6L 2.084 1.14−478.4−809.2W4 1.987 1.39−325.6W13-4L 1.975 1.32−447.7−805.9W5-4L 1.980 1.37−341.5W13-5L 2.026 1.24−487.6−830.8W5-5L 2.043 1.33−355.9W13-6L 2.084 1.15−490.8−839.9W6-4L 1.988 1.38−357.1−632.9W14-4L 1.968 1.31−475.0−824.5W6-5L 2.040 1.30−366.6−639.0W14-5L 2.028 1.23−496.6−850.0W6-6L 2.083 1.23−370.4−640.5W14-6L 2.085 1.15−502.9−858.9W7-4L 1.988 1.36−381.1−663.9W15-4L 1.975 1.31−472.7−850.9W7-5L 2.036 1.29−390.4−669.0W15-5L 2.026 1.24−507.5−872.4W7-6L 2.086 1.21−396.4−673.5W15-6L 2.085 1.14−512.9−882.2W8-4L1.970 1.35−404.5−692.8W16-4L 1.969 1.31−493.0−867.4W8-5L 2.035 1.28−412.6−699.3W16-5L 2.030 1.23−504.5−896.0W8-6L 2.088 1.19−417.3−703.4W16-6L 2.085 1.15−516.9−910.5W9-4L 1.975 1.35−417.6−713.9W17-4L 1.972 1.30−495.1−891.2W9-5L 2.030 1.26−432.9−728.1W17-5L 2.035 1.23−507.7−910.5W9-6L 2.085 1.17−439.9−733.2W17-6L 2.085 1.14−524.7−921.4W10-4L 1.971 1.33−430.8−737.4W18-4L 1.969 1.30−504.5−910.9W10-5L 2.029 1.26−451.9−756.1W18-5L 2.028 1.23−531.4−938.9W10-6L 2.081 1.16−454.2−759.3W18-6L2.0841.14−550.2−960.9W11-4L 1.969 1.33−443.4−758.7W11-5L 2.028 1.25−462.6−780.4W11-6L2.0871.15−466.4−783.1aThe numbers next to W and L are,respectively,the number of water molecules in the cluster and the number of those water molecules that are directly coordinated to the metal ionbR Ni –O is the average distance between Ni and the O atoms of water molecules,and q Ni is the NBO charge on Ni in the [Ni(H 2O)n ]2+cluster.Bond distances and NBO charges are given in Åand au/e ,respectivelycΔE and ΔE solv are the hydration energy in the gaseous and aqueous phases,respectively;the latter was obtained at the PCM-B3LYP/aVDZ level of theory.All of the energies listed are in kcal/mol and were calculated for a temperature of 298K and a pressure of 1atm2 Page 4of 9J Mol Model (2016) 22:2For n =18,the coordination numbers of the second hydration shell are 9and 12for the stable conformers of [Ni(H 2O)18]2+.Among all configurations,the [Ni(H 2O)6(H 2O)12]2+conformer (W18-6L in Fig.1)is the most stable (note that more con-formers are presented in the ESM ).For the larger hydrated clusters [Ni(H 2O)n ]2+(n =13–18),four-and five-coordinate conformers were considered too,but the DFT calculations showed that six-coordinate conformers are still the most stable of the possible conformers.Bond distance and NBO analyses of the [Ni(H 2O)n ]2+clustersThe mean Ni –O bond distance (R Ni –O )for the first hydration shell is an important influence on the hydration characteristics of Ni 2+.In order to study the effect of the central Ni 2+on charge transfer,natural bond orbital (NBO)charge population analyses were performed.As a consequence,we analyzed the hydration characteristics of the [Ni(H 2O)n ]2+clusters based on how the Ni –O distance varied with n and cluster conforma-tion,as well as on the results of the NBO charge population analyses (see Fig.3).As shown in Fig.3and Table 1,for the stable conformers of the [Ni(H 2O)n ]2+clusters,R Ni –O varies greatly (from 1.915Åto 2.083Å)as n increases from 1to 6.The reason for this is that the interactions of the Ni 2+ion with the water molecules gradually weaken as the number of water molecules in the cluster increases.As n increases from6to 12,the R Ni –O values for the six-coordinate conformers range from 2.081Åto2.088Å.Indeed,the Ni –O distance remains between 2.084Åand 2.085Åas n is increased from 12to 18for the six-coordinate conformers.In other words,increasing the number of water molecules beyond six has very little effect on the Ni –O distance.Actually,similar behavior is also seen for the Ni –O distance with four-and five-coordinated con-formers.This behavior shows that the water molecules of the outer hydration shell exert little influence on the structure of the inner hydration shell when the first hydration shell of Ni 2+is saturated (i.e.,contains six water molecules).The results from the NBO charge population analyses shown in Fig.3and Table 1indicate that the charge density on Ni 2+for the stable conformers decreases rapidly from 1.72e −to 1.23e −as n increases from 1to 6.The interactions between Ni 2+and the water molecules gradually weaken as n increases up to 6(i.e.,while the first hydration shell remains unsaturated).However,the value of q Ni varies from 1.23e −to 1.14e −as n increases from 6to 12,although the trend is still a decrease with n .Finally,as n increases from 12to 18,the charge density of Ni 2+barely changes:it remains around 1.145e −.Similar behavior of the charge density on Ni is also observed for the four-and five-coordinate isomers.Again,these results suggest that the water molecules of the outer hydration shell have no effect on the structure of the inner hydration shell when the inner shell is saturated.That is,while there is significant charge transfer between Ni 2+and the water molecules of the first hydration shell,the water molecules of the outer solvation shell have almost no impact on the charge density on Ni 2+.0.00.51.01.52.02.5Energy/eVN o r m a l i z e d a b s o r p t i o nNi (NO 3)2-0.5M; Ni (NO 3)2-3.0M; NiSO 4-2.2M Ni (NO 3)2⋅6H 2Oa-1.5-1.0-0.50.00.51.01.5k 2χ(k )(Å-2)k(Å-1)Ni (NO 3)2-0.5M; Ni (NO 3)2-3.0M; NiSO 4-2.2M Ni (NO 3)2⋅6H 2Ob820084008600880090002345678910012345624681012 Ni (NO 3)2-0.5M; Ni (NO 3)2-3.0M; NiSO 4-2.2M Ni (NO 3)2⋅6H 2OR/Å|χ(R )|(Å-3)cFig.4a –c Experimental EXAFS results for aqueous solutions of Ni(NO 3)2(0.5M,3.0M)and NiSO 4(2.2M)and for the solid Ni(NO 3)2·6H 2O.a Normalized Ni K αedge absorption spectra;b EXAFS k -space spectra;c EXAFS R -space spectra (with the phase shift correction applied)R N i -O /Ån /H 2Oq N i /e-n /H 2OFig.3Mean Ni –O bond lengths (left )and charge densities on Ni (q Ni )obtained from natural bond orbital (NBO)charge population analyses (right )for the[Ni(H 2O)n ]2+(n =1–18)clusters with four (4L ),five (5L ),or six (6L )water molecules directly coordinated to the metal ionJ Mol Model (2016) 22:2 Page 5of 9 2In summary,the bond and energy parameters of [Ni(H 2O)n ]2+clusters obtained by DFT calculations indicated that the water molecules of the outer solvation shell have little impact on the structure of the inner solvation shell when n =6–12and have almost no influence when n ≥12.Therefore,we can conclude that the most stable first hydration shell contains six water molecules in an octahedral configuration,and that the molecules in this inner shell are not easily influenced by the water molecules in the outer solvation shell.The structure of this second hydration shell is relatively unstable except that it possesses a symmetrical structure and presents hydrogen bonding.EXAFS analysis of Ni(II)in aqueous solutions and the solid phaseWe obtained Ni K αedge EXAFS spectra for aqueous solu-tions of Ni(NO 3)2(at concentrations of 0.5M and 3.0M)and NiSO 4(at the approximate saturated concentration of 2.2M).The EXAFS spectrum of the solid Ni(NO 3)2·6H 2O was also collected and analyzed to provide qualitative information about the local environment of Ni 2+,and then detailed fitting of the experimental data was performed.The measured Ni K αedge absorption data were isolated by Fourier filtering to re-move the smooth background,and the results were normal-ized by dividing the data by the smooth background,as shown in Fig.4a .The resulting EXAFS data,χ(k ),are plotted against k ,the photoelectron wave vector,in Fig.4b .The various datasets show no obvious differences in the signal-to-noise ratio,due to the small differences in their signal-to-background ratios present in Fig.4a .The EXAFS curves for the solid salt and the solutions are exactly the same,reflecting the similarity of the first coordination spheres of these nickel compounds.The EXAFS curves were analyzed using the Fourier trans-form procedure,where k n χ(k )was transformed with n =2.Figure 4c shows the Fourier transform for each dataset in Fig.4b in the k range 2.2–10.5Å−1.The lower limit of this range was chosen to exclude the large near-edge feature,which probably has a different physical origin than that of the EXAFS phenomenon.The first and most intense peak,centered at 2.02Å(with the phase shift correction applied)in Fig.4c ,may correspond to the average distance of the six water molecules in the first solvation shell according to X-ray diffraction results.The second peak,at around 4.0Å,can be attributed to the second coordination layer of Ni 2+.In order to obtain precise data on the local coordination environment of Ni 2+,we performed detailed fitting of the EXAFS data.To fit the experimental EXAFS data effectively,the first coordination shell of Ni 2+was taken into consideration.Because of multiple scattering,attempts to fit the peaks located above 3.0Ådid not yield accurate structural parameters.The fits to the EXAFS data in k -space and R -space (with phase correction performed)are shown in Figs.5and 6,respec-tively.The parameters obtained from these fits are listed in Table 2,and the fitting weight was 2in all cases.In order to confirm the fitting reliability,the structures of Ni(NO3)2·6H2O (ICSD:9127)and NiSO4·6H2O (ICSD:89698)crystal were used as standard structure to fit the raw data of Ni(NO3)2and NiSO4aqueous solutions and Ni(NO3)2·6H2O solid included in the plots of k -and R -space in Figs.5and 6,respectively.The results of fitting the EXAFS spectra in R -space (see Fig.6)show a prominent peak that can be assigned to the distance between Ni and the O atoms in the first shell.Also,the Fourier-transformed spectra show a peak at around 2.58Å(a shoulder on the first peak)corresponding to the distance0369|χ(R )|(Å-3)R/ÅNi(NO 3)2-0.5M;60369Ni(NO 3)2-3.0M;|χ(R )|(Å-3)R/Å0369NiSO 4-2.2M|χ(R )|(Å-3)R/Å0246242462460369Ni(NO 3)2·6H 2O|χ(R )|(Å-3)R/ÅFig.6Results of fitting the Ni K αedge EXAFS spectra of aqueous solutions of Ni(NO 3)2(0.5M,3.0M)and NiSO 4(2.2M)and solid Ni(NO 3)2·6H 2O in R -space.The Fourier-transformed spectra were fitted in the R range 1.3–3.2Åand phase shift correction was performed.The solid lines are the experimental data and the dashed lines are the fitting results of the fitting procedure-101Ni(NO 3)2-0.5M;k 2χ(k )(Å-2)k(Å-1)-101Ni(NO 3)2-3.0M;k 2χ(k )(Å-2)k(Å-1)-11k 2χ(k )(Å-2)k(Å-1)NiSO 4-2.2M46810468104681046810-11Ni(NO 3)2·6H 2Ok 2χ(k )(Å-2)k(Å-1)Fig.5Results of fitting the Ni K αedge EXAFS spectra of aqueous solutions of Ni(NO 3)2(0.5M,3.0M)and NiSO 4(2.2M)and solid Ni(NO 3)2·6H 2O in k -space.The solid lines are the experimental data and the dashed lines are the results of the fitting procedure2 Page 6of 9J Mol Model (2016) 22:2between Ni and the H atoms in the first shell;the reason for the small magnitude of the peak at2.58Åis the poor backscat-tering ability of H atoms.Refined values for the full set of parameters that define the short-range peaks corresponding to the distances Ni–O and Ni–H are presented in Table2. Statistical errors in the structural parameters were estimated from the confidence intervals in parameter space,as shown in Table2.The contribution of the first solvation shell in aqueous Ni(NO3)2solutions and in solid Ni(NO3)2·6H2O was modeled by an oxygen shell containing approximately6.0atoms at distances of2.041~2.044Åfrom the Ni2+as well as a hydro-gen shell containing approximately12.0atoms at distances of 2.582~2.585Åfrom the Ni2+.Meanwhile,the results of fitting the EXAFS data for an approximately saturated NiSO4aque-ous solution indicated that the local structure around the Ni2+ comprised6.0oxygen atoms at a distance of2.040Åand12.0 hydrogen atoms at a distance of2.591Åfrom the metal ion. These results are in good accord with those for nickel nitrate. The accuracy and reliability of the fitting procedure are highlighted by the agreement between the theoretical EXAFS spectra and experimental data,as presented in Figs.5and6.Since the crystalline hydrate shows long-range order,all of the features appear better resolved in the spectrum for the Ni(NO3)2·6H2O solid sample.Moreover,the results of fitting the datasets for the Ni(NO3)2and NiSO4aqueous solutions are similar to those obtained for the solid Ni(NO3)2·6H2O,indicating that their local coordination environments are also similar.This means that the solid and the aqueous solutions have very similar first coordination spheres around the Ni2+in terms of the coordinated number,the type of neighbors pres-ent,and the local geometry.At the same time,a comparison of the peaks in Figs.5and6with the optimal fitting results in Table2suggests that there is almost no difference between them.Thus,we can conclude that none of the water molecules in the solvation shell are replaced by an anion(SO42−or NO3−).Consequently,our results have led to a better under-standing of the hydrated structure of the Ni2+in nickel com-pounds in aqueous solutions.If we compare the results obtained in this work with those provided by other similar studies(see Table3[5,6,16]),we find that the coordination numbers of Ni2+in various Ni(II) compounds in aqueous solution are all approximately equal to 6.0,whether DFT,CPMD,or EXAFS is used to determine these parameters.Also,whichever method is used,the Ni–O distance is found to lie between2.040Åand2.090Å.In our work,the Ni–O distance obtained via DFT calculations is in good accord with the Ni–O distance derived from EXAFS experiments,and both of them agree well with the correspond-ing results in the literature.Therefore,we can conclude that the first coordination shell of Ni2+comprises six water mole-cules that form an octahedral structure at a coordination dis-tance of around2.05Åfrom the Ni2+ion.Table3The coordination numbers and Ni···O distances for Ni2+in various Ni(II)compounds in aqueous solution,as derived using different methods Ni(II)compound Method Coordination number R Ni–O(Å)ReferenceNiCl2EXAFS 6.2±1.0 2.060±0.010[16]Ni(NO3)2EXAFS 6.6 2.055±0.010[6]NiCl2CPMD 6.0 2.060[5]NiCl2DFT 6.0 2.090±0.020[5]Ni(NO3)2EXAFS 6.0 2.042This work NiSO4EXAFS 6.0±0.6 2.041±0.007This work NiSO4DFT 6.0 2.083This workTable2Optimal EXAFS parameters for aqueous solutions ofNi(NO3)2(0.5M,3.0M) and NiSO4(2.2M)and solid Ni(NO3)2·6H2O a Species Distance Structural parametersN R(Å)Δσ2(Å2)ΔE0(eV)R factor k range(Å−1)Ni(NO3)2(0.5M)Ni–O 6.0(0.7) 2.044(0.006)0.0053−4.890.0002 2.2–10.3 Ni–H12.0(1.3) 2.585(0.006)Ni(NO3)2(3.0M)Ni–O 6.0(0.6) 2.041(0.008)0.0046−2.540.0004 2.2-–10.2 Ni–H11.9(1.3) 2.583(0.008)NiSO4(2.2M)Ni–O 6.0(0.5) 2.040(0.012)0.0063 2.200.0013 2.2–10.4 Ni–H12.0(2.2) 2.591(0.012)Ni(NO3)2·6H2O Ni–O 6.0(0.6) 2.041(0.007)0.0051−2.800.0004 2.2–10.5 Ni–H11.9(1.3) 2.582(0.007)a N is the coordination number,Δσ2is the Debye–Waller factor,R is the Ni–O or Ni–H distance,ΔEis the inner potential correctionJ Mol Model (2016) 22:2 Page7of9 2。