Skip to content
BY 4.0 license Open Access Published by De Gruyter Open Access April 24, 2019

Aqueous Micro-hydration of Na+(H2O)n=1-7 Clusters: DFT Study

  • Tahoon M.A. EMAIL logo , Gomaa E.A. and Suleiman M.H.A.
From the journal Open Chemistry


Sodium ion micro-solvated clusters, [Na(H2O) n]+, n = 1–7, were completed by (DFT) density functional theory at B3LYP/6-311+G(d,p) level in the gaseous phase. At the ambient situation, the four, five and six micro-solvated configurations can convert from each other. The investigation of the sequential water binding energy on Na+ obviously indicates that the influence of Na+ on the neighboring water molecules goes beyond the first solvation layer with the hydration number of 5. The hydration number of Na+ is 5 and the hydration space (rNa-O) is 2.43 Å. The current study displays that all our simulations have an brilliant harmony with the diffraction result from X-ray scattering study. The vibration frequency of H2O solvent was also determined. This work is important for additional identification of the Na+(H2O)n clusters in aqueous medium.

1 Introduction

Micro-hydration studies of charged and neutral chemical ions and molecules are an important tool to interpret mechanisms, energetic, structural and spectroscopic properties of hydration at atomic levels. As the dissolved solute is placed in water solvent, there is an arrangement of the vicinity water molecules to form hydrogen bonds between the solute and solvent. As a result strong hydrogen bonded H2O mesh is formed around the dissolved solute due to the electron arrangement of the solute. Recently, information of solvation sphere structure have been determined by several techniques like first principal quantum chemical calculations and cluster spectroscopy. The interaction between solute and surrounding solvent molecules is interpreted on the basis of information obtained about the structural properties of these hydrated clusters. The interaction between solute and its surrounded solvent molecules is the main reason of the solvation phenomenon [1, 2, 3, 4, 5].

The construction and binding energy of fine ion-water clusters have a consideration in the last years [6, 7, 8] due to their consequence in interpretting the manner of separate ions in chemical and biological systems. Sodium ion aqueous solutions have an abundant portion of contemplation due to their consequence in many fields: manufacture, electrochemistry, biology, and pharmaceutical. Many trial and ideal algorithms have been estimate for the contemplation of sodium ion aqueous solutions. Many trial techniques contain X-ray scattering, neutron diffraction, EXAFS and NMR [9] which recognize the coordination number (CN) and solvation distance (rNa-O) of Na+(H2O)n , in which the rNa-O is around 0.243 and the CN is from 4 to 8. The difference of CN is found to be hanging on the concentration of sodium salt. Though, the outcome of sodium ion concentration on the CN is not studied until now. Theoretical studies of sodium ions in water have been achieved with different methods which propose a smaller rNa-O from 2.24 to 2.39 Å [10,11]. With a larger uncertainty, the second solvation shell of Na+ ion in aqueous solution is also calculated [12]. In this effort, the structure of Na+(H2O)n with n = 1 –7 are calculated with DFT calculations so as to recognize the correct CN of sodium ion in water. The greatest contestants for every important configuration size are expected. Agreeing to the structural analysis results, authors suggest information around hydration structure, for example coordination number (CN), r Na-O and energy for different hydrated clusters of sodium ion.

2 Computational protocol

Geometry optimizations of Na+(H2O)n were captured using DFT calculations at B3LYP [13,14] and the 6 –311+G(d, p) base set level [15]. The starting configuration of the Na+(H2O)1 –2 configurations were met via changing the position of H2O solvent with consideration to Na+. The form of the larger clusters were reproduced from the smaller ones by joining water molecules to the Na+ through Na–O interaction and other water molecules through OH-O(H2O) hydrogen bonds at different place. The optimized lowest energy geometry is reached by changing the initial geometry and confirming that convergence to the similar energy was reached within 10-6 H also confirming that there were no imaginary frequencies.. The RMS internal forces for optimized geometries were 17x10-5, 11x106, 11x10-6, 25x10-6, 62x10-7, 13x10-6 and 39x10-6 for Na+(H2O), Na+(H2O)2, Na+(H2O)3, Na+(H2O)4b, Na+(H2O)5b, Na+(H2O)6c and Na+(H2O)7a, respectively. In method to reproof the achievement of the B3LYP functional, the configuration of Na+(H2O)n=1-7 were also optimized using BLYP functional basis sets, which supply results concurring with those of the B3LYP functional [16, 17, 18]. All structures are completed by using the computational software package Gaussian09 [19]. Authors used the Material Studio 3.2 to perform MD simulation [20]. The number of H2O molecules in the first solvation sphere for sodium ion is determined by MD simulation in the solution phase. Material Studio 3.2 (Accelrys, Inc.) is used for the construction of simulation system that is a periodic box with 18.786 X 18.786 X 18.786 Å dimensions and containing two Na+ and two Cl- ions surrounded by 221 H2O solvent molecules. Na+ and Cl- ions are enough separated from each other in very dilute solutions. 6.9 Å is the initial distance between two ions Na+ and Cl- for the simulation. 298 K is the used temperature for the simulation of the system while the period of MD simulation is 50 ps with 1 fs step size. Cycles of 50 ps are followed until the coordination number of Na+ ion is reached. Optimization and dynamics of the system box were performed using UFF level and thermostat used was Nose. Conductor-like polarizable continuum model (CPCM) is performed to clear the effect of macroscopic solvation.

Ethical approval: The conducted research is not related to either human or animal use.

3 Results and discussion

3.1 Hydrated structures

The most proper functional for the current work is the hybrid B3LYP which plays a very important role to define different structural properties. The H2O solvents are delivered to the middle sodium ion in a step wise method holding in opinion the termination goal to dissolve the consequence of solvent. The water molecule is added to the middle ion in dissimilar thinkable means and the full constructional optimization is complete with DFT at the B3LYP level of theory. The Cartesian coordinates of the stable Na+–(H2O)n clusters at DFT/B3LYP/6-311+G (d,p) level of theory are shown in Table S1 in the Supplementary Materials. The optimized configuration and structure parameters were showed in Figure 1 and Table 1. Now we will apportionment with the thermodynamics parameter, the Gibbs free energy change of hydration (ΔGhyd), the enthalpy change of hydration (ΔHhyd), energy change of hydration (ΔEhyd) and entropy change of hydration (AShyd). These parameters are of universal attention beside there are experimentally calculated parameters for solute hydration. The obtained numbers of these parameters are shown in Table 2 at DFT/B3LYP/6-311+G (d,p) level of theory. The thermodynamic parameters of the Na+–(H2O)n clusters are calculated according to the next equations:

Figure 1 Optimized geometries of hydrated sodium ion clusters at DFT/B3LYP/6-311+G(d,p) levels of theory.
Figure 1

Optimized geometries of hydrated sodium ion clusters at DFT/B3LYP/6-311+G(d,p) levels of theory.

Table 1

Calculated values of different structural, energies and thermodynamic parameters of Na+–nH2O (n =1–7) hydrated clusters at DFT/B3LYP/6-311+G(d,p) level of theory basis function.

SystemGhyd / kJ.mol-1x103Shyd / cal.mol-1.K-1Hhyd / kJ.mol-1x103Ehyd / kJ.mol-1x103
N a +(H2O)7 a-1830.931152.735-1830.740-1830.742
Table 2

Calculated values of the Gibbs free energy change of hydration (ΔGhyd), the enthalpy change of hydration (ΔHhyd), energy change of hydration (ΔEhyd), entropy change of hydration (ΔShyd) and bond length of Na+(H2O)-1-7 hydrated clusters at DFT/B3LYP/6-311+G(d,p) level of theory basis function.

SystemΔGhyd/kJ.mol-1ΔShyd/cal.mol-1.K-1AHhyd/kJ.mol-1ΔEhyd/kJ.mol-1Bond length /Å
N a +(H2O)6 a-7503.68-176.261-7718.97-7705.8432.279
N a +(H2O)6 c-7522.058-172.699-7732.098-7716.3452.298

Where Gsolute(H2O)n,Hsolute(H2O)n,Ssolute(H2O)nand Esolute(H2O)nare Gibbs free energy, enthalpy, entropy and energy of hydrated Na+(H2O)n clusters respectively. Gsolute, Hsolute, Ssolute and Esolute are the same parameters for a single sodium ion. GH2O, HH2O, SH2O and E H 2 O are the same parameters for water molecule.

The energy change of hydration (ΔEhyd) is enlarged as presented in Table 1 by the accumulation of water molecules. The identical action is seen for further parameters ΔGhyd ΔShyd and ΔHhyd. The hydration distance rNa-O is increasing with the increase of water

molecules, number n The first hydration space between Na+ and oxygen of water molecular (rNa-o) of Na+(H2O) is 2.189 Å The greatest stable structure of Na+(H2O)n=2 is linear with hydration distance 2.210 Å, and for Na+(H2O)n=3 is trigonal planar with hydration space 2.216 Å. As n rises to 4, three categories of stable structures, including three-coordinated conformers in the interior shell (Na+(H2O)4a), tetrahedron (Na+(H2O)4b) and two-coordinated conformers in interior shell (Na+(H2O)4c). The rNa-o of Na+(H2O)4b is 2.269 Å, which is longer than that of Na+(H2O)4a and Na+(H2O)4c. The most stable structure of Na+(H2O)4 is Na+(H2O)4b and the minor stable structure is Na+(H2O)4c with an energy variance of 8.157 kcal/mol parallel to that of Na+(H2O)4b. 5 water molecules are coordinated with Na+, which forms first hydration coat with the rNa-O 2.244 Å in Na+(H2O)5a. The second two structures; Na+(H2O)5b has a tetrahedron interior shell and, Na+(H2O)5c has a trigonal interior shell with the second shell water molecules with each accepting two hydrogen bonds from the interior shell which creates a more dense and constant structure. The rNa-o of Na+(H2O)5b and Na+(H2O)5c is 2.259 Å and 2.182 Å, respectively. Na+(H2O)5b is the most stable structure of five coordinated clusters. For six coordinated configurations, four types of stable conformers, Na+(H2O)6a, Na+(H2O)6b, Na+(H2O)6c and Na+(H2O)6d, are obtainable. In this work, each configuration has a six-coordinated hydration configuration with rNa-O 2.238 for Na+(H2O)6a, 2.262 for Na+(H2O)6b, 2.261 Na+(H2O)6c and 2.245 for Na+(H2O)6d. Na+(H2O)6c is the greatest stable configuration of six coordinated clusters. For seven water molecules (n=7), the greatest stable construction is Na+(H2O)7c which has a five coordinated interior shell and two exterior water molecules connected to the inside molecules by hydrogen bonds. The slight stable configuration is Na+(H2O)7d with energy variance 6.378 kcal/mol from Na+(H2O)7c. The further two configurations are Na+(H2O)7a and Na+(H2O)7b with seven and six coordinated water molecules in the interior shell. The obtained quantities of hydration free energy (ΔΔGhyd) of the hydrated clusters rise with the increasing of the H2O molecules numbers, indicating the interaction between solvent and dissolved ion and additional interactions between solvent molecules by H-bonds [21, 22, 23, 24]. When the H2O solvent molecules are added, the hydration tends toward more exothermic and, in this way, the solvation energy per one H2O solvent molecule finishes up remarkably smaller in magnitude. The previous tendency possibly appears due to H2O–H2O repulsion when the primary solvation shell is totally full by H2O solvent. The zero value of incremental free energy of hydration could not be as it is essentially the variance among the electronic energy of the successive metal ion complex minus the energy of a single water molecule as set in the next eq.


Hence, with a particular final aim to acquire a stronger representation, the free energy of hydration (ΔΔGhyd) that arises from the step wise addition of solvent molecules is shown in Figure 2. The value of (ΔΔGhyd) for the hydrated clusters, Na+(H2O)n, grows meaningfully as the length of the individual water particle ties to the solute particle. The polarization of the Na+ drives outside the solvation primary shell though it is difficult to expect the sodium metal ion solvation number from this figure. Figure 2 shows that (ΔΔGhyd) with uncertain behavior with increasing the water molecules until n=5. After n=5, (ΔΔGhyd) has a perfect behavior. These features not only provide that the sodium ion mostly cooperates with its adjacent water molecules, but also suggest that the saturated hydration sphere mainly occurs when n =5.2. This occurrence advises that structural properties of the approximate complete solvent shell for Na+(H2O)n clusters would not actually differ with extra water molecules as n > 5. It is decided that the saturated hydration number is 5.2 in the first hydration coat for Na+(H2O)n. To determine the effect of macroscopic hydration on sodium ion,popular conductor-like polarizable continuum model (CPCM) are applied to find optimized geometries. It is observed that bulk hydration of sodium ion adopting macroscopic solvent models like the polarized continuum model (CPCM) at the DFT/B3LYP/6-311+G(d,p) level of electronic structure theory does not change the geometrical parameters significantly. The electrostatic interaction between the wave function of the solute and dielectric model of bulk solvent that is generated from a number of surface charges on a definite elements of the cavity is taken in consideration by PCM model.. The O –Na+ bond length of Na+(H2O)n is calculated by applying the CPCM model, and there is an increase in its values (the bond become longer). The O – Na+ bond length is found to be 2.317 Å, 2.328 Å and 2.334 Å for Na+(H2O), Na+(H2O)2 and Na+(H2O)3 respectively. The O – Na+ bond length is found to be 2.387 Å, 2.377 Å, 2.379 and 2.386 Å for Na+(H2O)4, Na+(H2O)5, Na+(H2O)6and Na+(H2O)7 respectively. The elongation of O– Na+ may be as a result of solvent-solvent interaction which effect on the solute-solvent interaction and make the solute (Na+)-solvent(0) bond become longer.

Figure 2 The relation between incremental hydration energy (ΔΔGhyd) and the number of water molecules in Na+(H2O)n=1-7 clusters at DFT/B3LYP/6-311+G(d,p) level of the theory.
Figure 2

The relation between incremental hydration energy (ΔΔGhyd) and the number of water molecules in Na+(H2O)n=1-7 clusters at DFT/B3LYP/6-311+G(d,p) level of the theory.

3.2 Radial distribution function (RDF)

The coordination number of the first solvation shell is found to be 5 according to the quantum electronic configuration

for Na+ solvated ion. The classical MD simulation has been performed to confirm this result for aqueous Na+ solution to obtain a good image about the configuration and the coordination number of the solvation layers that surrounding the solvated ion. Usually the coordination number calculations in various solvents is done according to the partial radial distribution function, gαβ. a and β are molecules of different sorts in which β molecule has a spherical width dr, with a separation r from a molecule and the nαβ is the coordination number which can be determined by the integration of the RDF [25], gαβ (r) with respect to r as


where, ρβ is the number density of atom type ρ. The measured RDF acquired from the present recognized classical MD simulation is shown in Figure 3. The first solvation peak is located at 2.2 Å but a bit more than the value of gas phase specifys that the solvation produces a slight density of the first solvation layer. The sodium ion in the aqueous medium is rigid and stable as indicated from the high intensity behavior of the first solvation layer peak. The integrated value of the radial distribution function indicates that the primary hydration layer of sodium ion is satisfied by five H2O molecules. Consequently, five H2O molecules is the correct solvation number of designated ion in aqueous environment. Figure 3 shows the sequentially coordination number n(r) of the hydrated sodium ion. From the figure, it is seen that, n(r) integrates to five oxygens at around 2.2 Å. Therefore, the sodium ion first hydration layer is constructed to have five H2O molecules as obtained from RDF.

Figure 3 The relation between radial distribution function (g(r)Na-O) and the distance (r) obtained from the UFF-based classical MD Simulation.
Figure 3

The relation between radial distribution function (g(r)Na-O) and the distance (r) obtained from the UFF-based classical MD Simulation.

3.3 IR spectrum

IR can support in defining the time of proton transmission from the solute molecule to solvent water molecules, by the occurrence of aqueous proton creating new peaks in the IR band. Matching the simulated IR spectra with that of gas phase IR spectra of Na+nH2O clusters can aid in confirming the configurations expected. IR spectrum simulated is constructed on harmonic calculations. To account for the anharmonic nature of the chemical bonds, a scaling element requests be combined to the considered spectrum. The IR spectrum of Na+(H2O)n=1-7 clusters and single water molecule at DFT/B3LYP/6-311+G(d,p) level of theory is seen in Figure 4 and the frequencies are tabulated in Table 3. The symmetric stretching vibration (vsym) and asymmetric stretching vibration (vasym) of a single water molecule is at 3340.47 and 3409.39 cm –1, respectively while the symmetric scissoring vibration is at 1437.19 cm –1. These vibrations are adjacent to the experimental standards (3657 and 3756 cm–1) [26]. When Na+ attached with n=l–3 water molecules to form the first hydration sphere, the parallels vsym are 3798.56, 3806.76 and 3803.99 cm –1 and the v asym are 3883.20, 3893.60, 3887.67 cm –1. It is obviously detected that these matching frequencies of Na+(H2O)n=1-3 parallel to that of

Figure 4 The IR spectrum of (a) H2O; (b) Na+(H2O); (c) Na+(H2O)2; (d) Na+(H2O)3; (e) Na+(H2O)4b; (f) Na+(H2O)5b; (g) Na+(H2O)6c; (h) Na+(H2O)7a.
Figure 4

The IR spectrum of (a) H2O; (b) Na+(H2O); (c) Na+(H2O)2; (d) Na+(H2O)3; (e) Na+(H2O)4b; (f) Na+(H2O)5b; (g) Na+(H2O)6c; (h) Na+(H2O)7a.

Table 3

The vibration frequencies of Na+(H2O)n=1-7 at DFT/B3LYP/6-311+G(d,p) level of theory.

Na+(H2O)228.21-35.74-240.54-302.02-317.47-377.69-419.40-444.30-1672.56-1673.83 3805.82-3806.76-3893.60-3893.89
Na+(H2O)4b38.41-43.87-47.42-47.49-65.70-91.17-92.23-100.42-163.14-216.39-228.52 231.05-267.17-279.90-280.25-291.85-353.47-380.72-380.83-396.10-1659.45-1660.29-1660.33-1662.77-3815.97-3816.03-3816.09-3817.38-3913.58-3913.68-3913.85-3914.06
Na+(H2O)5b28.10-40.74-50.19-52.05-77.89-90.30-98.00-146.61-162.63-179.35-187.17 216.41-221.64-226.37-231.56-248.21-261.31-277.98-294.51-311.52-358.98 393.77-503.18-540.07-664.92-681.10-1640.58-1652.15-1656.04-1656.99-1687.34-3648.52-3680.15-3790.33-3818.16-3818.73-3890.51-3892.99-3895.37-3918.18-3918.20
Na+(H2O)6c25.74-25.75-36.84-68.33-72.52-72.53-114.59-139.10-153.06-153.11-175.00-175.06-199.24-208.06-221.83-226.31-273.97-251.07-251.78-278.41-278.43-333.81-375.82-375.84-486.60-522.62-534.19-645.78-649.08-667.96-668.00-1637.95-1638.75-1645.49-1645.50-1682.60-1683.06-3660.30-3660.32-3688.25 -3692.36-3792.32-3792.33-3893.47-3893.48-3896.88-3896.92-3899.31-3899.44
Na1H2O)7a58.94-68.28-80.80-90.75-104.53-111.78-128.81-139.49-143.40-168.90-188.43-211.04-233.88-246.99-257.00-271.79-277.53-281.60-301.92-308.63-322.63-346.35.349.80-368.23-370.70-408.84-434.49-474.48-488.88-531.15-534.17-547.03-680.67-697.21-718.64-774.98-781.72-890.00-1611.72-1617.81-1623.81 -1638.26-1676.53-1679.92-1691.14-3475.54-3529.57-3562.58-3612.59-3635.33-3689.58-3739.43-3864.42-3870.47-3872.19-3876.93-3883.93-3890.12 -3905.10

the single water molecular have a red shift Additionally, this occurrence was too stated in other arrangements Mm+(H2O)n [26,27]. In the meantime, the vsym and vasym have a blue shift with growing the number of hydrated water molecules from 1 to 3. For Na+(H2O)4b the vsym is at 3817.38 cm-1 and the vasym is at 3913.58 cm-1. For Na+(H2O)5b vsym and vasym are at 3818.16 and 3818.13, correspondingly. For Na+(H2O)6c the vsym is at 3792.33 cm1 and the vasym is at 3893.47 cm1. For Na+(H2O)7a the vsym is at 3739.43 cm1 and the vasym is at 3864.42 cm-1. For the solvation phenomenon by five water molecules, significant changes with the intensity form and major peaks of H2O are fundamentally repressed and numbers are blue shifted.Similarly, particular intensities for the main peaks are altered. This outcome may be predictable due to the formation of the first solvation sphere layer to the adding of water molecule to Na+(H2O)4. In conclusion, the results obtained by the current study can provide an important vision for a thorough understanding of several chemical methods related to the hydration of sodium ion, particularly concerning ion concentration, in the wide area of chemical physics containing biological and atmospheric phenomena.

4 Conclusions

In the current study we scanned the progression of geometrical parameters and the sub-atomic level free energies of solvation for the optimized sodium ion aqueous clusters with n =1-7 at DFT/B3LYP/6-311+G(d,p) basis sets of the theory. By the addition of an extra water molecule to central sodium ion, there is a decrease in the Na-O distance. There is an agreement between our geometry optimizations for sodium ion and previous experimental results. Both indicate that sodium ion has five water molecules in the primary solvation sphere. There is no change in the coordination number due to solvation as approved by the calculated coordination number by force field classical MD simulation. The predictable equilibrium Na-oxygen space of 2.2 Å at the current level of theory is in bright covenant with the outcome of diffraction for the hydrated clusters. The correct prediction of sodium ion coordination number is obtained from the combination of results picked up from RDF and the quantum chemical DFT calculations of hydration free energy. DFT/B3LYP/6-311+G(d,p) basis sets is used for prediction of H2O molecule and Na+(H2O)n clusters infrared bands. The matching frequencies of Na+(H2O)n paralleled that of the single water molecule have an affinity for red shift. The additional hydrogen bonds formed between water moleculesshowed the lesser vibration frequency seen in the IR bands. The consequence of the work could make progress in predicting the hydration progression of alkali metal ions that happens in biological and atmospheric sciences, and the work could be an excellent addition in the current scientific folder of chemical and physical investigations.


The authors would like to express their gratitude to King Khalid University, Saudi Arabia for providing administrative and technical support. The authors would like to acknowledge Dr. Ahmed Al-Mubasher, the supervisor of joint programs at King Khalid University for his support to this work. Also Chemistry Dept. members of King Khalid University must be acknowledged.

  1. Conflict of interest: Authors declare no conflict of interest.

  2. Supplemental Material: The online version of this article offers supplementary material ( ).


[1] Gomaa E.A., Tahoon M.A., Negm A., Aqueous Micro-Solvation of Li+ Ions: Thermodynamics and Energetic Studies of Li+-(H2O)n (n=1-6) Structures, J. Mol. Liq., 2017, 11, 741-748.10.1016/j.molliq.2017.06.061Search in Google Scholar

[2] Headrick J.M., et al., Spectral Signatures of Hydrated Proton Vibrations in Water Clusters, Science, 2005, 308, 1765 –1769.10.1126/science.1113094Search in Google Scholar PubMed

[3] Miyazaki M., Fujii A., Ebata T., Mikami N., Infrared Spectroscopic Evidence for Protonated Water Clusters Forming Nanoscale Cages, Science, 2004, 304, 1134–1137.10.1126/science.1096037Search in Google Scholar PubMed

[4] Robertson W.H., Diken E.G., Price E.A., Shin J.W., Johnson M.A., Spectroscopic Determination of the OH – Solvation Shell in the OH –.(H2O) n Clusters, Science, 2003, 299, 1367 –1372.10.1126/science.1080695Search in Google Scholar PubMed

[5] Weber J.M., Kelley J.A., Nielson S.B.,Ayotte P., Johnson M.A., Isolating the Spectroscopic Signature of a Hydration Shell With the Use of Clusters: Superoxide Tetrahydrate, Science, 2000, 287, 2461 – 2463.10.1126/science.287.5462.2461Search in Google Scholar PubMed

[6] Marcus Y., Effect of Ions on the Structure of Water: Structure Making and Breaking, Chem. Rev., 2009, 109, 1346-1370.10.1021/cr8003828Search in Google Scholar PubMed

[7] Zhu F., et al., The investigation of structure and IR spectra for hydrated potassium ion clusters K+(H2O)n=1–16 by density functional theory, Eur. Phys. J. D., 2016, 70, 246.10.1140/epjd/e2016-60529-7Search in Google Scholar

[8] Bakker H.J., Skiner J.L., Vibrational Spectroscopy as a Probe of Structure and Dynamics in Liquid Water, Chem. Rev., 2010, 110, 1498-1517.10.1021/cr9001879Search in Google Scholar PubMed

[9] Ohtaki H., Radnai T., Structure and dynamics of hydrated ions, Chem. Rev., 1993, 93, 1157-1204.10.1021/cr00019a014Search in Google Scholar

[10] Bankura A., Carnevale V., Klein M.L., Hydration structure of Na+ and K+ from ab initio molecular dynamics based on modern density functional theory, Mol. Phys., 2014, 112, 1448-1456.10.1080/00268976.2014.905721Search in Google Scholar

[11] Azam S.S., ul Zaheer H., Fatmi M.Q., Classical and QM/MM MD simulations of sodium(l) and potassium(l) ions in aqueous solution, J. Mol. Liq., 2010, 153, 95-100.10.1016/j.molliq.2010.01.005Search in Google Scholar

[12] Zhou Y., et al., Structure of aqueous sodium metaborate solutions: X-ray diffraction study, Russ. J. Phys. Chem. A, 2012, 86, 1236-1244.10.1134/S0036024412060349Search in Google Scholar

[13] Becke A.D., Density-functional thermochemistry. III. The role of exact exchange, J. Chem. Phys., 1993, 98, 5648- 5652.10.1063/1.464913Search in Google Scholar

[14] Lee C., Yang W., Parr R.G., Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density, Phys. Rev. B, 1988, 37, 785.10.1103/PhysRevB.37.785Search in Google Scholar

[15] Ditchfield R., Hehre W.J., Pople J.A., Self-Consistent Molecular-Orbital Methods. IX. An Extended Gaussian-Type Basis for Molecular-Orbital Studies of Organic Molecules, J. Chem. Phys., 1971, 54, 724-728.10.1063/1.1674902Search in Google Scholar

[16] Chai J.D., Head-Gordon M., Long-range corrected hybrid density functionals with damped atom–atom dispersion corrections, Phys. Chem. Chem. Phys., 2008, 10, 6615-6620.10.1039/b810189bSearch in Google Scholar PubMed

[17] Zeng Z., et al., Microsolvation of LiBO2 in water: anion photoelectron spectroscopy and ab initio calculations, Phys. Chem. Chem. Phys., 2015, 17, 9135-9147.10.1039/C5CP00020CSearch in Google Scholar

[18] Zeng Z., et al., Photoelectron Spectroscopy and ab initio Calculations of Li(H2O)n– and Cs(H2O)n– (n = 1–6) Clusters, J. Phys. Chem. A, 2015, 119, 2845-2856.10.1021/jp512177jSearch in Google Scholar PubMed

[19] Frisch M.J., Trucks G.W., Schlegel H.B., et al., Gaussian 09, Revision C.01 (Gaussian, Inc., Wallingford CT, 2010.Search in Google Scholar

[20] Gonfa G., Bustam M.A., Muhammad N., Ullah S., Effect of task specific thiocyanate based ionic liquids on relative volatility of cyclohexane and benzene azeotropic mixture, J. Mol. Liq., 2017, 238, 208-21410.1016/j.molliq.2017.05.007Search in Google Scholar

[21] Gomaa E.A., Tahoon M.A., Ion association and solvation behavior of copper sulfate in binary aqueous–methanol mixtures at different temperatures, J. Mol. Liq., 2016, 214, 19-23.10.1016/j.molliq.2015.11.046Search in Google Scholar

[22] Gomaa E.A., Abu-Qarn R.M., Ionic association and thermodynamic parameters for solvation of vanadyl sulfate in ethanol-water mixtures at different temperatures, J. Mol. Liq., 2017, 232, 319-324.10.1016/j.molliq.2017.02.085Search in Google Scholar

[23] Gomaa E.A., Tahoon M.A., Shokr A., Ionic association and solvation study of CoSO4 in aqueous - organic solvents at different temperatures, J. Chemical Data Collections, 2016, 3-4, 58-67.10.1016/j.cdc.2016.06.005Search in Google Scholar

[24] Gomaa E.A., Negm A., Tahoon M.A., Conductometric and volumetric study of copper sulphate in aqueous ethanol solutions at different temperatures, J. Taibah Univ. Sci., 2017, 11:5, 741-748, DOI: 10.1016/j.jtusci.2016.08.00710.1016/j.jtusci.2016.08.007Search in Google Scholar

[25] James C., Amal R.A., Reghunathan R., Hubert J.I., Jayakumar V.S., Structural conformation and vibrational spectroscopic studies of 2,6-bis(p-N,N-dimethyl benzylidene)cyclohexanone using density functional theory, J Raman Spectrosc., 2006, 37, 1381–1392.10.1002/jrs.1554Search in Google Scholar

[26] Soloveichik P., O'Donnell B.A., Lester M.I., Infrared Spectrum and Stability of the H2O–HO Complex: Experiment and Theory, j. Phys. Chem. A., 2010, 114,1529-1538.10.1021/jp907885dSearch in Google Scholar PubMed

[27] Walter R.S., Pillai E.D., Duncan M.A., Solvation Dynamics in Ni+(H2O)n Clusters Probed with Infrared Spectroscopy, J. Am. Chem. Soc, 2005, 127, 16599-16610.10.1021/ja0542587Search in Google Scholar PubMed

Received: 2018-06-25
Accepted: 2018-11-27
Published Online: 2019-04-24

© 2019 Tahoon M.A., Gomaa E.A., Suleiman M.H.A., published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 Public License.

Downloaded on 4.3.2024 from
Scroll to top button