Hydrated Sodium Ion Clusters [Na+(H2O)n (n = 1-6)]: An ab initio Study on Structures and Non-covalent Interaction

Abstract

Structural, thermodynamic, and vibrational characteristics of water clusters up to six water molecules incorporating a single sodium ion [Na⁺(H₂O)_n (n = 1-6)] are calculated using a comprehensive genetic algorithm combined with density functional theory on global search, followed by high-level ab initio calculation. For n ≥ 4, the coordinated water molecules number for the global minimum of clusters is 4 and the outer water molecules connecting with coordinated water molecules by hydrogen bonds. The charge analysis reveals the electron transfer between sodium ions and water molecules, providing an insight into the variations of properties of O-H bonds in clusters. Moreover, the simulated infrared (IR) spectra with anharmonic correction are in good agreement with the experimental results. The O-H stretching vibration frequencies show redshifts comparing with a free water molecule, which is attributed to the non-covalent interactions, including the ion-water interaction, and hydrogen bonds. Our results exhibit the comprehensive geometries, energies, charge, and anharmonic vibrational properties of Na⁺(H₂O)_n (n = 1-6), and reveal a deeper insight of non-covalent interactions.

Keywords: IR spectra; anharmonic effect; hydrated sodium cluster; natural bond orbital; stabilization energy.

Figure 1

The structures and symmetries of Na⁺(H₂O)_n (n = 1–6) optimized at MP2/aug-cc-pVDZ level of theory. Blue, red, and green balls denote hydrogen, oxygen, and sodium atoms, respectively. The black dashed lines represent hydrogen bonds.

Figure 2

The NBO overlapping and electron transfer in 1+0+0 calculated at the MP2/aug-cc-pVQZ level of theory. (A) ${\text{Na}}_1^{+}$(s) → σ^*(O₂-H₃). (B) ${\text{Na}}_1^{+}$(s) → σ^*(O₂-H₄). (C) σ(O₂-H₃) → ${\text{Na}}_1^{+}$(sp^0.66)^*. (D) σ(O₂-H₄) → ${\text{Na}}_1^{+}$(sp^0.66)^*.

Figure 3

Charge density difference of six small hydrated sodium ion clusters. Yellow and blue spaces represent the electron accumulation and depletion regions, respectively.

Figure 4

Anharmonic correctional IR spectra of 1+0+0, 2+0+0, 3+0+0 and a free water molecule calculated at MP2/aug-cc-pVDZ level of theory.

Figure 5

Anharmonic correctional IR spectra of 3+1+0, 4+0+0 calculated at MP2/aug-cc-pVDZ level of theory and experimental spectrum.

Figure 6

Anharmonic correctional IR spectra of 4+1+0, 3+1+1, 3+2+0(1), 5+0+0(1), 3+2+0(2), and 5+0+0(2) calculated at MP2/aug-cc-pVDZ level of theory and experimental spectrum.

Figure 7

Anharmonic correctional IR spectra of eight isomers for n = 6 shown in Figure 1 calculated at MP2/aug-cc-pVDZ level of theory.