Structure and Spectroscopy of Hydrated Sodium Ions at Different Temperatures and the Cluster Stability Rules

Abstract

The sodium cation plays an important role in several physiological processes. Understanding its solvation may help understanding ion selectivity in sodium channels that are pivotal for nerve impulses. This paper presents a thorough investigation of over 75 isomers of gas-phase Na(+)(H2O)(n=1-8) clusters, whose optimized structures, energies, and (harmonic) vibrational frequencies were computed quantum mechanically at the full MP2/6-31++G(d,p) level of theory. From these data, we have calculated the temperature effects on the cluster thermodynamic functions, and thus the equilibrium Boltzmann distribution for each n. For a selected number of isomers, we have corrected the calculations for basis set superposition error (BSSE) to obtain accurate clustering energies, in excellent agreement with experiment. The computed clusters are overwhelmingly 4-coordinated, as opposed to bulk liquid water, where sodium cations are believed to be mostly 5- or 6-coordinated. To explain this, we suggest the "cluster stability rules", a set of coordination-number-dependent hydrogen-bond (HB) strengths that can be obtained using a single BSSE correction. Assuming additivity and transferability, these reproduce the relative stability of most of our computed isomers. These rules enable us to elucidate the trends in HB strengths, outlining the major determinants of cluster stability. For n = 4 and 5, we have also performed anharmonic vibrational calculations (VPT2) to compare with available photodissociation infrared spectra of these gas-phase clusters. The comparison suggests that the experiments actually monitor a mixture of predominantly 3-coordinated isomers, which is quite remote from the computed Boltzmann distribution, particularly at low temperatures. Surprisingly, for these experiments, water evaporation pathways can rationalize the non-equilibrium isomer distribution. The equilibrium isomer distribution is, in turn, rationalized by the entropy of internal rotations of "dangling" water molecules.

Three‐body expansion of the fragment molecular orbital method combined with density‐functional tight‐binding

“…In this work, the accuracy of FMO‐DFTB/MD has been evaluated for solvated sodium cation, and 100 ps MD simulations have been performed to obtain the radial distribution and coordination number of sodium cation in solution. The obtained coordination number of sodium (6.5) is in reasonable agreement with other studies (5–6) . Adding periodic boundary conditions (PBC) to FMO/MD in future will be useful; at present, the use of PBC in QM/MD is not available in production GAMESS‐US, although some development of PBC for FMO has been reported …”

“…The obtained coordination number of sodium (6.5) is in reasonable agreement with other studies (5)(6). [88][89][90][91] Adding periodic boundary conditions (PBC) to FMO/MD in future will be useful; at present, the use of PBC in QM/MD is not available in production GAMESS-US, although some development of PBC for FMO has been reported. [98,99]…”

“…There are many studies on the CN of O around Na ; it is suggested on the basis of simulations that it is between 5 and 6 . The values in DFTB and FMO3‐DFTB are slightly overestimated, and the FMO2‐DFTB value is much overestimated.…”

“…There are many studies on the CN of O around Na 1 ; it is suggested on the basis of simulations that it is between 5 and 6. [88][89][90][91] The values in DFTB and FMO3-DFTB are slightly overestimated, and the FMO2-DFTB value is much overestimated. This is in agreement with the results of relative energies and Mulliken charges discussed above.…”

Theoretical infrared spectrum of the ethanol hexamer

“…Details of our Tempo code were first published in our work on the structures of protonated methanol clusters. [36,37] This program has been applied successfully to ammonia clusters [38,39] and protonated ammonia clusters. [40][41][42] It should be noted that the free energies, G k (T), can be also calculated using the module freqchk of Gaussian programs.…”