Single-Ion Thermodynamics from First Principles: Calculation of the Absolute Hydration Free Energy and Single-Electrode Potential of Aqueous Li+ Using ab Initio Quantum Mechanical/Molecular Mechanical Molecular Dynamics Simulations

A recently proposed thermodynamic integration (TI) approach formulated in the framework of quantum mechanical/molecular mechanical molecular dynamics (QM/MM MD) simulations is applied to study the structure, dynamics, and absolute intrinsic hydration free energy Δ_s G_M⁺,wat^◦ of the Li⁺ ion at a correlated ab initio level of theory. Based on the results, standard values (298.15 K, ideal gas at 1 bar, ideal solute at 1 molal) for the absolute intrinsic hydration free energy [Formula: see text] of the proton, the surface electric potential jump χ_wat^◦ upon entering bulk water, and the absolute single-electrode potential [Formula: see text] of the reference hydrogen electrode are calculated to be -1099.9 ± 4.2 kJ·mol^-1, 0.13 ± 0.08 V, and 4.28 ± 0.04 V, respectively, in excellent agreement with the standard values recommended by Hünenberger and Reif on the basis of an extensive evaluation of the available experimental data (-1100 ± 5 kJ·mol^-1, 0.13 ± 0.10 V, and 4.28 ± 0.13 V). The simulation results for Li⁺ are also compared to those for Na⁺ and K⁺ from a previous study in terms of relative hydration free energies ΔΔ_s G_M⁺,wat^◦ and relative electrode potentials [Formula: see text]. The calculated values are found to agree extremely well with the experimental differences in standard conventional hydration free energies ΔΔ_s G_M⁺,wat^• and redox potentials [Formula: see text]. The level of agreement between simulation and experiment, which is quantitative within error bars, underlines the substantial accuracy improvement achieved by applying a highly demanding QM/MM approach at the resolution-of-identity second-order Møller-Plesset perturbation (RIMP2) level over calculations relying on purely molecular mechanical or density functional theory (DFT) descriptions. A detailed analysis of the structural and dynamical properties of the Li⁺ hydrate indicates that a correct description of the solvation structure and dynamics is achieved as well at this level of theory. Consideration of the QM/MM potential-energy components also shows that the partitioning into QM and MM zones does not induce any significant energetic artifact for the system considered.

Erbium(III) in aqueous solution: an ab initio molecular dynamics study

Structural and dynamical properties of the erbium(III) ion in water have been obtained by means of ab initio quantum mechanical charge field molecular dynamics (QMCF-MD) simulations for the ground state and an excited state. The quality of the simulations has been monitored by recording UV/vis and Raman spectra of dilute solutions of ErCl3 and Er(NO3)3 in water and by comparison with EXAFS data from literature. Slight deviations between these data can be mainly attributed to relativistic effects, which are not sufficiently considered by the methodological framework. In both simulations, a mixture of coordination numbers eight and nine and a ligand exchange on the picosecond range are observed. The strength of the Er-ligand bond is considerably lower than that of trivalent transition metal ions but higher than that for La(III) and Ce(III) in aqueous solution. The main difference between ground state and excited state is the ligand exchange rate of the first shell. The second hydration shell is stable in both cases but with significantly different properties.

Computational study of the cerium(III) ion in aqueous environment

This work comprises the first quantum chemical simulation study of the Ce3+ ion in aqueous environment. The structural and dynamical properties have been investigated by means of the quantum mechanical charge field (QMCF) molecular dynamics (MD) approach and the results, where applicable, have been compared to experimental data. Besides conventional analytical tools, angular radial distribution functions have been employed to gain deeper insight into the structure of the hydrate. The ion-oxygen stretching motion's wavenumber, further characterising the Ce-O bond, is in excellent agreement with experimental results, same as the structural values obtained from the simulation.

A QMCF-MD investigation of the structure and dynamics of Ce4+ in aqueous solution

A quantum-mechanical charge-field molecular dynamics simulation has been performed for a tetravalent Ce ion in aqueous solution. In this framework, the complete first and second hydration spheres are treated by ab initio quantum mechanics supplemented by an electrostatic embedding technique, making the construction of non-Coulombic solute-solvent potentials unnecessary. During the 10 ps of simulation time, the structural aspects of the solution were analyzed by various methods. Experimental results such as the mean Ce-O bond distance and the predicted first-shell coordination number were compared to the results obtained from the simulation resolving some ambiguities in the literature. The dynamics of the system were characterized by mean ligand residence times and frequency/force constant calculations. Furthermore, Ce-O and Ce-H angular radial distribution plots were employed, yielding deeper insight into the structural and dynamical aspects of the system.

Exploring the thermodynamic derivatives of the structure factor of dense protein solutions

Using small-angle X-ray scattering data of concentrated solutions of the protein lysozyme taken at different pressures and temperatures, the isothermal pressure derivative and the isobaric temperature derivative of the structure factor S(q) were determined. The pressure derivative of S(q) allows us to test various models for the triplet correlation function g(3). Significant differences were found in comparison to simple liquids reflecting the more complex interaction potential in dense protein solutions.

Hydration of trivalent lanthanum revisited - An ab initio QMCF-MD approach

The previously investigated La³⁺-hydrate has been re-evaluated by means of the quantum mechanical charge field (QMCF) molecular dynamics (MD) approach. Improved description of the hydration characteristics has been realised by including the full second hydration shell into the quantum mechanically treated region and by introducing the influence of the surrounding bulk via an electrostatic embedding technique. Analytical tools such as the ligand angular radial distribution analysis have been employed to gain deeper insight into the structural features of the hydrate. La³⁺ simultaneously forms nona- and decahydrates with capped trigonal and quadratic prismatic structure, besides small amounts of an octahydrate.

Simulation of Ir(III) in Aqueous Solution: The Most Inert Ion Hydrate

The ab initio quantum mechanical charge field (QMCF) molecular dynamics (MD) approach at Hartree-Fock level was used to simulate the tripositive iridium ion in aqueous solution, evaluating structure and dynamics of its hydrate complex. The Ir-OH2 force constant was of particular interest because of the observed high inertness of Ir(iii) in aqueous solution. Iridium forms three hydration shells. Six water molecules coordinate the ion in the first hydration shell in a well defined octahedral geometry, and no exchanges took place during the simulation time of 15 ps. The second hydration shell is very flexible, however, with a mean residence time of a water molecule of 3.6 ps. The third shell can be identified only by a slight ordering effect. This investigation classified the Ir-OH2 force constant as the strongest ion-OH2 bond known to date.

Structural and dynamical aspects of the unsymmetric hydration of Sb(III): an ab initio quantum mechanical charge field molecular dynamics simulation

An ab initio quantum mechanical charge field molecular dynamics (QMCF MD) simulation was performed to investigate the behavior of the Sb(3+) ion in aqueous solution. The simulation reveals a significant influence of the residual valence shell electron density on the solvation structure and dynamics of Sb(3+). A strong hemidirectional behavior of the ligand binding pattern is observed for the first hydration shell extending up to the second hydration layer. The apparent domain partitioned structural behavior was probed by solvent reorientational kinetics and three-body distribution functions. The three-dimensional hydration space was conveniently segmented such that domains having different properties were properly resolved. The approach afforded a fair isolation of localized solvent structural and dynamical motifs that Sb(3+) seems to induce to a remarkable degree. Most intriguing is the apparent impact of the lone pair electrons on the second hydration shell, which offers insight into the mechanistic aspects of hydrogen bonding networks in water. Such electronic effects observed in the hydration of Sb(3+) can only be studied by applying a suitable quantum mechanical treatment including first and second hydration shell as provided by the QMCF ansatz.

Structure and dynamics of the U4+ ion in aqueous solution: an ab initio quantum mechanical charge field molecular dynamics study

The structure and dynamics of the stable four-times positively charged uranium(IV) cation in aqueous solution have been investigated by ab initio quantum mechanical charge field (QMCF) molecular dynamics (MD) simulation at the Hartree-Fock double-zeta quantum mechanical level. The QMCF-MD approach enables investigations with the accuracy of a quantum mechanics/molecular mechanics approach without the need for the construction of solute-solvent potentials. Angular distribution functions; radial distribution functions; coordination numbers of the first, second, and third shell (9, 19, and 44, respectively); coordination number distribution functions; tilt- and Theta-angle distribution functions; as well as local density corrected triangle distribution functions have been employed for the evaluation of the hydrated ion's structure. Special attention was paid to the determination of the geometry of the first hydration layer, and the results were compared to experimental large-angle X-ray scattering and extended X-ray absorption fine structure data. The solvent dynamics around the ion were also investigated using mean ligand residence times and related data and, resulting from the unavailability of any experimental data, were compared to ions with similar properties.