Modeling molecular and ionic absolute solvation free energies with quasichemical theory bounds

Quasichemical theory ͑QCT͒ provides a framework that can be used to partition the influence of the solvent surrounding an ion into near and distant contributions. Within QCT, the solvation properties of the ion are expressed as a sum of configurational integrals comprising only the ion and a small number of solvent molecules. QCT adopts a particularly simple form if it is assumed that the clusters undergo only small thermal fluctuations around a well-defined energy minimum and are affected exclusively in a mean-field sense by the surrounding bulk solvent. The fluctuations can then be integrated out via a simple vibrational analysis, leading to a closed-form expression for the solvation free energy of the ion. This constitutes the primitive form of quasichemical theory ͑pQCT͒, which is an approximate mathematical formulation aimed at reproducing the results from the full many-body configurational averages of statistical mechanics. While the results from pQCT from previous applications are reasonable, the accuracy of the approach has not been fully characterized and its range of validity remains unclear. Here, a direct test of pQCT for a set of ion models is carried out by comparing with the results of free energy simulations with explicit solvent. The influence of the distant surrounding bulk on the cluster comprising the ion and the nearest solvent molecule is treated both with a continuum dielectric approximation and with free energy perturbation molecular dynamics simulations with explicit solvent. The analysis shows that pQCT can provide an accurate framework in the case of a small cation such as Li + . However, the approximation encounters increasing difficulties when applied to larger cations such as Na + , and particularly for K + . This suggests that results from pQCT should be interpreted with caution when comparing ions of different sizes.

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Assessing the accuracy of approximate treatments of ion hydration based on primitive quasichemical theory

Roux

2010

“…7,82 Third, we plan to couple this QM/MM approach to computations of solvation free energies via quasi-chemical theory. 19,20,83 In the quasi-chemical approach, the solvation free energy is exactly partitioned into inner-shell, outer-shell packing, and outer-shell long-range contributions. The conditioning inherent in this partitioning allows for a mean-field treatment of the long-range contribution.…”

Section: Summary and Discussionmentioning

confidence: 99%

“…This paper is part of a series developing and exploiting computational methods for calculating the electronic and thermodynamic properties of ions in water. 19,20 Future work will focus on ion binding in proteins.…”

Section: Introductionmentioning

confidence: 99%

Polarization and charge transfer in the hydration of chloride ions

Zhao

Rogers

Beck

2010

Self Cite

A theoretical study of the structural and electronic properties of the chloride ion and water molecules in the first hydration shell is presented. The calculations are performed on an ensemble of configurations obtained from molecular dynamics simulations of a single chloride ion in bulk water. The simulations utilize the polarizable AMOEBA force field for trajectory generation, and MP2-level calculations are performed to examine the electronic structure properties of the ions and surrounding waters in the external field of more distant waters. The ChelpG method is employed to explore the effective charges and dipoles on the chloride ions and first-shell waters. The Quantum Theory of Atoms in Molecules (QTAIM) is further utilized to examine charge transfer from the anion to surrounding water molecules. The clusters extracted from the AMOEBA simulations exhibit high probabilities of anisotropic solvation for chloride ions in bulk water. From the QTAIM analysis, 0.2 elementary charges are transferred from the ion to the first-shell water molecules. The default AMOEBA model overestimates the average dipole moment magnitude of the ion compared with the estimated quantum mechanical value. The average magnitude of the dipole moment of the water molecules in the first shell treated at the MP2 level, with the more distant waters handled with an AMOEBA effective charge model, is 2.67 D. This value is close to the AMOEBA result for first-shell waters (2.72 D) and is slightly reduced from the bulk AMOEBA value (2.78 D). The magnitude of the dipole moment of the water molecules in the first solvation shell is most strongly affected by the local water-water interactions and hydrogen bonds with the second solvation shell, rather than by interactions with the ion.

“…[81][82][83][84][85][86] For the calculation of single-ion hydration free energies, two main strategies have been explored to date for achieving such a combination. The most common approach is the cluster-continuum approach, 53,56,[87][88][89][90][91] often referred to as a particular instance of quasi-chemical theory, [92][93][94] in which QM energy calculations are performed on small ion-water clusters (different sizes and geometries) and the bulk intrinsic hydration free energy is calculated by subsequently embedding the cluster configurations into a CE solvent environment. The second approach relies on Car-Parrinello 95 (CPMD) or Born-Oppenheimer 96 (BOMD) molecular dynamics simulations, performed at the density-functional theory (DFT) level.…”

Section: Introductionmentioning

confidence: 99%

Absolute proton hydration free energy, surface potential of water, and redox potential of the hydrogen electrode from first principles: QM/MM MD free-energy simulations of sodium and potassium hydration

Hofer

Hünenberger

2018

103

The absolute intrinsic hydration free energy G • H + ,wat of the proton, the surface electric potential jump χ • wat upon entering bulk water, and the absolute redox potential V • H + ,wat of the reference hydrogen electrode are cornerstone quantities for formulating single-ion thermodynamics on absolute scales. They can be easily calculated from each other but remain fundamentally elusive, i.e., they cannot be determined experimentally without invoking some extra-thermodynamic assumption (ETA). The Born model provides a natural framework to formulate such an assumption (Born ETA), as it automatically factors out the contribution of crossing the water surface from the hydration free energy. However, this model describes the short-range solvation inaccurately and relies on the choice of arbitrary ion-size parameters. In the present study, both shortcomings are alleviated by performing first-principle calculations of the hydration free energies of the sodium (Na + ) and potassium (K + ) ions. The calculations rely on thermodynamic integration based on quantum-mechanical molecular-mechanical (QM/MM) molecular dynamics (MD) simulations involving the ion and 2000 water molecules. The ion and its first hydration shell are described using a correlated ab initio method, namely resolution-of-identity second-order Møller-Plesset perturbation (RIMP2). The next hydration shells are described using the extended simple point charge water model (SPC/E). The hydration free energy is first calculated at the MM level and subsequently increased by a quantization term accounting for the transformation to a QM/MM description. It is also corrected for finite-size, approximate-electrostatics, and potentialsummation errors, as well as standard-state definition. These computationally intensive simulations provide accurate first-principle estimates for G • H + ,wat , χ • wat , and V • H + ,wat , reported with statistical errors based on a confidence interval of 99%. The values obtained from the independent Na + and K + simulations are in excellent agreement. In particular, the difference between the two hydration free energies, which is not an elusive quantity, is 73.9 ± 5.4 kJ mol 1 (K + minus Na + ), to be compared with the experimental value of 71.7 ± 2.8 kJ mol 1 . The calculated values of G • H + ,wat , χ • wat , and V • H + ,wat ( 1096.7 ± 6.1 kJ mol 1 , 0.10 ± 0.10 V, and 4.32 ± 0.06 V, respectively, averaging over the two ions) are also in remarkable agreement with the values recommended by Reif and Hünenberger based on a thorough analysis of the experimental literature ( 1100 ± 5 kJ mol 1 , 0.13 ± 0.10 V, and 4.28 ± 0.13 V, respectively). The QM/MM MD simulations are also shown to provide an accurate description of the hydration structure, dynamics, and energetics. Published by AIP Publishing.