Ion Solvation Thermodynamics from Simulation with a Polarizable Force Field Gaurav Chopra 07 February 2005 CS 379 A Alan GrossfeildPengyu Ren Jay W. Ponder

Ion Solvation : Why do we care? Ion Solvation: Relative stability of ions as a function of solvent and force field Surface & environmental chemistry Study of molecules such as surfactants, colloids and polyelectrolyte Biologically: Structure and function of nucleic acids, proteins and lipid membranes Thermodynamics: Development of continuum solvation models – Interested in Free Energy of Solvation for individual ionic species

Why Simulate? Motivation: Solvation free energy of salts known experimentally but cannot separate into individual contributions of ions Molecular dynamics used to resolve this using Polarizable Force Field (AMOEBA) Simulations with CHARMM27 and OPLS-AA done for comparison Ions: K+, Na+ and Cl- Solvent: Water (TIP3P model for non-polarizable force field) and Formamide

Molecular Model and Force Field N-body Problem Inclusion of Polarization: e.g. binding of a charged ligand polarizes receptor part -by inducing point dipoles -by changing the magnitude of atomic charges -by changing the position of atomic charges 3N x 3N Matrix Non-bonded two body interactions

Summary of the paper Experiments and standard molecular mechanics force fields (non-polarizable) cannot give correct values for ion solvation free energy for an ion AMOEBA parameters reproduce in vacuo quantum mechanical results, experimental ion- cluster solvation enthalpies, and experimental solvation energies for whole salt Result: Best estimation of ion-solvation free energy for ions using AMOEBA

Ion Solvation Thermodynamics Experimental: Extra- thermodynamic Assumptions Cation and Anion Identical Solvation Thermodynamics Tetraphenyl Arsonium Tetraphenyl Borate (TATB) Differential near IR: Anions better solvated than cations Estimation of proton solvation: entropies of H+ and OH- are equal in water and then use self-consistent analysis Born equation: Effective ionic radii = crystal radii + constant Advantage: avoids the use of reference salt Disadvantage: Data deviate from Born equations and constants reset Cluster Pair Approximation Simulation: Using TINKER 3.9 High-level quantum mechanicsQM/MM Methods Atomic Multipole Optimized Energetics for Biomolecular Applications (AMOEBA) AMOEBA VdW parameters: High-level QM (Na+, K+) Experimental Cluster Hydration enthalpies combined with solvent parameters using neat-liquid and gas-phase cluster simulation (Cl-)

Force Field Parameters AMOEBA Force Field Each atom has a permanent partial charge, dipole and quadrupole moment Represents electronic many-body effects Self-consistent dipole polarization procedure Repulsion-dispersion interaction between pairs of non-bonded atoms uses buffered 14-7 potential AMOEBA dipole Polarizabilities of Potassium, sodium and chloride ions is set to 0.78, 0.12 and 4.00 cubic Ang.

Cluster Calculations Stochastic Molecular dynamics of clusters of 1-6 water molecules with a single chloride ion Velocity Verlet implementation of Langevin dynamics used to integrate equations of motion Hydration enthalpy of water molecules n = number of water molecules = average potential energy over simulations with n waters and a chloride ion

Molecular Dynamics and Free Energy Simulation For each value of  energy minimization is performed until RMS gradient per atom is less than 1 kcal/(mol A) AMOEBA took more than 7 days, OPLS-AA and CHARMM27 took less than a day Final structure for = 1 particle growth simulation used as starting structure for each trajectory in the charging portion Statistical Uncertainity E = potential energy of system N = number of points in time series s = statistical efficiency

Ion Solvent Dimers Results Gas-phase behavior gives ion-solvent interaction without statistical sampling High level QM only possible for gas phase unless implicit solvent model used Table 2: Overestimated values Ion-oxygen separation > 2.3 Ang.: less electrostatic attraction than TIP3P water Molecular orbital calculations problematic for chloride

Cation-Amide Dimers Results

Chloride-Water Clusters Results Van der Waals parameters for chloride ion compared with enthalpy of formation of chloride-water dimer as molecular orbital calculations is problematic

Ion Solvation Results

Solvent Structure around ions g(r) = radial distribution function

To quote Albert Einstein: The properties of water [and aqueous solutions] are not only strange but perhaps stranger than what we can conceive Q & A