Ion Solvation Thermodynamics from Simulation with a Polarizable Force Field

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

2. 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

3. 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

4. Molecular Model and Force Field N-body Problem Non-bonded two body interactions 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

5. 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

6. 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-)

7. 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.

8. 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 <E(n,Cl)> = average potential energy over simulations with n waters and a chloride ion

9. Molecular Dynamics and Free Energy Simulation For each value of l 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 l = 1 particle growth simulation used as starting structure for each trajectory in the charging portion E = potential energy of system Statistical Uncertainity N = number of points in time series s = statistical efficiency

10. 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

11. Cation-Amide Dimers Results

12. 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

13. Ion Solvation Results

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

15. 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