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Ion Solvation Thermodynamics from Simulation with a Polarizable Force Field PowerPoint Presentation

Ion Solvation Thermodynamics from Simulation with a Polarizable Force Field

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### Ion Solvation Thermodynamics from Simulation with a Polarizable Force Field

Alan Grossfeild Pengyu Ren Jay W. Ponder

Gaurav Chopra

07 February 2005

CS 379 A

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

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

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

- 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

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

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

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

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

Solvent Structure around ions

g(r) = radial distribution function

The properties of water [and aqueous solutions] are not only strange but perhaps stranger than what we can conceive

Q & A

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