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

Gaurav ChopraGaurav Chopra

07 February 200507 February 2005

CS 379 ACS 379 A

Alan Grossfeild Pengyu Ren Jay W. Ponder

Ion Solvation : Why do we care?Ion Solvation : Why do we care?

Ion Solvation: Relative stability of ions as a Ion Solvation: Relative stability of ions as a function of solvent and function of solvent and force fieldforce fieldSurface & environmental chemistrySurface & environmental chemistryStudy of molecules such as surfactants, colloids Study of molecules such as surfactants, colloids and polyelectrolyteand polyelectrolyteBiologically: Structure and function of nucleic Biologically: Structure and function of nucleic acids, proteins and lipid membranesacids, proteins and lipid membranesThermodynamics: Development of continuum Thermodynamics: Development of continuum solvation models – Interested in Free Energy of solvation models – Interested in Free Energy of Solvation for individual ionic speciesSolvation for individual ionic species

Why Simulate?Why Simulate?

MotivationMotivation: Solvation free energy of salts known : Solvation free energy of salts known experimentally but cannot separate into experimentally but cannot separate into individual contributions of ionsindividual contributions of ionsMolecular dynamics used to resolve this using Molecular dynamics used to resolve this using Polarizable Force FieldPolarizable Force Field (AMOEBA) (AMOEBA)Simulations with CHARMM27 and OPLS-AA Simulations with CHARMM27 and OPLS-AA done for comparisondone for comparisonIons: K+, Na+ and Cl-Ions: K+, Na+ and Cl-Solvent: Water (TIP3P model for non-polarizable Solvent: Water (TIP3P model for non-polarizable force field) and Formamideforce field) and Formamide

Molecular Model and Force FieldMolecular Model and Force FieldN-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 paperSummary of the paper

Experiments and standard molecular mechanics Experiments and standard molecular mechanics force fields (non-polarizable) cannot give correct force fields (non-polarizable) cannot give correct values for ion solvation free energy for an ionvalues for ion solvation free energy for an ion

AMOEBA parameters reproduce in vacuo AMOEBA parameters reproduce in vacuo quantum mechanical results, experimental ion-quantum mechanical results, experimental ion-cluster solvation enthalpies, and experimental cluster solvation enthalpies, and experimental solvation energies for whole saltsolvation energies for whole salt

Result: Best estimation of ion-solvation free Result: Best estimation of ion-solvation free energy for ions using AMOEBA energy for ions using AMOEBA

Ion Solvation Thermodynamics

Experimental: Extra-

thermodynamic Assumptions

Simulation: Using TINKER 3.9

Cation and AnionIdentical Solvation Thermodynamics

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

Cluster Pair Approximation

High-level quantum

mechanicsQM/MM Methods

Atomic Multipole Optimized

Energetics for Biomolecular Applications(AMOEBA)

TetraphenylArsonium

Tetraphenyl Borate(TATB)

Differential near IR: Anions better

solvated than cations

Advantage: avoids the use of

reference saltDisadvantage:

Data deviate from Born equations and constants

reset

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 ParametersForce 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 CalculationsCluster Calculations

Stochastic Molecular dynamics of clusters Stochastic Molecular dynamics of clusters of 1-6 water molecules with a single of 1-6 water molecules with a single chloride ionchloride ion

Velocity Verlet implementation of Langevin Velocity Verlet implementation of Langevin dynamics used to integrate equations of dynamics used to integrate equations of motionmotion

Hydration enthalpy of water moleculesn = number of water molecules<E(n,Cl)> = average potential energy over simulations with n waters and a chloride ion

Molecular Dynamics and Free Molecular Dynamics and Free Energy SimulationEnergy 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 seriess = statistical efficiency

Ion Solvent Dimers ResultsIon 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 ResultsCation-Amide Dimers Results

Chloride-Water Clusters ResultsChloride-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 ResultsIon Solvation Results

Solvent Structure around ionsSolvent 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