Transcript Ion Solvation Thermodynamics from Simulation with a Polarizable

Ion Solvation Thermodynamics from
Simulation with a Polarizable Force Field
Alan Grossfeild
Pengyu Ren
Gaurav Chopra
07 February 2005
CS 379 A
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 ClSolvent: 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 ioncluster 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:
Extrathermodynamic
Assumptions
Cation and Anion
Identical Solvation
Thermodynamics
Tetraphenyl
Arsonium
Tetraphenyl Borate
(TATB)
Estimation of
proton solvation:
entropies of H+
and OH- are equal
in water and then
use selfconsistent
analysis
Differential near
IR: Anions better
solvated than
cations
Simulation: Using
TINKER 3.9
Born equation:
Effective ionic
radii = crystal
radii + constant
Cluster Pair
Approximation
Advantage:
avoids the use of
reference salt
Disadvantage:
Data deviate from
Born equations
and constants
reset
High-level
quantum
mechanics
QM/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
<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
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