Upload
maja
View
26
Download
0
Tags:
Embed Size (px)
DESCRIPTION
Short- and long -ranged Coulomb interactions in models for ionic solutions and water. John D. Weeks Institute for Physical Science and Technology and Department of Chemistry and Biochemistry University of Maryland. Water Jocelyn Rodgers. Polar Molecular Liquids Zhonghan Hu. - PowerPoint PPT Presentation
Citation preview
Short- and long-ranged Coulomb interactions
in models for ionic solutions and waterJohn D. Weeks
Institute for Physical Science and Technology and Department of Chemistry and Biochemistry
University of Maryland
WaterJocelyn Rodgers
Polar Molecular Liquids
Zhonghan Hu
Take home message
• LMF theory provided a general framework for understanding equilibrium properties of realistic simulation models with strong Coulomb interactions
• LMF theory is a mapping from a full system with Coulomb interactions in an external field to a mimic system with truncated Coulomb interactions in an effective external field
R contains a mean-field average over long-ranged slowly-varying parts of Coulomb interactions
• LMF theory generalizes both reaction field and Wolf truncations of Coulomb interactions and standard Poisson-Boltzmann treatments and corrects main errors often seen in both methods
• LMF theory is derived from a controlled and physically suggestive truncation of the exact YBG hierarchy relating forces to general density profiles in nonuniform systems; much more accurate than standard superposition approximation truncations
Coulomb interactions in molecular simulation modelsMolecular models: strong Coulomb interactions at short
distances compete with other strong intermolecular interactions -- LJ cores, covalent bonds …
YNYCHC
CT
• Strong short-ranged Coulomb forces dominate wide class of interesting phenomena: H-bonds in water, effective attraction between like-charged walls, ion pairing and chain formation near ionic fluid critical point …
• Want total force on molecular charged site at r and not just Coulomb force on infinitesimal test charge considered in classical electrostatics
Simplest idea: Truncate Coulomb interactions and hope for the best! Cf. Ion reaction field methods (Hummer), Wolf truncations, Force-matching truncations (Voth)
Truncation captures local liquid structure in uniform LJ fluidw(r) = u0(r) +
u1(r)
Map from long to short in uniform LJ system
w(r) u0(r)
1
u0(r)
u1(r)
Attractive forces cancel
J. D. Weeks, D. Chandler, and H. C. Andersen,J. Chem. Phys. 54, 5237 (1971).
Soft-sphere u0(r) accurate everywhereHard-sphere ud(r) accurate except in first peak near contact
LJ= 3.166 AqH =0.424lOH=1 A
Classical water models use point charges to describe both
short-ranged H-bonds and long-ranged dipolar forcesExtended Simple Point
Charge (SPC/E) Model
H-bonds in SPC/E water result from frustrated ion pairing
Max gOO =2.75AProperly truncated Coulomb interactions can describe local H-bonds well but not long-ranged dipolar forces
Long range of Coulomb forces causes problems
1/r = v0(r) + v1(r) Truncation of Coulomb potential using Gaussian charge
distribution
v1(r) is electrostatic potential fromGaussian charge distribution with
width
Truncated “short” models replace 1/r by v0(r)
• Screened Coulomb core potential v0(r) = 1/r - v1(r) combines with other strong core interactions.
• Force from v0(r) approaches bare Coulomb force for r <
Choosingmin ≈ nearest neighbor spacing in short water will capture local ion pairing,
hydrogen bonding etc!
Simulations of bulk short water use v0(r) only:Assumes complete cancellation of long-ranged forces
= 4.5 A
Short water gives very good description of local H-bond network
while ignoring all effects of long-ranged dipolar interactions:
Ideal local model to test classical network picture
Very good description of dipole angle correlations
in bulk water as well!
Site-site radial distribution functions for Acetonitrile
YNYCHC
CT
Truncated model describes ion pairing in uniform SAPM
Effective attraction between like-charged ions at very low density
Details of molecular cores and Coulomb potentials on scale a ≈ d2 importantMain features can be captured by mimic system of N + and N - “ions” with short ranged properly truncated Coulomb interactions (Strong Coupling Approximation)
J. Weis & D.LevesqueChem. Phys. Lett 336,523 (2001)
Truncation captures local liquid structure in uniform LJ fluidw(r) = u0(r) +
u1(r)
Map from long to short in uniform LJ system
w(r) u0(r)
1
u0(r)
u1(r)
Attractive forces cancel
FPush from effective wall field can give same density profile
FUncanceled attractive forces pull from bulk liquidPossible drying transition
But effective field is needed in nonuniform system
Truncated models need effective Local Molecular Field (LMF)
to account for uncanceled effects of long-ranged forces
(r;[]) = R(r;[R]) In principle exactchoice for R!
Choose R so that:
w(r) = u0(r) + u1(r)
Effective field R in LMF theory is a mean-field average over slowly-varying component v1(r)
r
r´
LMF theory determines R from mean-field average over slowly-varying u1
Controlled use of mean field ideas by proper choice of u1
Theory for Coulomb interactions needs only single LMF equation for restructured electrostatic potential
involving total charge densityconvolution of full chargedensity and Gaussian-smoothed Coulomb potential
convolution of full Coulomb potential and Gaussian-smoothed charge density
LMF restructured potential satisfies Poisson’s equation
but with a Gaussian-smoothed charge density!
Integrate YBG hierarchy
Lee, McCammon, and Rossky, J. Chem. Phys. 80, 4448 (1984)
Water and short water models near hydrophobic wallsSPC/E water (with 2D Ewald) and
short water confined between hydrophobic walls; LJ 9-3 potential
Local H-bond structure near wall (1 broken H-bond) generates dipole layerLocal structure should be well captured by short water− −
Competition between local H-bond structure and long-ranged dipolar forces important for
electrostatic properties
• Short system accounts only for local H-bonds• Neglects competing long-ranged effects of dipole layers out to ∞ in x- and y- directions
• This is precisely what an effective LMF can capture!
LMF affects long-wavelength orientations of H-bond network
Gaussian-smoothing of charge density cancels out simulation noise and atomic scale fluctuations to reveal underlying long-ranged electrostatics
A self-consistent VR applies a smooth reorienting torque on water molecules mimicking the action of a dipole layer
Smooth form should permit efficient solutions of LMF equation
LMF theory and classical electrostatics: why does it work so well?
We show effective field R in LMF theory satisfies Poisson’s equation
but with a Gaussian-smoothed (over scale ) charge density • Classical electrostatics smoothes over molecular scale fluctuations in
deriving basic equations for polarization field P and other dielectric properties
=
Purcell: ElectricityAnd Magnetism 1963
• LMF theory provides a general conceptual framework that shows how to carry out such smoothing in general environments and using realistic molecular models.• may be a fundamental length scale in molecular electrostatics
Relation to standard PB treatments
LMF theory correct two main errors in PB theory:
1. Poisson part: Poisson’s equation averages over full Coulomb interaction with nonuniform single particle density; OK for interaction with infinitesimal test charge but not for finite charges on molecular sites --- Main error in PB treatment
2. Boltzmann part: Density in PB theory given by Boltzmann factor of effective field. This approximation only accurate at very low density near ideal gas limit. LMF theory uses simulations or DFT to determine correct density response to effective field
LMF theory reduces exactly to PB treatment of a dilute system when is set equal to zero
exact
≈0
≈0
Derivation of LMF equation
exact
Choose R so that:
exact
r
r´
Strong coupling approximation (SCA): R≈0 “complete force-cancellation” Ignore all effects of u1 on structure
LMF is theory for mapping; not resulting structure.
Self-consistent equation Controlled use of mean field theory
Simulations of bulk short water use SCA:Assumes complete cancellation of long-ranged forces
Short water gives very good description of local H-bond network
while ignoring all effects of long-ranged dipolar interactions
= 4.5 A
Very good description of dipole angle correlations
in bulk water as well
Acetonitrile CH3CN Model
YNYCHC
CT
3.92 D
A. M. Nikitin and A P. Lyubartsev, J. Comp. Chem. Vol 28, 2020-2026, (2007)
Partial Charges:
HC 0.1904 CT -0.5503
YC 0.4917 YN -0.5126
Expt. Density: 0.777 g/cm^3
Expt. Evaporation Heat: 7.98 kcal/mol
Cal. Density:
0.782 g/cm^3 1% higher
Cal. Evaporation Heat:8.21 kcal/mol 3% higher
Work done by Zhonghan HU NSF CRC
Lee, McCammon, and Rossky, J. Chem. Phys. 80, 4448 (1984)
Water and short water models in nonuniform environmentsSPC/E water (with corrected 3D Ewald)
and short water confined between hydrophobic walls; LJ 9-3 potential
Local H-bond structure near wall (1 broken H-bond) generates dipole layerLocal structure should be well captured by short water− −
Electrostatic propertiesAway from the walls the net force from the dipole layers should be zero and the electrostatic potential should be
constant
Complete failure ofshort water!
Need effective field in nonuniform systems
Competition between local H-bond structure and long-ranged dipolar forces important for
electrostatic properties.
• Short system accounts only for local H-bonds• Neglects competing long-ranged effects of dipole layers out to ∞ in x- and y- directions
• This is precisely what an effective LMF can capture!
r
r´
LMF equation determines R from density-weighted average over slowly-varying u1
Controlled use of mean field ideas by proper choice of u1
• Derived by integrating exact YBG hierarchy equation relating singlet density gradients to forces and nonuniform pair correlations• Self-consistent equation effectively closes hierarchy• Theory very accurate when u1 is slowly varying over range of nearest-neighbor pair correlations• LMF is theory for accurate mapping; not resulting structure• Strong-coupling (force cancellation) approximation: ignore all effects of u1 on structure • u1 important for thermodynamics and long wavelength structure
Cf electrostatic potential
LMF theory for Coulomb interactions alone greatly simplifies when same is used for all charges
convolution of full Coulomb potential and Gaussiansmoothed charge density
Theory reduces to single self-consistent LMF equation for restructured electrostatic potentialVR defined with bare charge density
convolution of bare charge density and Gaussian smoothed Coulomb potential
LMF effective potential satisfies Poisson’s equation using Gaussian smoothed charge density!
Define bare charge density and exploit simple form of Coulomb interaction
Gaussian-smoothing of charge density in LMF theory cancels out simulation noise and atomic
scale fluctuations to reveal underlying long-ranged electrostatics
A self-consistent VR applies a smooth reorienting torque on water molecules, mimicking the action of a dipole layer
Smooth form should permit efficient solutions of LMF equation
LMF describes water confined by hydrophilic Pt(111) surfaces
R(x,y,z) ≈ 0(x,y,z) + R1(z)
Water in applied electric field: an even greater challenge
•Sensitive probe of effects of VR
•Wall spacing adjusted to yield B in center
•Similar to study by Yeh & Berkowitz that lead to corrected 3D Ewald; used as benchmark for our work here
•Can determine a dielectric constant:
Negative dielectric constant predicted for short water for using standard formula! LMF theory in excellent agreement with full Ewald.
LMF theory corrects very poor results for short water in electric field
Acetonitrile Liquid-vapor film
• Langevin dynamics simulation of a polymer (Np = 100) immersed in an
ionic solution• 44 “hydrophilic” polymer beads carry negative point charges located
near their surface • 56 uncharged “hydrophobic” beads interact via the attractive
Lennard-Jones potential
• Molar salt concentrations CM = 0.01-0.1M, giving 7000-10000 salt
ions in cell (GCMC)• Salt diameter is 1/5 of the polymer bead diameter• The box sides are aligned with the polymer axes of inertia, RG2 =
(I1 + I2 + I3)/2mNp
Charged polymer simulation model
Work done by Natasha Denesyuk
Polymer and ion density distributions
Hydrophobic Hydrophilic
Counter-ions
Co-ions
• Hydrophobic species form a dense core
• Hydrophilic species stay on the surface• Counter-ions aggregate near the polymer surface• Both counter- and co-ions are expelled from the
polymer interior
z
Grand Canonical System Neutrality• The mimic system does NOT have to be strictly neutral (Ewald requires strict neutrality)• Truncated Coulomb interactions alone results in a loss of counterions
in the simulation box• Adding the LMF restores the missing counterions
• SPC/E water and CH3CN can be very accurately described by short-ranged mimic system in effective external field• Effective field accounts for mean field average of special
long-ranged slowly varying component of Coulomb interactions• Effective field satisfies Poisson’s equation with Gaussian-smoothed charge density• Effective field corrects major errors in electrostatic properties of nonuniform systems from simple truncations of long-ranged forces. • No Ewald sums etc. needed in mimic simulations• LMF method adapted to open-source DL-Poly MD code and in-house Langevin MD polymer simulation code• Further work on ions, water, dipolar fluids near silica surfaces, charged polymers, etc. in progress • LMF theory provides a unified conceptual framework for wide class of nonuniform molecular fluids: ions, polymer and water models,…
Conclusions
qd
Y.-G. Chen and J.D. WeeksPNAS 103, 7560 (2006)
J.C. Rodgers, C. Kaur,Y.-G. Chen and J.D. WeeksPhys. Rev. Lett. 97, 097801(2006)
Ionic solutions: effective attraction between
like-charged walls
Water in applied electric field: an even greater challenge
•Sensitive probe of effects of VR
•Wall spacing adjusted to yield B in center
•Similar to study by Yeh & Berkowitz that lead to corrected 3D Ewald; used as benchmark for our work here
•Can determine a dielectric constant:
Short water effectively ignores Epol and has major errors
• Long-ranged forces lead to Epol
• Over-ordering of dipoles in center (bulk) region without effects of Epol
• Incorrect treatment of Epol in short water amplified by low energy of polarized local H-bond network
Short water oxygen density profiles incorrect in applied field
Negative dielectric constant predicted for short water for using
standard formula! LMF theory in excellent agreement with full Ewald.
LMF tames applied field systems as well
Self-consistent VR generates weak force on molecules at center
Short water feels nearly full force from bare V everywhere