Modeling Proton Solvation in Water: Is This Easier Than Electron Solvation?

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Modeling Proton Solvation in Water Is This
Easier Than Electron Solvation?
Feng Wang Department of Chemistry Boston
University Greg A. Voth Center for Biophysical
modeling and Simulation University of Utah
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Outline

• Proton Chemistry (Why hydrated proton?)
• Multi State-Empirical Valence Bond (MS-EVB)
  Method
• Self-consistent Iterative-MS-EVB (SCI-MS-EVB)
• Interesting Results

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Why Hydrated Proton ?
Proton stays on the surface in the global minima
of (H2O)21H !
Ah haa! It seems solvated proton is easier!
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Proton Chemistry
Difficult

• Grotthuss mechanism.
• (hop and turn)
• Proposed by Danneel in 1905 100 years after
  Grotthuss proposed a similar mechanism describes
  water electrolysis.
• Very difficult to describe using conventional
  Molecular Dynamics force fields
• Bonding topology
• changes.
• Atom identity changes.

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Proton Chemistry
Difficult

• Grotthuss mechanism.
• (hop and turn)
• Proposed by Danneel in 1905 100 years after
  Grotthuss proposed a similar mechanism describes
  water electrolysis.
• Very difficult to describe using conventional
  Molecular Dynamics force fields
• Bonding topology
• changes.
• Atom identity changes.

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MS-EVB Description of H9O4
The one proton EVB matrix
Each state has different atomic charges and
molecular topologies.
(H9O4) Eigen, (H5O2) Zundel
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Multi-State Empirical Valence Bond Method (MS-EVB)

• Pioneer by Warshel (1991)
• Schmitt and Voth MS-EVB 1 (1998-1999)
• Day and Voth MS-EVB 2 (2002)
• Wu and Voth MS-EVB 3 (2007)

Time correlation function C(t) obtained from CPMD
(solid line) and EVB simulation (dashed line).
The inset contains the same correlation functions
for short times. (C,Dellago, MM. Naor and
G.Hummer PRL. 90, 105902,2003)
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His cell phone battery is pretty cool! Model
this!
MTI MicroFuel Cells demonstrated its direct
methanol micro fuel cell system prototype for
President Bush
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Direct Methanol

• NafionTM, developed by DuPont, is commonly used
  as the proton conducting membrane for direct
  methanol fuel cells.

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Structure of NafionTM membrane
H.J. Yeager, et. al., Perfluorinated Ionomer
Membranes ACS Symp. No.180, (American Chemical
Society Washington, DC, 1982)

• The hydrated polymer organizes into a hydrophobic
  region (A,green) composed of the perfluorinated
  alkane backbone, a hydrophilic/hydrophobic
  interface (B,blue) containing the perfluoroalkyl
  ether side chain, and the hydrophilic ionic
  region (C,red).

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Big Matrix Approach to Solve Multi-Proton EVB
Problem
A1B3, A1B4, A2B1
A1B1,
A1B2,
16 states required to describe
two independent (H9O4)
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Big Matrix Approach is Computationally
Intractable for Any Nontrivial Systems

• The matrix size scales like m n, where m is the
  number of EVB states per proton, n is the number
  of protons.
• In bulk, each proton typically requires 25
  states, thus we need 625x625 matrices for 2
  protons 390,625x390,625 matrices for 4 protons.

Our NafionTM simulation box contains 40 protons.
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Mission Impossible !
A multi-proton problem should not be more
difficult than a multi-electron problem?!
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Linear Scaling Approach (SCI-MS-EVB)

• ? Iterative solution of single proton problem

• Each EVB complex sees all other EVB complexes as
  arrays of effective particles.
• The charges and van der Waals parameters of each
  effective particle is a linear combination of
  that of a pure hydronium or a pure water
  according to its local EVB vector.
• The MS-EVB problem is solved for each EVB complex
  iteratively until the coefficients of each EVB
  complex converge.
• The forces of the overall system are calculated
  based on a self-consistent solution of all the
  EVB-complexes.

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Two Proton System
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Hellmann-Feynman Forces
Hellmann-Feynman theorem holds if the total
energy reaches a minimum with respect to all
coefficients cAi and cBi, simultaneously
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In Case of Overlapping
R
CA42 C B32
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Double Protonation Probability
1
1
3
4
4
3
B
A
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Next MD step
Determine basis states for each EVB-complex
Solve HEVB for each EVB-complex
Yes
Remove conflicting EVB states
No
Solve HEVB for each EVB-complex
No
Yes
Calculate Force
Converged ?
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Simulation of 0.44M HCl Solutions
Feng Wang, Gregory A. Voth J. Chem. Phys., 122,
144105 (2005)
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Is Two Protons Per Box Enough?

• For 0.44M

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Radial Distribution Functions of 0.44M HCl
Solutions
Unpublished
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Hydronium is Ambiphilic!
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Proton Paring ?!
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Put These Together
Unpublished
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Compare with CPMD Simulations
Unpublished
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Hydrogen Bond Network Inside NafionTM Membranes

• The hydronium ions, sulfonate head groups, and
  water form extended hydrogen bonded networks
  surrounded by the polymer backbone.
  Non-vehicular proton transport occurs within
  this H-bond network.

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Simulation of Poorly-hyrated NafionTM Membranes

• Employing SCI-MS-EVB, all 40 excess protons are
  treated with the MS-EVB method.

Matt Petersen, Feng Wang, Gregory A. Voth, in
preparation
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Sulfonic Oxygen/Hydronium Hydrogen Radial
Distribution
Excess Protons in Hydrated Nafion Matt K.
Petersen, Feng Wang, Nick P. Blake, Horia Metiu,
Gregory A. Voth J. Phys. Chem. B, 109, 3727 (2005)
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Acknowledgements

• Prof. Gregory A. Voth
• Prof. Kenneth D. Jordan
• Prof. H. Bernhard Schlegel
• Dr. Matt Petersen
• Dr. Sergey Izvekov