Multiscale Methods in Density Functional Theory:

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Multiscale Methods in Density Functional
Theory Molecular Electronics and Biological Ion
Channels
Thomas L. Beck Department of Chemistry University
of Cincinnati thomas.beck_at_uc.edu
Acknowledgments
NSF AFOSR DoD
People
Nimal Wijesekera, Karlis Mikkelsons, Guogang
Feng, Jian Yin, Zhifeng Kuang, Nobu Matsuno,
Jason Clohecy, Uma Mahankali
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Applications
Molecular Electronics Diodes, Wires, Transistors?
DV
I
e
Au
Au
S
S
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Ion transport through membrane channels
W

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P
M
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Comparison of the closed and open state of
Potassium channels
Closed KcsA channel
Open MthK channel
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HOLE search on KcsA(all figures below are
produced by modified HOLE program)
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Chloride Channel
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Poisson-Boltzmann Potential of StClC 1KPL in
Membrane
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Poisson-Boltzmann Potential of StClC 1KPL in
Membrane (63/136)
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Figure 8. Results of molecular dynamics runs at
400, 500, and 600 K on E. coli channel with added
hClC-2 proton sensor. Main protein was held
fixed while addition was allowed to move. Six
runs are superimposed for each temperature. Figure
s generated by DeepView v. 3.7b2
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HOLE search on StClC
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Alternative Approaches
Electrostatic continuum model
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Proposed Approach
Simple Moderate Complex

• PNP theory

200mV
?(e(r) ??(r) ) -4??(r) Szeci J(r,t)
-D?ci(r, t) b ?V(r)ci(r, t)
At steady-state dc(r,t)/dt 0, 0 ?.J
?.?ci(r, t) b ?V(r)ci(r) where VU zi e?
i 1,2.. N
static charge
mobile charge
Upon Slotboom transformation, 0 ?.eeff(r) (? ?
(r)) where eeff exp(- bV) and ?i exp (bV) ci
Laplace Equation
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Proposed Approach
Simple Moderate Complex
25.0 3.0 mM
Concentration (mM)
3-D PNP solver results shown
grid point
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Equations to Solve
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Kohn-Sham Equations
Nonlinear!
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Finite-difference representation (Poisson)
(Results from Taylor series expansion of the
function)
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2-d 4th order Laplacian
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(No Transcript)
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Iterative relaxation efficiency
Eigenvalues of update matrix (weighted Jacobi)
Longest wavelength modes
Critical slowing down
MG
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Multigrid V-cycle
MG accelerates convergence by decimating error
components with all wavelengths!
2 relaxations per level
Correct, relax
Restrict, relax
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Alternative cycles
V-cycle
Full multigrid (FMG) good preconditioning
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Efficiency
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Glycine (15 states)
Benzene dithiol (21 states)
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Electron density
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Convergence glycine, 15 states
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Polyelectrolyte simulation configuration bias
MC with multigrid Poisson-Boltzmann solution for
each configuration