representing molecules as atomic-scale electrical circuits with fluctuating-charge models
DESCRIPTION
Slides for my talk at the APS (March 2007) national meeting.TRANSCRIPT
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Representing molecules as atomic‐scale electrical circuits with fluctuating‐charge models
Jiahao ChenDepartment of Chemistry and Beckman Institute
University of Illinois at Urbana‐ChampaignAPS Meeting P19.5, 2007‐03‐07
Funding•NSF DMR‐03 25939 ITR•DOE DE‐FG02‐05ER46260
+
‐
q1
+
‐
q2
Acknowledgments•Todd Martínez•Martínez Group members
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Polarization and charge transfer in molecular mechanics (MM)
• Want to describe both polarization and charge transfer with reasonable computational cost
• Common models to describe polarization:– Charge‐on‐spring/Drude oscillator, e.g. Drude (1902)– Point‐polarizable dipole, e.g. Vesely (1977)– Chemical potential equilibration (CPE), a.k.a. fluctuating‐charge: Rappé and Goddard (1991); Rick, Stuart and Berne (1994)
• Only CPE models can account for both effects
P. Drude, The Theory of Optics, Longmans, Green and Co., New York (1902); F.J. Vesely, J. Comp. Phys. 24 (1977), 361‐371; A. K. Rappé, W. A. Goddard, III, J. Phys. Chem. 95(1991), 3358‐3363; S. W. Rick, S. J. Stuart, B. J. Berne, J. Chem. Phys. 101 (1994), 6141‐6156.
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A simple DC circuit
capacitorDC source
ground
+
‐CV
0 V
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A simple DC circuitWhat is the charge q on C?
capacitorDC source
ground
+
‐CV
0 V
chargeq
This Hamiltonian approach works for molecules too:fluctuating‐charge/electronegativity equilibration models
energy depletedfrom DC source
energy gainof capacitor
E = −qV + 12C−1q2
∂E
∂q= −V + C−1q = 0
∴ q = V C
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E =Xi
qiχi +1
2ηiq
2i
+1
2
Xi 6=j
qiqjJij
CPE models: The QEq model
+
‐χ1
μ
η1 q1
chemicalhardness
electronegativity
chemicalpotential
+
‐χ2
η2 q2
Coulombinteraction
J12
A. K. Rappé, W. A. Goddard III, J. Phys. Chem. 95 (1991), 3358‐3363.
sourceterm
capacitanceterm
QEq model for a diatomic molecule
Coulombterm
∂E
∂qi= μ
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QEq: wrong NaCl dissociation
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0R/Å
q/e
QEq
ab initio DMA0CASSCF(8/5)/6‐31G*
equilibrium geometry
QEq, R → ∞
DMA0 = distributed multipole analysis restricted to point charges onlyCASSCF = complete active space self‐consistent field method
J12 → 0+‐
+‐
+‐
+‐
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The QTPIE model: Motivation
J. Chen, T. J. Martínez, Chem. Phys. Lett., in press.
1. Introduce charge transfer variables qi =Xj
pji
2. Introduce overlap integral: explicit notion of distance
∂EQTPIE∂pji
= 0
EQEq =Xi
qiχi +1
2ηiq
2i +
Xi 6=jqiqjJij
=Xij
pjiχi +Xijk
1
2ηipjipki +
1
2
Xijkl
pkipljJij
EQTPIE =Xij
pjiχiSij +Xijk
1
2ηipjipki +
1
2
Xijkl
pkipljJij
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QTPIE: Correct NaCl asymptote
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0R/Å
q/e
QEq
QTPIE
ab initio
equilibrium geometry
QTPIE prediction improved over QEq without reoptimizingparameters, but variation is still slower than ab initio
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Water fragments correctly• Asymmetric dissociation: correct asymptotics, charge
transfer on OH fragment retained
‐1.0
‐0.5
0.0
0.5
1.0
0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5
R/Å
q/e equilibrium geometry
R
QEq
QTPIE
ab initio
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Water parameters transferable• Parameters transferable across geometries
‐1.0
‐0.8
‐0.6
‐0.4
‐0.2
0.0
0.2
0.4
0.6
0.8
1.0
0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0R/Å
q/e
HO H
QEq
QEq
QTPIEQTPIEDMA
DMA
H
O H
‐1.0
‐0.8
‐0.6
‐0.4
‐0.2
0.0
0.2
0.4
0.6
0.8
1.0
0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0R/Å
q/e
QEq
QEq
QTPIEQTPIEDMA
DMA
‐1.0
‐0.8
‐0.6
‐0.4
‐0.2
0.0
0.2
0.4
0.6
0.8
1.0
0.5 1.5 2.5 3.5 4.5R/Å
q/e
H
O H
QEq
QEq
QTPIEQTPIEDMA
DMA
H
O H
‐1.0
‐0.8
‐0.6
‐0.4
‐0.2
0.0
0.2
0.4
0.6
0.8
1.0
0.5 1.5 2.5 3.5 4.5R/Å
q/e
QEq
QEq
QTPIEQTPIEDMA
DMA
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Dipole polarizability of phenol• Response of dipole moment to external electric field
• QTPIE: overestimates less than QEq
zyx
6.99810.00000.000012.362110.756620.327013.675813.029824.6244
ab initio*QTPIEQEq
(ų)
*ab initiomethod: MP2/aug‐cc‐pVDZ
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Conclusions
• Fluctuating‐charge models are analogous to DC electrical circuits
• QTPIE (our new charge model) predicts correct dissociation behavior of atomic charges
• Explicit distance cutoff for electronegativitiesimproves qualitative behavior
Thank You
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QEq v. ab initio charges
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0R/Å
q/e
QEq
equilibrium geometry
MullikenDMA
Ideal dipole
ab initiocharges
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QEq1, a fluctuating charge model
• Given geometry, find charge distribution
• Minimization with fixed total charge defines Lagrange multiplier μ
1. A. K. Rappe, W. A. Goddard III, J. Phys. Chem. 95 (1991) 3358‐3363.
q5q4
q3
q2
q1
energy to charge atom Coulomb interaction
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QTPIE: charge transfer with polarization current equilibration
• Shift focus to charge transfer variables pji:– Charge accounting: where it came from, where it’s going
– Explicitly penalize long‐distance charge transfer
p12
p23
p34p45