Representing molecules as atomic-scale electrical circuits with fluctuating-charge models
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Representing molecules as atomic‐scale electrical circuits with fluctuating‐charge models Jiahao Chen Department of Chemistry and Beckman Institute University of Illinois at Urbana‐Champaign APS Meeting P19.5, 2007‐03‐07 Funding •NSF DMR‐03 25939 ITR •DOE DE‐FG02‐05ER46260 + ‐ q 1 + ‐ q 2 Acknowledgments •Todd Martínez •Martínez Group members
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Slides for my talk at the APS (March 2007) national meeting.
Transcript of Representing molecules as atomic-scale electrical circuits with fluctuating-charge models
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
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.
A simple DC circuit
capacitorDC source
ground
+
‐CV
0 V
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
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
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+‐
+‐
+‐
+‐
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
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
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
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
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
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
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
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
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
