Transcript A New Model for Charge Distributions in Molecular Systems

A New Model for Charge Distributions in Molecular Systems
Jiahao Chen, Todd J. Martínez
Department of Chemistry, Center for Advanced Theory and Molecular Simulation, Center for Biophysics and Computational Biology,
Frederick T. Seitz Materials Research Laboratory, Beckman Institute for Advanced Science and Technology
Introduction
•Need electrostatics for molecular modeling: Electron densities  partial charges
•QEq: A. K. Rappé, W. A. Goddard III, J. Phys. Chem. 95, 1991, 3358-3363
•Parameters: Mulliken electronegativities, Parr-Pearson hardnesses
•Popular and chemically intuitive, but has problems
•Objective: Fix QEq!
Sudden dissociation of NaCl.6H2O cluster
•Hexamer is smallest cluster needed to fully solvate NaCl
•Sudden limit of dissociation dynamics: no solvent reorganization
•Chlorine atom goes to zero as it moves away
•Charge on sodium changes only slightly: polarization effect from water
What’s Wrong?
•No HOMO-LUMO band gap: metallic bonding!
•No difference between , , metallic or ionic bonds
•No out-of-plane polarizability
•Physical difficulty in interpreting parameters, e.g. negative electron affinity of H
1.5
q/e
Our New Model, QTPIE
1.0
•Charge transfer pseudocurrent equilibration
•Distance-dependent electronegativities
•Detailed balance
equilibrium
geometry
0.5
QTPIE, Na
QTPIE, Cl
QEq, Na
QEq, Cl
0.0
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
-0.5
Amino acids: QEq v. ab initio
q(QEq)
0.8
NaCl Dissociation
•QEq: fractional charges at infinite separation limit
•QTPIE (this work): correct asymptotic limit, wrong decay behavior
•ab initio: decay behavior arises from nonadiabatic curve-crossing effects
•Experimental dipole moment used to fit parameters
1.0
0.6
q/e
0.8
CHx
0.0
0.6
NH2
S
Interpretation
•QEq: molecules as clusters of point fractional charges
•This work: network flow of quasistatic currents
O
O-2δ
η1
0.4
OH
-0.4
-2.0
equilibrium
geometry
N, NH
-0.2
-1.5
QTPIE (This work)
QEq
Mulliken
DMA0
Dipole
Experimental
C
0.4
0.2
10.0
R/Å
-1.0
•ab initio method: distributed multipole analysis restricted to multipoles only
(DMA0) and Mulliken charges from MP2-optimized geometries; 6-31G* basis set
•Generally good agreement, but QEq underestimates strong charges
1.0
9.0
H+δ
O
-0.6
H+δ
H
η2
H
0.2
-0.8
q(ab initio)
-1.0
-1.0
-0.5
0.0
0.5
1.0
1.5
0.0
1.0
2.0
3.0
Dipole Moments of Diatomics
•QEq benchmarked against experimental values for 94 molecules
•Qualitatively correct trend
•Poor agreement for high bond orders and radicals
•Reparameterization improved fit at expense of describing amino acids
5.0
µ(QEq)
4.0
LiI
LiBr
LiCl
NaI
NaBr
NaCl
3.5
3.0
CsF
2.5
q/e
R/Å
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
CF
-0.5
PN
µ(Expt.)
ClO NS
0.0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
•Study adiabatic dissociation of sodium chloride-water hexamer cluster
•Understand the physical basis of this model, esp. in statistical mechanics
•Develop connections to quantum-mechanical observables
•Explore relationships to ensemble density-functional theory
•Construct new models based on Janak’s Theorem and its consequences
•Look into statistical-mechanical treatment of multiple configurations
0.0
0.5
HF
HCl OH
CO HBrICl
BrF
HISH
IBr
ClF SO
NO
BrCl
Conclusions
•Reparameterization did not improve QEq
•Suggests fundamental problem in its premises
•Distance-dependent electronegativity gives correct asymptotics
•Challenges concept of electronegativity as an atom-specific quantity
•Empirical evidence for variations depending on bonding context
Future work
TIP3P
equilibrium
geometry
SiO
1.5
0.5
R/Å 8.0
RbF
KF
2.0
1.0
7.0
0.5
NaF
LiF
6.0
Water Dissociation
1.0
CsI
5.0
•Pull one hydrogen (H1) off into infinity suddenly
•Charge on H1 converges exponentially to zero far away
•Remaining hydroxyl radical retains polarization
CsBr RbI
KI
CsClRbBr
KBr
RbCl
KCl
4.5
4.0
3.5
4.0
4.5
5.0
-1.0
QTPIE, O
Mulliken, O
QTPIE, H1
Mulliken, H1
QEq, O
DMA0, O
QEq, H1
DMA0, H1
Acknowledgements
We thank the other members of the Martínez group for insightful discussions,
particularly J. D. Coe, C. Ko, B. G. Levine, P. Slavíček and A. K. Thompson.
This work was supported by the National Science Foundation under Award No.
DMR-03 25939 ITR, via the Materials Computation Center at the University of
Illinois at Urbana-Champaign.