Our New Model, QTPIE•Energy expression contains explicit geometry-dependent electronegativities•Antisymmetric charge-transfer (bond) variables pij instead of charge (site) variables qi

•Unconstrained minimization solves the model

•New picture of polarization as induced quasistatic currents rather than charge separation

Known limitations of existing models•No HOMO-LUMO band gap: high-temperature limit, all bonds are metallic•For chemical purposes, want low temperature limit:Below Fermi temperature, where TF ~ 105 K for electron gases•No difference between , , metallic or ionic bonds•Unable to describe out-of-plane polarizabilities•Difficulty in interpreting parameters, e.g. negative electron affinity of H in QEq

Jiahao Chen and Todd J. MartínezCenter for Advanced Theory and Molecular Simulation, Center for Biophysics and Computational Biology, Frederick T. Seitz Materials Research Laboratory, Beckman

Institute for Advanced Science and TechnologyDepartment of Chemistry, School of Chemical Sciences, University of Illinois at Urbana-Champaign (UIUC), 600 South Mathews Avenue, Urbana, Illinois 61801, USA

QTPIE: A fluctuating-charge model involving charge-transfer variables with correct asymptotics

AcknowledgementsWe thank the other members of the Martínez group, esp. B. Levine, and D. Miller (Lisy group), for insightful discussions.This work was supported by the National Science Foundation under Award No. DMR-03 25939 ITR, via the Materials Computation Center at UIUC. J. C. thanks the Graduate College of UIUC for a travel award.

Conclusions•Geometry-dependent electronegativity gives correct asymptotic behavior•Charge transfer variables offer network interpretation analogous to electric circuits•Simplified description in models requires nonlocal corrections to local quantities•Multiconfiguration effects important but unclear how to treat them in charge models

Connections with density functional theory (DFT)•Grand-canonical DFT can be used to construct fluctuating-charge models•Free energy corresponding to ensemble of states of different particle numbers

•For a minimal-basis diatomic, a restricted model gives electronegativity and hardness

•Recovers derivative discontinuity in zero temperature limit, i.e. non-interacting limit•Gives interpretation of temperature as tuning coupling strength, e.g. Hubbard models

Dissociation of NaCl molecule•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 QEq parameters, which were later used in QTPIE

Hq3

p21 p31

Hq2

Oq1

HH

O

Amino acids: QEq v. ab initio•Charge analyses of MP2/6-31G* and MP2/cc-pVDZ optimized geometries: distributed multipole analysis restricted to multipoles only (DMA0) and Mulliken populations•Best agreement for singly bonded species; increasingly poor descriptions of multiply-bonded, aromatic and highly polarized (charged) species•Reparameterization did not improve fit•Results suggest need for geometry-dependent parameterization of charge models

S

C

CHx

NH2

N, NH

OHO

q(ab initio)

q(QEq)

-1.0 -0.5 0.0 0.5 1.0 1.5-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

Sudden dissociation of NaCl.6H2O cluster•Hexamer is smallest cluster needed to fully solvate NaCl•Sudden limit of dissociation dynamics: no solvent reorganization•Charge on chlorine atom goes to zero as it moves away•Charge on sodium changes only slightly: polarization effects charge transfer in water

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0

R/Å

q/e

QTPIE, Na QTPIE, Cl

QEq, Na QEq, Cl

equilibriumgeometry

equilibriumgeometry

0.0

0.2

0.4

0.6

0.8

1.0

1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0R/Å

q/eQTPIE (This work)QEqMullikenDMA0DipoleExperimental

Asymmetric dissociation of water molecule•Pull one hydrogen (H1) off into infinity suddenly•QTPIE-calculated charge on H1 converges exponentially to zero far away•Remaining hydroxyl radical retains polarization

-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

QTPIE, O QTPIE, H1 QEq, O QEq, H1Mulliken, O Mulliken, H1 DMA0, O DMA0, H1

TIP3P equilibriumgeometry R

Charged systems: sodium ion : phenol -complexes

•The hydrogen bonding behavior of water to phenol changes in the presence of Na+

(3) and (5) preferred over (2) and (6) respectively (D. Miller, personal communication)•Excellent test structures for investigating status of charged reference parameters•Charges with Na+ reference superior to Na0 reference with constraint on total charge

Fluctuating-charge models•Need electrostatics for molecular modeling•Fluctuating-charge models offer coarse-grained description of electronic structureQEq: A. K. Rappé, W. A. Goddard III, J. Phys. Chem. 95, 1991, 3358-3363fluc-q: S. W. Rick, S. Stuart, B.J. Berne, J. Chem. Phys. 101, 1994, 6141-6156•Chemically important local quantities parameterize these modelsElectronegativities i and hardnesses i = Jii

Common featuresQuadratic, classical energy

Constrained minimization

Minimal basis representation

Analogy with electrical circuits•Charge transfer variables and classical currents have same pseudoscalar symmetry•QTPIE leads to electrical interpretation of atomic capacitors storing partial charges•Charging asymmetry due to band gap: potential difference between conductor ‘plates’•Circuit sum rules for equivalent circuits give coarse-grained effective circuit branches

O

H

O

H

O

H

H

O

H

O

HH

O

HNa

O

HNa

O

H

H

O

H

Na

(1)

(2)

(3)

(4)

(5)

(6)

O

HH

0

5

10

15

20

25

30

35

40

45

(1) (2) (3) (4) (5) (6)

µ/D

QTPIE, Na(0)

QTPIE, Na(+1)

QEq, Na(0)

QEq, Na(+1)

Mulliken/MP2/cc-pVDZ

LUMO

HOMO

+V

E

V

C+

C-

C+

C-

V

-1.0

-0.8-0.6

-0.4-0.2

S

CCHx

NHx

OHO

DMA, MP2/cc-pVDZ

QEq

-1.0-0.8-0.6-0.4-0.2 0.0 0.2 0.4 0.6 0.8 1.0

0.0

0.2

0.4

0.6

0.8

1.0

S

CCHx

NHx

OHO

-1.0 -0.5 0.0 0.5 1.0 1.5-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

DMA, MP2/6-31G*

QEq