Polarization eff ects are important in classical molecular dynamics simulations

Structure of water improved when polarization is accounted for, even if implicitly1

Needed to describe local environmental eff ects, e.g. hydration of chloride in water clusters2

•

•

Berendsen, H. J. C.; Grigera, J. R.; Straatsma, T. P. J. Phys. Chem. 91 (1987) 6269-71. Stuart, S. J.; Berne, B. J. J. Phys. Chem. 100 (1996) 11934 -11943. Yu, H.; van Gunsteren, W. F. Comput. Phys. Commun. 172 (2005) 69-85. Rappé, A. K.; Goddard, W. A. J. Phys. Chem. 95 (1991) 3358-3363. Chen, J.; Martínez, T. J. Chem. Phys. Lett. 438 (2007) 315-320. Lide, D. R. CRC Handbook of Chemistry and Physics, 73rd ed., 1992. Gubskaya, A. V.;Kusalik, P. G. J. Chem. Phys. 117 (2002) 5290-5302. Jorgensen, W. L.; et al., J. Chem. Phys. 79 (1983) 926-935. NIST Webbook. Murphy, W. F. J. Chem. Phys. 67 (1977) 5877-5882. Ren, P.; Ponder, J. W. J. Phys. Chem. B 107 (2003) 5933-5947.

1.

2.3.

4.5.6.7.8.9.10.11.

OPLS/FQPolarizable force fi eld

OPLS/AANon-polarizable force fi eld

How to represent explicit polarization?3

Polarizable point dipole models•

+q, α1 -q, α2

Induced dipoles calculated from site polarizabilitiesDrude oscillator/charge-on-spring/shell models•

charge -Q >> qmass m << M

charge q+Qmass M-m

spring kElectronegativity equalization/charge equilibration/fl uctuating-charge models

•

Model polarization as a type of charge transfer

electro-negativity

chemicalhardness screened

Coulombinteraction

(inverse)capacitance

electricpotential

electricalcircuits

atoms inmolecule

0 V

χ�2

η�1

η�2

QEq4, a typical fl uctuating-charge modelEnergy minimized with respect to charges subject to constraint on total charge Q

•

Jiahao Chen and Todd J. Martínez

QTPIE: A minimal extension of Goddard’s QEq model with correct dissociation

Department of Chemistry, Frederick Seitz Materials Research Laboratory, and the Beckman InstituteUniversity of Illinois at Urbana-Champaign

Screened Coulomb interactions•

s-type Slater orbitals•

Limitations of QEqNo out-of-plane dipole polarizabilityOverestimates in-plane dipole polarizabilityUnphysical charge distributions predicted for non-equilibrium geometriesCause: no distance penalty for charge transfer

••••

η�2

distance

η�2 η�2η�2

QTPIE5, our new charge modelCharge-transfer with polarization current equilibrationVoltage attenuates with increasing distance

••

η�2

voltage

distance

η�2

η�2η�2

Features of QTPIECorrect dissociation limit for uncharged fragmentsMinimally parameterized in terms of chemically meaningful quantities (electronegativites and hardnesses)Can obtain results for electrostatic properties comparable to those from more sophisticated force fi elds

••

•

Dissocation of water in QEq and QTPIECorrect asymptoticsCharge separation 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

QTPIE prediction improved over QEq without reoptimizing parameters ab initio = DMA charges from CASSCF(6/4)/STO-3G wavefunction

ab initioQEq

QTPIE

Dipole moment of water increases from 1.854 Debye6 in gas phase to 2.95±0.20 Debye7 at r.t.p. liquid phasePolarization enhances dipole momentWater models with implicit or no polarization can’t describe local electri-cal fl uctuations

•

••

Cooperative polarization in water

Replace implicit polarization in TIP3P8 by explicitly polarizable charges using QTPIE and QEq QTPIE, QEq implemented in TINKERReparameterized to reproduce ab initio dipole moments and anisotropic polarizabilities of a single water moleculeab initio = DF-LMP2/aug-cc-pVDZ

•

••

•

Creating a water model with QTPIE

New parameters forTIP3P/QTPIE and TIP3P/QEq

Mulliken electronegativities and Parr-Pearson hardnesses•

Mean dipole moment per water

TIP3P/QTPIE predicts dipoles wellSimpler, computationally cheaper, yet results comparable to AMOEBA•

Distance-dependent electronegativity diff erence leads to correct asympot-ic behavior of dissociating neutral fragmentsNew TIP3P/QTPIE water model predicts dipole moments better than TIP3P/QEq TIP3P/QTPIE models polarization eff ects with results comparable to more expensive force fi elds

•

•

•

Conclusions

AcknowledgmentsProf. Todd J. Martínez

Martínez GroupFunding from DOE DE-FG02-05ER46260

References

Water model AMOEBA TIP3P TIP3P/QEq TIP3P/QTPIENo. of electrostatics parameters 14 3 4 4

1.8

1.9

2.0

2.1

2.2

2.3

2.4

2.5

2.6

0 5 10 15 20 25 30 35 40

Number of water molecules, N

( /N)/Debye

TIP3P

AMOEBADF-LMP2/aug-cc-pVDZ

TIP3P/QTPIE

TIP3P/QEq

gas phase (experimental)

1.8

1.9

2.0

2.1

2.2

2.3

2.4

2.5

2.6

0 5 10 15 20 25 30 35 40

Number of water molecules, N

( /N)/Debye

TIP3P

AMOEBA

DF-LMP2/aug-cc-pVDZ

TIP3P/QTPIE

TIP3P/QEq

gas phase (experimental)

Dipole response of linear water chainsUse parameters from single water molecule to model chains of watersCompared with gas phase experimental data10, ab initio (DF-LMP2/aug-cc-pVDZ), and AMOEBA11, a point polarizable dipole force fi eld

••

eV Original4 QTPIE QEq Expt.9

χH 4.528 4.960 5.116 7.176χO 8.741 8.285 8.125 7.540ηH 13.890 10.125 10.125 12.844ηO 13.364 20.680 20.680 12.157

Planar

Twisted