QTPIE: A new charge model for arbitrary geometries and

systems

Jiahao Chen and Todd J. MartínezDepartment of Chemistry and the Beckman Institute

Poster: 7:30-9:30 tonight, BCEC Exhibit Hall B2, #107

Polarization effects are important in classical molecular

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

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

1Berendsen, H. J. C.; Grigera, J. R.; Straatsma, T. P. J. Phys. Chem. 91, 1987, 6269-71.2Stuart, S. J.; Berne, B. J. J. Phys. Chem. 100, 1996, 11934 -11943.

OPLS/AANon-polarizableforce field

TIP4P/FQPolarizableforce field

Polarizable point dipole models

Review: Yu, H.; van Gunsteren, W. F.; Comput. Phys. Commun. 172 (2005), 69-85.

+q, -q,

Induced dipoles calculated from site polarizabilities

fixedcalculated

How to represent explicit polarization in classical MD?

How to represent explicit polarization in classical MD?Polarizable point dipole modelsDrude

oscillator/charge-on-spring/shell models

Review: Yu, H.; van Gunsteren, W. F.; Comput. Phys. Commun. 172 (2005), 69-85.

spring k

charge -Q >> qmass m << M

charge q+Qmass M-m

calculated

Polarizable point dipole modelsDrude oscillator/charge-on-spring/shell

modelsElectronegativity equalization/charge

equilibration/fluctuating-charge models

o Model polarization as a type of charge transfer

Review: Yu, H.; van Gunsteren, W. F.; Comput. Phys. Commun. 172 (2005), 69-85.

calculated

How to represent explicit polarization in classical MD?

Fluctuating-charge models map molecules onto electrical

circuits

screenedCoulomb

interactionchemicalhardness

electro-negativity

More electropositive

More electronegative0 V

-

Volt

ag

e

+

moleculeelectric

potential(inverse)

capacitanceelectricalcircuits

Coulombinteraction

QEq, a typical fluctuating-charge modelEnergy minimized with respect to

charges subject to constraint on total charge Q

Screened Coulomb interactions

s-type Slater orbitals

Rappé, A. K.; Goddard, W. A., J. Phys. Chem. 95 (1991), 3358-3363.

Limitations of QEqNo out-of-plane dipole polarizabilityOverestimates in-plane dipole

polarizabilityUnphysical charge distributions

predicted for non-equilibrium geometries

Cause: no distance penalty for charge transfer

voltage

distance

QTPIE, our new charge modelCharge-transfer with polarization

current equilibrationVoltage attenuates with increasing

distance

J. Chen and T. J. Martínez, Chem. Phys. Lett. 438 (2007) 315-320.

voltage

distance

Features of QTPIE

Correct dissociation limit for uncharged fragments

Minimally parameterized in terms of chemically meaningful quantities (electronegativites and hardnesses)

Can obtain results for electrostatic properties comparable to those from more sophisticated force fields

Dissocation of H2O in QEq and QTPIE

Correct 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/eequilibrium geometry

R

QEq

QTPIE

ab initio

QTPIE prediction improved over QEq without reoptimizing parameters

ab initio = DMA charges from CASSCF(6/4)/STO-3G wavefunction

Cooperative polarization in water

Dipole moment of water increases from 1.854 Debye1 in gas phase to 2.95±0.20 Debye2 at r.t.p. liquid phase

Polarization enhances dipole moments

Water models with implicit or no polarization can’t describe local electrical fluctuations

1D. R. Lide, CRC Handbook of Chemistry and Physics, 73rd ed., 1992.2A. V. Gubskaya and P. G. Kusalik, J. Chem. Phys. 117 (2002) 5290-5302.

+

Creating a water model with QTPIE

Replace implicit polarization in TIP3P1 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 moleculeo ab initio = DF-LMP2/aug-cc-pVDZ

1Jorgensen, W. L.; et al., J. Chem. Phys. 79 (1983) 926-935.

New parameters forTIP3P/QTPIE and TIP3P/QEqMulliken electronegativities and

Parr-Pearson hardnesses

eV Original1 QTPIE QEq Expt.2

4.528 4.960 5.116 7.176

8.741 8.285 8.125 7.540

13.890 10.125

10.125

12.844

13.364 20.680

20.680

12.157

1Rappé, A. K.; Goddard, W. A., J. Phys. Chem. 95 (1991), 3358-3363.2Calculated from ionization potentials and electron affinities in NIST Webbook.

Dipole response of linear water chains

Use parameters from single water molecule to model chains of water molecules

Compared with:o Gas phase experimental data1

o Ab initio DF-LMP2/aug-cc-pVDZo AMOEBA2, a point polarizable dipole

force field1Murphy, W. F. J. Chem. Phys. 67, 1977, 5877-5882.2Ren, P.; Ponder, J. W. J. Phys. Chem. B 107, 2003, 5933-5947..

planar (0° twist)

twisted (90°)

Mean dipole moment per water

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)

planar

Mean dipole moment per water

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)

twisted

TIP3P/QTPIE predicts dipoles well

Simpler, yet comparable to AMOEBA

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)

planar

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)

twisted

Water model AMOEBA TIP3P TIP3P/QEq TIP3P/QTPIE

No. of nonzero electrostatics

parameters14 3 4 4

Conclusions

Distance-dependent electronegativity difference leads to correct asympotic behavior of dissociating neutral fragments

New TIP3P/QTPIE water model predicts dipole moments better than TIP3P/QEq

TIP3P/QTPIE models polarization effects with results comparable to more expensive force fields

Acknowledgments

Prof. Todd J. MartínezMartínez GroupFunding from DOE DE-FG02-

05ER46260

Poster

Tonight 7:30-9:30

BCEC Exhibit Hall B2

#107