Polarization and charge transfer in classical molecular dynamics

Jiahao ChenMartínez Group

Chemistry, MRL and Beckman, UIUC

Methods of computational chemistry

less variablesmore variables

H! = i!

H! = E!

directnumericalquadrature

ab initiotheories

semiempiricalmethods

density functional

theory

coarse-grained models

continuumelectrostatics

molecular models (MM)

classicalmoleculardynamics

finite element methods

coarse-grained

dynamics

numerical quadrature, e.g. real-time path

integral propagatorsab initio molecular dynamics

What is the charge distribution?

What does the system do?

Molecular models/force fields

covalent bond effectsE =

+

Typical energy function

noncovalent interactions

Molecular models/force fields

bond stretch angle torsion dihedrals

electrostatics dispersion

E = !

a!angles

!a("a ! "eq,a)2!

b!bonds

kb(rb ! req,b)2

!

i<j!atoms

qiqj

rij

!

d!dihedrals

!

n

lnd cos (n!)

+ -

++

+ +

Typical energy function

!

i<j!atoms

!ij

"#"ij

rij

$12

!#

"ij

rij

$6%

Unique to condensed phases, where most

chemistry and biology happens

Why care about polarization and charge transfer?

Polarization in chemistry• Effect of local environment in liquid phases

• Ex. 1: Stabilizes carbonium in lysozyme

• Ex. 2: Hydrates chloride in water clusters

OPLS/AAnon-polarizable

force field

TIP4P/FQpolarizableforce field

1. A Warshel and M Levitt J. Mol. Biol. 103 (1976), 227-249. 2. SJ Stuart and BJ Berne J. Phys. Chem. 100 (1996), 11934 -11943.

3 models for polarization

Review: H Yu and WF van Gunsteren Comput. Phys. Commun. 172 (2005), 69-85.

Drude oscillatorsor charge-on-spring

or shell modelsQ

q !Q

kR

Response = change in RReview: H Yu and WF van Gunsteren Comput. Phys. Commun. 172 (2005), 69-85.

Ideal spring

Inducible dipoles

!1 !2

µinduced,1 µinduced,2

Response = change in induced dipoles

Review: H Yu and WF van Gunsteren Comput. Phys. Commun. 172 (2005), 69-85.

Fluctuating charges

charge transfer = 0.5 charge transfer = 0.2 e

charge transfer = 0.9 e

-1.1

-0.3

+1.4

Response = change in atomic charges

!1, "1

!2, "2

!3, "3

Review: H Yu and WF van Gunsteren Comput. Phys. Commun. 172 (2005), 69-85.

Better Electrostatics

!

i<j!atoms

qiqj

rij

ModelPolari-zation

Charge transfer

Cost

Pairwise fixed charges

Drude oscillator

Inducible dipoles

Fluctuating charges

❙

✓ ❙ ❙

✓ ❙ ❙ ❙ ❙ ❙ ❙

✓ ✓ ❙ ❙ ❙

QEq, a fluctuating-charge model

AK Rappé and WA Goddard III J. Phys. Chem. 95 (1991), 3358-3363.

atomicelectronegativities

“voltages”

screenedCoulomb

interactions

E =!

i

qi!i +!

i<j

qiqjJij

Jij =!

R3!2

!2i (r1)!2

j (r2)|r1 ! r2| dr1dr2

!i(r) = Ni|r !Ri|ni!1e!!i|r!Ri|

QEq has wrong asymptotics

q =!1 ! !2

J11 + J22 ! J12

0.0

0.2

0.4

0.6

0.8

1.0

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0

R/Å

q/e

QEq

ab initio

Na ClR

asymptote ~ 0.43 ≠ 0

QTPIE: our new model

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

replace atomic electronegativities with

distance-dependent pairwise electronegativities

or “potential differences”

E =!

i

qi!i +!

i<j

qiqjJij

!

i<j

pji!ikijSij

Sij =!

R3!i(r)!j(r)dr

!i(r) = Ni|r !Ri|ni!1e!!i|r!Ri|

overlap integral

0.0

0.2

0.4

0.6

0.8

1.0

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0

R/Å

q/e

QEq

QTPIE

ab initio

QTPIE has correct limit

q =(!1 ! !2)S12

J11 + J22 ! J12

q =!1 ! !2

J11 + J22 ! J12

Na ClR

Execution times

J Chen and T J Martínez, in preparation.

0.01

0.1

1

10

100

1000

104

10 100 1000 104 105

TImes to solve the QTPIE model

Bond-space SVDBond-space COFAtom-space iterative solverAtom-space direct solver

Sol

utio

n tim

e (s

)

Number of atoms

N1.81N6.20

N

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

• Missing in models with implicit or no polarization

!"+

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

Polarization in water chains• Use parameters from single water molecule

to model chains of waters

• Compare QEq and QTPIE with:

๏ Gas phase experimental data1

๏ Ab initio DF-LMP2/aug-cc-pVDZ

๏ AMOEBA2, an inducible dipole model

๏ TIP3P, a common implicit polarization model

1. WF Murphy J. Chem. Phys. 67 (1977), 5877-5882.2. P Ren and JW Ponder J. Phys. Chem. B 107 (2003), 5933-5947.

H! = E!

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)

Charge transfer in 15 waters

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

1 3 5 7 9 11 13 15

Charges per molecule in chain of 15 water molecules

QTPIEQEqMulliken/DF-LMP2/aug-cc-pVDZ

Cha

rge

on N

th m

olec

ule

Molecule No. N

Summary

• Polarization and charge transfer are important effects usually neglected in classical MD

• Our new charge model corrects deficiencies in existing fluctuating-charge model at similar computational cost

• We obtain quantitative polarization and qualitative charge transfer trends in linear water chains

Acknowledgments

Prof. Todd J. MartínezMartínez Group and friends

$: DOE