Teaching an old water model new tricks: (pp)F3C, a simple

protonizable water. Julius Su, Goddard group

ff Subgroup presentation.

Proton dynamics are integral to the functionof many key systems

CsHSO4 solid acid

HSAPO-34 zeolite

Protein proton shuttle

Nafion polymer

Protonizable molecular dynamics: “difficult” effects

Essentially need a reactive ff over all solvent molecules!

bond breakingand forming

electrostatics

multibodyeffects andpolarization

+1/3

+1/3

+1/3

+1

ppF3C design philosophy

1. Use a simple validated water model.

2. Use additional terms for the protons and protonatable sites only.

3. Use terms easily implementable in current generation force fields.

+q

-2q

+q

extendeddescription

http://biot.alfred.edu/~lewis/BPTI_WEB_1/BPTI_0/Images/bpti_1.html

The polarizable proton (ppF3C) model: energy components

F3C water model (electrostatics, VDW)

Short range angular (bonding)

Polarizable proton shell (3-body effects)

simple extension of existing F3C model

The polarizable proton model: F3C portion

H+

proton interacts onlyas point charge

Electrostatics: pt charge

(kcal/mol) r0 (Å)O-O 0.1848 3.56H-H 0.1000 0.90

qH = +0.410e qH+ = 1.000e

qO = –0.820eVan der Waals: 12-6 interaction(no proton)

12 6

0 02R R

ER R

The polarizable proton model: short range angular

rprovides bonding dependence

21 cosbrE a e a = 88.7 kcal/molb = 0.60 Å-1

= 0.63

25 50 75 100 125 150 175

520

540

560

580

600

Escreenbased on previouslyobserved dependence

HOH normalvector

The polarizable proton model: polarizable shell

+q

shell(-1)

proton(+1) +q

one pt. charge perprotonatable site

rr’

21 1 1( ) Erf 2

2ij

iij ij e

rE k r r q

r r r

harmonic restoring force(polarizability)

Gaussian shell density(screening)

reproduces three body effectq = 4.02e, re = 0.92 Ak = 26274.2 kcal/mol/A2

PP-F3C fitting to monomer-proton geometries

r

5 10 15 20 25

100

200

300

400

500

600

0o 0o

0o

0o

2/N = 89.1good fit but slightly too tightly bound at long range.

PP-F3C fitting to dimer-proton geometries

50 100 150 200 250

200

400

600

800

1000

1200

12

34

5

12

34

5rDH

rDA

1 1 2 1 3 11 2 2 2 3 21 3 2 3 3 31 4 2 41 5 2 5

All angle combinations represented:

rDA

rDH

Scan over proton/water distances:

2/N = 45.2 excellent fit

Short range angular term: inversion barrier

= 0o = 90o = 180o

-208

-206

-204

-202

-200

-198

-196

-194

0 60 120 180

kcal

/mol

-182

-180

-178

-176

-174

-172

-170

-168

0 60 120 180

kcal

/molPP-F3C MP2/6-31G**

Ebarrier = 2.6 kcal/mol (PP-F3C) 4.1 kcal/mol (MP2/6-31G**)

get almost 2/3 of theinversion barrier correct

(r = 1.0 A,tetrahedral water)

Swapping equivalent protons

H+

H+

pick closest oxygen,random hydrogen on it.

accept swap with/E TP e

0

50

100

150

200

250

300

350

400

450

500

0 50 100 150

Histogram of E showsmost proposed swaps are “uphill”

E (kcal/mol)

Estimating a diffusion constant for H+

periodic water (12 A)3, 10 ps run298 K, Ewald sum.

proton is quicklytrapped between twowaters

can adjust hopping temperature to fit D=7.8x10-5 cm2/sec

-2.5

-1.5

-0.5

0.5

1.5

2.5

3.5

0 0.5 1 1.5 2 2.5 3 3.5 4

Log10 t / fs

Log1

0 <R

2> /

A2

T/103K D /10-5 cm2/sec

10 17.2

20 78.8

30 148.5

40 178.4

50 187.5

partial bonds and charges equivalent proton swapping

Reality vs. ppF3C

Reality vs. ppF3C

nonisotropic/nonuniformelectron density

anisotropic bonding term

partial bonds and charges equivalent proton swapping

polarizable species, point proton point species, polarizable proton

Reality vs. ppF3C

nonisotropic/nonuniformelectron density

anisotropic bonding term

partial bonds and charges equivalent proton swapping