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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