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 function
of many key systems
CsHSO4 solid acid
Protein proton shuttle
Nafion polymer
HSAPO-34 zeolite
Protonizable molecular dynamics: “difficult” effects
+1
bond breaking
and forming
+1/3
+1/3
multibody
effects and
polarization
+1/3
electrostatics
Essentially need a reactive ff over all solvent molecules!
ppF3C design philosophy
1. Use a simple validated water model.
-2q
+q
+q
2. Use additional terms
for the protons and
protonatable sites only.
extended
description
http://biot.alfred.edu/~lewis/BPTI_WEB_1/BPTI_0/Images/bpti_1.html
3. Use terms easily implementable in current generation force fields.
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+
Electrostatics: pt charge
Van der Waals: 12-6 interaction
(no proton)
6
  R0 12
 R0  
E      2  
 R 

R




proton interacts only
as point charge
qH = +0.410e
qO = –0.820e
qH+ = 1.000e
(kcal/mol) r0 (Å)
O-O
0.1848
3.56
H-H
0.1000
0.90
The polarizable proton model: short range angular
HOH
normal
vector
q
r
provides bonding dependence
f
E  ae
600
580
 br
1   cos q 
2
a = 88.7 kcal/mol
b = 0.60 Å-1
 = 0.63
DEscreen
based on previously
observed dependence
560
540
520
25
50
75
q
100
125
f
150
175
The polarizable proton model: polarizable shell
+q
r
proton
(+1)
r’
shell
(-1)
+q
one pt. charge per
protonatable site
1 1
rij 
1
2
E  k (r  r )   qi   Erf 2 
 rij rij

2
r
e 

harmonic restoring force
(polarizability)
reproduces three body effect
Gaussian shell density
(screening)
q = 4.02e, re = 0.92 A
k = 26274.2 kcal/mol/A2
q
PP-F3C fitting to monomer-proton geometries
r
f
q90o
S2/N
good fit but slightly too
tightly bound at long range.
= 89.1
600
500
400
300
200
100
q0o
f0o
f90o
5
10
15
20
25
PP-F3C fitting to dimer-proton geometries
1200
1000
All angle combinations represented:
800
3
4
600
2
5
1
1
rDH
2
5
3
4
11
12
13
14
15
rDA
Scan over proton/water distances:
rDH
400
200
rDA
50
100
150
200
250
S2/N = 45.2
excellent fit
21
22
23
24
25
31
32
33
Short range angular term: inversion barrier
(r = 1.0 A,
tetrahedral water)
q = 0o
q = 90o
-194
-196
-168
0
60
120
180
-170
-202
0
60
120
180
-172
PP-F3C
kcal/mol
kcal/mol
-198
-200
q = 180o
-174
MP2/6-31G**
-176
-204
-178
-206
-180
-208
-182
DEbarrier = 2.6 kcal/mol (PP-F3C)
4.1 kcal/mol (MP2/6-31G**)
get almost 2/3 of the
inversion barrier correct
Swapping equivalent protons
H+
H+
pick closest oxygen,
random hydrogen on it.
accept swap with
P  e DE / T
500
450
400
Histogram of DE shows
most proposed swaps
are “uphill”
350
300
250
200
150
100
50
0
0
50
100
DE (kcal/mol)
150
Estimating a diffusion constant for H+
3.5
Log10 <R2> / A2
2.5
proton is quickly
trapped between two
waters
periodic water (12 A)3, 10 ps run
298 K, Ewald sum.
1.5
0.5
-0.5 0
-1.5
-2.5
Log10 t / fs
0.5
1
1.5
2
2.5
3
3.5
T/103K
D /10-5 cm2/sec
10
17.2
20
78.8
30
148.5
40
178.4
50
187.5
4
can adjust hopping temperature to fit D=7.8x10-5 cm2/sec
Reality vs. ppF3C
partial bonds and charges
equivalent proton swapping
Reality vs. ppF3C
partial bonds and charges
equivalent proton swapping
nonisotropic/nonuniform
electron density
anisotropic bonding term
Reality vs. ppF3C
partial bonds and charges
equivalent proton swapping
nonisotropic/nonuniform
electron density
polarizable species, point proton
anisotropic bonding term
point species, polarizable proton