Polarization and charge transfer in classical molecular dynamics
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Transcript of Polarization and charge transfer in classical molecular dynamics
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