Transcript A polarizable QM/MM model for the global (H2O)N– potential surface John M.

A polarizable QM/MM model for the
global (H2O)N– potential surface
John M. Herbert
Department of Chemistry
Ohio State University
IMA Workshop
“Chemical Dynamics: Challenges & Approaches”
Minneapolis, MN
January 12, 2009
Acknowledgements
Group members:
Dr. Mary Rohrdanz
Dr. Chris Williams
Leif Jacobson
Adrian Lange
Ryan Richard
Katie Martins
Mark Hilkert
$$
CAREER
B.B.G.
2006
Dr. Chris
Williams
Leif
Jacobson
(H2O)n– vertical electron binding
energies (VEBEs)
6
2
eV
VEBE
VDE / /eV
100
30
15
200
50
20
11
0.0
-0.5
—VEBE / eV
– VDE (eV)
n
Isomer II
Isomer
?
-1.0
-1.5
Experiments
Johnson
-2.0
Neumark
n
n
I
Experiment:
Abrupt changes at n = 11 and n = 25
followed by smooth (?) extrapolation
-2.5
– VDE / eV =
–3.30 + 5.73 n–1/3
-3.0
-3.5
0.0
0.2
0.4
0.6
n -1/3
n-1/3
0.8
1.0
Johnson:
CPL 297, 90 (1998)
JCP 110, 6268 (1999)
Coe/Bowen:
JCP 92, 3980 (1990)
Neumark:
Science 307, 93 (2005)
(H2O)n– vertical electron binding
energies (VEBEs)
100
30
15
200
50
20
11
6
2
III
0.0
?
-0.5
—VEBE / eV
– VDE (eV)
n
-1.0
II
Experiments
Johnson
-1.5
-2.0
Neumark
I
Theory (1980s):
Surface to internal transition
occurs between n = 32
and n = 64
Simulation:
-2.5
Internal
-3.0
Surface
-3.5
0.0
0.2
0.4
0.6
n -1/3
n-1/3
0.8
1.0
Simulations:
Barnett, Landman, Jorter
JCP 88, 4429 (1988)
CPL 145, 382 (1988)
Theory (21st century version)
simulated absorption spectra for (H2O)N–
expt.
Turi & Borgis, JCP 117, 6186 (2002)
Interior (cavity) states are stable only for
T ≤ 100 K or n ≥ 200
J.V. Coe et al. Int. Rev. Phys. Chem. 27, 27 (2008)
Turi & Rossky, Science 309, 914 (2005)
Importance of the neutral water potential for
water cluster anions
V(anion)
V(neut)
VEBE
E(neut)
E(anion)
Global minima
(H2O)20– isomers
VEBE = 0.42 eV
E(anion) = 0.00 eV
E(neut) = 0.45 eV
V(anion)
V(neut)
VEBE
E(neut)
VEBE = 0.39 eV
E(anion) = 0.01 eV
E(neut) = 0.43 eV
E(anion)
VEBE = 0.72 eV
E(anion) = 0.03 eV
E(neut) = 0.78 eV
Global minima
e– correlation is more important for cavity states
correlation strength vs. e– binding motif
VEBE
(eV)
∆ = Ecorr(anion) - Ecorr(neutral)
(eV)
C.F. Williams & JMH,
J. Phys. Chem. A 112, 6171 (2008)
e– correlation is more important for cavity states
correlation strength vs. e– binding motif
surface states
VEBE
(eV)
∆ = Ecorr(anion) - Ecorr(neutral)
(eV)
C.F. Williams & JMH,
J. Phys. Chem. A 112, 6171 (2008)
e– correlation is more important for cavity states
correlation strength vs. e– binding motif
cavity states
VEBE
(eV)
∆ = Ecorr(anion) - Ecorr(neutral)
(eV)
C.F. Williams & JMH,
J. Phys. Chem. A 112, 6171 (2008)
Motivation for the new model
• The electron–water interaction potential has been analyzed
carefully, but almost always used in conjunction with simple, nonpolarizable water models (e.g., Simple Point Charge model, SPC).
– L. Turi & D. Borgis, J. Chem. Phys. 114, 7805 (2001); 117, 6186 (2002)
• A QM treatment of electron–water dispersion via QM Drude
oscillators provides ab initio quality VEBEs, but requires
expensive many-body QM
– F. Wang, T. Sommerfeld, K. Jordan, e.g.:
J. Chem. Phys. 116, 6973 (2002)
J. Phys. Chem. A 109, 11531 (2005)
• How far can we get with one-electron QM, using a polarizable
water model that performs well for neutral water clusters?
– AMOEBA water model: P. Ren & J. Ponder, J. Phys. Chem. B 107, 5933
(2003)
Electron–water pseudopotential
1) Construct a repulsive effective core potential representing the H2O
molecular orbitals:
(H2O)– wavefn.
O
H
H
nodeless
pseudo-wavefn.
Electron–water pseudopotential
1) Construct a repulsive effective core potential representing the H2O
molecular orbitals:
(H2O)– wavefn.
O
H
H
nodeless
pseudo-wavefn.
2) Use a density functional form for exchange attraction, e.g., the local
density (electron gas) approximation:
3) In practice these two functionals are fit simultaneously
AMOEBA electrostatics
Define multipole polytensors
and interaction polytensors
where i and j index MM atomic sites and
Then the double Taylor series that defines the multipole expansion of the
Coulomb interaction can be expressed as
Polarization
In AMOEBA,* polarization is represented via a linear-response dipole at
each MM site:
The total electrostatic interaction, including polarization, is
where
*P. Ren & J.W. Ponder, J. Phys. Chem. B 127, 5933 (2003)
Polarization work
The electric field at MM site i is
Some work is required to polarize the dipole in the presence of the field:
So the total electrostatic interaction is really
Electron–multipole interactions
To avoid a “polarization catastrophe” at short range, we employ a damped
Coulomb interaction:
Recovering a pairwise polarization model
In general within our model we have:
Imagine instead that each H2O has a single, isotropic polarizable dipole whose
value is induced solely by qelec:
Then the electron–water polarization interaction is
In practice we use an attenuated Coulomb potential, the effect of which
can be mimicked by an offset in the electron–water distance:
This is a standard ad hoc polarization potential that has been used in may
previous simulations.
Fourier Grid Simulations
• Simultaneous solution of
where i = 1, ..., NMM.
cI = vector of grid amplitudes for the wave function of
the Ith electronic state
H depends on the induced dipoles.
• Solution of the linear-response dipole equation is done via iterative matrix
operations. Dynamical propagation of the dipoles (i.e., an extendedLagrangian approach) is another possibility.
• Solution of the Schrödinger equation is accomplished via Fourier grid
method using a modified Davidson algorithm (periodically re-polarize the
subspace vectors)
• The method is fully variational provided that all polarization is done
self-consistently
A few comments about guns
Vertical e– binding energies for (H2O)N–
Exchange/repulsion fit to (H2O)2– VEBE
75 clusters from N=20 to N=35
Model VEBE / eV
34 clusters from N=2 to N=19
Ab initio VEBE / eV
Non-polarizable model: Turi & Borgis, J. Chem. Phys. 117, 6186 (2002)
Vertical e– binding energies for (H2O)N–
Exchange/repulsion fit to entire database of VEBEs
75 clusters from N=20 to N=35
Model VEBE / eV
34 clusters from N=2 to N=19
Ab initio VEBE / eV
Non-polarizable model: Turi & Borgis, J. Chem. Phys. 117, 6186 (2002)
Relative isomer energies
Relative isomer energies
Relative isomer energies
Analysis
electron–water polarization
(kcal/mol)
e– correlation is more important for cavity states
correlation strength vs. e– binding motif
surface states, n = 2–24
DFT geometries
VEBE
(eV)
∆ = Ecorr(anion) - Ecorr(neutral)
(eV)
C.F. Williams & JMH,
J. Phys. Chem. A 112, 6171 (2008)
e– correlation is more important for cavity states
correlation strength vs. e– binding motif
surface states, n = 2–24
DFT geometries
VEBE
(eV)
∆ = Ecorr(anion) - Ecorr(neutral)
(eV)
C.F. Williams & JMH,
J. Phys. Chem. A 112, 6171 (2008)
e– correlation is more important for cavity states
correlation strength vs. e– binding motif
surface states, n = 18–22
model Hamiltonian geometries
VEBE
(eV)
∆ = Ecorr(anion) - Ecorr(neutral)
(eV)
C.F. Williams & JMH,
J. Phys. Chem. A 112, 6171 (2008)
e– correlation is more important for cavity states
correlation strength vs. e– binding motif
cavity states, n = 28–34
model Hamiltonian geometries
VEBE
(eV)
∆ = Ecorr(anion) - Ecorr(neutral)
(eV)
C.F. Williams & JMH,
J. Phys. Chem. A 112, 6171 (2008)
e– correlation is more important for cavity states
correlation strength vs. e– binding motif
cavity states, n = 14, 24
DFT geometries
VEBE
(eV)
∆ = Ecorr(anion) - Ecorr(neutral)
(eV)
C.F. Williams & JMH,
J. Phys. Chem. A 112, 6171 (2008)
Quantifying electron–water dispersion
surface state, VEBE = 0.87 eV
fraction of total pairs
cavity state, VEBE = 0.58 eV
mainly just a bunch of
weak interactions
0.6
0.5
0.4
0.3
0.2
0.1
1
3
5
7
9
11
13
15
17
19
1
3
5
7
9
11
13
15
17
19
many stronger
correlations
SOMO pair correlation energy / meV
C.F. Williams & JMH, J. Phys. Chem. A 112, 6171 (2008)
Putting it all together:
water–
water
e––water
electrostatics
fit to exchange/
repulsion