a polarizable qm/mm model for the global (h 2 o) n – potential surface john m. herbert department...
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![Page 1: A polarizable QM/MM model for the global (H 2 O) N – potential surface John M. Herbert Department of Chemistry Ohio State University IMA Workshop “Chemical](https://reader035.vdocuments.net/reader035/viewer/2022062519/5697bfd61a28abf838cadf48/html5/thumbnails/1.jpg)
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, MNJanuary 12, 2009
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Acknowledgements
Group members:Dr. Mary RohrdanzDr. Chris WilliamsLeif JacobsonAdrian LangeRyan RichardKatie Martins Mark Hilkert
CAREER
$$
B.B.G.2006
Dr. ChrisWilliams Leif
Jacobson
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n -1/3
0.0 0.2 0.4 0.6 0.8
-3.5
-3.0
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
1.0
261115
2030
50100
200n
INeumark
JohnsonExperiments
– V
DE
(eV
)
Isomer I
VD
E /
eV
n
Johnson:CPL 297, 90 (1998)JCP 110, 6268 (1999)
Coe/Bowen:JCP 92, 3980 (1990)
Neumark:Science 307, 93 (2005)
Experiment:Abrupt changes at n = 11 and n = 25 followed by smooth (?) extrapolation– VDE / eV =
–3.30 + 5.73 n–1/3
(H2O)n– vertical electron binding energies (VEBEs)
n-1/3
Isomer I
?
VE
BE
/ eV
n—V
EB
E /
eV
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n -1/3
0.0 0.2 0.4 0.6 0.8
-3.5
-3.0
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
1.0
261115
2030
50100
200n
INeumark
JohnsonExperiments
Simulation:
Internal
Surface
III
II
– V
DE
(eV
)(H2O)n
– vertical electron binding energies (VEBEs)
n-1/3
—V
EB
E /
eV
Simulations: Barnett, Landman, Jorter JCP 88, 4429 (1988) CPL 145, 382 (1988)
Theory (1980s):Surface to internal transition
occurs between n = 32and n = 64
?
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Interior (cavity) states are stable only for T ≤ 100 K or n ≥ 200
Turi & Rossky, Science 309, 914 (2005)
simulated absorption spectra for (H2O)N–
Theory (21st century version)
Turi & Borgis, JCP 117, 6186 (2002)
expt.
J.V. Coe et al. Int. Rev. Phys. Chem. 27, 27 (2008)
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V(anion)
V(neut)
VEBE
E(anion)
E(neut)
Importance of the neutral water potential for water cluster anions
Global minima
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(H2O)20– isomers VEBE = 0.42 eV
E(anion) = 0.00 eVE(neut) = 0.45 eV
VEBE = 0.39 eV E(anion) = 0.01 eVE(neut) = 0.43 eV
VEBE = 0.72 eV E(anion) = 0.03 eVE(neut) = 0.78 eV
V(anion)
V(neut)
VEBE
E(anion)
E(neut)
Global minima
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e– correlation is more important for cavity states
∆ = Ecorr(anion) - Ecorr(neutral)
(eV)
VEBE(eV)
correlation strength vs. e– binding motif
C.F. Williams & JMH,J. Phys. Chem. A 112, 6171 (2008)
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∆ = Ecorr(anion) - Ecorr(neutral)
(eV)
VEBE (eV)
surface states
correlation strength vs. e– binding motif
e– correlation is more important for cavity states
C.F. Williams & JMH,J. Phys. Chem. A 112, 6171 (2008)
![Page 10: A polarizable QM/MM model for the global (H 2 O) N – potential surface John M. Herbert Department of Chemistry Ohio State University IMA Workshop “Chemical](https://reader035.vdocuments.net/reader035/viewer/2022062519/5697bfd61a28abf838cadf48/html5/thumbnails/10.jpg)
∆ = Ecorr(anion) - Ecorr(neutral)
(eV)
VEBE (eV)
cavity states
correlation strength vs. e– binding motif
e– correlation is more important for cavity states
C.F. Williams & JMH,J. Phys. Chem. A 112, 6171 (2008)
![Page 11: A polarizable QM/MM model for the global (H 2 O) N – potential surface John M. Herbert Department of Chemistry Ohio State University IMA Workshop “Chemical](https://reader035.vdocuments.net/reader035/viewer/2022062519/5697bfd61a28abf838cadf48/html5/thumbnails/11.jpg)
Motivation for the new model
• The electron–water interaction potential has been analyzed carefully, but almost always used in conjunction with simple, non-polarizable 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)
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Electron–water pseudopotential
O
H H
1) Construct a repulsive effective core potential representing the H2O molecular orbitals:
(H2O)– wavefn.
nodeless pseudo-wavefn.
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Electron–water pseudopotential
O
H H
1) Construct a repulsive effective core potential representing the H2O molecular orbitals:
(H2O)– wavefn.
nodeless pseudo-wavefn.
2) Use a density functional form for exchange attraction, e.g., the localdensity (electron gas) approximation:
3) In practice these two functionals are fit simultaneously
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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 theCoulomb interaction can be expressed as
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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)
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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
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Electron–multipole interactions
To avoid a “polarization catastrophe” at short range, we employ a dampedCoulomb interaction:
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Recovering a pairwise polarization modelIn general within our model we have:
Imagine instead that each H2O has a single, isotropic polarizable dipole whosevalue 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 mayprevious simulations.
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Fourier Grid Simulations
• Simultaneous solution of
where i = 1, ..., NMM.cI = vector of grid amplitudes for the wave function of
the Ith electronic stateH depends on the induced dipoles.
• Solution of the linear-response dipole equation is done via iterative matrixoperations. Dynamical propagation of the dipoles (i.e., an extended-Lagrangian approach) is another possibility.
• Solution of the Schrödinger equation is accomplished via Fourier gridmethod using a modified Davidson algorithm (periodically re-polarize thesubspace vectors)
• The method is fully variational provided that all polarization is done self-consistently
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A few comments about guns
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Vertical e– binding energies for (H2O)N–
Exchange/repulsion fit to (H2O)2– VEBE
34 clusters from N=2 to N=19 75 clusters from N=20 to N=35
Mod
el V
EB
E /
eV
Ab initio VEBE / eV
Non-polarizable model: Turi & Borgis, J. Chem. Phys. 117, 6186 (2002)
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Vertical e– binding energies for (H2O)N–
Exchange/repulsion fit to entire database of VEBEs
Ab initio VEBE / eV
Mod
el V
EB
E /
eV
34 clusters from N=2 to N=19 75 clusters from N=20 to N=35
Non-polarizable model: Turi & Borgis, J. Chem. Phys. 117, 6186 (2002)
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Relative isomer energies
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Relative isomer energies
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Relative isomer energies
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electron–water polarization
(kcal/mol)
Analysis
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∆ = Ecorr(anion) - Ecorr(neutral)
(eV)
VEBE (eV)
surface states, n = 2–24DFT geometries
correlation strength vs. e– binding motif
e– correlation is more important for cavity states
C.F. Williams & JMH,J. Phys. Chem. A 112, 6171 (2008)
![Page 29: A polarizable QM/MM model for the global (H 2 O) N – potential surface John M. Herbert Department of Chemistry Ohio State University IMA Workshop “Chemical](https://reader035.vdocuments.net/reader035/viewer/2022062519/5697bfd61a28abf838cadf48/html5/thumbnails/29.jpg)
∆ = Ecorr(anion) - Ecorr(neutral)
(eV)
VEBE (eV)
surface states, n = 2–24DFT geometries
correlation strength vs. e– binding motif
e– correlation is more important for cavity states
C.F. Williams & JMH,J. Phys. Chem. A 112, 6171 (2008)
![Page 30: A polarizable QM/MM model for the global (H 2 O) N – potential surface John M. Herbert Department of Chemistry Ohio State University IMA Workshop “Chemical](https://reader035.vdocuments.net/reader035/viewer/2022062519/5697bfd61a28abf838cadf48/html5/thumbnails/30.jpg)
∆ = Ecorr(anion) - Ecorr(neutral)
(eV)
VEBE (eV)
surface states, n = 18–22model Hamiltonian geometries
correlation strength vs. e– binding motif
e– correlation is more important for cavity states
C.F. Williams & JMH,J. Phys. Chem. A 112, 6171 (2008)
![Page 31: A polarizable QM/MM model for the global (H 2 O) N – potential surface John M. Herbert Department of Chemistry Ohio State University IMA Workshop “Chemical](https://reader035.vdocuments.net/reader035/viewer/2022062519/5697bfd61a28abf838cadf48/html5/thumbnails/31.jpg)
∆ = Ecorr(anion) - Ecorr(neutral)
(eV)
VEBE (eV)
cavity states, n = 28–34model Hamiltonian geometries
correlation strength vs. e– binding motif
e– correlation is more important for cavity states
C.F. Williams & JMH,J. Phys. Chem. A 112, 6171 (2008)
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∆ = Ecorr(anion) - Ecorr(neutral)
(eV)
VEBE (eV)
cavity states, n = 14, 24DFT geometries
correlation strength vs. e– binding motif
e– correlation is more important for cavity states
C.F. Williams & JMH,J. Phys. Chem. A 112, 6171 (2008)
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SOMO pair correlation energy / meV
0.1
0.2
0.3
0.4
0.5
0.6
cavity state, VEBE = 0.58 eV
frac
tion
of t
otal
pai
rs
1 3 5 7 9 11 13 15 17 19
surface state, VEBE = 0.87 eV
1 3 5 7 9 11 13 15 17 19
mainly just a bunch of weak interactions
many stronger correlations
Quantifying electron–water dispersion
C.F. Williams & JMH, J. Phys. Chem. A 112, 6171 (2008)
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Putting it all together:
water–water
e––waterelectrostatics
fit to exchange/repulsion