Chemical Reaction on the Born-Oppenheimer surface and beyond

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Chemical Reactionon the Born-Oppenheimer surface
and beyond

• ISSP
• Osamu Sugino

FADFT WORKSHOP 26th July
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Chemical Reaction

• On the (ground state) Born-Oppenheimer surface
• Thermally activated process Classical
• Beyond excited state potential surface
• Non-adiabatic reaction Quantum
• Dissipation (dephasing) Classical aspect

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Chemical Reactions on the BO surface
AB?C

• Potential energy surface
• Search for reaction path and determine the rate

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Thermally activated process

• Reaction coordinate
• Transition State Theory (TST) (1935)
• Thermodynamic treatment
• Boltzmann factor

Transition state
Q
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Thermodynamic integration
H1
H(Q)
H0
TS
1
Q
Other degrees of freedom
0
eq
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Thermodynamic integration
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cf. Fast growth algorithm
1. Thermodynamics second low
2. Jarzynskis identity(JCP56,5018(1997))
Other topics related to the free-energy To be
presented at FADFT Symposium presentations by
Y. Yoshimoto (phase transition) Y. Tateyama
(reaction)
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Free-energy vs. direct simulation

• Free-energy approach
• TS and Q need to be defined a priori
• Direct simulation
• The more important the more complex

• Solvated systems
• Water fluctuates
• Retarded interaction (dynamical correlation)

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An example of the direct simulation

• Chemical reaction at electrode-solution interface

To be presented by M. Otani, FADFT Symposium
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H3Oe-?H(ad)H2O
350K, BO dynamics
Redox reaction at Pt electrode-water interface
H2O
Hydronium ion (H3O) acid condition
Excess electrons (e-) negatively biased
condition
Volmer step of H2 evolution electrolysis
Pt
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H3Oe-?H(ad)H2O
Redox reaction at Pt electrode-water interface
H2O
Hydronium ion (H3O) acid condition
Excess electrons (e-) negatively biased
condition
Volmer step of H2 evolution electrolysis
Pt
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First-Principles MD simulation
H2O
H3O deficit in electrons Pt excess
electrons
H3O
H3Oe-
H(ad)H2O
F
Q
voltage
Pt
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H gets adsorbed and then water reorganizes
Too complicated to be required of direct
simulation
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Chemical reaction beyond BO

• Non-adiabatic dynamics

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Adiabaticity consideration
H3Oe-
H(ad)H2O
F
Q
Electrons cannot perfectly follow the ionic motion
Deviation from the Born-Oppenheimer picture
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Non-adiabaticity
adiabatic
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Wavefunction at tdt
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Overlap with adiabatic state
Non-adiabaticity is proportional to the rate of
change in H While it is reduced when two
eigenvalues are different
V2(r)
V1(r)
t
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Born-Oppenheimer Theory
Adiabatic base
Density matrix
Eq. of motion
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A representation of the density matrix
Effective nuclear Hamiltonian
Potential surfaces e and non-adiabatic couplings
are required
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Semiclassical approximation using the Wigner
representation
Nuclear wavepacket
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Semiclassical wavepacket dynamics
Semiclassical wavepacket dynamics requires first
order NACs
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An Ehrenfest dynamics simulation
H
Si-H s
Si
excitation
decay
Potential energy surface
Si-H s
distance from the surface
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8-layer slab
(2x2) unit cell
(Å)
Deviates from BO
s-electron
s-hole
Y. Miyamoto and OS (1999)
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How to compute NAC

• TDDFT linear response theory

To be presented by C. Hu, FADFT Symposium
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How to derive NAC in TDDFT?
Apply an artificial perturbation and see the
response
The sum-over-states (SOS) representation gives
Chernyak and Mukamel, JCP 112, 3572 (2000). Hu,
Hirai, OS, JCP(2007)
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NAC of H3 near the conical intersection
z
3
x
O
2
1
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Full Quantum Simulation
To be presented by H. Hirai, FADFT Symposium
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Summary

• Chemical reaction (phase transition, atomic
  diffusion)
• Free-energy approach has become more and more
  accessible
• Direct simulation is very important
• Non-adiabatic dynamics
• Still challenging but progress has been made for
  system with few degrees of freedom