1. Chemical Reaction on the Born-Oppenheimer surface and beyond ISSP Osamu Sugino FADFT WORKSHOP 26 th July

2. 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

3. Chemical Reactions on the BO surface Potential energy surface Search for reaction path and determine the rate A+B→C

4. Thermally activated process Reaction coordinate Transition State Theory (TST) (1935~) – Thermodynamic treatment – Boltzmann factor Transition state Q

5. Other degrees of freedom Q  eq TS H0H0 H1H1 H( Q )  Thermodynamic integration

7. 1. Thermodynamics second low ： 3. Crook’s identity( J.Stat.Phys.90,1481(1998) ) p:probability distribution 2. Jarzynski’s identity( JCP56,5018(1997) ) cf. Fast growth algorithm Other topics related to the free-energy: To be presented at FADFT Symposium presentations by Y. Yoshimoto (phase transition) Y. Tateyama (reaction)

8. 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)

9. An example of the direct simulation Chemical reaction at electrode- solution interface To be presented by M. Otani, FADFT Symposium

10. H 3 O + +e − →H(ad)+H 2 O Redox reaction at Pt electrode-water interface Hydronium ion (H 3 O + ) acid condition Excess electrons (e − ) negatively biased condition Volmer step of H 2 evolution electrolysis H2OH2O Pt 350K, BO dynamics

11. H 3 O + +e − →H(ad)+H 2 O Pt H2OH2O Redox reaction at Pt electrode-water interface Hydronium ion (H 3 O + ) acid condition Excess electrons (e − ) negatively biased condition Volmer step of H 2 evolution electrolysis

12. First-Principles MD simulation Pt H2OH2O H 3 O + deficit in electrons Pt excess electrons H3O+H3O+ Q F H 3 O + +e − H(ad)+H 2 O voltage

13. H gets adsorbed and then water reorganizes Too complicated to be required of direct simulation

14. Chemical reaction beyond BO Non-adiabatic dynamics

15. Adiabaticity consideration Q F H 3 O + +e − H(ad)+H 2 O Electrons cannot perfectly follow the ionic motion Deviation from the Born-Oppenheimer picture

16. adiabatic Non-adiabaticity

17. Wavefunction at t+  t

18. Non-adiabaticity is proportional to the rate of change in H While it is reduced when two eigenvalues are different ｔ V 1 (r) V 2 (r) Overlap with adiabatic state

19. Born-Oppenheimer Theory Adiabatic base Density matrix Eq. of motion

20. A representation of the density matrix Effective nuclear Hamiltonian Potential surfaces e and non-adiabatic couplings are required

21. Semiclassical approximation using the Wigner representation Nuclear wavepacket

22. Semiclassical wavepacket dynamics requires first order NACs Semiclassical wavepacket dynamics

23. An Ehrenfest dynamics simulation Potential energy surface distance from the surface excitation decay Si-H σ Si-H σ* Si H

24. (Å)(Å) 8-layer slab (2x2) unit cell Deviates from BO  electron  hole Y. Miyamoto and OS (1999)

25. How to compute NAC TDDFT linear response theory To be presented by C. Hu, FADFT Symposium

26. How to derive NAC in TDDFT? The sum-over-states (SOS) representation gives Chernyak and Mukamel, JCP 112, 3572 (2000). Hu, Hirai, OS, JCP(2007) Apply an artificial perturbation and see the response

27. NAC of H 3 near the conical intersection 1 2 3 z x O

28. Full Quantum Simulation To be presented by H. Hirai, FADFT Symposium

29. 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