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Chemical Reaction on the Born-Oppenheimer surface and beyond

Chemical Reaction on the Born-Oppenheimer surface and beyond. ISSP Osamu Sugino. FADFT WORKSHOP 26 th July. Chemical Reaction. On the (ground state) Born-Oppenheimer surface Thermally activated process : Classical Beyond: excited state potential surface Non-adiabatic reaction : Quantum

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Chemical Reaction on the Born-Oppenheimer surface and beyond

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  1. Chemical Reactionon the Born-Oppenheimer surface and beyond ISSP Osamu Sugino FADFT WORKSHOP 26th 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 A+B→C • Potential energy surface • Search for reaction path and determine the rate

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

  5. Thermodynamic integration H1 H(Q) H0 TS 1 Q Other degrees of freedom 0 eq

  6. Thermodynamic integration

  7. 3. Crook’s identity(J.Stat.Phys.90,1481(1998)) p:probability distribution cf. Fast growth algorithm 1. Thermodynamics second low： 2. Jarzynski’s 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)

  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. H3O++e−→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

  11. H3O++e−→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

  12. First-Principles MD simulation H2O H3O+ deficit in electrons Pt excess electrons H3O+ H3O++e− H(ad)+H2O F Q voltage Pt

  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 H3O++e− H(ad)+H2O F Q Electrons cannot perfectly follow the ionic motion Deviation from the Born-Oppenheimer picture

  16. Non-adiabaticity adiabatic

  17. Wavefunction at t+dt

  18. 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

  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 Semiclassical wavepacket dynamics requires first order NACs

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

  24. 8-layer slab (2x2) unit cell (Å) Deviates from BO s*-electron s-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? Apply an artificial perturbation and see the response The sum-over-states (SOS) representation gives Chernyak and Mukamel, JCP112, 3572 (2000). Hu, Hirai, OS, JCP(2007)

  27. NAC of H3 near the conical intersection z 3 x O 2 1

  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

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