Chemical Reactionon the Born-Oppenheimer surface and beyondISSPOsamu SuginoFADFT WORKSHOP 26th July

Chemical ReactionOn the (ground state) Born-Oppenheimer surfaceThermally activated process: ClassicalBeyond: excited state potential surfaceNon-adiabatic reaction: QuantumDissipation (dephasing): Classical aspect

Chemical Reactions on the BO surfacePotential energy surfaceSearch for reaction path and determine the rate

A+BC

Thermally activated processReaction coordinate

Transition State Theory (TST) (1935~)Thermodynamic treatmentBoltzmann factorTransition stateQ

Other degrees of freedomQ0eqTSH0H1H(Q)1Thermodynamic integration

Thermodynamic integration

1. Thermodynamics second low2. Jarzynskis identity(JCP56,5018(1997))cf. Fast growth algorithmOther topics related to the free-energy:To be presented at FADFT Symposium presentations by Y. Yoshimoto (phase transition) Y. Tateyama (reaction)

Free-energy vs. direct simulationFree-energy approachTS and Q need to be defined a priori

Direct simulationThe more important the more complex

Solvated systemsWater fluctuatesRetarded interaction (dynamical correlation)

An example of the direct simulationChemical reaction at electrode-solution interfaceTo be presented by M. Otani, FADFT Symposium

H3O++eH(ad)+H2ORedox reaction at Pt electrode-water interfaceHydronium ion (H3O+) acid conditionExcess electrons (e) negatively biased conditionVolmer step of H2 evolution electrolysisH2OPt350K, BO dynamics

H3O++eH(ad)+H2OPtH2ORedox reaction at Pt electrode-water interfaceHydronium ion (H3O+) acid conditionExcess electrons (e) negatively biased conditionVolmer step of H2 evolution electrolysis

First-Principles MD simulationPtH2OH3O+ deficit in electronsPt excess electronsH3O+QFH3O++eH(ad)+H2Ovoltage

H gets adsorbed and then water reorganizesToo complicated to be required of direct simulation

Chemical reaction beyond BONon-adiabatic dynamics

Adiabaticity consideration QFH3O++eH(ad)+H2OElectrons cannot perfectly follow the ionic motionDeviation from the Born-Oppenheimer picture

adiabaticNon-adiabaticity

Wavefunction at t+dt

Non-adiabaticity is proportional to the rate of change in HWhile it is reduced when two eigenvalues are differentV1(r)V2(r)Overlap with adiabatic state

Born-Oppenheimer TheoryAdiabatic baseDensity matrixEq. of motion

A representation of the density matrixEffective nuclear HamiltonianPotential surfaces e and non-adiabatic couplings are required

Semiclassical approximation using the Wigner representationNuclear wavepacket

Semiclassical wavepacket dynamics requires first order NACsSemiclassical wavepacket dynamics

An Ehrenfest dynamics simulationPotential energy surfacedistance from the surface excitationdecaySi-H Si-H *SiH

()8-layer slab(2x2) unit cellDeviates from BOs*-electrons-holeY. Miyamoto and OS (1999)

How to compute NACTDDFT linear response theoryTo be presented by C. Hu, FADFT Symposium

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

NAC of H3 near the conical intersection123zxO

Full Quantum SimulationTo be presented by H. Hirai, FADFT Symposium

SummaryChemical reaction (phase transition, atomic diffusion)Free-energy approach has become more and more accessibleDirect simulation is very importantNon-adiabatic dynamicsStill challenging but progress has been made for system with few degrees of freedom

High temperature, heavy element; practically the most important*