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Quantum non-adiabatic dynamics with conical intersections: Model Hamiltonians and beyond

One of the prevalent non-adiabatic features responsible for radiationless electronic transitions in large molecules of biological and technological significance is conical intersection topology. Conical intersections give rise to irreducibly quantum behavior which makes it impossible to use well established molecular dynamics techniques based on the Born-Oppenheimer approximation. In this talk, I will discuss some of the recent efforts in building simple, non-empirical, and accurate rate theories for describing non-adiabatic dynamics involving conical intersections. Starting from the linear vibronic model Hamiltonian and treating linear diabatic couplings perturbatively we have developed a simple analytical expression for evolution of electronic populations at finite temperature. The derived expression can be seen as a nonequilibrium generalization of Fermi's Golden Rule, and it has become a cornerstone of further extensions beyond linear vibronic coupling model Hamiltonian within a framework of direct quantum dynamics with Gaussian wave-packets.