title: A perturbative formalism for electronic transitions through conical intersections in a fully quadratic vibronic model.
abstract: We consider a fully quadratic vibronic model Hamiltonian for studying photoinduced electronic transitions through conical intersections. Using a second order perturbative approximation for diabatic couplings, we derive an analytical expression for the time evolution of electronic populations at a given temperature. This formalism extends upon a previously developed perturbative technique for a linear vibronic coupling Hamiltonian. The advantage of the quadratic model Hamiltonian is that it allows one to use separate quadratic representations for potential energy surfaces of different electronic states and a more flexible representation of interstate couplings. We explore features introduced by the quadratic Hamiltonian in a series of 2D models, and then apply our formalism to the 2,6-bis(methylene) adamantyl cation and its dimethyl derivative. The Hamiltonian parameters for the molecular systems have been obtained from electronic structure calculations followed by a diabatization procedure. The evolution of electronic populations in the molecular systems using the perturbative formalism shows a good agreement with that from variational quantum dynamics.
authors: Department of Physical and Environmental Sciences, University of Toronto Scarborough, Toronto, Ontario M1C 1A4, Canada.
authors: Julia S
authors: JS
authors: Endicott
authors: Department of Physical and Environmental Sciences, University of Toronto Scarborough, Toronto, Ontario M1C 1A4, Canada.
authors: Loïc
authors: L
authors: Joubert-Doriol
authors: Department of Physical and Environmental Sciences, University of Toronto Scarborough, Toronto, Ontario M1C 1A4, Canada.
authors: Artur F
authors: AF
authors: Izmaylov
mesh_terms: D020029:Base Pairing; D001554:Benzene / Q000737:chemistry; D004247:DNA / Q000737:chemistry; D019281:Dimerization; D004583:Electrons; D006219:Halogens / Q000737:chemistry; D008958:Models, Molecular; D011789:Quantum Theory; D055672:Static Electricity; D013816:Thermodynamics; D014867:Water / Q000737:chemistry
chemical_list: D006219:Halogens; D014867:Water; D004247:DNA; D001554:Benzene