Abstract
Nonadiabatic dynamics in the vicinity of conical intersections is of essential importance in photochemistry. It is well known that if the branching space is represented in polar coordinates, then for a geometry represented by angle θ, the corresponding adiabatic states are obtained from the diabatic states with the mixing angle θ/2. In an equivalent way, one can study the relation between the real rotation of diabatic states and the resulting nuclear gradient. In this work, we extend the concept to allow a complex rotation of diabatic states to form a nonstationary superposition of electronic states. Our main result is that this leads to an elliptical transformation of the effective potential energy surfaces; i.e., the magnitude of the initial nuclear gradient changes as well as its direction. We fully explore gradient changes that result from varying both θ and ϕ (the complex rotation angle) as a way of electronically controlling nuclear motion, through Ehrenfest dynamics simulations for benzene cation.
Highlights
Conical intersections are points of degeneracy between two electronic states which exist in molecules by nature[1−4] or can be induced by light.[5]
We have extended the idea of geometric rotation due to the real rotation of diabatic states and presented an analytical expression for the nuclear gradient of the energy of a complex superposition of two diabatic electronic states in the vicinity of a conical intersection
We have shown that the projection of this vector onto the real plane can be interpreted as the nuclear gradient in the branching space
Summary
Conical intersections are points of degeneracy between two (or more) electronic states which exist in molecules by nature[1−4] or can be induced by light.[5]. The adiabatic potential energy surfaces form a double cone with a vertex at the origin It is well-known that near a conical intersection the adiabatic states at a geometric polar angle of θ are constructed from the real rotation of two diabatic basis states with an angle θ/2.13−16. The fact that the nuclear gradient depends on the composition of the superposition could be used for coherent electronic control as θ and φ can both be changed experimentally in principle. We will demonstrate this idea with nonadiabatic dynamics simulations in benzene radical cation a typical example of a Jahn−Teller system.[17−20]. We will use the Ehrenfest method,[25] able to describe the coupled electron−nuclear dynamics of small organic molecules as previously exhibited.[12,26−28]
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
