We
present a dynamical simulation scheme to model the
highly correlated
excited state dynamics of linear polyenes. We apply it to investigate
the internal conversion processes of carotenoids following their photoexcitation.
We use the extended Hubbard-Peierls model,
, to describe the π-electronic system
coupled to nuclear degrees of freedom. This is supplemented by a Hamiltonian,
, that explicitly breaks both the particle-hole
and two-fold rotation symmetries of idealized carotenoid structures.
The electronic degrees of freedom are treated quantum mechanically
by solving the time-dependent Schrödinger equation using the
adaptive time-dependent DMRG (tDMRG) method, while nuclear dynamics
are treated via the Ehrenfest equations of motion. By defining adiabatic
excited states as the eigenstates of the full Hamiltonian,
, and diabatic excited states as
eigenstates
of
, we present a computational framework to
monitor the internal conversion process from the initial photoexcited
1
1B
u
+ state to the singlet triplet-pair states of carotenoids. We further
incorporate Lanczos-DMRG to the tDMRG-Ehrenfest method to calculate
transient absorption spectra from the evolving photoexcited state.
We describe in detail the accuracy and convergence criteria for DMRG,
and show that this method accurately describes the dynamical processes
of carotenoid excited states. We also discuss the effect of the symmetry-breaking
term,
, on the internal conversion process, and
show that its effect on the extent of internal conversion can be described
by a Landau–Zener-type transition. This methodological paper
is a companion to our more explanatory discussion of carotenoid excited
state dynamics in Manawadu, D.; Georges, T. N.; Barford, W. Photoexcited
State Dynamics and Singlet Fission in Carotenoids.
J. Phys.
Chem. A
2023,
127, 1342.