A Vibronic Coupling Model to Study the Nonadiabatic Dynamics of Polyenes

TL;DR

This study builds a two-state linear vibronic coupling model for polyenes from an extended Hubbard-Peierls Hamiltonian and benchmarks four quantum-classical dynamics methods against fully quantum SILP for trans-hexatriene. The analysis shows that surface-hopping approaches capture ultrafast nonadiabatic dynamics better than multi-trajectory Ehrenfest but all fail to reproduce the long-time quantum oscillations seen in SILP, with surface hopping tending to overestimate internal conversion. A parameter-scan reveals consistent trends: increasing the energy gap reduces transfer, while stronger intra-state coupling or stiffer modes shift crossing points and modulate population outcomes; MTE can align with SILP in some parameter regimes, whereas INT-FSSH and MASH track trends more robustly but still miss oscillatory details. The framework provides a scalable route to study larger polyenes and carotenoids by combining DMRG-derived surfaces with LVC dynamics, and outlines future work to include more electronic states and torsional modes for lycopene and zeaxanthin and to validate reduced-dimensional models against full quantum results.

Abstract

We develop a linear vibronic coupling (LVC) model for polyenes described by the extended Hubbard-Peierls Hamiltonian. This model is applied to trans-hexatriene to benchmark quantum-classical dynamics methods against fully quantum simulations. We find that surface-hopping methods describe short times more accurately than multi-trajectory Ehrenfest. No quantum-classical method obtains the long-time population oscillations found in fully quantum simulations. Varying the parameters of the LVC Hamiltonian, surface hopping reproduces the correct trends in the long-time dynamics across a wide range of parameters, but generally overestimates the degree of internal conversion. On the other hand, multi-trajectory Ehrenfest gives more accurate long-time populations in proximity to the hexatriene parameter set.

Figures (6)

• Figure 1: A schematic diagram of the normal coordinates of the ground state of the extended Hubbard-Peierls Hamiltonian, ordered by increasing energy. Each circle represents a carbon atom of hexatriene. Symmetric ($A_g$) modes are red and anti-symmetric ($B_u$) modes are blue. The lowest-energy mode, $Q_0$, is translational, so it is excluded from the LVC model.
• Figure 2: The cut of the potential energy surfaces of the two lowest-lying excited states along the highest energy symmetric mode, $Q_5$. The surfaces are calculated for the extended Hubbard-Peierls Hamiltonian. At the Franck-Condon point, the $1B_u$ lies $0.3~\unit{\eV}$ below the $2A_g$. However, increasing $Q_5$ results in the relaxation of the $2A_g$ below the $1B_u$, with the $2A_g$ minimum at about $0.1~\unit{\angstrom}$. The fit could be improved by including state-specific force constants and higher-order terms. However, \ref{['fig:hex_2state_q_comparison']} shows that the poorly-fitted region is rarely entered during dynamics.
• Figure 3: $1B_u$ diabat population plotted against time for four different nonadiabatic dynamics methods. The three quantum-classical methods (MTE, INT-FSSH, MASH) fail to reproduce the quantum oscillations. MTE overestimates the centre of the SILP oscillations, whereas the surface hopping methods underestimate it. The surface hopping methods describe initial dynamics through the avoided crossing slightly more accurately (see inset).
• Figure 4: Adiabatic (dotted) and diabatic (solid) potential energies against time for the two-state hexatriene LVC Hamiltonian, calculated with the quantum phonon SILP method. The diabats cross between $2$ and $3~\unit{\fs}$, while the adiabats show an avoided crossing. This is due to a fast increase in displacement on the optical mode, $Q_5$. The oscillations have a period of about $8~\unit{\fs}$, which is half that of the optical mode.
• Figure 5: Average coordinate positions against time for the two-state LVC model. (a) The lowest energy mode $Q_1$ oscillates with a time period around $60~\unit{\fs}$. (b) The optical mode $Q_5$ relaxes to about $0.1~\unit{\angstrom}$, which is the minimum of the $2A_g$ potential energy surface. Its faster oscillations with a period of $16~\unit{\fs}$ are the result of its steeper potential energy surface.