Dynamical Simulations of Carotenoid Photoexcited States Using Density Matrix Renormalization Group Techniques.

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, H^UVP, to describe the π-electronic system coupled to nuclear degrees of freedom. This is supplemented by a Hamiltonian, H^ϵ, 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, H^=H^UVP+H^ϵ, and diabatic excited states as eigenstates of H^UVP, we present a computational framework to monitor the internal conversion process from the initial photoexcited 11Bu+ 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, H^ϵ, 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.

Photoexcited State Dynamics and Singlet Fission in Carotenoids.

We describe our simulations of the excited state dynamics of the carotenoid neurosporene, following its photoexcitation into the "bright" (nominally 11Bu+) state. To account for the experimental and theoretical uncertainty in the relative energetic ordering of the nominal 11Bu+ and 21Ag- states at the Franck-Condon point, we consider two parameter sets. In both cases, there is ultrafast internal conversion from the "bright" state to a "dark" singlet triplet-pair state, i.e., to one member of the "2Ag" family of states. For one parameter set, internal conversion from the 11Bu+ to 21Ag- states occurs via the dark, intermediate 11Bu- state. In this case, there is a cross over of the 11Bu+ and 11Bu- diabatic energies within 5 fs and an associated avoided crossing of the S2 and S3 adiabatic energies. After the adiabatic evolution of the S2 state from predominately 11Bu+ character to predominately 11Bu- character, there is a slower nonadiabatic transition from S2 to S1, accompanied by an increase in the population of the 21Ag- state. For the other parameter set, the 21Ag- energy lies higher than the 11Bu+ energy at the Franck-Condon point. In this case, there is cross over of the 21Ag- and 11Bu+ energies and an avoided crossing of the S1 and S2 energies, as the S1 state evolves adiabatically from being of 11Bu+ character to 21Ag- character. We make a direct connection from our predictions to experimental observables by calculating the time-resolved excited state absorption. For the case of direct 11Bu+ to 21Ag- internal conversion, we show that the dominant transition at ca. 2 eV, being close to but lower in energy than the T1 to T1* transition, can be attributed to the 21Ag- component of S1. Moreover, we show that it is the charge-transfer exciton component of the 21Ag- state that is responsible for this transition (to a higher-lying exciton state), and not its triplet-pair component. These simulations are performed using the adaptive tDMRG method on the extended Hubbard model of π-conjugated electrons. The Ehrenfest equations of motion are used to simulate the coupled nuclei dynamics. We next discuss the microscopic mechanism of "bright" to "dark" state internal conversion and emphasize that this occurs via the exciton components of both states. Finally, we describe a mechanism relying on torsional relaxation whereby the strongly bound intrachain triplet-pairs of the "dark" state may undergo interchain exothermic dissociation.

Mechanical Bond Enhanced Lithium Halide Ion-Pair Binding by Halogen Bonding Heteroditopic Rotaxanes.

A family of novel halogen bonding (XB) and hydrogen bonding (HB) heteroditopic [2]rotaxane host systems constructed by active metal template (AMT) methodology, were studied for their ability to cooperatively recognise lithium halide (LiX) ion-pairs. 1 H NMR ion-pair titration experiments in CD3 CN:CDCl3 solvent mixtures revealed a notable "switch-on" of halide anion binding in the presence of a co-bound lithium cation, with rotaxane hosts demonstrating selectivity for LiBr over LiI. The strength of halide binding was shown to greatly increase with increasing number of halogen bond donors integrated into the interlocked cavity, where an all-XB rotaxane was found to be the most potent host for LiBr. DFT calculations corroborated these findings, determining the mode of LiX ion-pair binding. Notably, ion-pair binding was not observed with the corresponding XB/HB macrocycles alone, highlighting the cooperative, heteroditopic, rotaxane axle-macrocycle component mechanical bond effect as an efficient strategy for ion-pair recognition in general.

Singlet Triplet-Pair Production and Possible Singlet-Fission in Carotenoids.

Internal conversion from the photoexcited state to a correlated singlet triplet-pair state is believed to be the precursor of singlet fission in carotenoids. We present numerical simulations of this process using a π-electron model that fully accounts for electron-electron interactions and electron-nuclear coupling. The time-evolution of the electrons is determined rigorously using the time-dependent density matrix renormalization group method, while the nuclei are evolved via the Ehrenfest equations of motion. We apply this to zeaxanthin, a carotenoid chain with 18 fully conjugated carbon atoms. We show that the internal conversion of the primary photoexcited state, S2, to the singlet triplet-pair state occurs adiabatically via an avoided crossing within ∼50 fs with a yield of ∼60%. We further discuss whether this singlet triplet-pair state will undergo exothermic versus endothermic intra- or interchain singlet fission.