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We discuss the general features of the time-evolving reduced density matrix (RDM) of multistate systems coupled to dissipative environments and show that many important aspects of the dynamics are visualized effectively and transparently through coherence maps, defined as snapshots of the real and imaginary components of the RDM on the square grid of system sites. In particular, the spread, signs, and shapes of the coherence maps collectively characterize the state of the system and the nature of the dynamics, as well as the equilibrium state. The topology of the system is readily reflected in its coherence map. Rows and columns show the composition of quantum superpositions, and their filling indicates the extent of the surviving coherence. Linear combinations of imaginary RDM elements specify instantaneous population derivatives. The main diagonal comprises the incoherent component of the dynamics, while the upper/lower triangular areas give rise to coherent contributions that increase the purity of the RDM. In open systems, the coherence map evolves to a band surrounding the principal diagonal whose width decreases with increasing temperature and dissipation strength. We illustrate these behaviors with examples of 10-site model molecular aggregates with Frenkel exciton couplings, where the electronic states of each monomer are coupled to harmonic vibrational baths.

The efficient, directional transfer of absorbed solar energy between photosynthetic light-harvesting complexes continues to pose intriguing questions. In this work, we identify the pathways of energy flow between the B800 and B850 rings in the LH2 complex of Rhodopseudomonas molischianum using fully quantum mechanical path integral methods to simulate the excited-state dynamics of the 24 bacteriochlorophyll molecules and their coupling to 50 normal mode vibrations in each chromophore. While all pigments are identical, the tighter packing of the inner B850 ring is responsible for the thermodynamic stabilization of the inner ring. Molecular vibrations enable the 1-ps flow of energy to the B850 states, which would otherwise be kinetically inaccessible. A classical treatment of the vibrations leads to uniform equilibrium distribution of the excitation, with only 67% transferred to the inner ring. However, spontaneous fluctuations associated with the quantum motion of the nuclei increase the transfer efficiency to 90%.

For a multistate system coupled to a general environment through terms local in the system basis, we show that the time derivatives of populations are given in terms of imaginary components of coherences, i.e., off-diagonal elements of the reduced density matrix. When the process exhibits rate dynamics, we show that all state-to-state rates can be obtained from the early "plateau" values of these imaginary components. The evolution of the state populations is then obtained from the short-time simulation results and the solution of the kinetic equations with the computed rate matrix. These expressions generalize the reactive flux method and its nonequilibrium version to multistate processes and show that even in the completely incoherent limit of rate kinetics, the time evolution of populations is governed by coherences. Further, we show that by virtue of detailed balance, the short-time values of the imaginary components of coherences fully determine the equilibrium populations.

We report fully quantum mechanical simulations of excitation energy transfer within the peripheral light harvesting complex (LH2) of Rhodopseudomonas molischianum at room temperature. The exciton–vibration Hamiltonian comprises the 16 singly excited bacteriochlorophyll states of the B850 (inner) ring and the 8 states of the B800 (outer) ring with all available electronic couplings. The electronic states of each chromophore couple to 50 intramolecular vibrational modes with spectroscopically determined Huang–Rhys factors and to a weakly dissipative bath that models the biomolecular environment. Simulations of the excitation energy transfer following photoexcitation of various electronic eigenstates are performed using the numerically exact small matrix decomposition of the quasiadiabatic propagator path integral. We find that the energy relaxation process in the 24-state system is highly nontrivial. When the photoexcited state comprises primarily B800 pigments, a rapid intra-band redistribution of the energy sharply transitions to a significantly slower relaxation component that transfers 90% of the excitation energy to the B850 ring. The mixed character B850* state lacks the slow component and equilibrates very rapidly, providing an alternative energy transfer channel. This (and also another partially mixed) state has an anomalously large equilibrium population, suggesting a shift to lower energy by virtue of exciton–vibration coupling. The spread of the vibrationally dressed states is smaller than that of the eigenstates of the bare electronic Hamiltonian. The total population of the B800 band is found to decay exponentially with a 1/ e time of 0.5 ps, which is in good agreement with experimental results.

In aqueous solution, 2-(4-fluorophenylamino)-5-(2,4-dihydroxybenzeno)-1,3,4-thiadiazole (FABT) was found to emit dual emission and the longer wavelength emission was assigned to the combination of aggregation and conformational change. In a number of molecules that possess an intramolecular hydrogen bond between the proton donor and the acceptor, the longer wavelength emission is often observed due to the emission from the tautomer formed by excited state intramolecular proton transfer (ESIPT). Therefore, an analogue of FABT, 2-phenylamino-5-(2-hydroxybenzono)-1,3,4-thiadiazole (PHBT), was synthesized to determine the origin of the longer wavelength emission. The luminescence of PHBT and its methoxy derivatives was studied and compared with that of FABT. Theoretical calculations were also performed on both FABT and PHBT. Based on the experimental and theoretical investigations, the nonexistence of the keto tautomer in the ground state and the origin of the longer wavelength emission are divulged.

The modular path integral methodology is used to extend the well-known spin-boson dynamics to finite-length quantum Ising chains, where each spin is coupled to a dissipative harmonic bath. The chain is initially prepared in the ferromagnetic phase where all spins are aligned, and the magnetization is calculated with spin-spin coupling parameters corresponding to the paramagnetic phase, mimicking a quantum quench experiment. The observed dynamics is found to depend significantly on the location of the tagged spin. In the absence of a dissipative bath, the time evolution displays irregular patterns that arise from multiple frequencies associated with the eigenvalues of the chain Hamiltonian. Coupling of each spin to a harmonic bath leads to smoother dynamics, with damping effects that are stronger compared to those observed in the spin-boson model and more prominent in interior spins, a consequence of additional damping from the spin environment. Interior spins exhibit a transition from underdamped oscillatory to overdamped monotonic dynamics as the temperature, spin-bath, or spin-spin coupling is increased. In addition to these behaviors, a new dynamical pattern emerges in the evolution of edge spins with strong spin-spin coupling at low and intermediate temperatures, where the magnetization oscillates either above or below the equilibrium value.

In aqueous solution, 2-(4-fluorophenylamino)-5-(2,4-dihydroxybenzeno)-1,3,4-thiadiazole (FABT) was found to emit dual emission and the longer wavelength emission was assigned to the combination of aggregation and conformational change. In a number of molecules that possess an intramolecular hydrogen bond between the proton donor and the acceptor, the longer wavelength emission is often observed due to the emission from the tautomer formed by excited state intramolecular proton transfer (ESIPT). Therefore, an analogue of FABT, 2-phenylamino-5-(2-hydroxybenzono)-1,3,4-thiadiazole (PHBT), was synthesized to determine the origin of the longer wavelength emission. The luminescence of PHBT and its methoxy derivatives was studied and compared with that of FABT. Theoretical calculations were also performed on both FABT and PHBT. Based on the experimental and theoretical investigations, the nonexistence of the keto tautomer in the ground state and the origin of the longer wavelength emission are divulged.