Decoherence and Quantum Interference in a Four-Site Model System: Mechanisms and Turnovers

Seeking a quantum advantage with trapped-ion quantum simulations of condensed-phase chemical dynamics

Simulating the quantum dynamics of molecules in the condensed phase represents a longstanding challenge in chemistry. Trapped-ion quantum systems may serve as a platform for the analog-quantum simulation of chemical dynamics that is beyond the reach of current classical-digital simulation. To identify a 'quantum advantage' for these simulations, performance analysis of both analog-quantum simulation on noisy hardware and classical-digital algorithms is needed. In this Review, we make a comparison between a noisy analog trapped-ion simulator and a few choice classical-digital methods on simulating the dynamics of a model molecular Hamiltonian with linear vibronic coupling. We describe several simple Hamiltonians that are commonly used to model molecular systems, which can be simulated with existing or emerging trapped-ion hardware. These Hamiltonians may serve as stepping stones towards the use of trapped-ion simulators for systems beyond the reach of classical-digital methods. Finally, we identify dynamical regimes in which classical-digital simulations seem to have the weakest performance with respect to analog-quantum simulations. These regimes may provide the lowest hanging fruit to make the most of potential quantum advantages.

Multistate Energy Decomposition Analysis of Molecular Excited States

A multistate energy decomposition analysis (MS-EDA) method is described to dissect the energy components in molecular complexes in excited states. In MS-EDA, the total binding energy of an excimer or an exciplex is partitioned into a ground-state term, called local interaction energy, and excited-state contributions that include exciton excitation energy, superexchange stabilization, and orbital and configuration-state delocalization. An important feature of MS-EDA is that key intermediate states associated with different energy terms can be variationally optimized, providing quantitative insights into widely used physical concepts such as exciton delocalization and superexchange charge-transfer effects in excited states. By introducing structure-weighted adiabatic excitation energy as the minimum photoexcitation energy needed to produce an excited-state complex, the binding energy of an exciplex and excimer can be defined. On the basis of the nature of intermolecular forces through MS-EDA analysis, it was found that molecular complexes in the excited states can be classified into three main categories, including (1) encounter excited-state complex, (2) charge-transfer exciplex, and (3) intimate excimer or exciplex. The illustrative examples in this Perspective highlight the interplay of local excitation polarization, exciton resonance, and superexchange effects in molecular excited states. It is hoped that MS-EDA can be a useful tool for understanding photochemical and photobiological processes.

Excimer Energies

A multistate energy decomposition analysis (MS-EDA) method is introduced for excimers using density functional theory. Although EDA has been widely applied to intermolecular interactions in the ground state, few methods are currently available for excited-state complexes. Here, the total energy of an excimer state is separated into exciton excitation energy ΔE_Ex(|Ψ_X·Ψ_Y⟩*), resulting from the state interaction between locally excited monomer states |Ψ_X^*·Ψ_Y⟩ and |Ψ_X·Ψ_Y^*⟩ , a superexchange stabilization energy ΔE_SE, originating from the mutual charge transfer between two monomers |Ψ_X⁺·Ψ_Y⟩ and |Ψ_X^-·Ψ_Y⁺⟩ , and an orbital-and-configuration delocalization term ΔE_OCD due to the expansion of configuration space and block-localized orbitals to the fully delocalized dimer system. Although there is no net charge transfer in symmetric excimer cases, the resonance of charge-transfer states is critical to stabilizing the excimer. The monomer localized excited and charge-transfer states are variationally optimized, forming a minimal active space for nonorthogonal state interaction (NOSI) calculations in multistate density functional theory to yield the intermediate states for energy analysis. The present MS-EDA method focuses on properties unique to excited states, providing insights into exciton coupling, superexchange and delocalization energies. MS-EDA is illustrated on the acetone and pentacene excimer systems; three configurations of the latter case are examined, including the optimized excimer, a stacked configuration of two pentacene molecules and the fishbone orientation. It is found that excited-state energy splitting is strongly dependent on the relative energies of the monomer excited states and the phase-matching of the monomer wave functions.

Polariton-Mediated Electron Transfer via Cavity Quantum Electrodynamics

We investigate the polariton-mediated electron transfer reaction in a model system with analytic rate constant theory and direct quantum dynamical simulations. We demonstrate that the photoinduced charge transfer reaction between a bright donor state and dark acceptor state can be significantly enhanced or suppressed by coupling the molecular system to the quantized radiation field inside an optical cavity. This is because the quantum light-matter interaction can influence the effective driving force and electronic couplings between the donor state, which is the hybrid light-matter excitation, and the molecular acceptor state. Under the resonance condition between the photonic and electronic excitations, the effective driving force can be tuned by changing the light-matter coupling strength; for an off-resonant condition, the same effect can be accomplished by changing the molecule-cavity detuning. We further demonstrate that using both the electronic coupling and light-matter coupling helps to extend the effective couplings across the entire system, even for the dark state that carries a zero transition dipole. Theoretically, we find that both the counter-rotating terms and the dipole self-energy in the quantum electrodynamics Hamiltonian are important for obtaining an accurate polariton eigenspectrum as well as the polariton-mediated charge transfer rate constant, especially in the ultrastrong coupling regime.

Non-equilibrium relaxation of hot states in organic semiconductors: Impact of mode-selective excitation on charge transfer

The theoretical study of open quantum systems strongly coupled to a vibrational environment remains computationally challenging due to the strongly non-Markovian characteristics of the dynamics. We study this problem in the case of a molecular dimer of the organic semiconductor tetracene, the exciton states of which are strongly coupled to a few hundreds of molecular vibrations. To do so, we employ a previously developed tensor network approach, based on the formalism of matrix product states. By analyzing the entanglement structure of the system wavefunction, we can expand it in a tree tensor network state, which allows us to perform a fully quantum mechanical time evolution of the exciton-vibrational system, including the effect of 156 molecular vibrations. We simulate the dynamics of hot states, i.e., states resulting from excess energy photoexcitation, by constructing various initial bath states, and show that the exciton system indeed has a memory of those initial configurations. In particular, the specific pathway of vibrational relaxation is shown to strongly affect the quantum coherence between exciton states in time scales relevant for the ultrafast dynamics of application-relevant processes such as charge transfer. The preferential excitation of low-frequency modes leads to a limited number of relaxation pathways, thus "protecting" quantum coherence and leading to a significant increase in the charge transfer yield in the dimer structure.

Quantum coherence in ultrafast photo-driven charge separation

Coherent interactions are prevalent in photodriven processes, ranging from photosynthetic energy transfer to superexchange-mediated electron transfer, resulting in numerous studies aimed towards identifying and understanding these interactions. A key motivator of this interest is the non-statistical scaling laws that result from coherently traversing multiple pathways due to quantum interference. To that end, we employed ultrafast transient absorption spectroscopy to measure electron transfer in two donor-acceptor molecular systems comprising a p-(9-anthryl)-N,N-dimethylaniline chromophore/electron donor and either one or two equivalent naphthalene-1,8:4,5-bis(dicarboximide) electron acceptors at both ambient and cryogenic temperatures. The two-acceptor compound shows a statistical factor of 2.1 ± 0.2 rate enhancement at room temperature and a non-statistical factor of 2.6 ± 0.2 rate enhancement at cryogenic temperatures, suggesting correlated interactions between the two acceptors with the donor and with the bath modes. Comparing the charge recombination rates indicates that the electron is delocalized over both acceptors at low temperature but localized on a single acceptor at room temperature. These results highlight the importance of shielding the system from bath fluctuations to preserve and ultimately exploit the coherent interactions.

Redfield Treatment of Multipathway Electron Transfer in Artificial Photosynthetic Systems

Coherence effects on electron transfer in a series of symmetric and asymmetric two-, three-, four-, and five-site molecular model systems for photosystem I in cyanobacteria and green plants were studied. The total site energies of the electronic Hamiltonian were calculated using the density functional theory (DFT) formalism and included the zero point vibrational energies of the electron donors and acceptors. Site energies and couplings were calculated using a polarizable continuum model to represent various solvent environments, and the site-to-site couplings were calculated using fragment charge difference methods at the DFT level of theory. The Redfield formalism was used to propagate the electron density from the donors to the acceptors, incorporating relaxation and dephasing effects to describe the electron transfer processes. Changing the relative energies of the donor, intermediate acceptor, and final acceptor molecules in these assemblies has profound effects on the electron transfer rates as well as on the amplitude of the quantum oscillations observed. Increasing the ratio of a particular energy gap to the electronic coupling for a given pair of states leads to weaker quantum oscillations between sites. Biasing the intermediate acceptor energies to slightly favor one pathway leads to a general decrease in electron transfer yield.

Enhancing Singlet Fission Dynamics by Suppressing Destructive Interference between Charge-Transfer Pathways

We apply a real-time path-integral approach to investigate the charge-transfer (CT)-mediated singlet fission quantum dynamics in a model pentacene dimer. Our path-integral method gives reliable fission dynamics across various reaction regimes as well as a broad range of reorganization energies and temperatures. With this method, we investigated the destructive interference between the two CT-mediated fission pathways and discovered two mechanisms that can suppress this deleterious effect. First, increasing the energy gap between the two CT states effectively shuts down the high-lying CT pathway, leaving a better functioning low-lying CT pathway with a minimum amount of destructive interference. Second, intermolecular vibrations induce electronic coupling fluctuations, such that the destructive cancellations due to the different signs in static electronic couplings are suppressed. Our numerical results suggest that these two effects can enhance the fission rate up to three times. These findings reveal promising design principles for more efficient singlet fission materials.

Quantum dynamics of a hole migration through DNA: A single strand DNA model

A model predicting the behavior of a hole acting on the DNA strand was investigated. The hole-DNA interaction on the basis of a quantum-classical, non-linear DNA single strand model was described. The fact that a DNA molecule is formed by a furanose ring as its sugar, phosphate group and bases was taken into consideration. Based on the model, results were obtained for the probability of a hole location on the DNA base sequences, such as GTTGGG, GATGTGGG, GTTGTTGGG as well as on the sugar-phosphate groups mated with them.

Charge transport in molecular junctions: From tunneling to hopping with the probe technique

We demonstrate that a simple phenomenological approach can be used to simulate electronic conduction in molecular wires under thermal effects induced by the surrounding environment. This "Landauer-Büttiker's probe technique" can properly replicate different transport mechanisms, phase coherent nonresonant tunneling, ballistic behavior, and hopping conduction. Specifically, our simulations with the probe method recover the following central characteristics of charge transfer in molecular wires: (i) the electrical conductance of short wires falls off exponentially with molecular length, a manifestation of the tunneling (superexchange) mechanism. Hopping dynamics overtakes superexchange in long wires demonstrating an ohmic-like behavior. (ii) In off-resonance situations, weak dephasing effects facilitate charge transfer, but under large dephasing, the electrical conductance is suppressed. (iii) At high enough temperatures, kBT/ϵB > 1/25, with ϵB as the molecular-barrier height, the current is enhanced by a thermal activation (Arrhenius) factor. However, this enhancement takes place for both coherent and incoherent electrons and it does not readily indicate on the underlying mechanism. (iv) At finite-bias, dephasing effects may impede conduction in resonant situations. We further show that memory (non-Markovian) effects can be implemented within the Landauer-Büttiker's probe technique to model the interaction of electrons with a structured environment. Finally, we examine experimental results of electron transfer in conjugated molecular wires and show that our computational approach can reasonably reproduce reported values to provide mechanistic information.

Electronic coherence and the kinetics of inter-complex energy transfer in light-harvesting systems

Comparison of inter-complex excitation energy transfer rates obtained in a general system (original, red) and in an alternative parameterization of the system that preserves static coherence while eliminating dynamic coherence (SCP, black) reveals that static coherence largely governs the kinetics of incoherent inter-complex EET in model light-harvesting networks, whereas dynamic coherence plays only a minor role.

Interference and Molecular Transport-A Dynamical View: Time-Dependent Analysis of Disubstituted Benzenes

The primary issue in molecular electronics is measuring and understanding how electrons travel through a single molecule strung between two electrodes. A key area involves electronic interference that occurs when electrons can follow more than one pathway through the molecular entity. When the phases developed along parallel pathways are inequivalent, interference effects can substantially reduce overall conductance. This fundamentally interesting issue can be understood using classical rules of physical organic chemistry, and the subject has been examined broadly. However, there has been little dynamical study of such interference effects. Here, we use the simplest electronic structure model to examine the coherent time-dependent transport through meta- and para-linked benzene circuits, and the effects of decoherence. We find that the phase-caused coherence/decoherence behavior is established very quickly (femtoseconds), that the localized dephasing at any site reduces the destructive interference of the meta-linked species (raising the conductance), and that thermal effects are essentially ineffectual for removing coherence effects.

Single-molecule electronics: from chemical design to functional devices

The use of single molecules in electronics represents the next limit of miniaturisation of electronic devices, which would enable to continue the trend of aggressive downscaling of silicon-based electronic devices.

Microscopic theory of singlet exciton fission. II. Application to pentacene dimers and the role of superexchange

We apply our theoretical formalism for singlet exciton fission, introduced in the previous paper [T. C. Berkelbach, M. S. Hybertsen, and D. R. Reichman, J. Chem. Phys. 138, 114102 (2013)] to molecular dimers of pentacene, a widely studied material that exhibits singlet fission in the crystal phase. We address a longstanding theoretical issue, namely whether singlet fission proceeds via two sequential electron transfer steps mediated by charge-transfer states or via a direct two-electron transfer process. We find evidence for a superexchange mediated mechanism, whereby the fission process proceeds through virtual charge-transfer states which may be very high in energy. In particular, this mechanism predicts efficient singlet fission on the sub-picosecond timescale, in reasonable agreement with experiment. We investigate the role played by molecular vibrations in mediating relaxation and decoherence, finding that different physically reasonable forms for the bath relaxation function give similar results. We also examine the competing direct coupling mechanism and find it to yield fission rates slower in comparison with the superexchange mechanism for the dimer. We discuss implications for crystalline pentacene, including the limitations of the dimer model.

Study of DNA conducting properties: reversible and irreversible evolution

A hole transport through DNA base sequences was modeled. The fact that DNA consists of two polynucleotide strands was taken into consideration. Specific DNA base locations are determined in the model. The model predicts the behavior of a hole acting on the DNA chain, taking into account reversible and irreversible dynamics. It was shown that the transfer mechanisms depend on the sequence type and can be either of hopping nature or of superexchange one. Distance dependence of the hole transport relative rate on the number of hopping steps was investigated. The results obtained were compared with the experimental data. The investigation demonstrates the utilization of the formalism in practical problems for description of the charge migration through the different molecular sequences.