Combining the generalized quantum master equation approach with quasiclassical mapping Hamiltonian methods to simulate the dynamics of electronic coherences.

The generalized quantum master equation (GQME) approach provides a powerful general-purpose framework for simulating the inherently quantum mechanical dynamics of a subset of electronic reduced density matrix elements of interest in complex molecular systems. Previous studies have found that combining the GQME approach with quasiclassical mapping Hamiltonian (QC/MH) methods can dramatically improve the accuracy of electronic populations obtained via those methods. In this paper, we perform a complimentary study of the advantages offered by the GQME approach for simulating the dynamics of electronic coherences, which play a central role in optical spectroscopy, quantum information science, and quantum technology.

A Computational Study of the Electronic Energy and Charge Transfer Rates and Pathways in the Tetraphenyldibenzoperiflanthene/Fullerene Interfacial Dyad.

The electronic transition rates and pathways underlying interfacial charge separation in tetraphenyldibenzoperiflanthene:fullerene (DBP:C) blends are investigated computationally. The analysis is based on a polarization-consistent framework employing screened range-separated hybrid functional in a polarizable continuum model to parametrize Fermi's golden rule rate theory. The model considers the possible transitions within the 25 lowest excited states of a DBP:C dyad that are accessible by photoexcitation.

Cavity-modified Fermi's golden rule rate constants: Beyond the single mode approximation.

We extend our recently proposed theoretical framework for estimating cavity-modified equilibrium Fermi's golden rule (FGR) rate constants beyond the single cavity mode case to cases where the molecular system is coupled to multiple cavity modes. We show that the cumulative effect of simultaneous coupling to multiple modes can enhance FGR rate constants by orders of magnitude relative to the single mode case. We also present an analysis of the conditions necessary for maximizing this effect in the Marcus limit of FGR-based rate theory.

Mapping Molecular Hamiltonians into Hamiltonians of Modular cQED Processors.

We introduce a general method based on the operators of the Dyson-Masleev transformation to map the Hamiltonian of an arbitrary model system into the Hamiltonian of a circuit Quantum Electrodynamics (cQED) processor. Furthermore, we introduce a modular approach to programming a cQED processor with components corresponding to the mapping Hamiltonian. The method is illustrated as applied to quantum dynamics simulations of the Fenna-Matthews-Olson (FMO) complex and the spin-boson model of charge transfer.

Simulating Open Quantum System Dynamics on NISQ Computers with Generalized Quantum Master Equations.

We present a quantum algorithm based on the generalized quantum master equation (GQME) approach to simulate open quantum system dynamics on noisy intermediate-scale quantum (NISQ) computers. This approach overcomes the limitations of the Lindblad equation, which assumes weak system-bath coupling and Markovity, by providing a rigorous derivation of the equations of motion for any subset of elements of the reduced density matrix. The memory kernel resulting from the effect of the remaining degrees of freedom is used as input to calculate the corresponding non-unitary propagator.

Tensor-Train Thermo-Field Memory Kernels for Generalized Quantum Master Equations.

The generalized quantum master equation (GQME) approach provides a rigorous framework for deriving the exact equation of motion for any subset of electronic reduced density matrix elements (e.g., the diagonal elements).

Electronic absorption spectra from off-diagonal quantum master equations.

Quantum master equations (QMEs) provide a general framework for describing electronic dynamics within a complex molecular system. Off-diagonal QMEs (OD-QMEs) correspond to a family of QMEs that describe the electronic dynamics in the interaction picture based on treating the off-diagonal coupling terms between electronic states as a small perturbation within the framework of second-order perturbation theory. The fact that OD-QMEs are given in terms of the interaction picture makes it non-trivial to obtain Schrödinger picture electronic coherences from them.

An Accurate Linearized Semiclassical Approach for Calculating Cavity-Modified Charge Transfer Rate Constants.

We show that combining the linearized semiclasscial approximation with Fermi's golden rule (FGR) rate theory gives rise to a general-purpose cost-effective and scalable computational framework that can accurately capture the cavity-induced rate enhancement of charge transfer reactions that occurs when the molecular system is placed inside a microcavity. Both partial linearization with respect to the nuclear and photonic degrees of freedom and full linerization with respect to nuclear, photonic, and electronic degrees of freedom (the latter within the mapping Hamiltonian approach) are shown to be highly accurate, provided that the Wigner transforms of the product (WoP) of operators at the initial time is not replaced by the product of their Wigner transforms. We also show that the partial linearization method yields the quantum-mechanically exact cavity-modified FGR rate constant for a model system in which the donor and acceptor potential energy surfaces are harmonic and identical except for a shift in the equilibrium energy and geometry, if WoP is applied.

Simulating the dynamics of electronic observables via reduced-dimensionality generalized quantum master equations.

We describe a general-purpose framework for formulating the dynamics of any subset of electronic reduced density matrix elements in terms of a formally exact generalized quantum master equation (GQME). Within this framework, the effect of coupling to the nuclear degrees of freedom, as well as to any projected-out electronic reduced density matrix elements, is captured by a memory kernel and an inhomogeneous term, whose dimensionalities are dictated by the number of electronic reduced density matrix elements included in the subset of interest. We show that the memory kernel and inhomogeneous term within such GQMEs can be calculated from projection-free inputs of the same dimensionality, which can be cast in terms of the corresponding subsets of overall system two-time correlation functions.

Correlating Interfacial Charge Transfer Rates with Interfacial Molecular Structure in the Tetraphenyldibenzoperiflanthene/C Organic Photovoltaic System.

Organic photovoltaics (OPV) is an emerging solar cell technology that offers vast advantages such as low-cost manufacturing, transparency, and solution processability. However, because the performance of OPV devices is still disappointing compared to their inorganic counterparts, better understanding of how controlling the molecular-level morphology can impact performance is needed. To this end, one has to overcome significant challenges that stem from the complexity and heterogeneity of the underlying electronic structure and molecular morphology.

On simulating the dynamics of electronic populations and coherences via quantum master equations based on treating off-diagonal electronic coupling terms as a small perturbation.

Quantum master equations provide a general framework for describing the dynamics of electronic observables within a complex molecular system. One particular family of such equations is based on treating the off-diagonal coupling terms between electronic states as a small perturbation within the framework of second-order perturbation theory. In this paper, we show how different choices of projection operators, as well as whether one starts out with the time-convolution or the time-convolutionless forms of the generalized quantum master equation, give rise to four different types of such off-diagonal quantum master equations (OD-QMEs), namely, time-convolution and time-convolutionless versions of a Pauli-type OD-QME for only the electronic populations and an OD-QME for the full electronic density matrix (including both electronic populations and coherences).

A Road Map to Various Pathways for Calculating the Memory Kernel of the Generalized Quantum Master Equation.

The generalized quantum master equation (GQME) provides a powerful framework for simulating electronic energy, charge, and coherence transfer dynamics in molecular systems. Within this framework, the effect of the nuclear degrees of freedom on the time evolution of the electronic reduced density matrix is fully captured by a memory kernel superoperator. However, the actual memory kernel depends on the choice of projection operator and is therefore not unique.

Simulating energy transfer dynamics in the Fenna-Matthews-Olson complex via the modified generalized quantum master equation.

The generalized quantum master equation (GQME) provides a general and formally exact framework for simulating the reduced dynamics of open quantum systems. The recently introduced modified approach to the GQME (M-GQME) corresponds to a specific implementation of the GQME that is geared toward simulating the dynamics of the electronic reduced density matrix in systems governed by an excitonic Hamiltonian. Such a Hamiltonian, which is often used for describing energy and charge transfer dynamics in complex molecular systems, is given in terms of diabatic electronic states that are coupled to each other and correspond to different nuclear Hamiltonians.

Three-state harmonic models for photoinduced charge transfer.

A widely used strategy for simulating the charge transfer between donor and acceptor electronic states in an all-atom anharmonic condensed-phase system is based on invoking linear response theory to describe the system in terms of an effective spin-boson model Hamiltonian. Extending this strategy to photoinduced charge transfer processes requires also taking into consideration the ground electronic state in addition to the excited donor and acceptor electronic states. In this paper, we revisit the problem of describing such nonequilibrium processes in terms of an effective three-state harmonic model.

CTRAMER: An open-source software package for correlating interfacial charge transfer rate constants with donor/acceptor geometries in organic photovoltaic materials.

In this paper, we present CTRAMER (Charge-Transfer RAtes from Molecular dynamics, Electronic structure, and Rate theory)-an open-source software package for calculating interfacial charge-transfer (CT) rate constants in organic photovoltaic (OPV) materials based on ab initio calculations and molecular dynamics simulations. The software is based on identifying representative donor/acceptor geometries within interfacial structures obtained from molecular dynamics simulation of donor/acceptor blends and calculating the corresponding Fermi's golden rule CT rate constants within the framework of the linearized-semiclassical approximation. While the methods used are well established, the integration of these state-of-the-art tools originating from different disciplines to study photoinduced CT processes with explicit treatment of the environment, in our opinion, makes this package unique and innovative.

Benchmarking Quasiclassical Mapping Hamiltonian Methods for Simulating Cavity-Modified Molecular Dynamics.

Recent experimental realizations of strong coupling between optical cavity modes and molecular matter placed inside the cavity have opened exciting new routes for controlling chemical processes. Simulating the cavity-modified dynamics of complex chemical systems calls for the development of accurate, flexible, and cost-effective approximate numerical methods that scale favorably with system size and complexity. In this Letter, we test the ability of quasiclassical mapping Hamiltonian methods to serve this purpose.

Improving the Accuracy of Quasiclassical Mapping Hamiltonian Methods by Treating the Window Function Width as an Adjustable Parameter.

Mapping Hamiltonian methods for simulating electronically nonadiabatic molecular dynamics are based on representing the electronic population and coherence operators in terms of isomorphic mapping operators, which are given in terms of the auxiliary position and momentum operators. Adding a quasiclassical approximation then makes it possible to treat those auxiliary coordinates and momenta, as well as the nuclear coordinates and momenta, as classical-like phase-space variables. Within such quasiclassical mapping Hamiltonian methods, the initial sampling of the auxiliary coordinates and momenta and the calculation of expectation values of electronic observables at a later time are based on window functions whose functional form differ from one method to another.

Photoinduced Charge Transfer Dynamics in the Carotenoid-Porphyrin-C Triad via the Linearized Semiclassical Nonequilibrium Fermi's Golden Rule.

The nonequilibrium Fermi's golden rule (NE-FGR) describes the time-dependent rate coefficient for electronic transitions when the nuclear degrees of freedom start out in a nonequilibrium state. In this paper, the linearized semiclassical (LSC) approximation of the NE-FGR is used to calculate the photoinduced charge transfer (CT) rates in the carotenoid-porphyrin-C molecular triad dissolved in explicit tetrahydrofuran. The initial nonequilibrium state corresponds to impulsive photoexcitation from the equilibrated ground state to the ππ* state, and the porphyrin-to-C and carotenoid-to-C CT rates are calculated.

On the Interplay between Electronic Structure and Polarizable Force Fields When Calculating Solution-Phase Charge-Transfer Rates.

We present a comprehensive analysis of the interplay between the choice of an electronic structure method and the effect of using polarizable force fields vs. nonpolarizable force fields when calculating solution-phase charge-transfer (CT) rates. The analysis is based on an integrative approach that combines inputs from electronic structure calculations and molecular dynamics simulations and is performed in the context of the carotenoid-porphyrin-C molecular triad dissolved in an explicit tetrahydrofuran (THF) liquid solvent.

Simulating Absorption Spectra of Multiexcitonic Systems via Quasiclassical Mapping Hamiltonian Methods.

In this paper, we compare the ability of different quasiclassical mapping Hamiltonian methods to accurately simulate the absorption spectra of multiexcitonic molecular systems. Two distinctly different approaches for simulating the absorption spectra are considered: (1) a perturbative approach, which relies on the first-order perturbation theory with respect to the field-matter interaction; (2) a nonperturbative approach, which mimics the experimental measurement of the absorption spectra from the free-induction decay that follows a short laser pulse. The methods compared are several variations of the linearized semiclassical (LSC) method, the symmetrical quasiclassical (SQC) method, and the mean-field (Ehrenfest) method.

A Nonperturbative Methodology for Simulating Multidimensional Spectra of Multiexcitonic Molecular Systems via Quasiclassical Mapping Hamiltonian Methods.

We present a new methodology for simulating multidimensional electronic spectra of complex multiexcitonic molecular systems within the framework of quasiclassical mapping Hamiltonian (QC/MH) methods. The methodology is meant to be cost-effective for molecular systems with a large number of nuclear degrees of freedom undergoing nonequilibrium nonadiabatic dynamics on multiple coupled anharmonic electronic potential energy surfaces, for which quantum-mechanically exact methods are not feasible. The methodology is based on a nonperturbative approach to field-matter interaction, which mimics the experimental measurement of those nonlinear time-resolved spectra via phase cycling and can accommodate laser pulses of arbitrary shape and intensity.