Effective modeling of open quantum systems by low-rank discretization of structured environments.

The accurate description of the interaction of a quantum system with its environment is a challenging problem ubiquitous across all areas of physics and lies at the foundation of quantum mechanics theory. Here, we pioneer a new strategy to create discrete low-rank models of the system-environment interaction, by exploiting the frequency and time domain information encoded in the fluctuation-dissipation relation connecting the system-bath correlation function and the spectral density. We demonstrate the effectiveness of our methodology by combining it with tensor-network methodologies and simulating the quantum dynamics of complex excitonic systems in a highly structured bosonic environment.

Interconnection between Polarization-Detected and Population-Detected Signals: Theoretical Results and Ab Initio Simulations.

Most of spectroscopic signals are specified by the nonlinear laser-induced polarization. In recent years, population-detection of signals becomes a trend in femtosecond spectroscopy. Polarization-detected (PD) and population-detected signals are fundamentally different, because they are determined by photoinduced processes acting on disparate time scales.

Tensor-Train Format Hierarchical Equations of Motion Formalism: Charge Transfer in Organic Semiconductors via Dissipative Holstein Models.

Hierarchical Equations of Motion (HEOM) in the Tensor-Train (TT) representation is applied to study the charge-transfer dynamics in organic semiconductors (OSCs). The theoretical formulation as well as the basic computational aspects of HEOM-TT are discussed in detail. Charge transfer in OSCs is modeled using dissipative polaronic models that incorporate the effects of both high- and low-frequency molecular vibrations, and it is simulated in a fully quantum and nonperturbative manner, which has not been studied intensively.

High accuracy exponential decomposition of bath correlation functions for arbitrary and structured spectral densities: Emerging methodologies and new approaches.

This study investigates the decomposition of bath correlation functions (BCFs) in terms of complex exponential functions, with an eye on the realistic modeling of open quantum systems based on the hierarchical equations of motion. We introduce the theoretical background of various decomposition schemes in both time and frequency domains and assess their efficiency and accuracy by demonstrating the decomposition of various BCFs. We further develop a new procedure for the decomposition of BCFs originating from highly structured spectral densities with a high accuracy and compare it with existing fitting techniques.

Finite temperature dynamics in a polarized sub-Ohmic heat bath: A hierarchical equations of motion-tensor train study.

The dynamics of the sub-Ohmic spin-boson model under polarized initial conditions at finite temperatures is investigated by employing both analytical tools and the numerically accurate hierarchical equations of motion-tensor train method. By analyzing the features of nonequilibrium dynamics, we discovered a bifurcation phenomenon, which separates two regimes of the dynamics. It is found that before the bifurcation time, increasing temperature slows down the population dynamics, while the opposite effect occurs after the bifurcation time.

Thermo-Field Dynamics Approach to Photo-induced Electronic Transitions Driven by Incoherent Thermal Radiation.

The effects of thermal light-matter interaction on the dynamics of photo-induced electronic transitions in molecules are investigated using a novel first principles approach based on the thermo-field dynamics description of both the molecular vibrational modes and of the radiation field. The developed approach permits numerically accurate simulations of quantum dynamics of electronic/excitonic systems coupled to nuclear and photonic baths kept at different temperatures. The baths can be described by arbitrary spectral densities and can have any system-bath coupling strengths.

Current-induced bond rupture in single-molecule junctions: Effects of multiple electronic states and vibrational modes.

Current-induced bond rupture is a fundamental process in nanoelectronic architectures, such as molecular junctions, and scanning tunneling microscopy measurements of molecules at surfaces. The understanding of the underlying mechanisms is important for the design of molecular junctions that are stable at higher bias voltages and is a prerequisite for further developments in the field of current-induced chemistry. In this work, we analyze the mechanisms of current-induced bond rupture employing a recently developed method, which combines the hierarchical equations of motion approach in twin space with the matrix product state formalism and allows accurate, fully quantum mechanical simulations of the complex bond rupture dynamics.

Hierarchical equations of motion approach to hybrid fermionic and bosonic environments: Matrix product state formulation in twin space.

We extend the twin-space formulation of the hierarchical equations of motion approach in combination with the matrix product state representation [R. Borrelli, J. Chem.

Efficient quantum dynamics simulations of complex molecular systems: A unified treatment of dynamic and static disorder.

We present a unified and highly numerically efficient formalism for the simulation of quantum dynamics of complex molecular systems, which takes into account both temperature effects and static disorder. The methodology is based on the thermo-field dynamics formalism, and Gaussian static disorder is included into simulations via auxiliary bosonic operators. This approach, combined with the tensor-train/matrix-product state representation of the thermalized stochastic wave function, is applied to study the effect of dynamic and static disorders in charge-transfer processes in model organic semiconductor chains employing the Su-Schrieffer-Heeger (Holstein-Peierls) model Hamiltonian.

Transparent and Colorless Dye-Sensitized Solar Cells Exceeding 75% Average Visible Transmittance.

Most photovoltaic (PV) technologies are opaque to maximize visible light absorption. However, see-through solar cells open additional perspectives for PV integration. Looking beyond maximizing visible light harvesting, this work considers the human eye photopic response to optimize a selective near-infrared sensitizer based on a polymethine cyanine structure (VG20-C ) to render dye-sensitized solar cells (DSSCs) fully transparent and colorless.

Simulation of Time- and Frequency-Resolved Four-Wave-Mixing Signals at Finite Temperatures: A Thermo-Field Dynamics Approach.

We propose a new approach to simulate four-wave-mixing signals of molecular systems at finite temperatures by combining the multiconfigurational Ehrenfest method with the thermo-field dynamics theory. In our approach, the four-time correlation functions at finite temperatures are mapped onto those at zero temperature in an enlarged Hilbert space with twice the vibrational degrees of freedom. As an illustration, we have simulated three multidimensional spectroscopic signals, time- and frequency-resolved fluorescence spectra, transient-absorption pump-probe spectra, and electronic two-dimensional (2D) spectra at finite temperatures, for a conical intersection-mediated singlet fission model of a rubrene crystal.

Simulation of Nonlinear Femtosecond Signals at Finite Temperature via a Thermo Field Dynamics-Tensor Train Method: General Theory and Application to Time- and Frequency-Resolved Fluorescence of the Fenna-Matthews-Olson Complex.

Addressing needs of contemporary nonlinear femtosecond optical spectroscopy, we have developed a fully quantum, numerically accurate wave function-based approach for the calculation of third-order spectroscopic signals of polyatomic molecules and molecular aggregates at finite temperature. The systems are described by multimode nonadiabatic vibronic-coupling Hamiltonians, in which diagonal terms are treated in harmonic approximation, while off-diagonal interstate couplings are assumed to be coordinate independent. The approach is based on the Thermo Field Dynamics (TFD) representation of quantum mechanics and tensor-train (TT) machinery for efficient numerical simulation of quantum evolution of systems with many degrees of freedom.

Expanding the Range of Hierarchical Equations of Motion by Tensor-Train Implementation.

The non-equilibrium thermo-field dynamics formulation of the hierarchical equations of motion combined with the tensor-train representation of the density matrix is discussed, and a new numerical integration scheme is introduced. The numerical methodology is based on an adaptive low-rank Galerkin reduction scheme and can preserve linear invariants (such as the trace of the density matrix). The method is applied to the study of the charge transfer dynamics in model pentacene molecular aggregates.

Hierarchical Equations-of-Motion Method for Momentum System-Bath Coupling.

For a broad class of quantum models of practical interest, we demonstrate that the Hamiltonian of the system nonlinearly coupled to a harmonic bath through the system and bath coordinates can be equivalently mapped into the Hamiltonian of the system bilinearly coupled to the bath through the system and bath momenta. We show that the Hamiltonian with bilinear system-bath momentum coupling can be treated by the hierarchical equations-of-motion (HEOM) method and present the corresponding proof-of-principle simulations. The developed methodology creates the opportunity to scrutinize a new family of nonlinear quantum systems by the numerically accurate HEOM method.

Probing photoinduced proton coupled electron transfer process by means of two-dimensional resonant electronic-vibrational spectroscopy.

We develop a detailed theoretical model of photo-induced proton-coupled electron transfer (PPCET) processes, which are at the basis of solar energy harvesting in biological systems and photovoltaic materials. Our model enables us to analyze the dynamics and the efficiency of a PPCET reaction under the influence of a thermal environment by disentangling the contribution of the fundamental electron transfer and proton transfer steps. In order to study quantum dynamics of the PPCET process under an interaction with the non-Markovian environment, we employ the hierarchical equations of motion.

Reliable Predictions of Benzophenone Singlet-Triplet Transition Rates: A Second-Order Cumulant Approach.

Fermi golden rule and second-order cumulant expansion of the time-dependent density matrix have been used to compute from first principles the rate of intersystem crossing in benzophenone, using minimum-energy geometries and normal modes of vibrations computed at the TDDFT/CAM-B3LYP level. Both approaches yield reliable values of the S decay rate, the latter being almost in quantitative agreement with the results of time-dependent spectroscopic measurements (0.154 ps observed vs 0.

Proton tunneling in a two-dimensional potential energy surface with a non-linear system-bath interaction: Thermal suppression of reaction rate.

We consider a proton transfer (PT) system described by a proton transfer reaction (PTR) coordinate and a rate promoting vibrational (RPV) coordinate interacting with a non-Markovian heat bath. While dynamics of PT processes has been widely discussed using two-dimensional potential energy surfaces, the role of the heat bath, in particular, in a realistic form of the system-bath interaction has not been well explored. Previous studies are largely based on a one-dimensional model and linear-linear system-bath interaction.

Tunable Redox Potential, Optical Properties, and Enhanced Stability of Modified Ferrocene-Based Complexes.

We report a series of ferrocene-based derivatives and their corresponding oxidized forms in which the introduction of simple electron donating groups like methyl or -butyl units on cyclopentadienyl-rings afford great tunability of Fe/Fe redox potentials from +0.403 V down to -0.096 V versus saturated calomel electrode.

Density matrix dynamics in twin-formulation: An efficient methodology based on tensor-train representation of reduced equations of motion.

The twin-formulation of quantum statistical mechanics is employed to describe a new methodology for the solution of the equations of motion of the reduced density matrix in their hierarchical formulation. It is shown that the introduction of tilde operators and of their algebra in the dual space greatly simplifies the application of numerical techniques for the propagation of the density matrix. The application of tensor-train representation of a vector to solve complex quantum dynamical problems within the framework of the twin-formulation is discussed.

Origin of Unexpectedly Simple Oscillatory Responses in the Excited-State Dynamics of Disordered Molecular Aggregates.

Unraveling the many facets of coherent and incoherent exciton motion in an ensemble of chromophores is an inherently complex quantum mechanical problem that has triggered a vivid debate on the role of quantum effects in molecular materials and biophysical systems. Here the dynamics of a statistical ensemble of molecular aggregates consisting of identical chromophores is investigated within a new theoretical framework. Taking account of intrinsic properties of the system, the Hamiltonian of the aggregate is partitioned into two mutually commuting vibrational and vibronic operators.

Transient and Enduring Electronic Resonances Drive Coherent Long Distance Charge Transport in Molecular Wires.

It is shown that the yields of oxidative damage observed in double-stranded DNA oligomers consisting of two guanines separated by adenine-thymine (A:T) bridges of various lengths are reliably accounted for by a multistep mechanism, in which transient and nontransient electronic resonances induce charge transport and solvent relaxation stabilizes the hole transfer products. The proposed multistep mechanism leads to results in excellent agreement with the observed yield ratios for both the short and the long distance regime; the almost distance independence of yield ratios for longer bridges ( n ≥ 3) is the consequence of the significant energy decrease of the electronic levels of the bridge, which, as the bridge length increases, become quasi-degenerate with those of the acceptor and donor groups (enduring resonance). These results provide significant guidelines for the design of novel DNA sequences to be employed in organic electronics.

Hole Hopping Rates in Organic Semiconductors: A Second-Order Cumulant Approach.

Second-order cumulant expansion of the time dependent reduced density matrix has been employed to evaluate hole hopping rates in pentacene, tetracene, picene, and rubrene homodimers. The cumulant expansion is a full quantum mechanical approach, which enables the use of the whole set of nuclear coordinates in computations and the inclusion of both the effects of the equilibrium position displacements and of normal mode mixing upon hole transfer. The time dependent populations predicted by cumulant approach are in good agreement with those obtained by numerical solution of time dependent Schrödinger equation, even for ultrafast processes, where the Fermi Golden Rule fails.

Dynamics of Coupled Electron-Boson Systems with the Multiple Davydov D Ansatz and the Generalized Coherent State.

The dynamics of a coupled electron-boson system is investigated by employing a multitude of the Davydov D trial states, also known as the multi-D Ansatz, and a second trial state based on a superposition of the time-dependent generalized coherent state (GCS Ansatz). The two Ansätze are applied to study population dynamics in the spin-boson model and the Holstein molecular crystal model, and a detailed comparison with numerically exact results obtained by the (multilayer) multiconfiguration time-dependent Hartree method and the hierarchy equations of motion approach is drawn. It is found that the two methodologies proposed here have significantly improved over that with the single D Ansatz, yielding quantitatively accurate results even in the critical cases of large energy biases and large transfer integrals.

Simulation of Quantum Dynamics of Excitonic Systems at Finite Temperature: an efficient method based on Thermo Field Dynamics.

Quantum electron-vibrational dynamics in molecular systems at finite temperature is described using an approach based on Thermo Field Dynamics theory. This formulation treats temperature effects in the Hilbert space without introducing the Liouville space. The solution of Thermo Field Dynamics equations with a novel technique for the propagation of Tensor Trains (Matrix Product States) is implemented and discussed.