Search

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.

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. A key experimental quantity that relies on the ability to obtain accurate Schrödinger picture electronic coherences is the absorption spectrum. In this paper, we propose using a recently introduced procedure for extracting Schrödinger picture electronic coherences from interaction picture inputs to calculate electronic absorption spectra from the electronic dynamics generated by OD-QMEs. The accuracy of the absorption spectra obtained this way is studied in the context of a biexciton benchmark model, by comparing spectra calculated based on time-local and time-nonlocal OD-QMEs to spectra calculated based on a Redfield-type QME and the non-perturbative and quantum-mechanically exact hierarchical equations of motion method.

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. Furthermore, calculating the memory kernel can be done in multiple ways that use different forms of projection-free inputs. Although the electronic dynamics is invariant to those choices when quantum-mechanically exact projection-free inputs are used, this is not the case when they are obtained via more feasible semiclassical or mixed quantum-classical approximate methods. Furthermore, the accuracy and numerical stability of the resulting electronic dynamics has been observed to be sensitive to the above-mentioned choices when approximate methods are used to calculate the projection-free inputs. In this article, we provide a systematic road map to 30 possible pathways for calculating the memory kernel and highlight how they are related as well as the ways in which they differ. We also compare the performance of different pathways in the context of the spin-boson benchmark model, with the projection-free inputs obtained via a mapping Hamiltonian linearized semiclassical method. In this case, we find that expressing the memory kernel with an exponential operator where the projection operator precedes the Liouvillian yields the most accurate and most numerically stable results.

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). In the context of electronic dynamics, the memory kernel and inhomogeneous term of the GQME introduce the implicit coupling to nuclear motion or dynamics of electronic density matrix elements that are projected out (e.g., the off-diagonal elements), allowing for efficient quantum dynamics simulations. Here, we focus on benchmark quantum simulations of electronic dynamics in a spin-boson model system described by various types of GQMEs. Exact memory kernels and inhomogeneous terms are obtained from short-time quantum-mechanically exact tensor-train thermo-field dynamics (TT-TFD) simulations. The TT-TFD memory kernels provide insights on the main sources of inaccuracies of GQME approaches when combined with approximate input methods and pave the road for development of quantum circuits that could implement GQMEs on digital quantum computers.

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. However, different methods also differ with respect to the way in which they treat the window width. More specifically, while the window width is treated as an adjustable parameter within the symmetrical quasiclassical (SQC) method, this has not been the case for methods based on the linearized semiclasscial (LSC) approximation. In the present study, we investigate the effect that turning the window width into an adjustable parameter within LSC-based methods has on their accuracy compared to SQC. The analysis is performed in the context of the spin-boson and Fenna-Matthews-Olson (FMO) complex benchmark models. We find that treating the window width in LSC-based methods as an adjustable parameter can make their accuracy comparable to that of the SQC method.

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-C60 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-C60 and carotenoid-to-C60 CT rates are calculated. Our results show that accounting for the nonequilibrium nature of the initial state significantly enhances the transition rate of the porphyrin-to-C60 CT process. We also derive the instantaneous Marcus theory (IMT) from LSC NE-FGR, which casts the CT rate coefficients in terms of a Marcus-like expression, with explicitly time-dependent reorganization energy and reaction free energy. IMT is found to reproduce the CT rates in the system under consideration remarkably well.

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

Quasi-classical mapping Hamiltonian methods have recently emerged as a promising approach for simulating electronically nonadiabatic molecular dynamics. The classical-like dynamics of the overall system within these methods makes them computationally feasible, and they can be derived based on well-defined semiclassical approximations. However, the existence of a variety of different quasi-classical mapping Hamiltonian methods necessitates a systematic comparison of their respective advantages and limitations. Such a benchmark comparison is presented in this paper. The approaches compared include the Ehrenfest method, the symmetrical quasi-classical (SQC) method, and five variations of the linearized semiclassical (LSC) method, three of which employ a modified identity operator. The comparison is based on a number of popular nonadiabatic model systems; the spin-boson model, a Frenkel biexciton model, and Tully’s scattering models 1 and 2. The relative accuracy of the different methods is tested by comparing with quantum-mechanically exact results for the dynamics of the electronic populations and coherences. We find that LSC with the modified identity operator typically performs better than the Ehrenfest and standard LSC approaches. In comparison to SQC, these modified methods appear to be slightly more accurate for condensed phase problems, but for scattering models there is little distinction between them., Journal of Chemical Theory and Computation, 16 (5), ISSN:1549-9618, ISSN:1549-9626

The special pair, a bacteriochlorophyll a (BChl) dimer found at the core of bacterial reaction centers, is known to play a key role in the functionality of photosystems as a precursor to the photosynthesis process. In this paper, we analyze the inherent affinity of the special pair to rectify the intrapair photo-induced charge transfer (CT). In particular, we show that the molecular environment affects the nuclear geometry, resulting in symmetry breaking between the two possible intrapair CT processes. To this end, we study the relationships of the intrapair CT and the molecular geometry with respect to the effective dielectric constant provided by the molecular environment. We identify the special pair structural feature that breaks the symmetry between the two molecules, leading to CT rectification. Excited state energies, oscillator strengths, and electronic coupling values are obtained via time-dependent density functional theory, employing a recently developed framework based on a screened range-separated hybrid functional within a polarizable continuum model (SRSH-PCM). We analyze the rectification capability of the special pair by calculating the CT rates using a first-principles-based Fermi's golden rule approach.

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). The fact that those OD-QMEs are given in terms of the interaction picture makes it non-trivial to obtain Schrodinger picture electronic coherences from them. To address this, we also extend a procedure for extracting Schrodinger picture electronic coherences from interaction picture populations recently introduced by Trushechkin in the context of time-convolutionless Pauli-type OD-QME to the other three types of OD-QMEs. The performance of the aforementioned four types of OD-QMEs is explored in the context of the Garg–Onuchic–Ambegaokar benchmark model for charge transfer in the condensed phase across a relatively wide parameter range. The results show that time-convolution OD-QMEs can be significantly more accurate than their time-convolutionless counterparts, particularly in the case of Pauli-type OD-QMEs, and that rather accurate Schrodinger picture coherences can be obtained from interaction picture electronic inputs.

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. Within the M-GQME approach, the effect of the nuclear degrees of freedom on the time evolution of the electronic density matrix is fully captured by a memory kernel superoperator, which can be obtained from short-lived (compared to the time scale of energy/charge transfer) projection-free inputs. In this paper, we test the ability of the M-GQME to predict the energy transfer dynamics within a seven-state benchmark model of the Fenna–Matthews–Olson (FMO) complex, with the short-lived projection-free inputs obtained via the Ehrenfest method. The M-GQME with Ehrenfest-based inputs is shown to yield accurate results across a wide parameter range. It is also found to dramatically outperform the direct application of the Ehrenfest method and to provide better-behaved convergence with respect to memory time in comparison to an alternative implementation of the GQME approach previously applied to the same FMO model.

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. We do so within the framework of nonequilibrium Fermi’s golden rule (NE-FGR) in the context of photoinduced charge transfer in the carotenoid–porphyrin–C60 (CPC60) molecular triad dissolved in explicit tetrahydrofuran (THF). To this end, we consider different ways for obtaining a three-state harmonic model from the equilibrium autocorrelation functions of the donor–acceptor, donor–ground, and acceptor–ground energy gaps, as obtained from all-atom molecular dynamics simulations of the CPC60/THF system. The quantum-mechanically exact time-dependent NE-FGR rate coefficients for two different charge transfer processes in two different triad conformations are then calculated using the effective three-state model Hamiltonians as well as a hierarchy of more approximate expressions that lead to the instantaneous Marcus theory limit. Our results show that the photoinduced charge transfer in CPC60/THF can be described accurately by the effective harmonic three-state models and that nuclear quantum effects are small in this system.

Spectral peaks of the special pair (P) and adjacent pigments in the bacterial reaction center (BRC) are investigated computationally. We employ a novel framework based on a polarization-consistent treatment of the dielectric environment, combining the polarizable continuum model (PCM) with time-dependent screened range-separated hybrid (SRSH) density functional theory. Our calculations quantitatively reproduce recently measured spectral peak splits between P excitonic states and spectral asymmetries within the pairs of excited states of the adjacent bacteriochlorophyll a (BChl) and bacteriopheophytin a (BPhe) pigments. For the special pair, a splitting energy between the absorptive state and a blue-shifted semidark state of 0.07 eV is found in close agreement with the measured value. The spectral asymmetries within the pseudosymmetric pairs of BChl and BPhe pigments are interpreted to result from locally different effective dielectric environments in the A and the B branch, where the latter are exposed to a lesser polarizing environment. We base our analysis on X-ray-resolved structures and where the effect of neighboring pigments on the electronic structure is addressed through an effective dielectric environment. We show that the spectral trends are only reproduced using a polarization-consistent framework based on a screened range-separated hybrid functional, whereas B3LYP-PCM energies fail to provide the correct trends.

Bacteriochlorophyll a (Bchl a) and chlorophyll a (Chl a) play important roles as light absorbers in photosynthetic antennae and participate in the initial charge-separation steps in photosynthetic reaction centers. Despite decades of study, questions remain about the interplay of electronic and vibrational states within the Q-band and its effect on the photoexcited dynamics. Here we report results of polarized two-dimensional electronic spectroscopic measurements, performed on penta-coordinated Bchl a and Chl a and their interpretation based on state-of-the-art time-dependent density functional theory calculations and vibrational mode analysis for spectral shapes. We find that the Q-band of Bchl a is comprised of two independent bands, that are assigned following the Gouterman model to Qx and Qy states with orthogonal transition dipole moments. However, we measure the angle to be ∼75°, a finding that is confirmed by ab initio calculations. The internal conversion rate constant from Qx to Qy is found to be 11 ps−1. Unlike Bchl a, the Q-band of Chl a contains three distinct peaks with different polarizations. Ab initio calculations trace these features back to a spectral overlap between two electronic transitions and their vibrational replicas. The smaller energy gap and the mixing of vibronic states result in faster internal conversion rate constants of 38–50 ps−1. We analyze the spectra of penta-coordinated Bchl a and Chl a to highlight the interplay between low-lying vibronic states and their relationship to photoinduced relaxation. Our findings shed new light on the photoexcited dynamics in photosynthetic systems where these chromophores are primary pigments.

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. We simulated the spontaneous emission dynamics of an atom confined to a microcavity via five different variations of the linearized semiclassical (LSC) method. Our main finding is that recently proposed LSC-based methods which use a modified form of the identity operator are reasonably accurate and perform significantly better than the Ehrenfest and standard LSC methods, without significantly increasing computational costs. These methods are therefore highly promising as a general purpose tool for simulating cavity-modified dynamics of complex chemical systems.

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

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 letter, the linearized semiclassical (LSC) approximation of the NE-FGR is used to calculate the photoinduced charge transfer rates in the carotenoid-porphyrin-C60 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-C60 and the carotenoid-to-C60 charge transfer rates are calculated. Our results show that accounting for the nonequilibrium nature of the initial state significantly enhances the transition rate of the porphyrin-to-C60 CT process. We also derive the instantaneous Marcus theory (IMT) from LSC NE-FGR, which casts the CT rate coefficients in terms of a Marcus-like expression, with explicitly time-dependent reorganization energy and reaction free energy. IMT is found to reproduce the CT rates in the system under consideration remarkably well.

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. The comparison is performed in the context of a biexcitonic model and a seven-excitonic model of the Fenna-Matthews-Olson (FMO) complex. The accuracy of the various methods is tested by comparing their predictions to the quantum-mechanically exact results obtained via the hierarchy of the equations of motion (HEOM) method, as well as to the results based on the Redfield quantum master equation. The results show that the LSC-based quasiclassical mapping Hamiltonian methods can yield the accurate and robust absorption spectra in the high-temperature and/or slow-bath limit, where the nuclear degrees of freedom can be treated as classical.

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. The ability of different QC/MH methods to accurately simulate two-dimensional and pump-probe electronic spectra within the proposed methodology is compared in the context of a biexcitonic benchmark model that includes both the singly excited and doubly excited electronic states. The QC/MH methods compared include five variations of the linearized semiclassical (LSC) method and the mean-field (Ehrenfest) method. The results show that LSC-based methods are significantly more accurate than the mean-field method and can yield quantitatively accurate two-dimensional and pump-probe spectra when nuclear degrees of freedom can be treated as classical-like.

Charge transfer rate constants were calculated for the carotenoid-porphyrin-C

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 letter, the linearized semiclassical (LSC) approximation of the NE-FGR is used to calculate the photoinduced charge transfer rates in the carotenoid-porphyrin-C60 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-C60 and the carotenoid-to-C60 charge transfer rates are calculated. Our results show that accounting for the nonequilibrium nature of the initial state significantly enhances the transition rate of the porphyrin-to-C60 CT process. We also derive the instantaneous Marcus theory (IMT) from LSC NE-FGR, which casts the CT rate coefficients in terms of a Marcus-like expression, with explicitly time-dependent reorganization energy and reaction free energy. IMT is found to reproduce the CT rates in the system under consideration remarkably well.

The arrangement of organic molecules at the donor-acceptor interface in an organic photovoltaic (OPV) cell can have a strong effect on the generation of charge carriers and thereby cell performance. In this paper, we report the molecular-level exploration of the ensemble of interfacial donor-acceptor pair geometries and the charge-transfer (CT) rates to which they give rise. Our approach combines molecular-dynamics simulations, electronic structure calculations, machine learning, and rate theory. This approach is applied to the boron subphthalocyanine chloride (donor) and ${\mathrm{C}}_{60}$ (acceptor) OPV system. We find that the interface is dominated by a previously unreported donor-acceptor pair edge geometry, which contributes significantly to device performance in a manner that depends on the initial conditions. Quantitative relations between the morphology and CT rates are established, which can be used to advance the design of more efficient OPV devices.

In this work, we investigate the ability of different quasiclassical mapping Hamiltonian methods to simulate the dynamics of electronic transitions through conical intersections. The analysis is carried out within the framework of the linear vibronic coupling (LVC) model. The methods compared are the Ehrenfest method, the symmetrical quasiclassical method, and several variations of the linearized semiclassical (LSC) method, including ones that are based on the recently introduced modified representation of the identity operator. The accuracy of the various methods is tested by comparing their predictions to quantum-mechanically exact results obtained via the multiconfiguration time-dependent Hartree (MCTDH) method. The LVC model is found to be a nontrivial benchmark model that can differentiate between different approximate methods based on their accuracy better than previously used benchmark models. In the three systems studied, two of the LSC methods are found to provide the most accurate description of electronic transitions through conical intersections.

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. The applicability and feasibility of such reduced-dimensionality GQMEs is demonstrated on the two-state spin-boson benchmark model. To this end, we compare and contrast the following four types of GQMEs: (1) a full density matrix GQME, (2) a single-population scalar GQME, (3) a populations-only GQME, and (4) a subset GQME for any combination of populations and coherences. Using a method based on the mapping Hamiltonian approach and linearized semiclassical approximation to calculate the projection-free inputs, we find that while single-population GQMEs and subset GQMEs containing only one population are less accurate, they can still produce reasonable results and that the accuracy of the results obtained via the populations-only GQME and a subset GQME containing both populations is comparable to that obtained via the full density matrix GQMEs.

Efficient organic photovoltaics (OPVs) require broadband charge photogeneration with near-unity quantum yield. This can only be achieved by exploiting all pathways that generate charge. Electron transfer from organic donors to acceptors has been well-studied and is considered the primary path to charge photogeneration in OPVs. In contrast, much less is known about the hole transfer pathway. Here we study charge photogeneration in an archetypical system comprising tetraphenyldibenzoperiflanthene: C70 blends using our recently developed multispectral two dimensional electronic spectroscopy (M-2DES), supported by time-dependent density functional theory and fully quantum-mechanical Fermi’s golden rule rate calculations. Our approach identifies in real time two rapid charge transfer pathways that are confirmed through computational analysis. Surprisingly, we find that both electron and hole transfer occur with comparable rates and efficiencies, facilitated by donor-acceptor electronic interactions. Our results highlight the importance of the hole transfer pathway for optimizing the efficiency of OPV devices employing small-molecule heterojunctions.

We investigated the charge-transfer dynamics between distinctive excited states of a carotenoid–porphyrin–C60 molecular triad in tetrahydrofuran solvent. Our approach combines all-atom molecular dy...

The symmetrical quasi-classical (SQC) method recently proposed by Miller and Cotton allows one to simulate nonadiabatic dynamics based on an algorithm with classical-like scaling with respect to system size. This is made possible by casting the electronic degrees of freedom in terms of mapping variables that can be propagated in a classical-like manner. While SQC was shown to be rather accurate when applied to benchmark models with harmonic electronic potential energy surfaces, it was also found to become inaccurate and to suffer numerical instabilities when applied to anharmonic systems. In this paper, we propose an extended SQC (E-SQC) methodology for overcoming those discrepancies by describing the anharmonic nuclear modes, which are coupled to the electronic degrees of freedom, in terms of classical-like mapping variables. The accuracy of E-SQC relative to standard SQC is demonstrated on benchmark models with quartic and Morse potential energy surfaces.

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 ideas from different disciplines to study photoinduced CT between excited states and explicit environment, in our opinion, makes this package unique and innovative. The software also provides tools for plotting other observables of interest. After outlining the features and implementation details, usage and performance of the software are demonstrated with results from an example OPV system., The following article has been submitted to The Journal of Chemical Physics. After it is published, it will be found at XX

In this paper, we report on the implementation of a novel compute-to-learn pedagogy, which is based upon the theories of situated cognition and meaningful learning. The compute-to-learn pedagogy is designed to simulate an authentic research experience as part of the undergraduate curriculum, including project development, teamwork, peer review, and publication. The compute-to-learn pedagogy was piloted during the Fall 2015 semester within a one-semester, peer-led honors studio environment that uses active learning strategies to encourage cooperation and collaboration among students as they learn how to program. The rationale behind the pedagogy, lessons learned, and adjustments made based on three iterations of its execution, and its initial assessment through end-of-semester interviews are discussed.

Selective fluorination of organic semiconducting molecules is proposed as a means to achieving enhanced hole mobility. Naphthalene is examined here as a root molecular system with fluorination performed at various sites. Our quantum chemical calculations show that selective fluorination can enhance attractive intermolecular interactions while reducing charge trapping. Those observations suggest a design principle whereby fluorination is utilized for achieving high charge mobilities in the crystalline form. The utility of this design principle is demonstrated through an application to perylene, which is an important building block of organic semiconducting materials. We also show that a quantum mechanical perspective of nuclear degrees of freedom is crucial for a reliable description of charge transport.

Using polarized 2D spectroscopy and state-of-the-art TDDFT calculations to uncover the vibronic structure of primary photosynthetic pigments and its effect on ultrafast photoexcited dynamics., Bacteriochlorophyll a (Bchl a) and chlorophyll a (Chl a) play important roles as light absorbers in photosynthetic antennae and participate in the initial charge-separation steps in photosynthetic reaction centers. Despite decades of study, questions remain about the interplay of electronic and vibrational states within the Q-band and its effect on the photoexcited dynamics. Here we report results of polarized two-dimensional electronic spectroscopic measurements, performed on penta-coordinated Bchl a and Chl a and their interpretation based on state-of-the-art time-dependent density functional theory calculations and vibrational mode analysis for spectral shapes. We find that the Q-band of Bchl a is comprised of two independent bands, that are assigned following the Gouterman model to Qx and Qy states with orthogonal transition dipole moments. However, we measure the angle to be ∼75°, a finding that is confirmed by ab initio calculations. The internal conversion rate constant from Qx to Qy is found to be 11 ps–1. Unlike Bchl a, the Q-band of Chl a contains three distinct peaks with different polarizations. Ab initio calculations trace these features back to a spectral overlap between two electronic transitions and their vibrational replicas. The smaller energy gap and the mixing of vibronic states result in faster internal conversion rate constants of 38–50 ps–1. We analyze the spectra of penta-coordinated Bchl a and Chl a to highlight the interplay between low-lying vibronic states and their relationship to photoinduced relaxation. Our findings shed new light on the photoexcited dynamics in photosynthetic systems where these chromophores are primary pigments.

We present a modified approach for simulating electronically nonadiabatic dynamics based on the Nakajima-Zwanzig generalized quantum master equation (GQME). The modified approach utilizes the fact that the Nakajima-Zwanzig formalism does not require casting the overall Hamiltonian in system-bath form, which is arguably neither natural nor convenient in the case of the Hamiltonian that governs nonadiabatic dynamics. Within the modified approach, the effect of the nuclear degrees of freedom on the time evolution of the electronic reduced density operator is fully captured by a memory kernel super-operator. A methodology for calculating the memory kernel from projection-free inputs is developed. Simulating the electronic dynamics via the modified approach, with a memory kernel obtained using exact or approximate methods, can be more cost effective and/or lead to more accurate results than direct application of those methods. The modified approach is compared to previously proposed GQME-based approaches, and its robustness and accuracy are demonstrated on a benchmark spin-boson model with a memory kernel which is calculated within the Ehrenfest method.

Nonequilibrium Fermi's golden rule (NE-FGR) describes the transition between a photoexcited bright donor electronic state and a dark acceptor electronic state when the nuclear degrees of freedom start out in a nonequilibrium state. In this article, we derive a new expression for NE-FGR within the framework of the linearized semiclassical approximation. The new expression opens the door for applications of NE-FGR in complex condensed-phase molecular systems described in terms of anharmonic force fields. We show that the linearized semiclassical expression for NE-FGR yields the exact fully quantum-mechanical result for the canonical Marcus model, where the coupling between donor and acceptor is assumed constant (the Condon approximation) and the donor and acceptor potential energy surfaces are parabolic and identical except for a shift in the equilibrium energy and geometry. For this model, we also present a comprehensive comparison between the linearized semiclassical expression and a hierarchy of more approximate expressions, in both normal and inverted regions and over a wide range of initial nonequilibrium states, temperatures, and frictions.

Charge transfer rate constants were calculated for the carotenoid-porphyrin-C60 (CPC60) molecular triad dissolved in explicit tetrahydrofuran. The calculation was based on mapping the all-atom anharmonic Hamiltonian of this system onto the spin-boson Hamiltonian. The mapping was based on discretizing the spectral density from the time correlation function of the donor-acceptor potential energy gap, as obtained from all-atom molecular dynamics simulations. Different spin-boson Hamiltonians were constructed for each of the possible transitions between the three excited electronic states in two different triad conformations. The rate constants of three possible transitions were calculated via the quantum-mechanically exact Fermi's golden rule (FGR), as well as a progression of more approximate expressions that lead to the classical Marcus expression. The advantage of the spin-boson approach is that once the mapping is established, the quantum-mechanically exact FGR and the hierarchy of approximations are known in closed form. The classical Marcus charge transfer rate constants obtained with the spin-boson Hamiltonians were found to reproduce those obtained from all-atom simulations with the linearized semiclassical approximation, thereby confirming the equivalence of the two approaches for this system. Within the spin-boson Hamiltonian, we also found that the quantum-mechanically exact FGR rate constants were significantly enhanced compared to the classical Marcus theory rate constants for two out of three transitions in one of the two conformations under consideration. The results confirm that mapping to the spin-boson model can yield accurate predictions for charge transfer rate constants in a system as complex as CPC60 dissolved in tetrahydrofuran.

Range-separated hybrid (RSH) functionals have been shown to overcome the tendency of traditional density functional theory to underestimate the fundamental orbital gap. More recently, the screened RSH (SRSH) approach has been developed as a means to extend these functionals to address the effect of the electrostatic environment on the fundamental gap. Here, we report a scheme that combines the SRSH formulation with the polarized continuum model (PCM) within a consistent framework for addressing long-range screened electrostatic interactions, which is further improved by optimal tuning (OT). The quantitative predictive power of the new OT-SRSH-PCM scheme is demonstrated by addressing fundamental gaps in thin films of organic semiconducting materials. This is especially impressive as the approach is based on single molecule calculations. We also discuss the advantages of this approach over alternative schemes combining PCM with RSH. In particular, we show that it avoids the well-documented tendency of standard OT to collapse the range separation parameter when performed within a dielectric continuum.

In this article, we present a comprehensive comparison between the linearized semiclassical expression for the equilibrium Fermi's golden rule rate constant and the progression of more approximate expressions that lead to the classical Marcus expression. We do so within the context of the canonical Marcus model, where the donor and acceptor potential energy surface are parabolic and identical except for a shift in both the free energies and equilibrium geometries, and within the Condon region. The comparison is performed for two different spectral densities and over a wide range of frictions and temperatures, thereby providing a clear test for the validity, or lack thereof, of the more approximate expressions. We also comment on the computational cost and scaling associated with numerically calculating the linearized semiclassical expression for the rate constant and its dependence on the spectral density, temperature, and friction.

The dependence of charge-transfer states on interfacial geometry at the phthalocyanine/fullerene organic photovoltaic system is investigated. The effect of deviations from the equilibrium geometry of the donor-donor-acceptor trimer on the energies of and electronic coupling between different types of interfacial electronic excited states is calculated from first-principles. Deviations from the equilibrium geometry are found to destabilize the donor-to-donor charge transfer states and to weaken their coupling to the photoexcited donor-localized states, thereby reducing their ability to serve as charge traps. At the same time, we find that the energies of donor-to-acceptor charge transfer states and their coupling to the donor-localized photoexcited states are either less sensitive to the interfacial geometry or become more favorable due to modifications relative to the equilibrium geometry, thereby enhancing their ability to serve as gateway states for charge separation. Through these findings, we eludicate how interfacial geometry modifications can play a key role in achieving charge separation in this widely studied organic photovoltaic system.

Charge transfer (CT) states formed at the donor/acceptor heterointerface are key for photocurrent generation in organic photovoltaics (OPV). Our calculations show that interfacial donor-to-donor CT states in the phthalocyanine-fullerene OPV system may be more stable than donor-to-acceptor CT states and that they may rapidly recombine, thereby constituting a potentially critical and thus far overlooked loss mechanism. Our results provide new insight into processes that may compete with charge separation, and suggest that the efficiency for charge separation may be improved by destabilizing donor-to-donor CT states or decoupling them from other states.

Ionization potentials (IP) and electron affinities (EA) of organic molecules with applications in photovoltaic devices are calculated using modern density functional theory (DFT). Calculated frontier orbital energies are compared to experimentally determined IPs and EAs at gas phase and thin film environments. Gas phase frontier orbital energies calculated with widely-used DFT functionals accidentally coincide with thin film measurements, reproducing condensed phase results for the wrong reasons. Recently developed range separated hybrid (RSH) functionals, on the other hand, provide gas phase frontier orbital energies that correspond properly to measured IPs and EAs. We also employ a polarizable continuum model to address the effects of the electrostatic environment in the solid state. We find that the environmentally-corrected RSH orbital energies compare well with thin film experimental measurements.

In this Letter, we combine the recently introduced transfer tensor method with the mixed quantum-classical Liouville method. The resulting protocol provides an accurate, general, flexible and robust new route for simulating the reduced dynamics of the quantum subsystem for arbitrarily long times, starting with computationally feasible short-time mixed quantum-classical Liouville dynamical maps. The accuracy and feasibility of the methodology are demonstrated on a spin-boson benchmark model.

The generalized quantum master equation (GQME) provides a powerful framework for simulating electronically nonadiabatic molecular dynamics. 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. In this paper, we consider two different procedures for calculating the memory kernel of the GQME from projection-free inputs obtained via the combination of the mapping Hamiltonian (MH) approach and the linearized semiclassical (LSC) approximation. The accuracy and feasibility of the two procedures are demonstrated on the spin-boson model. We find that although simulating the electronic dynamics by direct application of the two LSC-based procedures leads to qualitatively different results that become increasingly less accurate with increasing time, restricting their use to calculating the memory kernel leads to an accurate description of the electronic dynamics. Comparison with a previously proposed procedure for calculating the memory kernel via the Ehrenfest method reveals that MH/LSC methods produce memory kernels that are better behaved at long times and lead to more accurate electronic dynamics.