Applicability of the Caldeira-Leggett Model to Vibrational Spectroscopy in Solution

PyCTRAMER: A Python package for charge transfer rate constant of condensed-phase systems from Marcus theory to Fermi's golden rule

In this work, we introduce PyCTRAMER, a comprehensive Python package designed for calculating charge transfer (CT) rate constants in disordered condensed-phase systems at finite temperatures, such as organic photovoltaic (OPV) materials. PyCTRAMER is a restructured and enriched version of the CTRAMER (Charge-Transfer RAtes from Molecular dynamics, Electronic structure, and Rate theory) package [Tinnin et al. J. Chem. Phys. 154, 214108 (2021)], enabling the computation of the Marcus CT rate constant and the six levels of the linearized semiclassical approximations of Fermi's golden rule (FGR) rate constant. It supports various types of intramolecular and intermolecular CT transitions from the excitonic states to CT state. Integrating quantum chemistry calculations, all-atom molecular dynamics (MD) simulations, spin-boson model construction, and rate constant calculations, PyCTRAMER offers an automatic workflow for handling photoinduced CT processes in explicit solvent environments and interfacial CT in amorphous donor/acceptor blends. The package also provides versatile tools for individual workflow steps, including electronic state analysis, state-specific force field construction, MD simulations, and spin-boson model construction from energy trajectories. We demonstrate the software's capabilities through two examples, highlighting both intramolecular and intermolecular CT processes in prototypical OPV systems.

How proton transfer impacts hachimoji DNA

Hachimoji DNA is a synthetic nucleic acid extension of DNA, formed by an additional four bases, Z, P, S, and B, that can encode information and sustain Darwinian evolution. In this paper, we aim to look into the properties of hachimoji DNA and investigate the probability of proton transfer between the bases, resulting in base mismatch under replication. First, we present a proton transfer mechanism for hachimoji DNA, analogous to the one presented by Löwdin years prior. Then, we use density functional theory to calculate proton transfer rates, tunnelling factors and the kinetic isotope effect in hachimoji DNA. We determined that the reaction barriers are sufficiently low that proton transfer is likely to occur even at biological temperatures. Furthermore, the rates of proton transfer of hachimoji DNA are much faster than in Watson-Crick DNA due to the barrier for Z-P and S-B being 30% lower than in G-C and A-T. Suggesting that proton transfer occurs more frequently in hachimoji DNA than canonical DNA, potentially leading to a higher mutation rate.

Discretized hierarchical equations of motion in mixed Liouville-Wigner space for two-dimensional vibrational spectroscopies of liquid water

A model of a bulk water system describing the vibrational motion of intramolecular and intermolecular modes is constructed, enabling analysis of its linear and nonlinear vibrational spectra as well as the energy transfer processes between the vibrational modes. The model is described as a system of four interacting anharmonic oscillators nonlinearly coupled to their respective heat baths. To perform a rigorous numerical investigation of the non-Markovian and nonperturbative quantum dissipative dynamics of the model, we derive discretized hierarchical equations of motion in mixed Liouville-Wigner space, with Lagrange-Hermite mesh discretization being employed in the Liouville space of the intramolecular modes and Lagrange-Hermite mesh discretization and Hermite discretization in the Wigner space of the intermolecular modes. One-dimensional infrared and Raman spectra and two-dimensional terahertz-infrared-visible and infrared-infrared-Raman spectra are computed as demonstrations of the quantum dissipative description provided by our model.

Quantum Tunnelling Effects in the Guanine-Thymine Wobble Misincorporation via Tautomerism

The misincorporation of a noncomplementary DNA base in the polymerase active site is a critical source of replication errors that can lead to genetic mutations. In this work, we model the mechanism of wobble mispairing and the subsequent rate of misincorporation errors by coupling first-principles quantum chemistry calculations to an open quantum systems master equation. This methodology allows us to accurately calculate the proton transfer between bases, allowing the misincorporation and formation of mutagenic tautomeric forms of DNA bases. Our calculated rates of genetic error formation are in excellent agreement with experimental observations in DNA. Furthermore, our quantum mechanics/molecular mechanics model predicts the existence of a short-lived "tunnelling-ready" configuration along the wobble reaction pathway in the polymerase active site, dramatically increasing the rate of proton transfer by a hundredfold, demonstrating that quantum tunnelling plays a critical role in determining the transcription error frequency of the polymerase.

Generalized Langevin equation with a nonlinear potential of mean force and nonlinear memory friction from a hybrid projection scheme

We introduce a hybrid projection scheme that combines linear Mori projection and conditional Zwanzig projection techniques and use it to derive a generalized Langevin equation (GLE) for a general interacting many-body system. The resulting GLE includes (i) explicitly the potential of mean force (PMF) that describes the equilibrium distribution of the system in the chosen space of reaction coordinates, (ii) a random force term that explicitly depends on the initial state of the system, and (iii) a memory friction contribution that splits into two parts: a part that is linear in the past reaction-coordinate velocity and a part that is in general nonlinear in the past reaction coordinates but does not depend on velocities. Our hybrid scheme thus combines all desirable properties of the Zwanzig and Mori projection schemes. The nonlinear memory friction contribution is shown to be related to correlations between the reaction-coordinate velocity and the random force. We present a numerical method to compute all parameters of our GLE, in particular the nonlinear memory friction function and the random force distribution, from a trajectory in reaction coordinate space. We apply our method on the dihedral-angle dynamics of a butane molecule in water obtained from atomistic molecular dynamics simulations. For this example, we demonstrate that nonlinear memory friction is present and that the random force exhibits significant non-Gaussian corrections. We also present the derivation of the GLE for multidimensional reaction coordinates that are general functions of all positions in the phase-space of the underlying many-body system; this corresponds to a systematic coarse-graining procedure that preserves not only the correct equilibrium behavior but also the correct dynamics of the coarse-grained system.

Time-Dependent Friction Effects on Vibrational Infrared Frequencies and Line Shapes of Liquid Water

From ab initio simulations of liquid water, the time-dependent friction functions and time-averaged nonlinear effective bond potentials for the OH stretch and HOH bend vibrations are extracted. The obtained friction exhibits not only adiabatic contributions at and below the vibrational time scales but also much slower nonadiabatic contributions, reflecting homogeneous and inhomogeneous line broadening mechanisms, respectively. Intermolecular interactions in liquid water soften both stretch and bend potentials compared to the gas phase, which by itself would lead to a red-shift of the corresponding vibrational bands. In contrast, nonadiabatic friction contributions cause a spectral blue shift. For the stretch mode, the potential effect dominates, and thus, a significant red shift when going from gas to the liquid phase results. For the bend mode, potential and nonadiabatic friction effects are of comparable magnitude, so that a slight blue shift results, in agreement with well-known but puzzling experimental findings. The observed line broadening is shown to be roughly equally caused by adiabatic and nonadiabatic friction contributions for both the stretch and bend modes in liquid water. Thus, the quantitative analysis of the time-dependent friction that acts on vibrational modes in liquids advances the understanding of infrared vibrational frequencies and line shapes.

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). The fact that those OD-QMEs are given in terms of the interaction picture makes it non-trivial to obtain Schrödinger picture electronic coherences from them. To address this, we also extend a procedure for extracting Schrödinger 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 Schrödinger picture coherences can be obtained from interaction picture electronic inputs.

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. 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.

Caldeira-Leggett model vs ab initio potential: A vibrational spectroscopy test of water solvation

We present a semiclassically approximate quantum treatment of solvation with the purpose of investigating the accuracy of the Caldeira-Leggett model. We do that by simulating the vibrational features of water solvation by means of two different approaches. One is entirely based on the adoption of an accurate ab initio potential to describe water clusters of increasing dimensionality. The other one consists of a model made of a central water molecule coupled to a high-dimensional Caldeira-Leggett harmonic bath. We demonstrate the role of quantum effects in the detection of water solvation and show that the computationally cheap approach based on the Caldeira-Leggett bath is only partially effective. The main conclusion of the study is that quantum methods associated with high-level potential energy surfaces are necessary to correctly study solvation features, while simplified models, even if attractive owing to their reduced computational cost, can provide some useful insights but are not able to come up with a comprehensive description of the solvation phenomenon.

Quantifying Early Time Quantum Decoherence Dynamics through Fluctuations

We introduce a general but simple relation between the timescale for quantum coherence loss and the initial fluctuations of operators that couple a quantum system with a surrounding bath. The relation allows the prediction and measurement of early time decoherence dynamics for any open quantum system, through purity, without reconstructing the system's many-body density matrix. It is applied to predict the decoherence time for basic models-the Holstein chain, spin-boson and Caldeira-Legget models-commonly employed to capture electronic, vibrational, and vibronic dynamics in molecules. Such development also offers a practical platform to test the ability of approximate quantum dynamics methods to capture decoherence. In particular, a class of mixed quantum-classical schemes for molecular dynamics where the bath is treated classically, such as Ehrenfest dynamics, are shown to correctly capture short-time decoherence when the initial conditions are sampled from the Wigner distribution. These advances provide a useful platform to develop decoherence times for molecular processes and to test approximate molecular dynamics methods.

Vibrational spectroscopy via the Caldeira-Leggett model with anharmonic system potentials

The Caldeira-Leggett (CL) model, which describes a system bi-linearly coupled to a harmonic bath, has enjoyed popularity in condensed phase spectroscopy owing to its utmost simplicity. However, the applicability of the model to cases with anharmonic system potentials, as it is required for the description of realistic systems in solution, is questionable due to the presence of the invertibility problem [F. Gottwald et al., J. Phys. Chem. Lett. 6, 2722 (2015)] unless the system itself resembles the CL model form. This might well be the case at surfaces or in the solid regime, which we here confirm for a particular example of an iodine molecule in the atomic argon environment under high pressure. For this purpose we extend the recently proposed Fourier method for parameterizing linear generalized Langevin dynamics [F. Gottwald et al., J. Chem. Phys. 142, 244110 (2015)] to the non-linear case based on the CL model and perform an extensive error analysis. In order to judge on the applicability of this model in advance, we give practical empirical criteria and discuss the effect of the potential renormalization term. The obtained results provide evidence that the CL model can be used for describing a potentially broad class of systems.

Exact vs. asymptotic spectral densities in the Garg-Onuchic-Ambegaokar charge transfer model and its effect on Fermi's golden rule rate constants

The Garg-Onuchic-Ambegaokar model [J. Chem. Phys. 83, 4491 (1985)] has been used extensively for benchmarking methods aimed at calculating charge transfer rates. Within this model, the donor and acceptor diabats are described as shifted parabolas along a single primary mode, which is bilinearly coupled to a harmonic bath consisting of secondary modes, characterized by an Ohmic spectral density with exponential cutoff. Rate calculations for this model are often performed in the normal mode representation, with the corresponding effective spectral density given by an asymptotic expression derived at the limit where the Ohmic bath cutoff frequency is much larger than the primary mode frequency. We compare Fermi's golden rule rate constants obtained with the asymptotic and exact effective spectral densities. We find significant deviations between rate constants obtained from the asymptotic spectral density and those obtained from the exact one in the deep inverted region. Within the range of primary mode frequencies commonly employed, we find that the discrepancies increase with decreasing temperature and with decreasing primary mode frequency.

Nonadiabatic Dynamics in Atomistic Environments: Harnessing Quantum-Classical Theory with Generalized Quantum Master Equations

The development of methods that can efficiently and accurately treat nonadiabatic dynamics in quantum systems coupled to arbitrary atomistic environments remains a significant challenge in problems ranging from exciton transport in photovoltaic materials to electron and proton transfer in catalysis. Here we show that our recently introduced MF-GQME approach, which combines Ehrenfest mean field theory with the generalized quantum master equation framework, is able to yield quantitative accuracy over a wide range of charge-transfer regimes in fully atomistic environments. This is accompanied by computational speed-ups of up to 3 orders of magnitude over a direct application of Ehrenfest theory. This development offers the opportunity to efficiently investigate the atomistic details of nonadiabatic quantum relaxation processes in regimes where obtaining accurate results has previously been elusive.