Theory of torsional non-Condon electron transfer: A generalized spin-boson Hamiltonian and its nonadiabatic limit solution

Use of QM/MM Surface Hopping Simulations to Understand Thermally Activated Rare-Event Nonadiabatic Transitions in the Condensed Phase

We implement a rare-event sampling scheme for quantifying the rate of thermally activated nonadiabatic transitions in the condensed phase. Our Quantum mechanics/molecular mechanics (QM/MM) methodology uses the recently developed Interface for NonAdiabatic QM/MM in Solvent (INAQS) package to interface an elementary electronic structure package and a popular open-source molecular dynamics software (GROMACS) to simulate an electron transfer event between two stationary ions in a solution of acetonitrile solvent molecules. Nonadiabatic effects are implemented through a surface hopping scheme, and our simulations allow further quantitative insight into the participation ratio of a solvent and the effect of ion separation distance as far as facilitating electron transfer. We also demonstrate that the standard gas-phase approaches for treating frustrated hops and velocity reversal must be refined when working in the condensed phase with many degrees of freedom. The code and methodology developed here can be easily expanded upon and modified to incorporate other systems and should provide a great deal of new insight into a wide variety of condensed phase nonadiabatic phenomena.

Modified Fermi's golden rule rate expressions

Fermi's golden rule (FGR) serves as the basis for many expressions of spectroscopic observables and quantum transition rates. The utility of FGR has been demonstrated through decades of experimental confirmation. However, there still remain important cases where the evaluation of a FGR rate is ambiguous or ill-defined. Examples are cases where the rate has divergent terms due to the sparsity in the density of final states or time dependent fluctuations of system Hamiltonians. Strictly speaking, assumptions of FGR are no longer valid for such cases. However, it is still possible to define modified FGR rate expressions that are useful as effective rates. The resulting modified FGR rate expressions resolve a long standing ambiguity often encountered in using FGR and offer more reliable ways to model general rate processes. Simple model calculations illustrate the utility and implications of new rate expressions.

Electron transfer and spin-orbit coupling: Can nuclear motion lead to spin selective rates?

We investigate a spin-boson inspired model of electron transfer, where the diabatic coupling is given by a position-dependent phase, e^iWx. We consider both equilibrium and nonequilibrium initial conditions. We show that, for this model, all equilibrium results are completely invariant to the sign of W (to infinite order). However, the nonequilibrium results do depend on the sign of W, suggesting that photo-induced electron transfer dynamics with spin-orbit coupling can exhibit electronic spin polarization (at least for some time).

Effects of Structural Dynamics on Charge Carrier Transfer in B-DNA: A Combined MD and RT-TDDFT Study

Hole transfer along the axis of duplex DNA has been the focus of physical chemistry research for decades, with implications in diverse fields, from nanotechnology to cell oxidative damage. Computational approaches are particularly amenable for this problem, to complement experimental data for interpretation of transfer mechanisms. To be predictive, computational results need to account for the inherent mobility of biological molecules during the time frame of experimental measurements. Here, we address the structural variability of B-DNA and its effects on hole transfer in a combined molecular dynamics (MD) and real-time time-dependent density functional theory (RT-TDDFT) study. Our results show that quantities that characterize the charge transfer process, such as the time-dependent dipole moment and hole population at a specific site, are sensitive to structural changes that occur on the nanosecond time scale. We extend the range of physical properties for which such a correlation has been observed, further establishing the fact that quantitative computational data on charge transfer properties should include statistical averages. Furthermore, we use the RT-TDDFT results to assess an efficient tight-binding method suitable for high-throughput predictions. We demonstrate that charge transfer, although affected by structural variability, on average, remains strong in AA and GG dimers.

Multifaceted aspects of charge transfer

Charge transfer and charge transport are by far among the most important processes for sustaining life on Earth and for making our modern ways of living possible. Involving multiple electron-transfer steps, photosynthesis and cellular respiration have been principally responsible for managing the energy flow in the biosphere of our planet since the Great Oxygen Event. It is impossible to imagine living organisms without charge transport mediated by ion channels, or electron and proton transfer mediated by redox enzymes. Concurrently, transfer and transport of electrons and holes drive the functionalities of electronic and photonic devices that are intricate for our lives. While fueling advances in engineering, charge-transfer science has established itself as an important independent field, originating from physical chemistry and chemical physics, focusing on paradigms from biology, and gaining momentum from solar-energy research. Here, we review the fundamental concepts of charge transfer, and outline its core role in a broad range of unrelated fields, such as medicine, environmental science, catalysis, electronics and photonics. The ubiquitous nature of dipoles, for example, sets demands on deepening the understanding of how localized electric fields affect charge transfer. Charge-transfer electrets, thus, prove important for advancing the field and for interfacing fundamental science with engineering. Synergy between the vastly different aspects of charge-transfer science sets the stage for the broad global impacts that the advances in this field have.

Multiscale modelling reveals higher charge transport efficiencies of DNA relative to RNA independent of mechanism

In this study, we compare the charge transport properties of multiple double-stranded (ds)RNA sequences with corresponding dsDNA sequences. Recent studies have presented a contradictory picture of relative charge transport efficiencies in A-form DNA : RNA hybrids and dsDNA. Using a multiscale modelling framework, we compute conductance of dsDNA and dsRNA using Landauer formalism in the coherent limit and Marcus-Hush theory in the incoherent limit. We find that dsDNA conducts better than dsRNA in both the charge transport regimes. Our analysis shows that the structural differences in the twist angle and slide of dsDNA and dsRNA are the main reasons behind the higher conductance of dsDNA in the incoherent hopping regime. In the coherent limit however, for the same base pair length, the conductance of dsRNA is higher than that of dsDNA for the morphologies where dsRNA has a smaller end-to-end length relative to that of dsDNA.

Chemical Reaction Rates for Systems with Spin-Orbit Coupling and an Odd Number of Electrons: Does Berry's Phase Lead to Meaningful Spin-Dependent Nuclear Dynamics for a Two State Crossing?

Within the context of a simple avoided crossing, we investigate the effect of a complex-valued diabatic coupling in determining spin-dependent rate constants and scattering states. We find that, if the molecular geometry is not linear and the Berry force is not zero, one can find significant spin polarization of the products. This study emphasizes that, when analyzing nonadiabatic reactions with spin orbit coupling (and a complex-valued Hamiltonian), one must consider how Berry force affects nuclear motion-at least in the context of gas phase reactions. Work is currently ongoing as far as extrapolating these conclusions to the condensed phase, where interesting spin selection has been observed in recent years.

Gating That Suppresses Charge Recombination-The Role of Mono-N-Arylated Diketopyrrolopyrrole

Suppressing the charge recombination (CR) that follows an efficient charge separation (CS) is of key importance for energy, electronics, and photonics applications. We focus on the role of dynamic gating for impeding CR in a molecular rotor, comprising an electron donor and acceptor directly linked via a single bond. The media viscosity has an unusual dual effect on the dynamics of CS and CR in this dyad. For solvents with intermediate viscosity, CR is 1.5-3 times slower than CS. Lowering the viscosity below ∼0.6 mPa s or increasing it above ∼10 mPa s makes CR 10-30 times slower than CS. Ring rotation around the donor-acceptor bond can account only for the trends observed for nonviscous solvents. Media viscosity, however, affects not only torsional but also vibrational modes. Suppressing predominantly slow vibrational modes by viscous solvents can impact the rates of CS and CR to a different extent. That is, an increase in the viscosity can plausibly suppress modes that are involved in the transition from the charge-transfer (CT) to the ground state, i.e., CR, but at the same time are not important for the transition from the locally excited to the CT state, i.e., CS. These results provide a unique example of synergy between torsional and vibronic modes and their drastic effects on charge-transfer dynamics, thus setting paradigms for controlling CS and CR.

Implausibility of the vibrational theory of olfaction

The vibrational theory of olfaction assumes that electron transfer occurs across odorants at the active sites of odorant receptors (ORs), serving as a sensitive measure of odorant vibrational frequencies, ultimately leading to olfactory perception. A previous study reported that human subjects differentiated hydrogen/deuterium isotopomers (isomers with isotopic atoms) of the musk compound cyclopentadecanone as evidence supporting the theory. Here, we find no evidence for such differentiation at the molecular level. In fact, we find that the human musk-recognizing receptor, OR5AN1, identified using a heterologous OR expression system and robustly responding to cyclopentadecanone and muscone, fails to distinguish isotopomers of these compounds in vitro. Furthermore, the mouse (methylthio)methanethiol-recognizing receptor, MOR244-3, as well as other selected human and mouse ORs, responded similarly to normal, deuterated, and (13)C isotopomers of their respective ligands, paralleling our results with the musk receptor OR5AN1. These findings suggest that the proposed vibration theory does not apply to the human musk receptor OR5AN1, mouse thiol receptor MOR244-3, or other ORs examined. Also, contrary to the vibration theory predictions, muscone-d30 lacks the 1,380- to 1,550-cm(-1) IR bands claimed to be essential for musk odor. Furthermore, our theoretical analysis shows that the proposed electron transfer mechanism of the vibrational frequencies of odorants could be easily suppressed by quantum effects of nonodorant molecular vibrational modes. These and other concerns about electron transfer at ORs, together with our extensive experimental data, argue against the plausibility of the vibration theory.

The requisite electronic structure theory to describe photoexcited nonadiabatic dynamics: nonadiabatic derivative couplings and diabatic electronic couplings

Electronically photoexcited dynamics are complicated because there are so many different relaxation pathways: fluorescence, phosphorescence, radiationless decay, electon transfer, etc. In practice, to model photoexcited systems is a very difficult enterprise, requiring accurate and very efficient tools in both electronic structure theory and nonadiabatic chemical dynamics. Moreover, these theoretical tools are not traditional tools. On the one hand, the electronic structure tools involve couplings between electonic states (rather than typical single state energies and gradients). On the other hand, the dynamics tools involve propagating nuclei on multiple potential energy surfaces (rather than the usual ground state dynamics). In this Account, we review recent developments in electronic structure theory as directly applicable for modeling photoexcited systems. In particular, we focus on how one may evaluate the couplings between two different electronic states. These couplings come in two flavors. If we order states energetically, the resulting adiabatic states are coupled via derivative couplings. Derivative couplings capture how electronic wave functions change as a function of nuclear geometry and can usually be calculated with straightforward tools from analytic gradient theory. One nuance arises, however, in the context of time-dependent density functional theory (TD-DFT): how do we evaluate derivative couplings between TD-DFT excited states (which are tricky, because no wave function is available)? This conundrum was recently solved, and we review the solution below. We also discuss the solution to a second, pesky problem of origin dependence, whereby the derivative couplings do not (strictly) satisfy translation variance, which can lead to a lack of momentum conservation. Apart from adiabatic states, if we order states according to their electronic character, the resulting diabatic states are coupled via electronic or diabatic couplings. The couplings between diabatic states |ΞA⟩ and |ΞB⟩ are just the simple matrix elements, ⟨ΞA|H|ΞB⟩. A difficulty arises, however, because constructing exactly diabatic states is formally impossible and constructing quasi-diabatic states is not unique. To that end, we review recent advances in localized diabatization, which is one approach for generating adiabatic-to-diabatic (ATD) transformations. We also highlight outstanding questions in the arena of diabatization, especially how to generate multiple globally stable diabatic surfaces.

Charge transfer in model peptides: obtaining Marcus parameters from molecular simulation

Charge transfer within and between biomolecules remains a highly active field of biophysics. Due to the complexities of real systems, model compounds are a useful alternative to study the mechanistic fundamentals of charge transfer. In recent years, such model experiments have been underpinned by molecular simulation methods as well. In this work, we study electron hole transfer in helical model peptides by means of molecular dynamics simulations. A theoretical framework to extract Marcus parameters of charge transfer from simulations is presented. We find that the peptides form stable helical structures with sequence dependent small deviations from ideal PPII helices. We identify direct exposure of charged side chains to solvent as a cause of high reorganization energies, significantly larger than typical for electron transfer in proteins. This, together with small direct couplings, makes long-range superexchange electron transport in this system very slow. In good agreement with experiment, direct transfer between the terminal amino acid side chains can be dicounted in favor of a two-step hopping process if appropriate bridging groups exist.

Fluctuations in biological and bioinspired electron-transfer reactions

Central to theories of electron transfer (ET) is the idea that nuclear motion generates a transition state that enables electron flow to proceed, but nuclear motion also induces fluctuations in the donor-acceptor (DA) electronic coupling that is the rate-limiting parameter for nonadiabatic ET. The interplay between the DA energy gap and DA coupling fluctuations is particularly noteworthy in biological ET, where flexible protein and mobile water bridges take center stage. Here, we discuss the critical timescales at play for ET reactions in fluctuating media, highlighting issues of the Condon approximation, average medium versus fluctuation-controlled electron tunneling, gated and solvent relaxation controlled electron transfer, and the influence of inelastic tunneling on electronic coupling pathway interferences. Taken together, one may use this framework to establish principles to describe how macromolecular structure and structural fluctuations influence ET reactions. This framework deepens our understanding of ET chemistry in fluctuating media. Moreover, it provides a unifying perspective for biophysical charge-transfer processes and helps to frame new questions associated with energy harvesting and transduction in fluctuating media.

Condensed-phase relaxation of multilevel quantum systems. I. An exactly solvable model

An analytically solvable model of multilevel condensed-phase quantum dynamics relevant to vibrational relaxation and electron transfer is presented. Exact solutions are derived for the reduced system density matrix dynamics of a degenerate N-level quantum system characterized by nearest-neighbor hopping and off-diagonal coupling (which is linear in the bath coordinates) to a harmonic oscillator bath. We demonstrate that for N> 2 the long-time steady-state system site occupation probabilities are not the same for all sites; that is, they are distributed in a non-Boltzmann manner, which depends on the initial conditions and the number of levels in the system. Although the system-bath Hamiltonian considered here is restricted in form, the availability of an exact solution enables us to study the model in all regions of an extensive parameter space.

Condensed-Phase Relaxation of Multilevel Quantum Systems. II. Comparison of Path Integral Calculations and Second-Order Relaxation Theory for a Nondegenerate Three-Level System

An exactly solvable model of multisite condensed-phase vibrational relaxation was studied in Paper I (Peter, S.; Evans, D. G.; Coalson, R. D. J. Phys. Chem. B 2006, 110, 18758.), where it was shown that long-time steady-state site populations of a degenerate N-level system are not equal (hence, they are non-Boltzmann) and depend on the initial preparation of the system and the number of sites that it comprises. Here we consider a generalization of the model to the case of a nondegenerate three-level system coupled to a high-dimensional bath: such a model system has direct relevance to a large class of donor-bridge-acceptor electron transfer processes. Because the quantum dynamics of this system cannot be computed analytically, we compare numerically exact path integral calculations to the predictions of second-order time-local relaxation theory. For modest system-bath coupling strengths, the two sets of results are in excellent agreement. They show that non-Boltzmann long-time steady-state site populations are obtained when the level splitting is small but nonzero, whereas at larger values of the system bias (asymmetry) these populations become Boltzmann distributed.

Three-centered model of ultrafast photoinduced charge transfer: Continuum dielectric approach

A theoretical description of photoinduced charge transfer involves explicit treating both the optical formation of the nuclear wave packet on the excited free energy surface and its ensuing dynamics. The reaction pathway constitutes two-stage charge transfer between three centers. Manifestations of fractional charge transfer at first stage are explored. An expression for time dependent rate constant of photoinduced charge transfer is found in the framework of the linear dielectric continuum model of the medium. The model involves both the intramolecular vibrational reorganization and the Coulombic interaction of the transferred charge with the medium polarization fluctuations and allows to express the rate in terms of intramolecular reorganization parameters and complex dielectric permittivity. The influence of the vibrational coherent motion in the locally excited state on the charge transfer dynamics has been explored. The dependence of the ultrafast photoinduced charge transfer dynamics on the excitation pulse carrier frequency (spectral effect) has been investigated. The spectral effect has been shown to depend on quantity of the fractional charge.