Aqueous solvation dynamics with a quantum mechanical Solute: Computer simulation studies of the photoexcited hydrated electron

A size-consistent multi-state mapping approach to surface hopping

We develop a multi-state generalization of the recently proposed mapping approach to surface hopping (MASH) for the simulation of electronically nonadiabatic dynamics. This new approach extends the original MASH method to be able to treat systems with more than two electronic states. It differs from previous approaches in that it is size consistent and rigorously recovers the original two-state MASH in the appropriate limits. We demonstrate the accuracy of the method by applying it to a series of model systems for which exact benchmark results are available, and we find that the method is well suited to the simulation of photochemical relaxation processes.

Recovering Marcus Theory Rates and Beyond without the Need for Decoherence Corrections: The Mapping Approach to Surface Hopping

It is well-known that fewest-switches surface hopping (FSSH) fails to correctly capture the quadratic scaling of rate constants with diabatic coupling in the weak-coupling limit, as expected from Fermi's golden rule and Marcus theory. To address this deficiency, the most widely used approach is to introduce a "decoherence correction", which removes the inconsistency between the wave function coefficients and the active state. Here we investigate the behavior of a new nonadiabatic trajectory method, called the mapping approach to surface hopping (MASH), on systems that exhibit an incoherent rate behavior. Unlike FSSH, MASH hops between active surfaces deterministically and can never have an inconsistency between the wave function coefficients and the active state. We show that MASH not only can describe rates for intermediate and strong diabatic coupling but also can accurately reproduce the results of Marcus theory in the golden-rule limit, without the need for a decoherence correction. MASH is therefore a significant improvement over FSSH in the simulation of nonadiabatic reactions.

Empirically Optimized One-Electron Pseudopotential for the Hydrated Electron: A Proof-of-Concept Study

Mixed quantum-classical molecular dynamics simulations have been important tools for studying the hydrated electron. They generally use a one-electron pseudopotential to describe the interactions of an electron with the water molecules. This approximation shows both the strength and weakness of the approach. On the one hand, it enables extensive statistical sampling and large system sizes that are not possible with more accurate ab initio molecular dynamics methods. On the other hand, there has (justifiably) been much debate about the ability of pseudopotentials to accurately and quantitatively describe the hydrated electron properties. These pseudopotentials have largely been derived by fitting them to ab initio calculations of an electron interacting with a single water molecule. In this paper, we present a proof-of-concept demonstration of an alternative approach in which the pseudopotential parameters are determined by optimizing them to reproduce key experimental properties. Specifically, we develop a new pseudopotential, using the existing TBOpt model as a starting point, which correctly describes the hydrated electron vertical detachment energy and radius of gyration. In addition to these properties, this empirically optimized model displays a significantly modified solvation structure, which improves, for example, the prediction of the partial molar volume.

Nonadiabatic Dynamics in a Continuous Circularly Polarized Laser Field with Floquet Phase-Space Surface Hopping

Nonadiabatic chemical reactions involving continuous circularly polarized light (cw CPL) have not attracted as much attention as dynamics in unpolarized/linearly polarized light. However, including circularly (in contrast to linearly) polarized light allows one to effectively introduce a complex-valued time-dependent Hamiltonian, which offers a new path for control or exploration through the introduction of Berry forces. Here, we investigate several inexpensive semiclassical approaches for modeling such nonadiabatic dynamics in the presence of a time-dependent complex-valued Hamiltonian, beginning with a straightforward instantaneous adiabatic fewest-switches surface hopping (IA-FSSH) approach (where the electronic states depend on position and time), continuing to a standard Floquet fewest switches surface hopping (F-FSSH) approach (where the electronic states depend on position and frequency), and ending with an exotic Floquet phase-space surface hopping (F-PSSH) approach (where the electronic states depend on position, frequency, and momentum). Using a set of model systems with time-dependent complex-valued Hamiltonians, we show that the Floquet phase-space adiabats are the optimal choice of basis as far as accounting for Berry phase effects and delivering accuracy. Thus, the F-PSSH algorithm sets the stage for future modeling of nonadiabatic dynamics under strong externally pumped circular polarization.

Observation of a transient intermediate in the ultrafast relaxation dynamics of the excess electron in strong-field-ionized liquid water

A unified picture of the electronic relaxation dynamics of ionized liquid water has remained elusive despite decades of study. Here, we employ sub-two-cycle visible to short-wave infrared pump-probe spectroscopy and ab initio nonadiabatic molecular dynamics simulations to reveal that the excess electron injected into the conduction band (CB) of ionized liquid water undergoes sequential relaxation to the hydrated electron s ground state via an intermediate state, identified as the elusive p excited state. The measured CB and p-electron lifetimes are 0.26 ± 0.02 ps and 62 ± 10 fs, respectively. Ab initio quantum dynamics yield similar lifetimes and furthermore reveal vibrational modes that participate in the different stages of electronic relaxation, with initial relaxation within the dense CB manifold coupled to hindered translational motions whereas subsequent p-to-s relaxation facilitated by librational and even intramolecular bending modes of water. Finally, energetic considerations suggest that a hitherto unobserved trap state resides ~0.3-eV below the CB edge of liquid water. Our results provide a detailed atomistic picture of the electronic relaxation dynamics of ionized liquid water with unprecedented time resolution.

Incorporating Berry Force Effects into the Fewest Switches Surface-Hopping Algorithm: Intersystem Crossing and the Case of Electronic Degeneracy

We present a preliminary surface-hopping approach for modeling intersystem crossing (ISC) dynamics between four electronic states: one singlet and one (triply degenerate) triplet. In order to incorporate all Berry force effects, the algorithm requires that, when moving along an adiabatic surface associated with the triplet manifold, one must also keep track of a quasi-diabatic index (akin to a "m_s" quantum number) for each trajectory. For a simple model problem, we find that a great deal of new physics can be captured by our algorithm, setting the stage for larger, more realistic (or perhaps even ab initio) simulations in the future.

Flexible boundary layer using exchange for embedding theories. II. QM/MM dynamics of the hydrated electron

The FlexiBLE embedding method introduced in Paper I [Z. Shen and W. J. Glover, J. Chem. Phys. 155, 224112 (2021)] is applied to explore the structure and dynamics of the aqueous solvated electron at an all-electron density functional theory Quantum Mechanics/Molecular Mechanics level. Compared to a one-electron mixed quantum/classical description, we find the dynamics of the many-electron model of the hydrated electron exhibits enhanced coupling to water OH stretch modes. Natural bond orbital analysis reveals this coupling is due to significant population of water OH σ^* orbitals, reaching 20%. Based on this, we develop a minimal frontier orbital picture of the hydrated electron involving a cavity orbital and important coupling to 4-5 coordinating OH σ^* orbitals. Implications for the interpretation of the spectroscopy of this interesting species are discussed.

Direct coherent switching with decay of mixing for intersystem crossing dynamics of thioformaldehyde: The effect of decoherence

We evaluate the effect of electronic decoherence on intersystem crossing in the photodynamics of thioformaldehyde. First, we show that the state-averaged complete-active-space self-consistent field electronic structure calculations with a properly chosen active space of 12 active electrons in 10 active orbitals can predict the potential energy surfaces and the singlet-triplet spin-orbit couplings quite well for CH₂S, and we use this method for direct dynamics by coherent switching with decay of mixing (CSDM). We obtain similar dynamical results with CSDM or by adding energy-based decoherence to trajectory surface hopping, with the population of triplet states tending to a small steady-state value over 500 fs. Without decoherence, the state populations calculated by the conventional trajectory surface hopping method or the semiclassical Ehrenfest method gradually increase. This difference shows that decoherence changes the nature of the results not just quantitatively but qualitatively.

Time-Derivative Couplings for Self-Consistent Electronically Nonadiabatic Dynamics

Electronically nonadiabatic dynamics methods based on a self-consistent potential, such as semiclassical Ehrenfest and coherent switching with decay of mixing, have a number of advantages but are computationally slower than approximations based on an unaveraged potential because they require evaluation of all components of the nonadiabatic coupling vector. Here we introduce a new approximation to the self-consistent potential that does not have this computational drawback. The new approximation uses time-derivative couplings evaluated by overlap integrals of electronic wave functions to approximate the nonadiabatic coupling terms in the equations of motion. We present a numerical test of the method for ethylene that shows there is little loss of accuracy in the ensemble-averaged results. This new approximation to the self-consistent potential makes direct dynamics calculations with self-consistent potentials more efficient for complex systems and makes them practically affordable for some cases where the cost was previously too high.

State-pairwise decoherence times for nonadiabatic dynamics on more than two electronic states

Independent trajectory (IT) nonadiabatic molecular dynamics simulation methods are powerful tools for modeling processes involving transitions between electronic states. Incorporation and refinement of decoherence corrections into popular IT methods, e.g., Ehrenfest dynamics and trajectory surface hopping, is an important means of improving their accuracies. In this work, we identify a new challenge in the development of such decoherence corrections; when a system exists in a coherent superposition of three or more electronic states, coherences may decay unphysically when the decoherence correction is based on decoherence times assigned on a state-wise basis. As a solution, we introduce decoherence corrected Ehrenfest schemes based on decoherence times assigned on a state-pairwise basis. By application of these methods to a set of very simple one-dimensional model problems, we show that one of these state-pairwise methods ("collapse to a block") correctly describes the loss of coherence between all pairs of states in our multistate model problems, whereas a method based on a state-wise description of coherence loss does not. The new one-dimensional models introduced here can serve as useful tests for other decoherence correction schemes.

To unravel the connection between the non-equilibrium and equilibrium solvation dynamics of tryptophan: success and failure of the linear response theory of fluorescence Stokes shift

The connections between the non-equilibrium solvation dynamics upon optical transitions and the system's equilibrium fluctuations are explored in aqueous liquid. Linear response theory correlates time-dependent fluorescence with the equilibrium time correlation functions. In the previous work [T. Li, J. Chem. Theory Comput., 2017, 13, 1867], Stokes shift was explicitly decomposed into the contributions of various order time correlation functions on the excited state surface. Gaussian fluctuations of the solute-solvent interactions validate linear response theory. Correspondingly, the deviation of the Gaussian statistics causes the inefficiency of linear response evaluation. The above mechanism is thoroughly tested in this study. By employing molecular simulations, multiple non-equilibrium processes, not necessarily initiated from the ground state equilibrium minimum, were examined for tryptophan. Both the success and failure of linear response theory are found for this simple system and the mechanism is analyzed. These observations, assisted by the width dynamics, the initial state linear response approach, and the variation of the solvation structures, integrally verify the virtue of the excited state Gaussian statistics on the dynamics of Stokes shift.

Linear Response Theory for Decomposition Energies of Stokes Shift in Proteins

In aqueous solution, fluorescence Stokes shift experiments monitor the relaxation of the solute-solvent interactions upon photon excitation of the solute chromophore. Linear response (LR) theory expects the identical dynamics between the Stokes shift and the system's spontaneous fluctuations. Whether this identity guarantees similar dynamics between the nonequilibrated and equilibrium processes for the decomposition energy of the Stokes shift is the main focus of this study. In our previous work [Li, T. J. Chem. Theory Comput. 2017, 13, 1867-1873], Stokes shift is properly correlated with various order time-correlation functions. As a continuation, its decomposition energy from the subsystem is further represented as the full summation of all of the cross-time correlation functions between the decomposition energy and the total solute-solvent interactions. Gaussian statistics of the total solute-solvent interactions ensure the same decay rates among the odd orders not only for the time-correlation functions but also for the cross-time correlation functions, validating the LR of the Stokes shift and the decompositions, respectively. The above mechanism is verified by molecular dynamics simulations in the protein Staphylococcus nuclease and is robust even as the decomposed energy associated with an individual residue exhibits typical non-Gaussian properties. Further examinations reveal the consistent molecular motions for a specific residue over the nonequilibrium and equilibrium processes, which are responsible for the nonequilibrium dynamics of the associated decomposed energy. Our results show the appropriateness of LR on finer molecular scales.

Nonadiabatic Dynamics in a Laser Field: Using Floquet Fewest Switches Surface Hopping To Calculate Electronic Populations for Slow Nuclear Velocities

We investigate two well-known approaches for extending the fewest switches surface hopping (FSSH) algorithm to periodic time-dependent couplings. The first formalism acts as if the instantaneous adiabatic electronic states were standard adiabatic states, which just happen to evolve in time. The second formalism replaces the role of the usual adiabatic states by the time-independent adiabatic Floquet states. For a set of modified Tully model problems, the Floquet FSSH (F-FSSH) formalism gives a better estimate for both transmission and reflection probabilities than the instantaneous adiabatic FSSH (IA-FSSH) formalism, especially for slow nuclear velocities. More importantly, only F-FSSH predicts the correct final scattering momentum. Finally, in order to use Floquet theory accurately, we find that it is crucial to account for the interference between wavepackets on different Floquet states. Our results should be of interest to all those interested in laser-induced molecular dynamics.

Partial Molar Volume of the Hydrated Electron

The partial molar volume of the hydrated electron was investigated with pulse radiolysis and transient absorption by measuring the pressure dependence of the equilibrium constant for e^-_aq + NH₄⁺ ⇔ H + NH₃. At 2 kbar pressure, the equilibrium constant decreases relative to 1 bar by only 6%. Using tabulated molar volumes for ammonia and ammonium, we have the result V̅(e^-_aq) - V̅(H) = 11.3 cm³/mol at 25 °C, confirming that V̅(e^-_aq) is positive and even larger than the hydrophobic H atom. Assuming on the basis of recent molecular dynamics simulations that the molar volume of the H atom is somewhat less than that of H₂, we estimate V̅(e^-_aq) = 26 ± 6 cm³/mol. The positive molar volume is consistent with an electron that exists largely in a small solvent void (cavity), ruling out a recent model ( Larsen , R. E. ; Glover , W. J. ; Schwartz , B. J. Science 2010 , 329 , 65 - 69 ) that suggests a noncavity structure with negative molar volume.

Observation of dissociative quasi-free electron attachment to nucleoside via excited anion radical in solution

Damage to DNA via dissociative electron attachment has been well-studied in both the gas and condensed phases; however, understanding this process in bulk solution at a fundamental level is still a challenge. Here, we use a picosecond pulse of a high energy electron beam to generate electrons in liquid diethylene glycol and observe the electron attachment dynamics to ribothymidine at different stages of electron relaxation. Our transient spectroscopic results reveal that the quasi-free electron with energy near the conduction band effectively attaches to ribothymidine leading to a new absorbing species that is characterized in the UV-visible region. This species exhibits a nearly concentration-independent decay with a time constant of ~350 ps. From time-resolved studies under different conditions, combined with data analysis and theoretical calculations, we assign this intermediate to an excited anion radical that undergoes N1-C1′ glycosidic bond dissociation rather than relaxation to its ground state.

Radiation-induced low-energy electrons in solution are implicated in DNA damage, but their relaxation dynamics are not well understood. Here the authors observe how quasi-free electrons dissociate glycosidic bonds via an excited nucleoside anion radical, whereas solvated electrons reside on the nucleoside as a relatively stable anion radical.

Structure of the aqueous electron

A cavity or excluded-volume structure best explains the experimental properties of the aqueous or “hydrated” electron.

A post Gurney quantum mechanical perspective on the electrolysis of water: ion neutralization in solution

Electron fluxes crossing the interface between a metallic conductor and an aqueous environment are important in many fields; hydrogen production, environmental scanning tunnelling microscopy, scanning electrochemical microscopy being some of them. Gurney (Gurney 1931 Proc. R. Soc. Lond.134, 137 (doi:10.1098/rspa.1931.0187)) provided in 1931 a scheme for tunnelling during electrolysis and outlined conditions for it to occur. We measure the low-voltage current flows between gold electrodes in pure water and use the time-dependent behaviour at voltage switch-on and switch-off to evaluate the relative contribution to the steady current arising from tunnelling of electrons between the electrodes and ions in solution and from the neutralization of ions adsorbed onto the electrode surface. We ascribe the larger current contribution to quantum tunnelling of electrons to and from ions in solution near the electrodes. We refine Gurney's barrier scheme to include solvated electron states and quantify energy differences using updated information. We show that Gurney's conditions would prevent the current flow at low voltages we observe but outline how the ideas of Marcus (Marcus 1956 J. Chem. Phys.24, 966-978 (doi:10.1063/1.1742723)) concerning solvation fluctuations enable the condition to be relaxed. We derive an average barrier tunnelling model and a multiple pathways tunnelling model and compare predictions with measurements of the steady-state current-voltage relation. The tunnelling barrier was found to be wide and low in agreement with other experimental studies. Applications as a biosensing mechanism are discussed that exploit the fast tunnelling pathways along molecules in solution.

Electronic Excited State Lifetimes of Anionic Water Clusters: Dependence on Charge Solvation Motif

An ongoing controversy about water cluster anions concerns the electron-binding motif, whether the charge center is localized at the surface or within the cluster interior. Here, mixed quantum-classical dynamics simulations have been carried out for a wide range of cluster sizes (n ≤ 1000) for (H₂O)_n^- and (D₂O)_n^-, based on a nonequilibrium first-order rate constant approach. The computed data are in good general agreement with time-resolved photoelectron imaging results (n ≤ 200). The analysis reveals that, for surface state electrons, the cluster size dependence of the excited state electronic energy gap and the magnitude of the nonadiabatic couplings have compensating influences on the excited state lifetimes: the excited state lifetime for surface states reaches a minimum for n ∼ 150 and then increases for larger clusters. It is concluded that the electron resides in a surface-localized motif in all of these measured clusters, dominating at least up to n = 200.

Efficient Criterion To Evaluate Linear Response Theory in Optical Transitions

The role of the Gaussian statistics on the solvation dynamics upon the photon excitation of the chromophore is deeply explored. The linear response theory for the fluorescence Stokes shift is investigated. An analytical formulism is presented to recast Stokes shift into the contributions of the equilibrium time correlation functions of the solute-solvent interactions on the excited-state surface, and the latter is further reformed and depicted by the time relaxation of the moment. As the first application of the formulism in the molecular dynamics simulations, it is verified that the efficiency of the linear response theory relies on the Gaussian characteristics of the dominant moments in terms of the Stokes shift, which is identified by the same relaxation dynamics between those moments and the linear order one. The comparisons between the above observations on the linearity of Stokes shift and the explanations in the literature are discussed. The key finding is the development of explicit criterion to measure the appropriateness of applying linear response theory.

Quantifying solvated electrons' delocalization

The electron delocalization range EDR(r;u_av) (left) captures the spin density (right) of an electron delocalized over u_av = 5.77 Å on the surface of an (H₂O)₂₀⁻ cluster.

Relaxation mechanism of the hydrated electron

The relaxation dynamics of the photoexcited hydrated electron have been subject to conflicting interpretations. Here, we report time-resolved photoelectron spectra of hydrated electrons in a liquid microjet with the aim of clarifying ambiguities from previous experiments. A sequence of three ultrashort laser pulses (~100 femtosecond duration) successively created hydrated electrons by charge-transfer-to-solvent excitation of dissolved anions, electronically excited these electrons via the s→p transition, and then ejected them into vacuum. Two distinct transient signals were observed. One was assigned to the initially excited p-state with a lifetime of ~75 femtoseconds, and the other, with a lifetime of ~400 femtoseconds, was attributed to s-state electrons just after internal conversion in a nonequilibrated solvent environment. These assignments support the nonadiabatic relaxation model.

Solvated electrons at the water-air interface: surface versus bulk signal in low kinetic energy photoelectron spectroscopy

Time-resolved photoelectron spectroscopy at low kinetic energies (≲5 eV) is applied to dilute iodide solutions with different surface and bulk contributions. The results indicate a pronounced surface sensitivity. Signals assigned to solvated electrons near the liquid surface decay rapidly on a sub-ps timescale. In contrast to the literature, a long-lived surface solvated electron at 1.6 eV binding energy is not observed.

HYDRATION FREE ENERGY AND ABSORPTION SPECTRUM OF AN EXTRA ELECTRON IN WATER BY QUANTUM-CONTINUUM MODEL

In this paper, the hydration energy of electron and absorption spectrum at room temperature have been estimated by quantum-continuum model. Taking a number of negatively charged water clusters as the quantum part, the hydration energy is calculated at high levels associated with IPCM and IEFPCM. The optical absorption spectrum is calculated by TDDFT with different basis sets. The vertical detachment energy and cluster reorganization energy in gas phase are also investigated. The results have been discussed by comparing with the experimental observations.

Unveiling Electron Promiscuity

Although the wave-like proclivity of electrons for delocalization is familiar to every student of chemistry, it seems that electrons may have less respect for atomic and molecular boundaries than one might have considered proper. The boundaries in question include those between H-bonded dimers and within hydrated clusters, as well as those of aqueous cavities, colloidal suspensions, and macroscopic air-water and oil-water interfaces. Unveiling the promiscuous behavior of electrons at such frontiers may both raise eyebrows and demand acknowledgment.