Controlling Extraction of Rare Earth Elements Using Functionalized Aryl-vinyl Phosphonic Acid Esters.

Ligands that can discriminate between individual rare earth elements are important for production of these critical elements. A set of aryl-vinyl phosphonic acid ligands for extracting rare earth elements were designed and synthesized under the hypothesis that the strength of the rare earth-ligand interactions could be tuned by changing the dipole moment of the ligand. The ligands were synthesized via a two-step reaction procedure using a Heck coupling reaction to functionalize vinyl phosphonic acid, followed by Steglich esterification to obtain high-purity styryl phosphonic acid monoesters with varying dipole moments along the P-C bond. The metal binding strength and composition of the rare earth complexes formed with these styryl phosphonic acid monoesters were experimentally studied by liquid-liquid extraction techniques, while DFT calculations were performed to determine the dipole moments of the free and complexed ligands and the electronic structure of the complexes formed. All three prepared ligands were much stronger extracting agents for europium(III) than the dialkylphosphonic acids usually used for this separation. However, the order of increasing extraction strength was found to match the order of the decreasing calculated dipole moment along the P-C bond of the three styryl-based ligands, rather than correlating with increasing ligand basicity, as reflected by the pKa of the ligands. These findings suggest that this approach can be used to systematically alter the extraction strength of aromatic phosphonic monoesters for rare earth element purification.

Mediating Photochemical Reaction Rates at Lewis Acidic Rare Earths by Selective Energy Loss to 4f-Electron States.

Manifesting chemical differences in individual rare earth (RE) element complexes is challenging due to the similar sizes of the tripositive cations and the corelike 4f shell. We disclose a new strategy for differentiating between similarly sized Dy3+ and Y3+ ions through a tailored photochemical reaction of their isostructural complexes in which the f-electron states of Dy3+ act as an energy sink. Complexes RE(hfac)3(NMMO)2 (RE = Dy (2-Dy) and Y (2-Y), hfac = hexafluoroacetylacetonate, and NMMO = N-methylmorpholine-N-oxide) showed variable rates of oxygen atom transfer (OAT) to triphenylphosphine under ultraviolet (UV) irradiation, as monitored by 1H and 19F NMR spectroscopies. Ultrafast transient absorption spectroscopy (TAS) identified the excited state(s) responsible for the photochemical OAT reaction or lack thereof. Competing sensitization pathways leading to excited-state deactivation in 2-Dy through energy transfer to the 4f electron manifold ultimately slows the OAT reaction at this metal cation. The measured rate differences between the open-shell Dy3+ and closed-shell Y3+ complexes demonstrate that using established principles of 4f ion sensitization may deliver new, selective modalities for differentiating the RE elements that do not depend on cation size.

Message-passing neural networks for high-throughput polymer screening.

Machine learning methods have shown promise in predicting molecular properties, and given sufficient training data, machine learning approaches can enable rapid high-throughput virtual screening of large libraries of compounds. Graph-based neural network architectures have emerged in recent years as the most successful approach for predictions based on molecular structure and have consistently achieved the best performance on benchmark quantum chemical datasets. However, these models have typically required optimized 3D structural information for the molecule to achieve the highest accuracy. These 3D geometries are costly to compute for high levels of theory, limiting the applicability and practicality of machine learning methods in high-throughput screening applications. In this study, we present a new database of candidate molecules for organic photovoltaic applications, comprising approximately 91 000 unique chemical structures. Compared to existing datasets, this dataset contains substantially larger molecules (up to 200 atoms) as well as extrapolated properties for long polymer chains. We show that message-passing neural networks trained with and without 3D structural information for these molecules achieve similar accuracy, comparable to state-of-the-art methods on existing benchmark datasets. These results therefore emphasize that for larger molecules with practical applications, near-optimal prediction results can be obtained without using optimized 3D geometry as an input. We further show that learned molecular representations can be leveraged to reduce the training data required to transfer predictions to a new density functional theory functional.

Molecular dynamics and charge transport in organic semiconductors: a classical approach to modeling electron transfer.

Organic photovoltaics (OPVs) are a promising carbon-neutral energy conversion technology, with recent improvements pushing power conversion efficiencies over 10%. A major factor limiting OPV performance is inefficiency of charge transport in organic semiconducting materials (OSCs). Due to strong coupling with lattice degrees of freedom, the charges form polarons, localized quasi-particles comprised of charges dressed with phonons. These polarons can be conceptualized as pseudo-atoms with a greater effective mass than a bare charge. We propose that due to this increased mass, polarons can be modeled with Langevin molecular dynamics (LMD), a classical approach with a computational cost much lower than most quantum mechanical methods. Here we present LMD simulations of charge transfer between a pair of fullerene molecules, which commonly serve as electron acceptors in OSCs. We find transfer rates consistent with experimental measurements of charge mobility, suggesting that this method may provide quantitative predictions of efficiency when used to simulate materials on the device scale. Our approach also offers information that is not captured in the overall transfer rate or mobility: in the simulation data, we observe exactly when and why intermolecular transfer events occur. In addition, we demonstrate that these simulations can shed light on the properties of polarons in OSCs. Much remains to be learned about these quasi-particles, and there are no widely accepted methods for calculating properties such as effective mass and friction. Our model offers a promising approach to exploring mass and friction as well as providing insight into the details of polaron transport in OSCs.

Close Packing of Nitroxide Radicals in Stable Organic Radical Polymeric Materials.

The relationship between the polymer network and electronic transport properties for stable radical polymeric materials has come under investigation owing to their potential application in electronic devices. For the radical polymer poly(2,2,6,6-tetramethylpiperidine-4-yl-1-oxyl methacrylate), it is unclear whether the radical packing is optimal for charge transport partially because the relationship between radical packing and molecular structure is not well-understood. Using the paramagnetic nitroxide radical as a probe of the polymer and synthetic techniques to control the radical concentration on the methyl methacrylate backbone, we investigate the dependence of radical concentration on molecular structure. The electron paramagnetic resonance data indicate that radicals in the PTMA assume a closest approach distance to each other when more than 60% of the backbone is populated with radical pendant groups. Below 60% coverage, the polymer rearranges to accommodate larger radical-radical spacing. These findings are consistent with theoretical calculations and help explain some experimentally determined electron-transport properties.

Quenching of the perylene fluorophore by stable nitroxide radical-containing macromolecules.

Stable nitroxide radical bearing organic polymer materials are attracting much attention for their application as next generation energy storage materials. A greater understanding of the inherent charge transfer mechanisms in such systems will ultimately be paramount to further advancements in the understanding of both intrafilm and interfacial ion- and electron-transfer reactions. This work is focused on advancing the fundamental understanding of these dynamic charge transfer properties by exploiting the fact that these species are efficient fluorescence quenchers. We systematically incorporated fluorescent perylene dyes into solutions containing the 2,2,6,6-tetramethylpiperidine-N-oxyl (TEMPO) radical and controlled their interaction by binding the TEMPO moiety into macromolecules with varying morphologies (e.g., chain length, density of radical pendant groups). In the case of the model compound, 4-oxo-TEMPO, quenching of the perylene excited state was found to be dominated by a dynamic (collisional) process, with a contribution from an apparent static process that is described by an ∼2 nm quenching sphere of action. When we incorporated the TEMPO unit into a macromolecule, the quenching behavior was altered significantly. The results can be described by using two models: (A) a collisional quenching process that becomes less efficient, presumably due to a reduction in the diffusion constant of the quenching entity, with a quenching sphere of action similar to 4-oxo-TEMPO or (B) a collisional quenching process that becomes more efficient as the radius of interaction grows larger with increasing oligomer length. This is the first study that definitively illustrates that fluorophore quenching by a polymer system cannot be explained using merely a classical Stern-Volmer approach but rather necessitates a more complex model.

Resonance Raman and temperature-dependent electronic absorption spectra of cavity and noncavity models of the hydrated electron.

Most of what is known about the structure of the hydrated electron comes from mixed quantum/classical simulations, which depend on the pseudopotential that couples the quantum electron to the classical water molecules. These potentials usually are highly repulsive, producing cavity-bound hydrated electrons that break the local water H-bonding structure. However, we recently developed a more attractive potential, which produces a hydrated electron that encompasses a region of enhanced water density. Both our noncavity and the various cavity models predict similar experimental observables. In this paper, we work to distinguish between these models by studying both the temperature dependence of the optical absorption spectrum, which provides insight into the balance of the attractive and repulsive terms in the potential, and the resonance Raman spectrum, which provides a direct measure of the local H-bonding environment near the electron. We find that only our noncavity model can capture the experimental red shift of the hydrated electron's absorption spectrum with increasing temperature at constant density. Cavity models of the hydrated electron predict a solvation structure similar to that of the larger aqueous halides, leading to a Raman O-H stretching band that is blue-shifted and narrower than that of bulk water. In contrast, experiments show the hydrated electron has a broader and red-shifted O-H stretching band compared with bulk water, a feature recovered by our noncavity model. We conclude that although our noncavity model does not provide perfect quantitative agreement with experiment, the hydrated electron must have a significant degree of noncavity character.

Simulating the formation of sodium:electron tight-contact pairs: watching the solvation of atoms in liquids one molecule at a time.

The motions of solvent molecules during a chemical transformation often dictate both the dynamics and the outcome of solution-phase reactions. However, a microscopic picture of solvation dynamics is often obscured by the concerted motions of numerous solvent molecules that make up a condensed-phase environment. In this study, we use mixed quantum/classical molecular dynamics simulations to furnish the molecular details of the solvation dynamics that leads to the formation of a sodium cation-solvated electron contact pair, (Na(+), e(-)), in liquid tetrahydrofuran following electron photodetachment from sodide (Na(-)). Our simulations reveal that the dominant solvent response is comprised of a series of discrete solvent molecular events that work sequentially to build up a shell of coordinating THF oxygen sites around the sodium cation end of the contact pair. With the solvent response described in terms of the sequential motion of single molecules, we are then able to compare the calculated transient absorption spectroscopy of the sodium species to experiment, providing a clear microscopic interpretation of ultrafast pump-probe experiments on this system. Our findings suggest that for solute-solvent interactions similar to the ones present in our study, the solvation dynamics is best understood as a series of kinetic events consisting of reactions between chemically distinct local structures in which key solvent molecules must be considered to be part of the identity of the reacting species.

Nature of sodium atoms/(Na(+), e(-)) contact pairs in liquid tetrahydrofuran.

With no internal vibrational or rotational degrees of freedom, atomic solutes serve as the simplest possible probe of a condensed-phase environment's influence on solute electronic structure. Of the various atomic species that can be formed in solution, the quasi-one-electron alkali atoms in ether solvents have been the most widely studied experimentally, primarily due to the convenient location of their absorption spectra at visible wavelengths. The nature of solvated alkali atoms, however, remains controversial: the consensus view is that solvated alkali atoms exist as (Na(+), e(-)) tight-contact pairs (TCPs), species in which the alkali valence electron is significantly displaced from the alkali nucleus and confined primarily by the first solvent shell. Thus, to shed light on the nature of alkali atoms in solution and to further our understanding of condensed-phase effects on solutes' electronic structure, we have performed mixed quantum/classical molecular dynamics simulations of sodium atoms in liquid tetrahydrofuran (Na(0)/THF). Our interest in this particular system stems from recent pump-probe experiments in our group, which found that the rate at which this species is solvated depends on how it was created ( Science 2008 , 321 , 1817 ); in other words, the solvation dynamics of this system do not obey linear response. Our simulations reproduce the experimental spectroscopy of this system and clearly indicate that neutral Na atoms exist as (Na(+), e(-)) TCPs in solution. We find that the driving force for the displacement of sodium's valence electron is the formation of a tight solvation shell around the partially exposed Na(+). On average, four THF oxygens coordinate the cation end of the TCP; however, we also observe fluctuations to other solvent coordination numbers. Furthermore, we find that species with different solvent coordination numbers have unique absorption spectra and that interconversion between species with different solvent coordination numbers requires surmounting a free energy barrier of several k(B)T. Taken together, our results suggest that the Na(0)/THF species with different solvent coordination numbers may be viewed as chemically distinct. Thus, we can explain the kinetics of Na TCP formation as being dictated by changes in the Na(+) solvent coordination number, and we can understand the dependence on initial conditions seen in the solvation dynamics of this system as resulting from the fact that the important solvent coordinate involves the motion of only a few molecules in the first solvation shell.

Does the hydrated electron occupy a cavity?

Since the discovery of the hydrated electron more than 40 years ago, a general consensus has emerged that the hydrated electron occupies a quasispherical cavity in liquid water. We simulated the electronic structure and dynamics of the hydrated electron using a rigorously derived pseudopotential to treat the electron-water interaction, which incorporates attractive oxygen and repulsive hydrogen features that have not been included in previous pseudopotentials. What emerged was a hydrated electron that did not reside in a cavity but instead occupied a approximately 1-nanometer-diameter region of enhanced water density. Both the calculated ground-state absorption spectrum and the excited-state spectral dynamics after simulated photoexcitation of this noncavity hydrated electron showed excellent agreement with experiment. The relaxation pathway involves a rapid internal conversion followed by slow ground-state cooling, the opposite of the mechanism implicated by simulations in which the hydrated electron occupies a cavity.

First principles multielectron mixed quantum/classical simulations in the condensed phase. I. An efficient Fourier-grid method for solving the many-electron problem.

We introduce an efficient multielectron first-principles based electronic structure method, the two-electron Fourier-grid (2EFG) approach, that is particularly suited for use in mixed quantum/classical simulations of condensed-phase systems. The 2EFG method directly solves for the six-dimensional wave function of a two-electron Hamiltonian in a Fourier-grid representation such that the effects of electron correlation and exchange are treated exactly for both the ground and excited states. Due to the simplicity of a Fourier-grid representation, the 2EFG is readily parallelizable and we discuss its computational implementation in a distributed-memory parallel environment. We show our method is highly efficient, being able to find two-electron wave functions in approximately 20 s on a modern desktop computer for a calculation this is equivalent to full configuration interaction (FCI) in a basis of 17 million Slater determinants. We benchmark the accuracy of the 2EFG by applying it to two electronic structure test problems: the harmonium atom and the sodium dimer. We find that even with a modest grid basis size, our method converges to the analytically exact solutions of harmonium in both the weakly and strongly correlated electron regimes. Our method also reproduces the low-lying potential energy curves of the sodium dimer to a similar level of accuracy as a valence CI calculation, thus demonstrating its applicability to molecular systems. In the following paper [W. J. Glover, R. E. Larsen, and B. J. Schwartz, J. Chem. Phys. 132, 144102 (2010)], we use the 2EFG method to explore the nature of the electronic states that comprise the charge-transfer-to-solvent absorption band of sodium anions in liquid tetrahydrofuran.

First principles multielectron mixed quantum/classical simulations in the condensed phase. II. The charge-transfer-to-solvent states of sodium anions in liquid tetrahydrofuran.

Gas-phase atomic anions lack bound electronic excited states, yet in solution many of these anions exhibit intense absorption bands due to the presence of excited states, referred to as charge-transfer-to-solvent (CTTS) states that are bound only by the presence of the solvent. CTTS spectra thus serve as delicate probes of solute-solvent interactions, but the fact that they are created by the interactions of a solute with many solvent molecules makes them a challenge to describe theoretically. In this paper, we use mixed quantum/classical molecular dynamics with the two-electron Fourier-grid (2EFG) electronic structure method presented in the previous paper [W. J. Glover, R. E. Larsen, and B. J. Schwartz, J. Chem. Phys. 132, 144101 (2010)] to simulate the CTTS states of a sodium anion in liquid tetrahydrofuran, Na(-)/THF. Since our 2EFG method is based on configuration interaction with single and double excitations in a grid basis, it allows for an exact treatment of the two valence electrons of the sodium anion. To simulate Na(-)/THF, we first develop a new electron-THF pseudopotential, and we verify the accuracy of this potential by reproducing the experimental absorption spectrum of an excess electron in liquid THF with near quantitative accuracy. We also are able to reproduce the CTTS spectrum of Na(-)/THF and find that the CTTS states of Na(-) exhibit a Rydberg-like progression due to the pre-existing long-range solvent polarization around the anion. We also find that the CTTS states are highly mixed with the disjoint electronic states supported by naturally occurring solvent cavities that exist in liquid THF. This mixing explains why the solvated electrons that are ejected following CTTS excitation appear with their equilibrium absorption spectrum. The mixing of the CTTS and solvent-cavity states also explains why the recombination of the electron and its geminate Na(0) partner occurs on slower time scales when photoexciting in the blue compared to in the red of the CTTS band: blue excitation accesses CTTS states whose charge densities lies further from the position of the anion, whereas red excitation accesses CTTS states that lie primarily within the anion's first solvation shell. Finally, we see that the radial character of the CTTS states near the Na(+) core matches that of Na(0), explaining why the spectrum of this species appears instantly after photoexciting Na(-).

The roles of electronic exchange and correlation in charge-transfer- to-solvent dynamics: Many-electron nonadiabatic mixed quantum/classical simulations of photoexcited sodium anions in the condensed phase.

The charge-transfer-to-solvent (CTTS) reactions of solvated atomic anions serve as ideal models for studying the dynamics of electron transfer: The fact that atomic anions have no internal degrees of freedom provides one of the most direct routes to understanding how the motions of solvent molecules influence charge transfer, and the relative simplicity of atomic electronic structure allows for direct contact between theory and experiment. To date, molecular dynamics simulations of the CTTS process have relied on a single-electron description of the atomic anion-only the electron involved in the charge transfer has been treated quantum mechanically, and the electronic structure of the atomic solute has been treated via pseudopotentials. In this paper, we examine the severity of approximating the electronic structure of CTTS anions with a one-electron model and address the role of electronic exchange and correlation in both CTTS electronic structure and dynamics. To do this, we perform many-electron mixed quantum/classical molecular dynamics simulations of the ground- and excited-state properties of the aqueous sodium anion (sodide). We treat both of the sodide valence electrons quantum mechanically and solve the Schrodinger equation using configuration interaction with singles and doubles (CISD), which provides an exact solution for two electrons. We find that our multielectron simulations give excellent general agreement with experimental results on the CTTS spectroscopy and dynamics of sodide in related solvents. We also compare the results of our multielectron simulations to those from one-electron simulations on the same system [C. J. Smallwood et al., J. Chem. Phys. 119, 11263 (2003)] and find substantial differences in the equilibrium CTTS properties and the nonadiabatic relaxation dynamics of one- and two-electron aqueous sodide. For example, the one-electron model substantially underpredicts the size of sodide, which in turn results in a dramatically different solvation structure around the ion. The one-electron model also misses the existence of an entire manifold of bound CTTS excited states and predicts an absorption spectrum that is blueshifted from that in the two-electron model by over 2 eV. Even the use of a quantum mechanics/molecular mechanics (QM/MM)-like approach, where we calculated the electronic structure with our CISD method using solvent configurations generated from the one-electron simulations, still produced an absorption spectrum that was shifted approximately 1 eV to the blue. In addition, we find that the two-electron model sodide anion is very polarizable: The instantaneous dipole induced by local fluctuating electric fields in the solvent reaches values over 14 D. This large polarizability is driven by an unusual solvation motif in which the solvent pushes the valence electron density far enough to expose the sodium cation core, a situation that cannot be captured by one-electron models that employ a neutral atomic core. Following excitation to one of the bound CTTS excited states, we find that one of the two sodide valence electrons is detached, forming a sodium atom:solvated electron contact pair. Surprisingly, the CTTS relaxation dynamics are qualitatively similar in both the one- and two-electron simulations, a result we attribute to the fact that the one-electron model does correctly describe the symmetry of the important CTTS excited states. The excited-state lifetime of the one-electron model, however, is over three times longer than that in the two-electron model, and the detachment dynamics in the two-electron model is correlated with the presence of solvent molecules that directly solvate the cationic atomic core. Thus, our results make it clear that a proper treatment of anion electron structure that accounts for electronic exchange and correlation is crucial to understanding CTTS electronic structure and dynamics.

The structure of the hydrated electron. Part 2. A mixed quantum/classical molecular dynamics embedded cluster density functional theory: single-excitation configuration interaction study.

Adiabatic mixed quantum/classical (MQC) molecular dynamics (MD) simulations were used to generate snapshots of the hydrated electron in liquid water at 300 K. Water cluster anions that include two complete solvation shells centered on the hydrated electron were extracted from the MQC MD simulations and embedded in a roughly 18 Ax18 Ax18 A matrix of fractional point charges designed to represent the rest of the solvent. Density functional theory (DFT) with the Becke-Lee-Yang-Parr functional and single-excitation configuration interaction (CIS) methods were then applied to these embedded clusters. The salient feature of these hybrid DFT(CIS)/MQC MD calculations is significant transfer (approximately 18%) of the excess electron's charge density into the 2p orbitals of oxygen atoms in OH groups forming the solvation cavity. We used the results of these calculations to examine the structure of the singly occupied and the lower unoccupied molecular orbitals, the density of states, the absorption spectra in the visible and ultraviolet, the hyperfine coupling (hfcc) tensors, and the infrared (IR) and Raman spectra of these embedded water cluster anions. The calculated hfcc tensors were used to compute electron paramagnetic resonance (EPR) and electron spin echo envelope modulation (ESEEM) spectra for the hydrated electron that compared favorably to the experimental spectra of trapped electrons in alkaline ice. The calculated vibrational spectra of the hydrated electron are consistent with the red-shifted bending and stretching frequencies observed in resonance Raman experiments. In addition to reproducing the visible/near IR absorption spectrum, the hybrid DFT model also accounts for the hydrated electron's 190-nm absorption band in the ultraviolet. Thus, our study suggests that to explain several important experimentally observed properties of the hydrated electron, many-electron effects must be accounted for: one-electron models that do not allow for mixing of the excess electron density with the frontier orbitals of the first-shell solvent molecules cannot explain the observed magnetic, vibrational, and electronic properties of this species. Despite the need for multielectron effects to explain these important properties, the ensemble-averaged radial wavefunctions and energetics of the highest occupied and three lowest unoccupied orbitals of the hydrated electrons in our hybrid model are close to the s- and p-like states obtained in one-electron models. Thus, one-electron models can provide a remarkably good approximation to the multielectron picture of the hydrated electron for many applications; indeed, the two approaches appear to be complementary.

Watching Na atoms solvate into (Na+,e-) contact pairs: untangling the ultrafast charge-transfer-to-solvent dynamics of Na- in tetrahydrofuran (THF).

With the large dye molecules employed in typical studies of solvation dynamics, it is often difficult to separate the intramolecular relaxation of the dye from the relaxation associated with dynamic solvation. One way to avoid this difficulty is to study solvation dynamics using an atom as the solvation probe; because atoms have only electronic degrees of freedom, all of the observed spectroscopic dynamics must result from motions of the solvent. In this paper, we use ultrafast transient absorption spectroscopy to investigate the solvation dynamics of newly created sodium atoms that are formed following the charge transfer to solvent (CTTS) ejection of an electron from sodium anions (sodide) in liquid tetrahydrofuran (THF). Because the absorption spectra of the sodide reactant, the sodium atom, and the solvated electron products overlap, we first examined the dynamics of the ejected CTTS electron in the infrared to build a detailed model of the CTTS process that allowed us to subtract the spectroscopic contributions of the sodide bleach and the solvated electron and cleanly reveal the spectroscopy of the solvated atom. We find that the neutral sodium species created following CTTS excitation of sodide initially absorbs near 590 nm, the position of the gas-phase sodium D-line, suggesting that it only weakly interacts with the surrounding solvent. We then see a fast solvation process that causes a red-shift of the sodium atom's spectrum in approximately 230 fs, a time scale that matches well with the results of MD simulations of solvation dynamics in liquid THF. After the fast solvation is complete, the neutral sodium atoms undergo a chemical reaction that takes place in approximately 740 fs, as indicated by the observation of an isosbestic point and the creation of a species with a new spectrum. The spectrum of the species created after the reaction then red-shifts on a approximately 10-ps time scale to become the equilibrium spectrum of the THF-solvated sodium atom, which is known from radiation chemistry experiments to absorb near approximately 900 nm. There has been considerable debate as to whether this 900-nm absorbing species is better thought of as a solvated atom or a sodium cation:solvated electron contact pair, (Na+,e-). The fact that we observe the initially created neutral Na atom undergoing a chemical reaction to ultimately become the 900-nm absorbing species suggests that it is better assigned as (Na+,e-). The approximately 10-ps solvation time we observe for this species is an order of magnitude slower than any other solvation process previously observed in liquid THF, suggesting that this species interacts differently with the solvent than the large molecules that are typically used as solvation probes. Together, all of the results allow us to build the most detailed picture to date of the CTTS process of Na- in THF as well as to directly observe the solvation dynamics associated with single sodium atoms in solution.

Moving solvated electrons with light: nonadiabatic mixed quantum/classical molecular dynamics simulations of the relocalization of photoexcited solvated electrons in tetrahydrofuran (THF).

Motivated by recent ultrafast spectroscopic experiments [Martini et al., Science 293, 462 (2001)], which suggest that photoexcited solvated electrons in tetrahydrofuran (THF) can relocalize (that is, return to equilibrium in solvent cavities far from where they started), we performed a series of nonequilibrium, nonadiabatic, mixed quantum/classical molecular dynamics simulations that mimic one-photon excitation of the THF-solvated electron. We find that as photoexcited THF-solvated electrons relax to their ground states either by continuous mixing from the excited state or via nonadiabatic transitions, approximately 30% of them relocalize into cavities that can be over 1 nm away from where they originated, in close agreement with the experiments. A detailed investigation shows that the ability of excited THF-solvated electrons to undergo photoinduced relocalization stems from the existence of preexisting cavity traps that are an intrinsic part of the structure of liquid THF. This explains why solvated electrons can undergo photoinduced relocalization in solvents like THF but not in solvents like water, which lack the preexisting traps necessary to stabilize the excited electron in other places in the fluid. We also find that even when they do not ultimately relocalize, photoexcited solvated electrons in THF temporarily visit other sites in the fluid, explaining why the photoexcitation of THF-solvated electrons is so efficient at promoting recombination with nearby scavengers. Overall, our study shows that the defining characteristic of a liquid that permits the photoassisted relocalization of solvated electrons is the existence of nascent cavities that are attractive to an excess electron; we propose that other such liquids can be found from classical computer simulations or neutron diffraction experiments.

Exploring the role of decoherence in condensed-phase nonadiabatic dynamics: a comparison of different mixed quantum/classical simulation algorithms for the excited hydrated electron.

Mixed quantum/classical (MQC) molecular dynamics simulation has become the method of choice for simulating the dynamics of quantum mechanical objects that interact with condensed-phase systems. There are many MQC algorithms available, however, and in cases where nonadiabatic coupling is important, different algorithms may lead to different results. Thus, it has been difficult to reach definitive conclusions about relaxation dynamics using nonadiabatic MQC methods because one is never certain whether any given algorithm includes enough of the necessary physics. In this paper, we explore the physics underlying different nonadiabatic MQC algorithms by comparing and contrasting the excited-state relaxation dynamics of the prototypical condensed-phase MQC system, the hydrated electron, calculated using different algorithms, including: fewest-switches surface hopping, stationary-phase surface hopping, and mean-field dynamics with surface hopping. We also describe in detail how a new nonadiabatic algorithm, mean-field dynamics with stochastic decoherence (MF-SD), is to be implemented for condensed-phase problems, and we apply MF-SD to the excited-state relaxation of the hydrated electron. Our discussion emphasizes the different ways quantum decoherence is treated in each algorithm and the resulting implications for hydrated-electron relaxation dynamics. We find that for three MQC methods that use Tully's fewest-switches criterion to determine surface hopping probabilities, the excited-state lifetime of the electron is the same. Moreover, the nonequilibrium solvent response function of the excited hydrated electron is the same with all of the nonadiabatic MQC algorithms discussed here, so that all of the algorithms would produce similar agreement with experiment. Despite the identical solvent response predicted by each MQC algorithm, we find that MF-SD allows much more mixing of multiple basis states into the quantum wave function than do other methods. This leads to an excited-state lifetime that is longer with MF-SD than with any method that incorporates nonadiabatic effects with the fewest-switches surface hopping criterion.

Projections of quantum observables onto classical degrees of freedom in mixed quantum-classical simulations: understanding linear response failure for the photoexcited hydrated electron.

We present a general analytic method for understanding how specific motions of a classical bath influence the dynamics of quantum-mechanical observables in mixed quantum-classical molecular dynamics simulations. We apply our method and develop expressions for the special case of quantum solvation, allowing us to examine how specific classical solvent motions couple to the equilibrium energy fluctuations and nonequilibrium energy relaxation of a quantum-mechanical solute. As a first application of our formalism, we investigate the motions of classical water underlying the equilibrium and nonequilibrium excited-state solvent response functions of the hydrated electron; the results allow us to explain why the linear response approximation fails for this system.

A computationally efficient exact pseudopotential method. I. Analytic reformulation of the Phillips-Kleinman theory.

Even with modern computers, it is still not possible to solve the Schrodinger equation exactly for systems with more than a handful of electrons. For many systems, the deeply bound core electrons serve merely as placeholders and only a few valence electrons participate in the chemical process of interest. Pseudopotential theory takes advantage of this fact to reduce the dimensionality of a multielectron chemical problem: the Schrodinger equation is solved only for the valence electrons, and the effects of the core electrons are included implicitly via an extra term in the Hamiltonian known as the pseudopotential. Phillips and Kleinman (PK) [Phys. Rev. 116, 287 (1959)]. demonstrated that it is possible to derive a pseudopotential that guarantees that the valence electron wave function is orthogonal to the (implicitly included) core electron wave functions. The PK theory, however, is expensive to implement since the pseudopotential is nonlocal and its computation involves iterative evaluation of the full Hamiltonian. In this paper, we present an analytically exact reformulation of the PK pseudopotential theory. Our reformulation has the advantage that it greatly simplifies the expressions that need to be evaluated during the iterative determination of the pseudopotential, greatly increasing the computational efficiency. We demonstrate our new formalism by calculating the pseudopotential for the 3s valence electron of the Na atom, and in the subsequent paper, we show that pseudopotentials for molecules as complex as tetrahydrofuran can be calculated with our formalism in only a few seconds. Our reformulation also provides a clear geometric interpretation of how the constraint equations in the PK theory, which are required to obtain a unique solution, are themselves sufficient to calculate the pseudopotential.