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

Simulating the Competitive Ion Pairing of Hydrated Electrons with Chaotropic Cations

Experiments show that the absorption spectrum of the hydrated electron (ehyd-) blue-shifts in electrolyte solutions compared with what is seen in pure water. This shift has been assigned to the ehyd-'s competitive ion-pairing interactions with the salt cation relative to the salt anion based on the ions' positions on the Hofmeister series. Remarkably, little work has been done investigating the ehyd-'s behavior when the salts have chaotropic cations, which should greatly change the ion-pairing interactions given that the ehyd- is a champion chaotrope. In this work, we remedy this by using mixed quantum/classical simulations to analyze the behavior of two different models of the ehyd- in aqueous RbF and RbI electrolyte solutions as a function of salt concentration. We find that the magnitude of the salt-induced spectral blue-shift is determined by a combination of the number of chaotropic Rb+ cations near the ehyd- and the number of salt anions near those cations so that the spectrum of the ehyd- directly reflects its local environment. We also find that the use of a soft-cavity ehyd- model predicts stronger competitive interactions with Rb+ relative to I- than a more traditional hard cavity model, leading to different predicted spectral shifts that should provide a way to distinguish between the two models experimentally. Our simulations predict that at the same concentration, salts with chaotropic cations should produce larger spectral blue-shifts than salts with kosmotropic cations. We also found that at high salt concentrations with chaotropic cations, the predicted blue-shift is greater when the salt anion is kosmotropic instead of chaotropic. Our goal is for this work to inspire experimentalists to make such measurements, which will help provide a spectroscopic means to distinguish between simulations models that predict different hydration structures for the ehyd-.

How Solvation Alters the Thermodynamics of Asymmetric Bond-Breaking: Quantum Simulation of NaK+ in Liquid Tetrahydrofuran

Gas-phase potential energy surfaces (PESs) are often used to provide an intuitive understanding of molecular chemical reactivity. Most chemical reactions, however, take place in solution, and it is unclear whether gas-phase PESs accurately represent chemical processes in solvent environments. In this work we use quantum simulations to investigate the dissociation energetics of NaK+ in liquid tetrahydrofuran (THF) to understand the degree to which solvent interactions alter the gas-phase picture. Using umbrella sampling and thermodynamic integration techniques, we construct condensed-phase free energy surfaces of NaK+ on THF in both the ground and electronic excited states. We find that solvation by THF completely alters the nature of the NaK+ bond by reordering the thermodynamic dissociation products. Reaching the thermodynamic dissociation limit in THF also requires a long-range charge transfer process that has no counterpart in the gas phase. Gas-phase PESs, even with perturbations, cannot adequately describe the reactivity of simple asymmetric molecules in solution.

Using Machine Learning to Understand the Causes of Quantum Decoherence in Solution-Phase Bond-Breaking Reactions

Decoherence is a fundamental phenomenon that occurs when an entangled quantum state interacts with its environment, leading to collapse of the wave function. The inevitability of decoherence provides one of the most intrinsic limits of quantum computing. However, there has been little study of the precise chemical motions from the environment that cause decoherence. Here, we use quantum molecular dynamics simulations to explore the photodissociation of Na2+ in liquid Ar, in which solvent fluctuations induce decoherence and thus determine the products of chemical bond breaking. We use machine learning to characterize the solute-solvent environment as a high-dimensional feature space that allows us to predict when and onto which photofragment the bonding electron will localize. We find that reaching a requisite photofragment separation and experiencing out-of-phase solvent collisions underlie decoherence during chemical bond breaking. Our work highlights the utility of machine learning for interpreting complex solution-phase chemical processes as well as identifies the molecular underpinnings of decoherence.

Solvation of magnesium chloride dimer in water: The case of anionic and neutral clusters

The structures of magnesium chloride dimer-water clusters, (MgCl2)2(H2O)n-/0, were investigated with size-selected anion photoelectron spectroscopy and theoretical calculations to understand the dissolution of magnesium chloride in water. The most stable structures were confirmed by comparing vertical detachment energies (VDEs) with the experimental measurements. A dramatic drop of VDE at n = 3 has been observed in the experiment, which is in accordance with the structural change of (MgCl2)2(H2O)n-. Compared to the neutral clusters, the excess electron induces two significant phenomena in (MgCl2)2(H2O)n-. First, the planar D2h geometry can be converted into a C3v structure at n = 0, making the Mg-Cl bonds easier to be broken by water molecules. More importantly, a negative charge-transfer-to-solvent process occurs after adding three water molecules (i.e., at n = 3), which leads to an obvious deviation in the evolution of the clusters. Such electron transfer behavior was noticed at n = 1 in monomer MgCl2(H2O)n-, indicating that the dimerization between two MgCl2 molecules can make the cluster more capable of binding electron. In neutral (MgCl2)2(H2O)n, this dimerization provides more sites for the added water molecules, which can stabilize the entire cluster and maintain its initial structure. Specifically, filling the coordination number to be 6 for Mg atoms can be seen as a link between structural preferences in the dissolution of the monomers, dimers, and extended bulk-state of MgCl2. This work represents an important step forward into fully understanding the solvation of MgCl2 crystals and other multivalent salt oligomers.

Competitive Ion Pairing and the Role of Anions in the Behavior of Hydrated Electrons in Electrolytes

Experiments have shown that in the presence of electrolytes, the hydrated electron's absorption spectrum experiences a blue shift whose magnitude depends on both the salt concentration and chemical identity. Previous computer simulations have suggested that the spectral blue shift results from the formation of (cation, electron) contact pairs and that the concentration dependence arises because the number of cations simultaneously paired with the electron increases with increasing concentration. In this work, we perform new simulations to build an atomistic picture that explains the effect of salt identity on the observed hydrated electron spectral shifts. We simulate hydrated electrons in the presence of both monovalent (Na⁺) and divalent (Ca²⁺) cations paired with both Cl^- and a spherical species representing ClO₄^- anions. Our simulations reproduce the experimental observations that divalent ions produce larger blue shifts of the hydrated electron's spectrum than monovalent ions with the same anion and that perchlorate salts show enhanced blue shifts compared to chloride salts with the same cation. We find that these observations can be explained by competitive ion pairing. With small kosmotropic cations such as Na⁺ and Ca²⁺, aqueous chloride salts tend to form (cation, anion) contact pairs, whereas there is little ion pairing between these cations and chaotropic perchlorate anions. Hydrated electrons also strongly interact with these cations, but if the cations are also paired with anions, this affects the free energy of the electron-cation interaction. With chloride salts, hydrated electrons end up in complexes containing multiple cations plus a few anions as well as the electron. Repulsive interactions between the electron and the nearby Cl^- anions reduce the cation-induced spectral blue shift of the hydrated electron. With perchlorate salts, hydrated electrons pair with multiple cations without any associated anions, leading to the largest possible cation-induced spectral blue shift. We also see that the reason multivalent cations produce larger spectral blue shifts than monovalent cations is because hydrated electrons are able to simultaneously pair with a larger number of multivalent cations due to a larger free energy of interaction. Overall, the interaction of hydrated electrons with electrolytes fits well with the Hofmeister series, where the electron behaves as an anion that is slightly more able to break water's H-bond structure than chloride.

Trap-Seeking or Trap-Digging? Photoinjection of Hydrated Electrons into Aqueous NaCl Solutions

It is well-known that when excess electrons are injected into an aqueous solution, they localize and solvate in ∼1 ps. Still debated is whether localization occurs via "trap-digging", in which the electron carves out a suitable localization site, or by "trap-seeking", where the electron prefers to localize at pre-existing low-energy trap sites in solution. To distinguish between these two possible mechanisms, we study the localization dynamics of excess electrons in aqueous NaCl solutions using both ultrafast spectroscopy and mixed quantum-classical molecular dynamics simulations. By introducing pre-existing traps in the form of Na⁺ ions, we can use the cation-induced blue-shift of the hydrated electron's absorption spectrum to directly monitor the site of electron localization. Our experimental and computational results show that the electron prefers to localize directly at the sites of Na⁺ traps; the presence of concentrated electrolytes otherwise has little impact on the way trap-seeking hydrated electrons relax following injection.

Hydrated Electrons in High-Concentration Electrolytes Interact with Multiple Cations: A Simulation Study

Experimental studies have demonstrated that the hydrated electron's absorption spectrum undergoes a concentration-dependent blue-shift in the presence of electrolytes such as NaCl. The blue-shift increases roughly linearly at low salt concentration but saturates as the solubility limit of the salt is approached. Previous attempts to understand the origin of the concentration-dependent spectral shift using molecular simulation have only examined the interaction between the hydrated electron and a single sodium cation, and these simulations predicted a spectral blue-shift that was an order of magnitude larger than that seen experimentally. Thus, in this paper, we first explore the reasons for the exaggerated spectral blue-shift when a simulated hydrated electron interacts with a single Na⁺. We find that the issue arises from nonpairwise additivity of the Na⁺-e^- and H₂O-e^- pseudopotentials used in the simulation. This effect arises because the solvating water molecules donate charge into the empty orbitals of Na⁺, lowering the effective charge of the cation and thus reducing the excess electron-cation interaction. Careful analysis shows, however, that although this nonpairwise additivity changes the energetics of the electron-Na⁺ interaction, the forces between the electron, Na⁺, and water are unaffected, so that mixed quantum/classical (MQC) simulations produce the correct structure and dynamics. With this in hand, we then use MQC simulations to explore the behavior of the hydrated electron as an explicit function of NaCl salt concentration. We find that the simulations correctly reproduce the observed experimental spectral shifting behavior. The reason for the spectral shift is that as the electrolyte concentration increases, the average number of cations simultaneously interacting in contact pairs with the hydrated electron increases from 1.0 at low concentrations to ∼2.5 near the saturation limit. As the number of cations that interact with the electron increases, the cation/electron interactions becomes slightly weaker, so that the corresponding Na⁺-e^- distance increases with increasing salt concentration. We also find that the dielectric constant of the solution plays little role in the observed spectroscopy, so that the electrolyte-dependent spectral shifts of the hydrated electron are directly related to the concentration-dependent number of closely interacting cations.

How Water-Ion Interactions Control the Formation of Hydrated Electron:Sodium Cation Contact Pairs

Although solvated electrons are a perennial subject of interest, relatively little attention has been paid to the way they behave in aqueous electrolytes. Experimentally, it is known that the hydrated electron's (e_aq^-) absorption spectrum shifts to the blue in the presence of salts, and the magnitude of the shift depends on the ion concentration and the identities of both the cation and anion. Does the blue-shift result from some type of dielectric effect from the bulk electrolyte, or are there specific interactions between the hydrated electron and ions in solution? Previous work has suggested that e_aq^- forms contact pairs with aqueous ions such as Na⁺, leading to the question of what controls the stability of such contact pairs and their possible connection to the observed spectroscopy. In this work, we use mixed quantum/classical simulations to examine the nature of Na⁺:e^- contact pairs in water, using a novel method for quantum umbrella sampling to construct e_aq^--ion potentials of mean force (PMF). We find that the nature of the contact pair PMF depends sensitively on the choice of the classical interactions used to describe the Na⁺-water interactions. When the ion-water interactions are slightly stronger, the corresponding cation:e^- contact pairs form at longer distances and become free energetically less stable. We show that this is because there is a delicate balance between solvation of the cation, solvation of e_aq^- and the direct electronic interaction between the cation and the electron, so that small changes in this balance lead to large changes in the formation and stability of e^--ion contact pairs. In particular, strengthening the ion-water interactions helps to maintain a favorable local solvation environment around Na⁺, which in turn forces water molecules in the first solvation shell of the cation to be unfavorably oriented toward the electron in a contact pair; stronger solvation of the cation also reduces the electronic overlap of e_aq^- with Na⁺. We also find that the calculated spectra of different models of Na⁺:e^- contact pairs do not shift monotonically with cation-electron distance, and that the calculated spectral shifts are about an order of magnitude larger than experiment, suggesting that isolated contact pairs are not the sole explanation for the blue-shift of the hydrated electron's spectrum in the presence of electrolytes.

Nonequilibrium Solvent Effects during Photodissociation in Liquids: Dynamical Energy Surfaces, Caging, and Chemical Identity

In the gas phase, potential energy surfaces can be used to provide insight into the details of photochemical reaction dynamics. In solution, however, it is unclear what potential energy surfaces, if any, can be used to describe even simple chemical reactions such as the photodissociation of a diatomic solute. In this paper, we use mixed quantum/classical (MQC) molecular dynamics (MD) to study the photodissociation of Na₂⁺ in both liquid Ar and liquid tetrahydrofuran (THF). We examine both the gas-phase potential surfaces and potentials of mean force (PMF), which assume that the solvent remains at equilibrium with the solute throughout the photodissociation process and show that neither resemble a nonequilibrium dynamical energy surface that is generated by taking the time integral of work. For the photodissociation of Na₂⁺ in liquid Ar, the dynamical energy surface shows clear signatures of solvent caging, and the degree of caging is directly related to the mass of the solvent atoms. For Na₂⁺ in liquid THF, local specific interactions between the solute and solvent lead to changes in chemical identity that create a kinetic trap that effectively prevents the molecule from dissociating. The results show that nonequilibrium effects play an important role even in simple solution-phase reactions, requiring the use of dynamical energy surface to understand such chemical events.

The Role of the Solvent in the Condensed-Phase Dynamics and Identity of Chemical Bonds: The Case of the Sodium Dimer Cation in THF

When a solute molecule is placed in solution, is it acceptable to presume that its electronic structure is essentially the same as that in the gas phase? In this paper, we address this question from a simulation perspective for the case of the sodium dimer cation (Na₂⁺) molecule in both liquid Ar and liquid tetrahydrofuran (THF). In previous work, we showed that, when local specific interactions between a solute and solvent are energetically on the order of a hydrogen bond, the solvent can become part of the chemical identity of the solute. Here, using mixed quantum/classical molecular dynamics simulations, we see that, for the Na₂⁺ molecule, solute-solvent interactions lead to two stable, chemically distinct coordination states (Na(THF)₄-Na(THF)₅⁺ and Na(THF)₅-Na(THF)₅⁺) that are not only stable themselves as gas-phase molecules but that also have a completely new electronic structure with important implications for the excited-state photodissociation of this molecule in the condensed phase. Furthermore, we show through a set of comparative classical simulations that treating the solute's bonding electron explicitly quantum mechanically is necessary to understand both the ground-state dynamics and chemical identity of this simple diatomic molecule; even use of the quantum-derived potential of mean force is insufficient to describe the behavior of the molecule classically. Finally, we calculate the results of a proposed transient hole-burning experiment that could be used to spectroscopically disentangle the presence of the different coordination states.

The Fluxional Nature of the Hydrated Electron: Energy and Entropy Contributions to Aqueous Electron Free Energies

There has been a great deal of recent controversy over the structure of the hydrated electron and whether it occupies a cavity or contains a significant number of interior waters (noncavity). The questions we address in this work are, from a free energy perspective, how different are these proposed structures? Do the different structures all lie along a single continuum, or are there significant differences (i.e., free energy barriers) between them? To address these questions, we have performed a series of one-electron calculations using umbrella sampling with quantum biased molecular dynamics along a coordinate that directly reflects the number of water molecules in the hydrated electron's interior. We verify that a standard cavity model of the hydrated electron behaves essentially as a hard sphere: the model is dominated by repulsion at short range such that water is expelled from a local volume around the electron, leading to a water solvation shell like that of a pseudohalide ion. The repulsion is much larger than thermal energies near room temperature, explaining why such models exhibit properties with little temperature dependence. On the other hand, our calculations reveal that a noncavity model is highly fluxional, meaning that thermal motions cause the number of interior waters to fluctuate from effectively zero (i.e., a cavity-type electron) to potentially above the bulk water density. The energetic contributions in the noncavity model are still repulsive in the sense that they favor cavity formation, so the fluctuations in structure are driven largely by entropy: the entropic cost for expelling water from a region of space is large enough that some water is still driven into the electron's interior. As the temperature is lowered and entropy becomes less important, the noncavity electron's structure is predicted to become more cavity-like, consistent with the observed temperature dependence of the hydrated electron's properties. Thus, we argue that although the specific noncavity model we study overestimates the preponderance of fluctuations involving interior water molecules, with appropriate refinements to correctly capture the true average number of interior waters and molar solvation volume, a fluxional model likely makes the most sense for understanding the various experimental properties of the hydrated electron.

Ab Initio Investigation of the Resonance Raman Spectrum of the Hydrated Electron

According to the conventional picture, the aqueous or "hydrated" electron, e^-(aq), occupies an excluded volume (cavity) in the structure of liquid water. However, simulations with certain one-electron models predict a more delocalized spin density for the unpaired electron, with no distinct cavity structure. It has been suggested that only the latter (non-cavity) structure can explain the hydrated electron's resonance Raman spectrum, although this suggestion is based on calculations using empirical frequency maps developed for neat liquid water, not for e^-(aq). All-electron ab initio calculations presented here demonstrate that both cavity and non-cavity models of e^-(aq) afford significant red-shifts in the O-H stretching region. This effect is nonspecific and arises due to electron penetration into frontier orbitals of the water molecules. Only the conventional cavity model, however, reproduces the splitting of the H-O-D bend (in isotopically mixed water) that is observed experimentally and arises due to the asymmetric environments of the hydroxyl moieties in the electron's first solvation shell. We conclude that the cavity model of e^-(aq) is more consistent with the measured resonance Raman spectrum than is the delocalized, non-cavity model, despite previous suggestions to the contrary. Furthermore, calculations with hybrid density functionals and with Hartree-Fock theory predict that non-cavity liquid geometries afford only unbound (continuum) states for an extra electron, whereas in reality this energy level should lie more than 3 eV below vacuum level. As such, the non-cavity model of e^-(aq) appears to be inconsistent with available vibrational spectroscopy, photoelectron spectroscopy, and quantum chemistry.

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.

Structure of the aqueous electron

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

Solvents can control solute molecular identity

For solution-phase chemical reactions, the solvent is often considered simply as a medium to allow the reactants to encounter each other by diffusion. Although examples of direct solvent effects on molecular solutes exist, such as the compression of solute bonding electrons due to Pauli repulsion interactions, the solvent is not usually considered a part of the chemical species of interest. We show, using quantum simulations of Na₂, that when there are local specific interactions between a solute and solvent that are energetically on the same order as a hydrogen bond, the solvent controls not only the bond dynamics but also the chemical identity of the solute. In tetrahydrofuran, dative bonding interactions between the solvent and Na atoms lead to unique coordination states that must cross a free energy barrier of ~8 k_BT-undergoing a chemical reaction-to interconvert. Each coordination state has its own dynamics and spectroscopic signatures, highlighting the importance of considering the solvent in the identity of condensed-phase chemical systems.

Short-Range Electron Correlation Stabilizes Noncavity Solvation of the Hydrated Electron

The hydrated electron, e^-_(aq), has often served as a model system to understand the influence of condensed-phase environments on electronic structure and dynamics. Despite over 50 years of study, however, the basic structure of e^-_(aq) is still the subject of controversy. In particular, the structure of e^-_(aq) was long assumed to be an electron localized within a solvent cavity, in a manner similar to halide solvation. Recently, however, we suggested that e^-_(aq) occupies a region of enhanced water density with little or no discernible cavity. The potential we developed was only subtly different from those that give rise to a cavity solvation motif, which suggests that the driving forces for noncavity solvation involve subtle electron-water attractive interactions at close distances. This leads to the question of how dispersion interactions are treated in simulations of the hydrated electron. Most dispersion potentials are ad hoc or are not designed to account for the type of close-contact electron-water overlap that might occur in the condensed phase, and where short-range dynamic electron correlation is important. To address this, in this paper we develop a procedure to calculate the potential energy surface between a single water molecule and an excess electron with high-level CCSD(T) electronic structure theory. By decomposing the electron-water potential into its constituent energetic contributions, we find that short-range electron correlation provides an attraction of comparable magnitude to the mean-field interactions between the electron and water. Furthermore, we find that by reoptimizing a popular cavity-forming one-electron model potential to better capture these attractive short-range interactions, the enhanced description of correlation predicts a noncavity e^-_(aq) with calculated properties in better agreement with experiment. Although much attention has been placed on the importance of long-range dispersion interactions in water cluster anions, our study reveals that largely unexplored short-range correlation effects are crucial in dictating the solvation structure of the condensed-phase hydrated electron.

A Simple ab Initio Model for the Solvated Electron in Methanol

The solvation structure of a solvated electron in methanol is investigated with ab initio calculations of small anion methanol clusters in a polarized dielectric continuum. We find that the lowest-energy structure in best agreement with experiment, calculated with CCSD, MP2, and B3LYP methods with aug-cc-pvdz basis set, is a tetrahedral arrangement of four methanol molecules with OH bonds oriented toward the center. The optimum distance from the tetrahedron center to the hydroxyl protons is ∼1.8 Å, significantly smaller than previous estimates. We are able to reproduce experimental radius of gyration Rg (deduced from optical absorption), vertical detachment energy, and resonance Raman frequencies. The electron paramagnetic resonance g-factor shift is qualitatively reproduced using density functional theory.

Hydrated Electrons in Water Clusters: Inside or Outside, Cavity or Noncavity?

In this work, we compare the applicability of three electron–water molecule pseudopotentials in modeling the physical properties of hydrated electrons. Quantum model calculations illustrate that the recently suggested Larsen–Glover–Schwartz (LGS) model and its modified m-LGS version have a too-attractive potential in the vicinity of the oxygen. As a result, LGS models predict a noncavity hydrated electron structure in clusters at room temperature, as seen from mixed one-electron quantum–classical molecular dynamics simulations of water cluster anions, with the electron localizing exclusively in the interior of the clusters. Comparative calculations using the cavity-preferring Turi–Borgis (TB) model predict interior-state and surface-state cluster isomers. The computed associated physical properties are also analyzed and compared to available experimental data. We find that the LGS and m-LGS potentials provide results that appear to be inconsistent with the size dependence of the experimental data. The simulated TB tendencies are qualitatively correct. Furthermore, ab initio calculations on static LGS noncavity structures indicate weak stabilization of the excess electron in regions where the LGS potential preferably and strongly binds the electron. TB calculations give stabilization energies that are in line with the ab initio results. In conclusion, we observe that the cavity-preferring pseudopotential model predicts cluster physical properties in better agreement with experimental data and ab initio calculations than the models predicting noncavity structures for the hydrated electron.

Response to "Comment on 'Going beyond the frozen core approximation: development of coordinate-dependent pseudopotentials and application to Na2(+)'" [J. Chem. Phys. 139, 147101 (2013)]

Stoll, Fuentealba, and Szentpály (SFS) argue that the coordinate-dependent pseudopotential we developed for the sodium dimer cation molecule is inferior to other potentials that have been presented in the literature for this molecule. The goal of our work, however, was to present a novel method for the development of rigorous coordinate-dependent pseudopotentials. Our method is designed to reproduce all-electron Hartree-Fock calculations without the inclusion of adjustable parameters. Moreover, our method starts from the superposition of unoptimized, non-norm-conserved atomic potentials, so that when complete, the resulting norm-conserving potential can reproduce an all-electron Hartree-Fock calculation without the inclusion of adjustable parameters. We chose the sodium dimer cation system as a proof of principle for our method, and showed that our method does indeed allow a one-electron calculation to correctly reproduce the all-electron Hartree-Fock calculation from bonding to the dissociation limit. Our purpose in developing this method is to use such potentials in condensed-phase mixed quantum/classical molecular dynamics simulations, where inclusion of valence polarization effects is unimportant or can be added on after the fact. Thus we do not claim that our method provides a potential that is superior to potentials that have been specifically constructed to go beyond the static exchange approximation and/or include valence polarization effects-such potentials are beyond the scope of our work. We also note that although we made a numerical error in the application of our method to Na2(+) in our original work [A. Kahros and B. J. Schwartz, J. Chem. Phys. 138, 054110 (2013)] that led to an overestimation of the magnitude of core polarization effects for this particular molecule, out method does work as derived for this molecule and the error does not affect the significance of our method or its general applicability.

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.

A computationally efficient exact pseudopotential method. II. Application to the molecular pseudopotential of an excess electron interacting with tetrahydrofuran (THF)

In the preceding paper, we presented an analytic reformulation of the Phillips-Kleinman (PK) pseudopotential theory. In the PK theory, the number of explicitly treated electronic degrees of freedom in a multielectron problem is reduced by forcing the wave functions of the few electrons of interest (the valence electrons) to be orthogonal to those of the remaining electrons (the core electrons); this results in a new Schrodinger equation for the valence electrons in which the effects of the core electrons are treated implicitly via an extra term known as the pseudopotential. Although this pseudopotential must be evaluated iteratively, our reformulation of the theory allows the exact pseudopotential to be found without ever having to evaluate the potential energy operator, providing enormous computational savings. In this paper, we present a detailed computational procedure for implementing our reformulation of the PK theory, and we illustrate our procedure on the largest system for which an exact pseudopotential has been calculated, that of an excess electron interacting with a tetrahyrdrofuran (THF) molecule. We discuss the numerical stability of several approaches to the iterative solution for the pseudopotential, and find that once the core wave functions are available, the full e(-)-THF pseudopotential can be calculated in less than 3 s on a relatively modest single processor. We also comment on how the choice of basis set affects the calculated pseudopotential, and provide a prescription for correcting unphysical behavior that arises at long distances if a localized Gaussian basis set is used. Finally, we discuss the effective e(-)-THF potential in detail, and present a multisite analytic fit of the potential that is suitable for use in molecular simulation.