William J. Glover

Does the Hydrated Electron Occupy a Cavity

Filling a Cavity Unlike liquid ammonia, water cannot sustain a steady concentration of isolated electrons. Nonetheless, high-energy irradiation can introduce a small number of free charges that engage in potent reductive chemistry and have clear spectroscopic signatures. The manner in which water solubilizes these hydrated electrons has remained uncertain, but the general consensus has been that repulsive interactions drive the nearest water molecules away, leaving the electron in a nearly spherical empty cavity. Larsen et al. (p. 65; see the Perspective by Jordan and Johnson) upend this consensus with simulations based on a more thorough potential function for modeling the competing attractions and repulsions between the electron and surrounding water. The calculations suggest that the hydrated electron actually draws water in, occupying a region denser than the pure bulk liquid. The model reproduces experimental spectral and dynamic observations as effectively as, and in some cases better than, the cavity framework. A long-standing model of the solvent geometry surrounding a free charge in water is questioned by new numerical simulations. 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 ~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.

Role of Rydberg states in the photochemical dynamics of ethylene.

We use the ab initio multiple spawning method with potential energy surfaces and nonadiabatic coupling vectors computed from multistate multireference perturbation theory (MSPT2) to follow the dynamics of ethylene after photoexcitation. We introduce an analytic formulation for the nonadiabatic coupling vector in the context of MSPT2 calculations. We explicitly include the low-lying 3s Rydberg state which has been neglected in previous ab initio molecular dynamics studies of this process. We find that although the 3s Rydberg state lies below the optically bright ππ* state, little population gets trapped on this state. Instead, the 3s Rydberg state is largely a spectator in the photodynamics, with little effect on the quenching mechanism or excited state lifetime. We predict the time-resolved photoelectron spectrum for ethylene and point out the signature of Rydberg state involvement that should be easily observed.

Raman spectra of ionic liquids: A simulation study of LaCl3 and its mixtures with alkali chlorides

Theoretical Raman spectra of the elpasolite-structured crystal Cs2NaLaCl6 and of molten mixtures of LaCl6 with NaCl and CsCl have been obtained from computer simulations in order to examine how the Raman spectra reflect the coordination structure around the La3+ ions. This system is a model for many other trivalent metal halides and for examining how the network structure of the pure melts is broken down by the addition of alkali halides with different structure-breaking powers. The results suggest a way of reconciling the conclusions of Raman studies about the structures of the melts with those of neutron and x-ray-diffraction studies, which have already been examined with the same simulation methods. The Raman spectra, both polarized and depolarized, are calculated from a model for the dependence of the polarizability of the system on the ionic coordinates which was inspired by electronic structure calculations of the polarizabilities of ions in a condensed phase environment. Some results on the lifetimes of the coordination complexes responsible for the appearance of the discrete Raman bands are discussed.

Ultrafast internal conversion in ethylene. II. Mechanisms and pathways for quenching and hydrogen elimination

Through a combined experimental and theoretical approach, we study the nonadiabatic dynamics of the prototypical ethylene (C(2)H(4)) molecule upon π → π(∗) excitation with 161 nm light. Using a novel experimental apparatus, we combine femtosecond pulses of vacuum ultraviolet and extreme ultraviolet (XUV) radiation with variable delay to perform time resolved photo-ion fragment spectroscopy. In this second part of a two part series, the XUV (17 eV < hν < 23 eV) probe pulses are sufficiently energetic to break the C-C bond in photoionization, or to photoionize the dissociation products of the vibrationally hot ground state. The experimental data is directly compared to excited state ab initio molecular dynamics simulations explicitly accounting for the probe step. Enhancements of the CH(2)(+) and CH(3)(+) photo-ion fragment yields, corresponding to molecules photoionized in ethylene (CH(2)CH(2)) and ethylidene (CH(3)CH) like geometries are observed within 100 fs after π → π(∗) excitation. Quantitative agreement between theory and experiment on the relative CH(2)(+) and CH(3)(+) yields provides experimental confirmation of the theoretical prediction of two distinct conical intersections and their branching ratio [H. Tao, B. G. Levine, and T. J. Martinez, J. Phys. Chem. A. 113, 13656 (2009)]. Evidence for fast, non-statistical, elimination of H(2) molecules and H atoms is observed in the time resolved H(2)(+) and H(+) signals.

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.

Between ethylene and polyenes - the non-adiabatic dynamics of cis-dienes

Using Ab Initio Multiple Spawning (AIMS) with a Multi-State Multi-Reference Perturbation theory (MS-MR-CASPT2) treatment of the electronic structure, we have simulated the non-adiabatic excited state dynamics of cyclopentadiene (CPD) and 1,2,3,4-tetramethyl-cyclopentadiene (Me4-CPD) following excitation to S1. It is observed that torsion around the carbon-carbon double bonds is essential in reaching a conical intersection seam connecting S1 and S0. We identify two timescales; the induction time from excitation to the onset of population transfer back to S0 (CPD: -25 fs, Me4-CPD: -71 fs) and the half-life of the subsequent population transfer (CPD: -28 fs, Me4-CPD: -48 fs). The longer timescales for Me4-CPD are a kinematic consequence of the inertia of the substituents impeding the essential out-of-plane motion that leads to the conical intersection seam. A bifurcation is observed on S1 leading to population transfer being attributable, in a 5 : 2 ratio for CPD and 7 : 2 ratio for Me4-CPD, to two closely related conical intersections. Calculated time-resolved photoelectron spectra are in excellent agreement with experimental spectra validating the simulation results.

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.

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.

Comment on “An electron-water pseudopotential for condensed phase simulation” [J. Chem. Phys. 86, 3462 (1987)]

Some time ago, Schnitker and Rossky derived a pseudopotential describing the interaction of an excess electron with water and used it to study the properties of the hydrated electron with molecular dynamics simulation. The derivation was based on ideas from electron-molecule scattering theory, with the wave function of the water-plus-electron system treated at the single-determinant Hartree–Fock level. Schnitker and Rossky’s application of this approach to water used the assumption that the pseudo-orbital associated with the pseudopotential is constant across each occupied molecular orbital of the water molecule, and this assumption leads to a particularly simple analytic form for the pseudopotential, which is given by Eq. 3 , below. Many properties of the hydrated electron have been understood in the context provided by the Schnitker and Rossky SR pseudopotential, although similar results have been seen with other pseudopotentials. With the published SR pseudopotential, the hydrated electron occupies a nearly spherical cavity and has a radius of gyration of 2.1 A. There are six water molecules in the first solvation shell, arranged quasioctahedrally in the so-called Kevan structure, with one hydrogen atom on each first-shell water pointing directly toward the hydrated electron’s center of mass see, e.g., Fig. 2 b . Recently, however, we discovered an error in the electron-water pseudopotential published by SR that dramatically changes the predicted properties of the hydrated electron. Thus, we believe it is worthwhile to comment on the nature of the error and to describe how the properties of the hydrated electron change when this error is corrected. Briefly, the error in the original paper is as follows: with the approximations made by SR, the part of the pseudopotential that accounts for the repulsion of the excess electron by the electrons in the occupied water molecular orbitals takes the form

Free Energies of Quantum Particles: The Coupled-Perturbed Quantum Umbrella Sampling Method.

We introduce a new simulation method called Coupled-Perturbed Quantum Umbrella Sampling that extends the classical umbrella sampling approach to reaction coordinates involving quantum mechanical degrees of freedom. The central idea in our method is to solve coupled-perturbed equations to find the response of the quantum systems wave function along a reaction coordinate of interest. This allows for propagation of the systems dynamics under the influence of a quantum biasing umbrella potential and provides a method to rigorously undo the effects of the bias to compute equilibrium ensemble averages. In this way, one can drag electrons into regions of high free energy where they would otherwise not go, thus enabling chemistry by fiat. We demonstrate the applicability of our method for two condensed-phase systems of interest. First, we consider the interaction of a hydrated electron with an aqueous sodium cation, and we calculate a potential of mean force that shows that an e(-):Na(+) contact pair is the thermodynamically favored product starting from either a neutral sodium atom or the separate cation and electron species. Second, we present the first determination of a hydrated electrons free-energy profile relative to an air/water interface. For the particular model parameters used, we find that the hydrated electron is more thermodynamically stable in the bulk rather than at the interface. Our analysis suggests that the primary driving force keeping the electron away from the interface is the long-range electron-solvent polarization interaction rather than the short-range details of the chosen pseudopotential.