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We present efficient analytical gradients of property-based diabatic states and couplings using a Lagrangian formalism. Unlike previous formulations, the method achieves a computational scaling that is independent of the number of adiabatic states used to construct the diabats. The approach is generalizable to other property-based diabatization schemes and electronic structure methods as long as analytical energy gradients are available and integral derivatives with the property operator can be formed. We also introduce a scheme to phase and reorder diabats to ensure their continuity between molecular configurations. We demonstrate this for the specific case of Boys diabatic states obtained from state-averaged complete active space self-consistent field electronic structure calculations with GPU acceleration in the TeraChem package. The method is used to test the Condon approximation for the hole transfer in an explicitly solvated model DNA oligomer.

The photoisomerization of isolated ethylene (ethene) was observed in real time from the Franck-Condon region in the

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.

We introduce Active Orbital Preservation for Multiconfigurational Self-Consistent Field (AOP-MCSCF), an automated approach to improving the consistency of active space orbitals over multiple molecular configurations. Our approach is based on maximum overlap with a reference set of active space orbitals taken from a single geometry of a chromophore in the gas phase and can be used to automatically preserve the appropriate orbitals of the chromophore across multiple thermally sampled configurations, even when the chromophore is solvated by quantum-mechanically treated water molecules. In particular, using the singular value decomposition of a Molecular Orbital (MO) overlap matrix between the system and reference, we rotate the MOs of the system to align with the reference active space orbitals and use the resulting rotated orbitals as an initial guess to a MCSCF calculation. We demonstrate the approach on aqueous p-hydroxybenzylidene-imidazolinone (HBI) and find that AOP-MCSCF converges to the “correct” orbitals for over 90% of 3000 thermally sampled configurations. In addition, we compute the linear absorption spectrum and find excellent agreement with new experimental measurements up to 5.4 eV (230 nm). We show that electrostatic contributions to the solvation energy of HBI largely explain the observed state-dependent solvatochromism.

We explore the convergence of the many-body expansion for a prototypical hole-transfer reaction between Zn(0) and Zn(I) in a condensed-phase environment. Poor convergence of state energies is seen when the adiabatic representation is used, which can be understood from the fragment single-point calculations at low orders of the many-body expansion incorrectly localizing charges compared to the full system, thus leading to qualitative errors in the electronic structure of the adiabatic states between fragments. Using a charge-localized representation of the electronic Hamiltonian, we introduce a diabatic many-body expansion method with quantitative accuracy for ground- and excited-state potential energy surfaces of a charge-transfer reaction. Combining with a multiconfigurational self-consistent field affords a fragmentation approach that scales quadratically with system size while retaining chemical accuracy (

Recent interest in polarizable embedding methods for electronic excited states has so far been focused on optical absorption and emission spectra calculations. To explore the suitability of these methods for excited-state reactions, we constructed a simple molecular system with an electronic crossing coupled to a polarizable species: the triatomic LiFBe. We found that current polarizable QM/MM methods inadequately describe the potential energy surfaces in this system, particularly close to the electronic crossing, so we developed a new polarizable embedding method called dynamically weighted polarizable QM/MM. The new method reproduces the potential energy surfaces of LiFBe from full-system multireference configuration interaction singles and doubles calculations with near-quantitative accuracy.

A fundamental understanding of the excited-state properties of molecular crystals is of central importance for their optoelectronics applications. In this study, we developed the electrostatically embedded generalized molecular fractionation (EE-GMF) method for the quantitative characterization of the excited-state properties of locally excited molecular clusters. The accuracy of the EE-GMF method is systematically assessed for oligoacene crystals. Our result demonstrates that the EE-GMF method is capable of providing the lowest vertical singlet (S

Many experiments have been carried out to display different colors of Proteorhodopsin (PR) and its mutants, but the mechanism of color tuning of PR was not fully elucidated. In this study, we applied the Electrostatically Embedded Generalized Molecular Fractionation with Conjugate Caps (EE-GMFCC) method to the prediction of excitation energies of PRs. Excitation energies of 10 variants of Blue Proteorhodopsin (BPR-PR105Q) in residue 105GLN were calculated with the EE-GMFCC method at the TD-B3LYP/6-31G* level. The calculated results show good correlation with the experimental values of absorption wavelengths, although the experimental wavelength range among these systems is less than 50 nm. The ensemble-averaged electric fields along the polyene chain of retinal correlated well with EE-GMFCC calculated excitation energies for these 10 PRs, suggesting that electrostatic interactions from nearby residues are responsible for the color tuning. We also utilized the GMFCC method to decompose the excitation energy contribution per residue surrounding the chromophore. Our results show that residues ASP97 and ASP227 have the largest contribution to the absorption spectral shift of PR among the nearby residues of retinal. This work demonstrates that the EE-GMFCC method can be applied to accurately predict the absorption spectral shifts for biomacromolecules.

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 ov...

The ultrafast excited state dynamics of the smallest polyene, trans-1,3-butadiene, were studied by femtosecond time-resolved photoelectron-photoion coincidence (TRPEPICO) spectroscopy. The evolution of the excited state wavepacket, created by pumping the bright 1Bu (ππ*) electronic state at its origin of 216 nm, is projected via one- and two-photon ionization at 267 nm onto several ionization continua. The results are interpreted in terms of Koopmans’ correlations and Franck-Condon factors for the excited and cationic states involved. The known predissociative character of the cation excited states is utilized to assign photoelectron bands to specific continua using TRPEPICO spectroscopy. This permits us to report the direct observation of the famously elusive S1(21Ag) dark electronic state during the internal conversion of trans 1,3-butadiene. Our phenomenological analysis permits the spectroscopic determination of several important time constants. We report the overall decay lifetimes of the 11Bu and 21Ag states and observe the re-appearance of the hot ground state molecule. We argue that the apparent dephasing time of the S2(11Bu) state, which leads to the extreme breadth of the absorption spectrum, is principally due to large amplitude torsional motion on the 1Bu surface in conjunction with strong non-adiabatic couplings via conical intersections, whereupon nuclear wavepacket revivals to the initial Franck-Condon region become effectively impossible. In Paper II [W. J. Glover et al., J. Chem. Phys. 148, 164303 (2018)], ab initio multiple spawning is used for on-the-fly computations of the excited state non-adiabatic wavepacket dynamics and their associated TRPEPICO observables, allowing for direct comparisons of experiment with theory.

The excited state non-adiabatic dynamics of the smallest polyene, trans 1,3-butadiene (BD), has long been the subject of controversy due to its strong coupling, ultrafast time scales and the difficulties that theory faces in describing the relevant electronic states in a balanced fashion. Here we apply Ab Initio Multiple Spawning (AIMS) using state-averaged complete active space multistate second order perturbation theory [SA-3-CAS(4/4)-MSPT2] which describes both static and dynamic electron correlation effects, providing a balanced description of both the initially prepared bright 11Bu (ππ*) state and non-adiabatically coupled dark 21Ag state of BD. Importantly, AIMS allows for on-the-fly calculations of experimental observables. We validate our approach by directly simulating the time resolved photoelectron-photoion coincidence spectroscopy results presented in Paper I [A. E. Boguslavskiy et al., J. Chem. Phys. 148, 164302 (2018)], demonstrating excellent agreement with experiment. Our simulations reveal that the initial excitation to the 11Bu state rapidly evolves via wavepacket dynamics that follow both bright- and dark-state pathways as well as mixtures of these. In order to test the sensitivity of the AIMS results to the relative ordering of states, we considered two hypothetical scenarios biased toward either the bright 1Bu or the dark 21Ag state. In contrast with AIMS/SA-3-CAS(4/4)-MSPT2 simulations, neither of these scenarios yields favorable agreement with experiment. Thus, we conclude that the excited state non-adiabatic dynamics in BD involves both of these ultrafast pathways.

We use one-electron non-adiabatic mixed quantum/classical simulations to explore the temperature dependence of both the ground-state structure and the excited-state relaxation dynamics of the hydrated electron. We compare the results for both the traditional cavity picture and a more recent non-cavity model of the hydrated electron and make definite predictions for distinguishing between the different possible structural models in future experiments. We find that the traditional cavity model shows no temperature-dependent change in structure at constant density, leading to a predicted resonance Raman spectrum that is essentially temperature-independent. In contrast, the non-cavity model predicts a blue-shift in the hydrated electron's resonance Raman O-H stretch with increasing temperature. The lack of a temperature-dependent ground-state structural change of the cavity model also leads to a prediction of little change with temperature of both the excited-state lifetime and hot ground-state cooling time of the hydrated electron following photoexcitation. This is in sharp contrast to the predictions of the non-cavity model, where both the excited-state lifetime and hot ground-state cooling time are expected to decrease significantly with increasing temperature. These simulation-based predictions should be directly testable by the results of future time-resolved photoelectron spectroscopy experiments. Finally, the temperature-dependent differences in predicted excited-state lifetime and hot ground-state cooling time of the two models also lead to different predicted pump-probe transient absorption spectroscopy of the hydrated electron as a function of temperature. We perform such experiments and describe them in Paper II [E. P. Farr et al., J. Chem. Phys. 147, 074504 (2017)], and find changes in the excited-state lifetime and hot ground-state cooling time with temperature that match well with the predictions of the non-cavity model. In particular, the experiments reveal stimulated emission from the excited state with an amplitude and lifetime that decreases with increasing temperature, a result in contrast to the lack of stimulated emission predicted by the cavity model but in good agreement with the non-cavity model. Overall, until ab initio calculations describing the non-adiabatic excited-state dynamics of an excess electron with hundreds of water molecules at a variety of temperatures become computationally feasible, the simulations presented here provide a definitive route for connecting the predictions of cavity and non-cavity models of the hydrated electron with future experiments.

We recently introduced a Dynamically Weighted Complete Active Space Self-Consistent Field (DW-CASSCF) electronic structure for excited-state dynamics. In this Communication, we reformulate analytical gradients at this level of theory using a Lagrangian approach, thereby reducing the required number of coupled-perturbed CASSCF calculations to one per state gradient. In addition, we derive and implement derivative couplings at the DW-CASSCF level for the first time. We demonstrate the new formulation of DW-CASSCF gradients by optimizing a conical intersection for the p-hydroxybenzylidene-imidazolinone anion, the green fluorescent protein chromophore, to shed light on its observed radiationless decay dynamics in the ultraviolet region.

The properties of the hydrated electron at the air/water interface are computed for both a cavity and a noncavity model using mixed quantum/classical molecular dynamics simulation. We take advantage of our recently developed formalism for umbrella sampling with a restrained quantum expectation value to calculate free-energy profiles of the hydrated electron's position relative to the water surface. We show that it is critical to use an instantaneous description of the air/water interface rather than the Gibbs' dividing surface to obtain accurate potentials of mean force. We find that noncavity electrons, which prefer to encompass several water molecules, avoid the interface where water molecules are scarce. In contrast, cavity models of the hydrated electron, which prefer to expel water, have a local free-energy minimum near the interface. When the cavity electron occupies this minimum, its absorption spectrum is quite red-shifted, its binding energy is significantly lowered, and its dynamics speed up quite a bit compared with the bulk, features that have not been found by experiment. The surface activity of the electron therefore serves as a useful test of cavity versus noncavity electron solvation.

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.

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.

Understanding how a solvent affects the quantum mechanics and reactivity of the chemical bonds of dissolved solutes is of fundamental importance to chemistry. To explore condensed-phase effects on a simple molecular solute, we have studied the six-dimensional two-electron wave function of the bonding electrons of the Na2 molecule in liquid argon via mixed quantum/classical simulation. We find that even though Ar is an apolar liquid, solvent interactions produce dipole moments on Na2 that can reach magnitudes over 1.4 D. These interactions also change the selection rules, induce significant motional-narrowing, and cause a large (26 cm−1) blue shift of the dimer’s vibrational spectrum relative to that in the gas phase. These effects cannot be captured via classical simulation, highlighting the importance of quantum many-body effects.

Adiabatic mixed quantum/classical molecular dynamics simulations were used to generate snapshots of the hydrated electron (e-) in liquid water at 300 K. Water cluster anions that include two complete solvation shells centered on the e- were extracted from these simulations and embedded in a matrix of fractional point charges designed to represent the rest of the solvent. Density functional theory and single-excitation configuration interaction methods were then applied to these embedded clusters. The salient feature of these hybrid calculations is significant transfer (ca. 0.18) of the excess electron's charge density into the O 2p orbitals in OH groups forming the solvation cavity. We used the results of these calculations to examine the structure of the molecular orbitals, the density of states, the absorption spectra in the visible and ultraviolet, the hyperfine coupling (hfc) tensors, and the IR and Raman spectra of the e-. The calculated hfc tensors were used to compute the EPR and ESEEM spectra for the e- that compared favorably to the experimental spectra of trapped e- in alkaline ice. The calculated vibrational spectra of the e- are consistent with the red-shifted bending and stretching frequencies observed in resonance Raman experiments. The model also accounts for the VIS and 190-nm absorption bands of the e-. Thus, our study suggests that to explain several important experimentally observed properties of the e-, many-electron effects must be accounted for., Comment: 68 pages, 12 figures + 16 more figures in the supplement (included) submitted to J Phys Chem A

© 2014 American Chemical Society. 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 system's wave function along a reaction coordinate of interest. This allows for propagation of the system's 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 electron's 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.

State averaged complete active space self-consistent field (SA-CASSCF) is a workhorse for determining the excited-state electronic structure of molecules, particularly for states with multireference character; however, the method suffers from known issues that have prevented its wider adoption. One issue is the presence of discontinuities in potential energy surfaces when a state that is not included in the state averaging crosses with one that is. In this communication I introduce a new dynamical weight with spline (DWS) scheme that mimics SA-CASSCF while removing energy discontinuities due to unweighted state crossings. In addition, analytical gradients for DWS-CASSCF (and other dynamically weighted schemes) are derived for the first time, enabling energy-conserving excited-state ab initio molecular dynamics in instances where SA-CASSCF fails.

We present a new algorithm for ab initio quantum nonadiabatic molecular dynamics that combines the best features of ab initio Multiple Spawning (AIMS) and Multiconfigurational Ehrenfest (MCE) methods. In this new method, ab initio multiple cloning (AIMC), the individual trajectory basis functions (TBFs) follow Ehrenfest equations of motion (as in MCE). However, the basis set is expanded (as in AIMS) when these TBFs become sufficiently mixed, preventing prolonged evolution on an averaged potential energy surface. We refer to the expansion of the basis set as "cloning," in analogy to the "spawning" procedure in AIMS. This synthesis of AIMS and MCE allows us to leverage the benefits of mean-field evolution during periods of strong nonadiabatic coupling while simultaneously avoiding mean-field artifacts in Ehrenfest dynamics. We explore the use of time-displaced basis sets, "trains," as a means of expanding the basis set for little cost. We also introduce a new bra-ket averaged Taylor expansion (BAT) to approximate the necessary potential energy and nonadiabatic coupling matrix elements. The BAT approximation avoids the necessity of computing electronic structure information at intermediate points between TBFs, as is usually done in saddle-point approximations used in AIMS. The efficiency of AIMC is demonstrated on the nonradiative decay of the first excited state of ethylene. The AIMC method has been implemented within the AIMS-MOLPRO package, which was extended to include Ehrenfest basis functions.

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.

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.

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(-).

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.

Through a combined experimental and theoretical approach, we study the nonadiabatic dynamics of the prototypical ethylene (C$_2$H$_4$) molecule upon $\pi \rightarrow \pi^*$ excitation with 161 nm light. Using a novel experimental apparatus, we combine femtosecond pulses of vacuum ultraviolet (VUV) 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 extreme ultraviolet (17 eV$ < h \nu < 23$ eV) probe pulses are sufficiently energetic to break the C-C bond in photoionization, or photoionize the dissociation products of the vibrationally hot ground state. The experimental data is directly compared to ab initio molecular dynamics simulations accounting for both the pump and probe steps. Enhancements of the CH$_2^+$ and CH$_3^+$ photoion 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 $\pi \rightarrow \pi^*$ 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 transition states and their branching ratio (Tao, et al. J. Phys. Chem. A. 113, 13656 (2009)). Fast, non-statistical, elimination of H$_2$ molecules and H atoms is observed in the time resolved H$_2^+$ and H$^+$ signals.

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.

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.

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

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.

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.

Ab initio multiple spawning provides a powerful and accurate way of describing the excited-state dynamics of molecular systems, whose strength resides in the proper description of coherence effects during nonadiabatic processes thanks to the coupling of trajectory basis functions. However, the simultaneous propagation of a large number of trajectory basis functions can be numerically inconvenient. We propose here an elegant and simple solution to this issue, which consists of (i) detecting uncoupled groups of coupled trajectory basis functions, and (ii) selecting stochastically one of these groups to continue the AIMS dynamics. We show that this procedure can reproduce the results of full AIMS dynamics in cases where the uncoupled groups of TBFs stay uncoupled throughout the dynamics (which is often the case in high dimensional problems). We present and discuss the aforementioned idea in detail and provide simple numerical applications on indole, ethylene and protonated formaldimine, highlighting the potential of stochastic-selection ab initio multiple spawning.