Understanding ion-transfer reactions in silver electrodissolution and electrodeposition from first-principles calculations and experiments.

The electrified aqueous/metal interface is critical in controlling the performance of energy conversion and storage devices, but an atomistic understanding of even basic interfacial electrochemical reactions challenges both experiment and computation. We report a combined simulation and experimental study of (reversible) ion-transfer reactions involved in anodic Ag corrosion/deposition, a model system for interfacial electrochemical processes generating or consuming ions. With the explicit modeling of the electrode potential and a hybrid implicit-explicit solvation model, the density functional theory calculations produce free energy curves predicting thermodynamics, kinetics, partial charge profiles, and reaction trajectories. The calculated (equilibrium) free energy barriers (0.2 eV), and their asymmetries, agree with experimental activation energies (0.4 eV) and transfer coefficients, which were extracted from temperature-dependent voltage-step experiments on Au-supported, Ag-nanocluster substrates. The use of Ag nanoclusters eliminates the convolution of the kinetics of Ag+(aq.) generation and transfer with those of nucleation or etch-pit formation. The results indicate that the barrier is controlled by the bias-dependent competition between partial solvation of the incipient ion, metal-metal bonding, and electrostatic stabilization by image charge, with the latter two factors weakened by stronger positive biases. We also report simulations of the bias-dependence of defect generation relevant to nucleating corrosion by removing an atom from a perfect Ag(100) surface, which is predicted to occur via a vacancy-adatom intermediate. Together, these experiments and calculations provide the first validated, accurate, molecular model of the central steps that govern the rates of important dissolution/deposition reactions broadly relevant across the energy sciences.

Predicting the X-ray Absorption Spectrum of Ozone with Single Configuration State Functions.

X-ray absorption spectra (XAS) of biradicaloid species are often thought to represent a challenge to theoretical methods. This has led to the testing of recently developed multireference techniques on the XAS of ozone, but reproduction of the experimental spectral profile has proven difficult. We utilize a minimal model consisting of a single configuration state function (CSF) per excited state to model core-level excitations of ozone, with the orbitals of each CSF optimized using the restricted open-shell Kohn-Sham (ROKS) method. This protocol leads to semiquantitative agreement with experimental XAS. In fact, we find that low-lying core-hole excited states in biradicaloids can be approximated with individual CSFs, despite the presence of multireference character in the ground state. We also report that the 1s → π* and 1s → σ* transitions have quite distinct widths for O3. This reveals the importance of sampling over a representative range of geometries from the vibrational ground state for properly assessing the accuracy of electronic structure methods against experiments instead of the popular procedure of uniformly broadening stick spectra at the equilibrium geometry.

When Is a Bond Broken? The Polarizability Perspective.

The question of when a chemical bond can be said to be broken is of fundamental chemical interest but has not been widely studied. Herein we propose that the maxima of static polarizability along bond dissociation coordinates naturally define cutoff points for bond rupture, as they represent the onset of localization of shared electron density into constituent fragments. Examples of computed polarizability maxima over the course of bond cleavage in main-group and transition metal compounds are provided, across covalent, dative and charge-shift bonds. The behavior along reaction paths is also considered. Overall, the static polarizability is found to be a sensitive reporter of electronic structure reorganization associated with bond stretching, and thus can serve as a metric for describing bond cleavage (or diagnose the absence of a chemical bond).

Probing C-I bond fission in the UV photochemistry of 2-iodothiophene with core-to-valence transient absorption spectroscopy.

The UV photochemistry of small heteroaromatic molecules serves as a testbed for understanding fundamental photo-induced chemical transformations in moderately complex compounds, including isomerization, ring-opening, and molecular dissociation. Here, a combined experimental-theoretical study of 268 nm UV light-induced dynamics in 2-iodothiophene (C4H3IS) is performed. The dynamics are experimentally monitored with a femtosecond extreme ultraviolet (XUV) probe that measures iodine N-edge 4d core-to-valence transitions. Experiments are complemented by density functional theory calculations of both the pump-pulse induced valence excitations and the XUV probe-induced core-to-valence transitions. Possible intramolecular relaxation dynamics are investigated by ab initio molecular dynamics simulations. Gradual absorption changes up to ∼0.5 to 1 ps after excitation are observed for both the parent molecular species and emerging iodine fragments, with the latter appearing with a characteristic rise time of 160 ± 30 fs. Comparison of spectral intensities and energies with the calculations identifies an iodine dissociation pathway initiated by a predominant π → π* excitation. In contrast, initial excitation to a nearby n⟂ → σ* state appears unlikely based on a significantly smaller oscillator strength and the absence of any corresponding XUV absorption signatures. Excitation to the π → π* state is followed by contraction of the C-I bond, enabling a nonadiabatic transition to a dissociative π→σC-I* state. For the subsequent fragmentation, a relatively narrow bond-length region along the C-I stretch coordinate between 230 and 280 pm is identified, where the transition between the parent molecule and the thienyl radical + iodine atom products becomes prominent in the XUV spectrum due to rapid localization of two singly occupied molecular orbitals on the two fragments.

Femtosecond symmetry breaking and coherent relaxation of methane cations via x-ray spectroscopy.

Understanding the relaxation pathways of photoexcited molecules is essential to gain atomistic-level insight into photochemistry. We performed a time-resolved study of ultrafast molecular symmetry breaking through geometric relaxation (Jahn-Teller distortion) on the methane cation. Attosecond transient absorption spectroscopy with soft x-rays at the carbon K-edge revealed that the distortion occurred within 10 ± 2 femtoseconds after few-femtosecond strong-field ionization of methane. The distortion activated coherent oscillations in the asymmetric scissoring vibrational mode of the symmetry-broken cation, which were detected in the x-ray signal. These oscillations were damped within 58 ± 13 femtoseconds because vibrational coherence was lost with the energy redistributing into lower-frequency vibrational modes. This study completely reconstructs the molecular relaxation dynamics of this prototypical example and opens avenues for exploring complex systems.

Ultrafast X-ray Spectroscopy of Intersystem Crossing in Hexafluoroacetylacetone: Chromophore Photophysics and Spectral Changes in the Face of Electron-Withdrawing Groups.

Intersystem crossings between singlet and triplet states represent a crucial relaxation pathway in photochemical processes. Herein, we probe the intersystem crossing in hexafluoro-acetylacetone with ultrafast X-ray transient absorption spectroscopy at the carbon K-edge. We observe the excited state dynamics following excitation with 266 nm UV light to the 1ππ* (S2) state with element and site-specificity using a broadband soft X-ray pulse produced by high harmonic generation. These results are compared to X-ray spectra computed from orbital optimized density functional theory methods. It is found that the electron-withdrawing fluorine atoms decongest the X-ray absorption spectrum by enhancing separation between features originating from different carbon atoms. This facilitates the elucidation of structural and electronic dynamics at the chromophore. The evolution of the core-to-valence resonances at the carbon K-edge reveals an ultrafast population transfer between the 1nπ* (S1) and 3ππ* (T1) states on a 1.6 ± 0.4 ps time scale, which is similar to the 1.5 ps time scale earlier observed for acetylacetone [ J. Am. Chem. Soc. 2017, 139, 16576-16583, DOI: 10.1021/jacs.7b07532]. It therefore appears that terminal fluorination has little influence on the intersystem crossing rate of the acetylacetone chromophore. In addition, the significant role of hydrogen-bond opened and twisted rotational isomers is elucidated in the excited state dynamics by comparison of the experimental transient X-ray spectra with theory.

Correction: Jahn-Teller distortion and dissociation of CCl4 + by transient X-ray spectroscopy simultaneously at the carbon K- and chlorine L-edge.

[This corrects the article DOI: 10.1039/D2SC02402K.].

Jahn-Teller distortion and dissociation of CCl4 + by transient X-ray spectroscopy simultaneously at the carbon K- and chlorine L-edge.

X-ray Transient Absorption Spectroscopy (XTAS) and theoretical calculations are used to study CCl4 + prepared by 800 nm strong-field ionization. XTAS simultaneously probes atoms at the carbon K-edge (280-300 eV) and chlorine L-edge (195-220 eV). Comparison of experiment to X-ray spectra computed by orbital-optimized density functional theory (OO-DFT) indicates that after ionization, CCl4 + undergoes symmetry breaking driven by Jahn-Teller distortion away from the initial tetrahedral structure (Td) in 6 ± 2 fs. The resultant symmetry-broken covalently bonded form subsequently separates to a noncovalently bound complex between CCl3 + and Cl over 90 ± 10 fs, which is again predicted by theory. Finally, after more than 800 fs, L-edge signals for atomic Cl are observed, indicating dissociation to free CCl3 + and Cl. The results for Jahn-Teller distortion to the symmetry-broken form of CCl4 + and formation of the Cl-CCl+ 3 complex characterize previously unobserved new species along the route to dissociation.

Computing x-ray absorption spectra from linear-response particles atop optimized holes.

State specific orbital optimized density functional theory (OO-DFT) methods, such as restricted open-shell Kohn-Sham (ROKS), can attain semiquantitative accuracy for predicting x-ray absorption spectra of closed-shell molecules. OO-DFT methods, however, require that each state be individually optimized. In this Communication, we present an approach to generate an approximate core-excited state density for use with the ROKS energy ansatz, which is capable of giving reasonable accuracy without requiring state-specific optimization. This is achieved by fully optimizing the core-hole through the core-ionized state, followed by the use of electron-addition configuration interaction singles to obtain the particle level. This hybrid approach can be viewed as a DFT generalization of the static-exchange (STEX) method and can attain ∼0.6 eV rms error for the K-edges of C-F through the use of local functionals, such as PBE and OLYP. This ROKS(STEX) approach can also be used to identify important transitions for full OO ROKS treatment and can thus help reduce the computational cost of obtaining OO-DFT quality spectra. ROKS(STEX), therefore, appears to be a useful technique for the efficient prediction of x-ray absorption spectra.

Revisiting the Performance of Time-Dependent Density Functional Theory for Electronic Excitations: Assessment of 43 Popular and Recently Developed Functionals from Rungs One to Four.

In this paper, the performance of more than 40 popular or recently developed density functionals is assessed for the calculation of 463 vertical excitation energies against the large and accurate QuestDB benchmark set. For this purpose, the Tamm-Dancoff approximation offers a good balance between computational efficiency and accuracy. The functionals ωB97X-D and BMK are found to offer the best performance overall with a root-mean square error (RMSE) of around 0.27 eV, better than the computationally more demanding CIS(D) wave function method with a RMSE of 0.36 eV. The results also suggest that Jacob's ladder still holds for time-dependent density functional theory excitation energies, though hybrid meta generalized-gradient approximations (meta-GGAs) are not generally better than hybrid GGAs. Effects of basis set convergence, gauge invariance correction to meta-GGAs, and nonlocal correlation (VV10) are also studied, and practical basis set recommendations are provided.

Relativistic Orbital-Optimized Density Functional Theory for Accurate Core-Level Spectroscopy.

Core-level spectra of 1s electrons of elements heavier than Ne show significant relativistic effects. We combine advances in orbital-optimized density functional theory (OO-DFT) with the spin-free exact two-component (X2C) model for scalar relativistic effects to study K-edge spectra of third period elements. OO-DFT/X2C is found to be quite accurate at predicting energies, yielding a ∼0.5 eV root-mean-square error versus experiment with the modern SCAN (and related) functionals. This marks a significant improvement over the >50 eV deviations that are typical for the popular time-dependent DFT (TDDFT) approach. Consequently, experimental spectra are quite well reproduced by OO-DFT/X2C, sans empirical shifts for alignment. OO-DFT/X2C combines high accuracy with ground state DFT cost and is thus a promising route for computing core-level spectra of third period elements. We also explored K and L edges of 3d transition metals to identify limitations of the OO-DFT/X2C approach in modeling the spectra of heavier atoms.

Software for the frontiers of quantum chemistry: An overview of developments in the Q-Chem 5 package.

This article summarizes technical advances contained in the fifth major release of the Q-Chem quantum chemistry program package, covering developments since 2015. A comprehensive library of exchange-correlation functionals, along with a suite of correlated many-body methods, continues to be a hallmark of the Q-Chem software. The many-body methods include novel variants of both coupled-cluster and configuration-interaction approaches along with methods based on the algebraic diagrammatic construction and variational reduced density-matrix methods. Methods highlighted in Q-Chem 5 include a suite of tools for modeling core-level spectroscopy, methods for describing metastable resonances, methods for computing vibronic spectra, the nuclear-electronic orbital method, and several different energy decomposition analysis techniques. High-performance capabilities including multithreaded parallelism and support for calculations on graphics processing units are described. Q-Chem boasts a community of well over 100 active academic developers, and the continuing evolution of the software is supported by an "open teamware" model and an increasingly modular design.

Revealing the nature of electron correlation in transition metal complexes with symmetry breaking and chemical intuition.

In this work, we provide a nuanced view of electron correlation in the context of transition metal complexes, reconciling computational characterization via spin and spatial symmetry breaking in single-reference methods with qualitative concepts from ligand-field and molecular orbital theories. These insights provide the tools to reliably diagnose the multi-reference character, and our analysis reveals that while strong (i.e., static) correlation can be found in linear molecules (e.g., diatomics) and weakly bound and antiferromagnetically coupled (monometal-noninnocent ligand or multi-metal) complexes, it is rarely found in the ground-states of mono-transition-metal complexes. This leads to a picture of static correlation that is no more complex for transition metals than it is, e.g., for organic biradicaloids. In contrast, the ability of organometallic species to form more complex interactions, involving both ligand-to-metal σ-donation and metal-to-ligand π-backdonation, places a larger burden on a theory's treatment of dynamic correlation. We hypothesize that chemical bonds in which inter-electron pair correlation is non-negligible cannot be adequately described by theories using MP2 correlation energies and indeed find large errors vs experiment for carbonyl-dissociation energies from double-hybrid density functionals. A theory's description of dynamic correlation (and to a less important extent, delocalization error), which affects relative spin-state energetics and thus spin symmetry breaking, is found to govern the efficacy of its use to diagnose static correlation.

Exploring spin symmetry-breaking effects for static field ionization of atoms: Is there an analog to the Coulson-Fischer point in bond dissociation?

Löwdin's symmetry dilemma is an ubiquitous issue in approximate quantum chemistry. In the context of Hartree-Fock (HF) theory, the use of Slater determinants with some imposed constraints to preserve symmetries of the exact problem may lead to physically unreasonable potential energy surfaces. On the other hand, lifting these constraints leads to the so-called broken symmetry solutions that usually provide better energetics, at the cost of losing information about good quantum numbers that describe the state of the system. This behavior has previously been extensively studied in the context of bond dissociation. This paper studies the behavior of different classes of HF spin polarized solutions (restricted, unrestricted, and generalized) in the context of ionization by strong static electric fields. We find that, for simple two electron systems, unrestricted Hartree-Fock (UHF) is able to provide a qualitatively good description of states involved during the ionization process (neutral, singly ionized, and doubly ionized states), whereas RHF fails to describe the singly ionized state. For more complex systems, even though UHF is able to capture some of the expected characteristics of the ionized states, it is constrained to a single Ms (diabatic) manifold in the energy surface as a function of field intensity. In this case, a better qualitative picture can be painted by using generalized Hartree-Fock as it is able to explore different spin manifolds and follow the lowest solution due to lack of collinearity constraints on the spin quantization axis.

Orbital Optimized Density Functional Theory for Electronic Excited States.

Density functional theory (DFT) based modeling of electronic excited states is of importance for investigation of the photophysical/photochemical properties and spectroscopic characterization of large systems. The widely used linear response time-dependent DFT (TDDFT) approach is, however, not effective at modeling many types of excited states, including (but not limited to) charge-transfer states, doubly excited states, and core-level excitations. In this perspective, we discuss state-specific orbital optimized (OO) DFT approaches as an alterative to TDDFT for electronic excited states. We motivate the use of OO-DFT methods and discuss reasons behind their relatively restricted historical usage (vs TDDFT). We subsequently highlight modern developments that address these factors and allow efficient and reliable OO-DFT computations. Several successful applications of OO-DFT for challenging electronic excitations are also presented, indicating their practical efficacy. OO-DFT approaches are thus increasingly becoming a useful route for computing excited states of large chemical systems. We conclude by discussing the limitations and challenges still facing OO-DFT methods, as well as some potential avenues for addressing them.

Electron-Nuclear Dynamics Accompanying Proton-Coupled Electron Transfer.

Although photoinduced proton-coupled electron transfer (PCET) plays an essential role in photosynthesis, a full understanding of the mechanism is still lacking due to the complex nonequilibrium dynamics arising from the strongly coupled electronic and nuclear degrees of freedom. Here we report the photoinduced PCET dynamics of a biomimetic model system investigated by means of transient IR and two-dimensional electronic-vibrational (2DEV) spectroscopies, IR spectroelectrochemistry (IRSEC), and calculations utilizing long-range-corrected hybrid density functionals. This collective experimental and theoretical effort provides a nuanced picture of the complicated dynamics and synergistic motions involved in photoinduced PCET. In particular, the evolution of the 2DEV line shape, which is highly sensitive to the mixing of vibronic states, is interpreted by accurate computational modeling of the charge separated state and is shown to represent a gradual change in electron density distribution associated with a dihedral twist that occurs on a 120 fs time scale.

Too big, too small, or just right? A benchmark assessment of density functional theory for predicting the spatial extent of the electron density of small chemical systems.

Multipole moments are the first-order responses of the energy to spatial derivatives of the electric field strength. The quality of density functional theory prediction of molecular multipole moments thus characterizes errors in modeling the electron density itself, as well as the performance in describing molecules interacting with external electric fields. However, only the lowest non-zero moment is translationally invariant, making the higher-order moments origin-dependent. Therefore, instead of using the 3 × 3 quadrupole moment matrix, we utilize the translationally invariant 3 × 3 matrix of second cumulants (or spatial variances) of the electron density as the quantity of interest (denoted by K). The principal components of K are the square of the spatial extent of the electron density along each axis. A benchmark dataset of the principal components of K for 100 small molecules at the coupled cluster singles and doubles with perturbative triples at the complete basis set limit is developed, resulting in 213 independent K components. The performance of 47 popular and recent density functionals is assessed against this Var213 dataset. Several functionals, especially double hybrids, and also SCAN and SCAN0 predict reliable second cumulants, although some modern, empirically parameterized functionals yield more disappointing performance. The H, Li, and Be atoms, in particular, are challenging for nearly all methods, indicating that future functional development could benefit from the inclusion of their density information in training or testing protocols.

Third-Order Møller-Plesset Theory Made More Useful? The Role of Density Functional Theory Orbitals.

The practical utility of Møller-Plesset (MP) perturbation theory is severely constrained by the use of Hartree-Fock (HF) orbitals. It has recently been shown that the use of regularized orbital-optimized MP2 orbitals and scaling of MP3 energy could lead to a significant reduction in MP3 error [Bertels, L. W.; J. Phys. Chem. Lett. 2019, 10, 4170 4176]. In this work, we examine whether density functional theory (DFT)-optimized orbitals can be similarly employed to improve the performance of MP theory at both the MP2 and MP3 levels. We find that the use of DFT orbitals leads to significantly improved performance for prediction of thermochemistry, barrier heights, noncovalent interactions, and dipole moments relative to the standard HF-based MP theory. Indeed, MP3 (with or without scaling) with DFT orbitals is found to surpass the accuracy of coupled-cluster singles and doubles (CCSD) for several data sets. We also found that the results are not particularly functional sensitive in most cases (although range-separated hybrid functionals with low delocalization error perform the best). MP3 based on DFT orbitals thus appears to be an efficient, noniterative O(N6) scaling wave-function approach for single-reference electronic structure computations. Scaled MP2 with DFT orbitals is also found to be quite accurate in many cases, although modern double hybrid functionals are likely to be considerably more accurate.

Accurate prediction of core-level spectra of radicals at density functional theory cost via square gradient minimization and recoupling of mixed configurations.

State-specific orbital optimized approaches are more accurate at predicting core-level spectra than traditional linear-response protocols, but their utility had been restricted due to the risk of "variational collapse" down to the ground state. We employ the recently developed square gradient minimization [D. Hait and M. Head-Gordon, J. Chem. Theory Comput. 16, 1699 (2020)] algorithm to reliably avoid variational collapse and study the effectiveness of orbital optimized density functional theory (DFT) at predicting second period element 1s core-level spectra of open-shell systems. Several density functionals (including SCAN, B3LYP, and ωB97X-D3) are found to predict excitation energies from the core to singly occupied levels with high accuracy (≤0.3 eV RMS error) against available experimental data. Higher excited states are, however, more challenging by virtue of being intrinsically multiconfigurational. We thus present a configuration interaction inspired route to self-consistently recouple single determinant mixed configurations obtained from DFT, in order to obtain approximate doublet states. This recoupling scheme is used to predict the C K-edge spectra of the allyl radical, the O K-edge spectra of CO+, and the N K-edge of NO2 with high accuracy relative to experiment, indicating substantial promise in using this approach for the computation of core-level spectra for doublet species [vs more traditional time dependent DFT, equation of motion coupled cluster singles and doubles (EOM-CCSD), or using unrecoupled mixed configurations]. We also present general guidelines for computing core-excited states from orbital optimized DFT.

The Ground State Electronic Energy of Benzene.

We report on the findings of a blind challenge devoted to determining the frozen-core, full configuration interaction (FCI) ground-state energy of the benzene molecule in a standard correlation-consistent basis set of double-ζ quality. As a broad international endeavor, our suite of wave function-based correlation methods collectively represents a diverse view of the high-accuracy repertoire offered by modern electronic structure theory. In our assessment, the evaluated high-level methods are all found to qualitatively agree on a final correlation energy, with most methods yielding an estimate of the FCI value around -863 mEH. However, we find the root-mean-square deviation of the energies from the studied methods to be considerable (1.3 mEH), which in light of the acclaimed performance of each of the methods for smaller molecular systems clearly displays the challenges faced in extending reliable, near-exact correlation methods to larger systems. While the discrepancies exposed by our study thus emphasize the fact that the current state-of-the-art approaches leave room for improvement, we still expect the present assessment to provide a valuable community resource for benchmark and calibration purposes going forward.