Δ-based composite models for calculating x-ray absorption and emission energies.

A practical ab initio composite method for modeling x-ray absorption and non-resonant x-ray emission is presented. Vertical K-edge excitation and emission energies are obtained from core-electron binding energies calculated with spin-projected ΔHF/ΔMP and outer-core ionization potentials/electron affinities calculated with electron propagator theory. An assessment of the combined methodologies against experiment is performed for a set of small molecules containing second-row elements.

Good Vibrations: Calculating Excited-State Frequencies Using Ground-State Self-Consistent Field Models.

The use of Δ-self-consistent field (SCF) approaches for studying excited electronic states has received a renewed interest in recent years. In this work, the use of this scheme for calculating excited-state vibrational frequencies is examined. Results from Δ-SCF calculations for a set of representative molecules are compared with those obtained using configuration interaction with single substitutions (CIS) and time-dependent density functional theory (TD-DFT) methods. The use of an approximate spin purification model is also considered for cases where the excited-state SCF solution is spin-contaminated. The results of this work demonstrate that an SCF-based description of an excited-state potential energy surface can be an accurate and cost-effective alternative to CIS and TD-DFT methods.

Assessing the performance of ΔSCF and the diagonal second-order self-energy approximation for calculating vertical core excitation energies.

Vertical core excitation energies are obtained using a combination of the ΔSCF method and the diagonal second-order self-energy approximation. These methods are applied to a set of neutral molecules and their anionic forms. An assessment of the results with the inclusion of relativistic effects is presented. For core excitations involving delocalized symmetry orbitals, the applied composite method improves upon the overestimation of ΔSCF by providing approximate values close to experimental K-shell transition energies. The importance of both correlation and relaxation contributions to the vertical core-excited state energies, the concept of local and nonlocal core orbitals, and the consequences of breaking symmetry are discussed.

Enhanced Reactivity for Aromatic Bromination via Halogen Bonding with Lactic Acid Derivatives.

We report a new method for regioselective aromatic bromination using lactic acid derivatives as halogen bond acceptors with N-bromosuccinimide (NBS). Several structural analogues of lactic acid affect the efficiency of aromatic brominations, presumably via Lewis acid/base halogen-bonding interactions. Rate comparisons of aromatic brominations demonstrate the reactivity enhancement available via catalytic additives capable of halogen bonding. Computational results demonstrate that Lewis basic additives interact with NBS to increase the electropositive character of bromine prior to electrophilic transfer. An optimized procedure using catalytic mandelic acid under aqueous conditions at room temperature was developed to promote aromatic bromination on a variety of arene substrates with complete regioselectivity.

Comparison of Linear Response Theory, Projected Initial Maximum Overlap Method, and Molecular Dynamics-Based Vibronic Spectra: The Case of Methylene Blue.

The simulation of optical spectra is essential to molecular characterization and, in many cases, critical for interpreting experimental spectra. The most common method for simulating vibronic absorption spectra relies on the geometry optimization and computation of normal modes for ground and excited electronic states. In this report, we show that the utilization of such a procedure within an adiabatic linear response (LR) theory framework may lead to state mixings and a breakdown of the Born-Oppenheimer approximation, resulting in a poor description of absorption spectra. In contrast, computing excited states via a self-consistent field method in conjunction with a maximum overlap model produces states that are not subject to such mixings. We show that this latter method produces vibronic spectra much more aligned with vertical gradient and molecular dynamics (MD) trajectory-based approaches. For the methylene blue chromophore, we compare vibronic absorption spectra computed with the following: an adiabatic Hessian approach with LR theory-optimized structures and normal modes, a vertical gradient procedure, the Hessian and normal modes of maximum overlap method-optimized structures, and excitation energy time-correlation functions generated from an MD trajectory. Because of mixing between the bright S1 and dark S2 surfaces near the S1 minimum, computing the adiabatic Hessian with LR theory and time-dependent density functional theory with the B3LYP density functional predicts a large vibronic shoulder for the absorption spectrum that is not present for any of the other methods. Spectral densities are analyzed and we compare the behavior of the key normal mode that in LR theory strongly couples to the optical excitation while showing S1/S2 state mixings. Overall, our study provides a note of caution in computing vibronic spectra using the excited-state adiabatic Hessian of LR theory-optimized structures and also showcases three alternatives that are less sensitive to adiabatic state mixing effects.

Using projection operators with maximum overlap methods to simplify challenging self-consistent field optimization.

Maximum overlap methods are effective tools for optimizing challenging ground- and excited-state wave functions using self-consistent field models such as Hartree-Fock and Kohn-Sham density functional theory. Nevertheless, such models have shown significant sensitivity to the user-defined initial guess of the target wave function. In this work, a projection operator framework is defined and used to provide a metric for non-aufbau orbital selection in maximum-overlap-methods. The resulting algorithms, termed the Projection-based Maximum Overlap Method (PMOM) and Projection-based Initial Maximum Overlap Method (PIMOM), are shown to perform exceptionally well when using simple user-defined target solutions based on occupied/virtual molecular orbital permutations. This work also presents a new metric that provides a simple and conceptually convenient measure of agreement between the desired target and the current or final SCF results during a calculation employing a maximum-overlap method.

New Photoelectron-Valence Electron Interactions Evident in the Photoelectron Spectrum of Gd2O.

Evidence of strong photoelectron-valence electron (PEVE) interactions has been observed in the anion photoelectron (PE) spectra of several lanthanide suboxide clusters, which are exceptionally complex from an electronic structure standpoint and are strongly correlated systems. The PE spectrum of Gd2O-, which should have relatively simple electronic structure because of its half-filled 4f subshell, exhibits numerous electronic transitions. The electron affinity determined from the spectrum is 0.26 eV. The intensities of transitions to excited states increase relative to the lower-energy states with lower photon energy, which is consistent with shakeup transitions driven by time-dependent electron-neutral interactions. A group of intense spectral features that lie between electron binding energies of 0.7 and 2.3 eV are assigned to transitions involving detachment of an electron from outer-valence σu and σg orbitals that have large Gd 6s contributions. The spectra show parallel transition manifolds in general, which is consistent with detachment from these orbitals. However, several distinct perpendicular transitions are observed adjacent to several of the vertical transitions. A possible explanation invoking interaction between the ejected electron and the high-spin neutral is proposed. Specifically, the angular momentum of electrons ejected from σu or σg orbitals, which is l = 1, can switch to l = 0, 2 with an associated change in the Ms of the remnant neutral, which is spin-orbit coupling between a free electron and the spin of a neutral.

Lanthanide Oxides: From Diatomics to High-Spin, Strongly Correlated Homo- and Heterometallic Clusters.

Small lanthanide (Ln) oxide clusters present both experimental and theoretical challenges because of their partially filled, core-like 4f n orbitals, a feature that results in a plethora of close-lying and fundamentally similar electronic states. These clusters provide a bottom-up approach toward understanding the electronic structure of defective or doped bulk material but also can offer a challenge to the theorists to find a method robust enough to capture electronic structure patterns that emerge from within the 4f n (0 < n < 14) series. In this Feature Article, we explore the electronic structures of small lanthanide oxide clusters that deviate from bulk stoichiometry using anion photoelectron spectroscopy and supporting density functional theory calculations. We will describe the evolution of electronic structure with oxidation and how LnxOy- cluster reactivities can be correlated with specific Ln-local orbital occupancies. These strongly correlated systems offer additional insights into how interactions between electrons and electronically complex neutrals can lead to detachment transitions that lie outside of the sudden one-electron detachment approximation generally assumed in anion photoelectron spectroscopy. With a better understanding of how we can control nominally forbidden transitions to sample an array of spin states, we suggest that more in-depth studies on the magnetic states of these systems can be explored. Extending these studies to other Ln-based materials with hidden magnetic phases, along with sequentially ligated single molecule magnets, could advance current understanding of these systems.

Versatile New Reagent for Nitrosation under Mild Conditions.

Here we report a new chemical reagent for transnitrosation under mild experimental conditions. This new reagent is stable to air and moisture across a broad range of temperatures and is effective for transnitrosation in multiple solvents. Compared with traditional nitrosation methods, our reagent shows high functional group tolerance for substrates that are susceptible to oxidation or reversible transnitrosation. Several challenging nitroso compounds are accessed here for the first time, including 15N isotopologues. X-ray data confirm that two rotational isomers of the reagent are configurationally stable at room temperature, although only one isomer is effective for transnitrosation. Computational analysis describes the energetics of rotamer interconversion, including interesting geometry-dependent hybridization effects.

ΔSCF Dyson orbitals and pole strengths from natural ionization orbitals.

The calculation of photoionization cross sections can play a key role in spectral assignments using modeling and simulation. In this work, we provide formal relationships between pole strengths, which are proportional to the photoionization cross section, and terms related to the natural ionization orbital model for ΔSCF calculations. A set of numerical calculations using the developed models is carried out. Pole strength values computed using the two approaches developed for ΔSCF calculations demonstrate excellent agreement with an electron propagator theory model.

Photoelectron Spectra of Gd2O2- and Nonmonotonic Photon-Energy-Dependent Variations in Populations of Close-Lying Neutral States.

Photoelectron spectra of Gd2O2- obtained with photon energies ranging from 2.033 to 3.495 eV exhibit numerous close-lying neutral states with photon-energy-dependent relative intensities. Transitions to these states, which fall within the electron binding energy window of 0.9 and 1.6 eV, are attributed to one- or two-electron transitions to the ground and low-lying excited neutral states. An additional, similar manifold of electronic states is observed in an electron binding energy window of 2.1-2.8 eV, which cannot be assigned to any simple one-electron transitions. This study expands on previous work on the Sm2O- triatomic, which has a more complex electronic structure because of the 4f6 subshell occupancy of each Sm center. Because of the simpler electronic structure from the half-filled 4f7 subshell occupancy in Gd2O2 and Gd2O2-, the numerous close-lying transitions observed in the spectra are better resolved, allowing a more detailed view of the changes in relative intensities of individual transitions with photon energy. With supporting calculations on numerous possible close-lying electronic states, we suggest a potential description of the strong photoelectron-valence electron interactions that may result in the photon-energy-dependent changes in the observed spectra.

Unveiling the coexistence of cis- and trans-isomers in the hydrolysis of ZrO2: A coupled DFT and high-resolution photoelectron spectroscopy study.

High-resolution anion photoelectron spectroscopy of the ZrO3H2 - and ZrO3D2 - anions and complementary electronic structure calculations are used to investigate the reaction between zirconium dioxide and a single water molecule, ZrO2 0/- + H2O. Experimental spectra of ZrO3H2 - and ZrO3D2 - were obtained using slow photoelectron velocity-map imaging of cryogenically cooled anions, revealing the presence of two dissociative adduct conformers and yielding insight into the vibronic structure of the corresponding neutral species. Franck-Condon simulations for both the cis- and trans-dihydroxide structures are required to fully reproduce the experimental spectrum. Additionally, it was found that water-splitting is stabilized more by ZrO2 than TiO2, suggesting Zr-based catalysts are more reactive toward hydrolysis.

Assessing the Calculation of Exchange Coupling Constants and Spin Crossover Gaps Using the Approximate Projection Model To Improve Density Functional Calculations.

This work evaluates the quality of exchange coupling constant and spin crossover gap calculations using density functional theory corrected by the approximate projection model. Results show that improvements using the approximate projection model range from modest to significant. This study demonstrates that, at least for the class of systems examined here, spin projection generally improves the quality of density functional theory calculations of J-coupling constants and spin crossover gaps. Furthermore, it is shown that spin projection can be important for both geometry optimization and energy evaluations. The approximate projection model provides an affordable and practical approach for effectively correcting spin-contamination errors in such calculations.

Exceptionally Complex Electronic Structures of Lanthanide Oxides and Small Molecules.

Lanthanide (Ln) oxide clusters and molecular systems provide a bottom-up look at the electronic structures of the bulk materials because of close parallels in the patterns of Ln 4fN subshell occupancy between the molecular and bulk Ln2O3 size limits. At the same time, these clusters and molecules offer a challenge to the theory community to find appropriate and robust treatments for the 4fN patterns across the Ln series. Anion photoelectron (PE) spectroscopy provides a powerful experimental tool for studying these systems, mapping the energies of the ground and low-lying excited states of the neutral relative to the initial anion state, providing spectroscopic patterns that reflect the Ln 4fN occupancy. In this Account, we review our anion PE spectroscopic and computational studies on a range of small lanthanide molecules and cluster species. The PE spectra of LnO- (Ln = Ce, Pr, Sm, Eu) diatomic molecules show spectroscopic signatures associated with detachment of an electron from what can be described as a diffuse Ln 6s-like orbital. While the spectra of all four diatomics share this common transition, the fine structure in the transition becomes more complex with increasing 4f occupancy. This effect reflects increased coupling between the electrons occupying the corelike 4f and diffuse 6s orbitals with increasing N. Understanding the PE spectra of these diatomics sets the stage for interpreting the spectra of polyatomic molecular and cluster species. In general, the results confirm that the partial 4fN subshell occupancy is largely preserved between molecular and bulk oxides and borides. However, they also suggest that surfaces and edges of bulk materials may support a low-energy, diffuse Ln 6s band, in contrast to bulk interiors, in which the 6s band is destabilized relative to the 5d band. We also identify cases in which the molecular Ln centers have 4fN+1 occupancy rather than bulklike 4fN, which results in weaker Ln-O bonding. Specifically, Sm centers in mixed Ce-Sm oxides or in SmxOy- (y ≤ x) clusters have this higher 4fN+1 occupancy. The PE spectra of these particular species exhibit a striking increase in the relative intensities of excited-state transitions with decreasing photon energy (resulting in lower photoelectron kinetic energy). This is opposite of what is expected on the basis of the threshold laws that govern photodetachment. We relate this phenomenon to strong electron-neutral interactions unique to these complex electronic structures. The time scale of the interaction, which shakes up the electronic configuration of the neutral, increases with decreasing electron momentum. From a computational standpoint, we point out that special care must be taken when considering Ln cluster and molecular systems toward the center of the Ln series (e.g., Sm, Eu), where treatment of electrons explicitly or using an effective core potential can yield conflicting results on competing subshell occupancies. However, despite the complex electronic structures associated with partially filled 4fN subshells, we demonstrate that inexpensive and tractable calculations yield useful qualitative insight into the general electronic structural features.

On the linear geometry of lanthanide hydroxide (Ln-OH, Ln = La-Lu).

Lanthanide hydroxides are key species in a variety of catalytic processes and in the preparation of corresponding oxides. This work explores the fundamental structure and bonding of the simplest lanthanide hydroxide, LnOH (Ln = La-Lu), using density functional theory calculations. Interestingly, the calculations predict that all structures of this series will be linear. Furthermore, these results indicate a valence electron configuration of σ2π4 for all LnOH compounds, suggesting that the lanthanide-hydroxide bond is best characterized as a covalent triple bond.

Electronic and Molecular Structures of the CeB6 Monomer.

The electronic and molecular structure of the CeB6 molecular unit has been probed by anion PE spectroscopy and DFT calculations to gain insight into structural and electronic relaxation on edge and corner sites of this ionic material. While boron in bulk lanthanide hexaboride materials assumes octahedral B63- units, the monomer assumes a less compact structure to delocalize the charge. Two competitive molecular structures were identified for the anion and neutral species, which include a boat-like structure and a planar or near-planar teardrop structure. Ce adopts different orbital occupancies in the two isomers; the boat-like structure has a 4f superconfiguration while the teardrop favors a 4f 6s occupancy. The B6 ligand in these structures carries a charge of -4 and -3, respectively. The teardrop structure, which was calculated to be isoenergetic with the boat structure, was most consistent with the experimental spectrum. B6-local orbitals crowd the energy window between the Ce 4f and 6s (HOMO) orbitals. A low-lying transition from the B-based orbitals is observed slightly less than 1 eV above the ground state. The results suggest that edge and corner conductivity involves stabilized, highly diffuse 6s orbitals or bands rather than the bulk-favored 5d band. High-spin and open-shell low-spin states were calculated to be very close in energy for both the anion and neutral, a characteristic that reflects how decoupled the 4f electron is from the B6 2p- and Ce 6s-based molecular orbitals.

Dispersion-Controlled Regioselective Acid-Catalyzed Intramolecular Hydroindolation of cis-Methindolylstyrenes To Access Tetrahydrobenzo[ cd]indoles.

Readily prepared cis-ß-(α',α'-dimethyl)-4'-methindolylstyrenes undergo acid-catalyzed intramolecular hydroindolation to afford tetrahydrobenzo[ cd]indoles. Our experimental and computational investigations suggest that dispersive interactions between the indole and styrene preorganize substrates such that 6-membered ring formation is preferred, apparently via concerted protonation and C-C bond formation. When dispersion is attenuated (by a substituent or heteroatom), regioselectivity erodes and competing oligomerization predominates for cis substrates. Similarly, all trans-configured substrates that we evaluated failed to cyclize efficiently.

A Tale of Two Stabilities: How One Boron Atom Affects a Switch in Bonding Motifs in CeO2B x- ( x = 2, 3) Complexes.

Boronyl (B≡O) ligands have garnered much attention as isoelectronic and isolobal analogues of CO and CN-, yet successful efforts in synthesizing metal boronyl complexes remain scarce. Anion photoelectron (PE) spectroscopy and density functional theory calculations were employed to investigate two small CeO2B x- ( x = 2, 3) complexes generated from laser ablation of a mixed Ce/B pressed powder target. The spectra reveal markedly different bonding upon incorporation of an additional B atom. Most interestingly, CeO2B2- was found to have a Ce(I) center coordinated to two monoanionic boronyl ligands in a bent geometry. This result was unexpected as previous studies suggest electron-rich metals are most suitable for stabilizing such ligands; furthermore, it is one of the first examples of an experimental metal-polyboronyl complex. Introducing another boron atom, however, favors a much different geometry in which Ce(II) coordinates an O2B33- unit through both the O and B atoms, which was evident in the markedly different PE spectra.