Study of MoNbOy (y = 2–5) Anion and Neutral Clusters Using Photoelectron Spectroscopy and Density Functional Theory Calculations: Impact of Spin Contamination on Single Point Calculations

Mapping spin contamination-free potential energy surfaces using restricted open-shell methods with Grassmannians

The Lagrange-based Grassmann interpolation (G-Int) method has been extended for open-shell systems using restricted open-shell (RO) methods. The performance of this method was assessed in constructing potential energy surfaces (PESs) for vanadium(II) oxide, benzyl radical, and methanesulfenyl chloride radical cation. The density matrices generated by G-Int when used as initial guesses for self-consistent field (SCF) calculations, exhibit superior performance compared to other traditional SCF initial guess schemes, such as SADMO, GWH, and CORE. Additionally, the energy obtained from the G-Int scheme satisfies the variational principle and outperforms the direct energy-based Lagrange interpolation approach. In the case of methanesulfenyl chloride radical cation, a unique example with a flat PES at the end region along the H-C-S-Cl dihedral angle, the use of an equally-spaced grid sampling leads to significant oscillations near the end of the interval due to the effects of Runge's phenomenon. Introducing an unequally-spaced grid sampling based on a scaled Gauss-Chebyshev quadrature effectively mitigated the Runge's phenomenon, making it suitable for combining with G-Int in constructing PESs for general applications. Thus, G-Int provides an efficient and robust strategy for building spin contamination-free PESs with consistent accuracy.

A Study of NbMo and NbMo- by Anion Photoelectron Spectroscopy

Photoelectron spectra of the niobium-molybdenum diatomic anion, obtained at 488 and 514 nm, display vibrationally resolved transitions from the ground state and one excited electronic state of the anion to the ground state and one excited electronic state of the neutral molecule. The electron affinity of NbMo is measured to be 1.130 ± 0.005 eV. Its ²Δ_3/2 spin-orbit component is observed to lie 870 ± 20 cm^-1 above its previously identified ²Δ_5/2 ground state. For ⁹³Nb⁹⁸Mo, vibrational energies measured for levels up to v = 4 for the ²Δ_5/2 and ²Δ_3/2 states give harmonic frequency and anharmonicity constant values of ω_e = 492 ± 12 cm^-1 and ω_ex_e = 8.0 ± 3.2 cm^-1, the former value corresponding to a force constant of 6.80 ± 0.35 mdyn/Å. These two vibrational parameters suggest a bond dissociation energy that is too low by at least a factor of 3, indicating that the ground state potential energy curve of NbMo deviates markedly from a Morse potential at higher energies. An excited electronic state of NbMo, assigned as a ²Σ⁺ state, is observed at 2900 ± 25 cm^-1 (T₀). Vibrational energies up to v = 8 in this excited state give values of ω_e = 544 ± 8 cm^-1 and ω_ex_e = 1.9 ± 1.2 cm^-1 for ⁹³Nb⁹⁸Mo. The former value corresponds to a high vibrational force constant of 8.30 ± 0.25 mdyn/Å. Both doublet states of the neutral molecule are accessed from the anion ground state, which is assigned as ¹Σ⁺. For the ⁹³Nb⁹⁸Mo^- anion, the fundamental vibrational frequency (ΔG_1/2) is 484 ± 15 cm^-1. Electron affinity data indicate that the bond dissociation energy of NbMo^- is 0.213 ± 0.005 eV greater than that of neutral NbMo, whose previously reported value then gives D₀ = 4.85 ± 0.27 eV for the anion. An excited state of the anion lying 3050 ± 25 cm^-1 (T₀) above its ground state is assigned as ³Δ, and the energies of its spin-orbit components above the ³Δ₃ lowest energy level are measured to be 450 ± 20 cm^-1 (³Δ₂) and 1100 ± 20 cm^-1 (³Δ₁). Their uneven spacing suggests that the energy of the ³Δ₂ level is lowered by interaction with a higher energy Ω = 2 anion state. The vibrational frequency (ΔG_1/2) for the ³Δ₁ and ³Δ₂ states is measured to be 433 ± 20 cm^-1. Bond length differences among the observed states are estimated from Franck-Condon fits to vibrational band intensity profiles. When combined with the previously reported NbMo bond length, these provide bond length estimates for the ground state of the anion (1.940 ± 0.025 Å) and for the observed excited states. These species offer extreme examples of multiple metal-metal bonding, with formal bond orders of 5¹/₂ for the ²Δ ground and ²Σ⁺ excited doublet states of NbMo, 6 for the singlet ground state of the anion, and 5 for its low-lying triplet state. The relationships among their bonding properties and those of related multiply bonded transition metal dimers are discussed.

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 Ln_xO_y^- 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.

Using anion photoelectron spectroscopy of cluster models to gain insights into mechanisms of catalyst-mediated H2 production from water

Metal oxide cluster models of catalyst materials offer a powerful platform for probing the molecular-scale features and interactions that govern catalysis. This perspective gives an overview of studies implementing the combination of anion photoelectron (PE) spectroscopy and density functional theory calculations toward exploring cluster models of metal oxides and metal-oxide supported Pt that catalytically drive the hydrogen evolution reaction (HER) or the water-gas shift reaction. The utility in the combination of these experimental and computational techniques lies in our ability to unambiguously determine electronic and molecular structures, which can then connect to results of reactivity studies. In particular, we focus on the activity of oxygen vacancies modeled by suboxide clusters, the critical mechanistic step of forming proximal metal hydride and hydroxide groups as a prerequisite for H2 production, and the structural features that lead to trapped dihydroxide groups. The pronounced asymmetric oxidation found in heterometallic group 6 oxides and near-neighbor group 5/group 6 results in higher activity toward water, while group 7/group 6 oxides form very specific stoichiometries that suggest facile regeneration. Studies on the trans-periodic combination of cerium oxide and platinum as a model for ceria supported Pt atoms and nanoparticles reveal striking negative charge accumulation by Pt, which, combined with the ionic conductivity of ceria, suggests a mechanism for the exceptionally high activity of this system towards the water-gas shift reaction.