Publications

Low-dimensional materials manifest structural anisotropy, quantum confinement, and tightly bound excitonic states, which make them attractive building blocks that can be assembled within three-dimensional laterally stitched heterostructures, stacked van der Waals solids, and complex moiré superlattices. Ion intercalation in the galleries between layered materials provides a means of modifying interlayer separation and coupling, but it is also known to drive the shearing of the layers. In this article, we explore the distinct ligand coordination environments afforded by vanadyl oxygens of singular [V₄O₁₀] sheets and examine how the size, polarizability, and stoichiometry of Group I cations sandwiched between such layers determine the interlocking of the sheets in stacked structures. Based on the topochemical insertion of alkali-metal ions into the layered λ-V₂O₅, we identify seven types of guest ion coordination sites discretized into four distinct regimes of interlayer shear in units of half octahedral widths. The coordination preferences of intercalated cations govern how they interlock 2D [V₄O₁₀] sheets and engender specific shear conformations. We present evidence that static and dynamic disorder in guest ion arrangement modulate the magnetic structure of the intercalated compounds based on electrostatic polarization, localization of charge and spin density, and lattice distortion. The results illustrate the use of topochemical ion insertion to modulate stacking relationships and magnetic transition characteristics.

Two-dimensional infrared spectroscopy offers unique capabilities for probing vibrational coupling in complex metal–ligand systems. In this paper, we combine two-dimensional infrared spectroscopy with vibrational perturbation theory to investigate vibrational coupling in a diiron trinitrosyl complex across three stable redox states. Although these systems are challenging for electronic structure methods, we demonstrate that key features of experimental 2D IR spectra can be accurately reproduced using reduced-dimensional anharmonic calculations with a small harmonic frequency scaling. Analysis reveals that N–O stretching modes maintain high locality across all redox states, with coupling patterns that directly reflect variations in Fe–N bond strength. Using curvilinear coordinate analysis, we demonstrate these differences result from systematic changes in cubic anharmonic force constants rather than mode delocalization. Our results establish N–O stretches as sensitive probes of metal–ligand bonding strength, expanding the toolkit for studying biologically relevant nitrosyl complexes.

Reactions of the metallodithiolate complex VO(bme-dach) (hereafter abbreviated as V, where bme-dach = N,N′-bis(2-mercaptoethyl)-1,4-diazacycloheptane) with [Pd^II(CH₃CN)₄](BF₄)₂ and [Pt^II(CH₃CN)₄](BF₄)₂ yield the V–M–V trimetallic compounds [VPdV](BF₄)₂ (2) and [VPtV](BF₄)₂ (3). Reaction of a similar metalloligand, VO(bme-daco) (hereafter abbreviated as V′ where bme-daco = N,N′-bis(2-mercaptoethyl)-1,5-diazacyclooctane) with [Ni^II(CH₃CN)₆](BF₄)₂ afforded the related salt [V′NiV′](BF₄)₂ (1). X-ray structural analyses revealed that cations in 1, 2, and 3 adopt a stairstep C_2h structure consisting of two terminal VO(N₂S₂) moieties bridged via thiolate sulfur to the group 10 metal ions. Weak ferromagnetic superexchange coupling (J = 0.282 cm^–1 for 1, 0.954 cm^–1 for 2, and 1.372 cm^–1 for 3) was observed between the two S = 1/2 V^IV centers separated by distances in the range of 5.9–6.3 Å, with J values varying following the order Ni < Pd < Pt. Frozen-solution EPR spectra measured on the more soluble [BArF₂₄]⁻ (BArF₂₄^– = tetrakis((3,5-trifluoromethyl)phenyl)borate) analogues revealed that the [VPtV]²⁺ cation exhibits a 15-line hyperfine splitting of 225 MHz at g = 4 in parallel mode, confirming exchange coupling between the two ⁵¹V, I = 7/2 nuclei. Density-functional theory (DFT) calculations indicate an S = 1 ground state for 1–3. These results demonstrate that the choice of paramagnetic metallodithiolate ligand and diamagnetic bridge in such trimetallic species influences the sign and magnitude of magnetic interactions.

Symbolic regression (SR) seeks interpretable analytical expressions that uncover the governing relationships within data, providing mechanistic insight beyond ‘black-box’ models. However, existing SR methods often suffer from two key limitations: (1) redundant representations that fail to capture mathematical equivalences and higher-order operand relations, breaking permutation invariance and hindering efficient learning; and (2) sparse rewards caused by incomplete incorporation of constraints that can only be evaluated on full expressions, such as constant fitting or physical-law verification. To address these challenges, we propose a unified framework, Graph-based Symbolic Regression (GSR), which compresses the search space through the permutation-invariant representations, expression graphs (EGs), that intrinsically encode expression equivalences via a term-rewriting system (TRS) and a directed acyclic graph (DAG) structure. GSR mitigates reward sparsity by employing a hybrid neural-guided Monte Carlo tree search (hnMCTS) on EGs, where constraint-informed neural guidance enables the direct incorporation of expression-level constraint priors, and an adaptive ϵ-UCB policy balances exploration and exploitation. Theoretical analyses establish the uniqueness of our proposed EG representation and the convergence of the hnMCTS algorithm. Experiments on synthetic and real-world scientific datasets demonstrate the efficiency and accuracy of GSR in discovering underlying expressions and adhering to physical laws, offering practical solutions for scientific discovery.