Laura Gagliardi

Iron–sulfur clusters play central roles in biological photosynthesis, respiration, and catalysis. The [Fe4S4(SCH3)4]2– cluster possesses a dense manifold of low-lying electronic states arising from strong magnetic interactions among the Fe centers, making its electronic structure challenging to describe theoretically. Previous multireference studies have generally optimized excited states individually while neglecting the interactions among low-lying states. In this work, we investigate the low-lying electronic states of [Fe4S4(SCH3)4]2– using localized active space state interaction singles (LASSIS) combined with pair-density functional theory (PDFT). By treating all states within a common model-space Hamiltonian, LASSIS generates a single set of orthogonal low-lying states. The resulting spin-state energies organize into distinct manifolds. The same overall pattern is obtained for active spaces ranging from 22 electrons in 20 orbitals to 54 electrons in 36 orbitals. To enable these calculations, we also implement GPU acceleration for the most computationally demanding components of the LASSIS workflow.

Calculations of many electronically excited states in solution require both a multiconfigurational treatment of the solute and an efficient treatment of solvent effects. Multiconfiguration pair-density functional theory (MC-PDFT) and its multistate, linearized extension (L-PDFT) can recover correlation beyond state-averaged complete active space self-consistent field theory (SA-CASSCF) at a fraction of the cost of multireference perturbation theory (e.g., CASPT2) or multireference configuration interaction. Here we combine MC-PDFT and L-PDFT with a nonequilibrium-treatment of the electrostatic solvation effect using the solvation model based on density (SMD). The resulting models are called MC-NSCRF-PDFT and L-NSCRF-PDFT, where NSCRF denotes the key state-specific excited-state nonequilibrium self-consistent reaction field step. We apply the new models to the solvatochromic shifts of the lowest valence excitations of formaldehyde, acetone, acrolein, and methylenecyclopropene and to the aqueous shifts of the lowest π → π* and n → π* transitions of cytosine. For vertical excitation energies in solution, MC-NSCRF-PDFT and L-NSCRF-PDFT give results that are in agreement with the far-more-expensive NSCRF model based on multistate CASPT2. These results show that MC-NSCRF-PDFT and L-NSCRF-PDFT can be used as accurate and computationally efficient methods for electronic excitation energies in the condensed phase.

Spin-phonon coupling governs magnetic relaxation in numerous systems, including single-molecule magnets and molecular spin qubits. In most cases, the accurate prediction of spin relaxation rates requires multireference electronic structure methods, but their computational cost has largely restricted such calculations to isolated molecules. Here we show that spin-phonon relaxation rates can be computed within a multireference density matrix embedding framework. We apply the approach to three cobalt- and two dysprosium-based single-molecule magnets and to a cobalt-based molecular crystal. Across all systems, treating only the first coordination sphere of the magnetic center at the multireference level reproduces spin relaxation rates in good agreement with non-embedded CASSCF calculations, while reducing the correlated problem to 10–68% of the total basis functions. Periodic calculations further demonstrate that spin relaxation rates can be computed for a molecular crystal using an embedded active space of only 259 basis functions out of a total of 2569. These results show that multireference density matrix embedding extends quantitative spin-phonon relaxation calculations from isolated molecules to molecular crystals.

Predicting which molecular species will form under a given set of synthetic conditions requires determining their thermodynamic stability relative to precursors and competing products. For complex molecular systems in solution, this requires both accurate electronic-structure calculations and sufficient configurational sampling. Here, we investigate two hexanuclear Ce/Ti clusters that form under different synthetic conditions: a yellow Ce ^IV ₄ Ti ₂ cluster obtained under mild conditions and a red Ce ^III ₂ Ti ₄ cluster, presented here for the first time, that requires higher temperature, longer reaction times, and increased Ti precursor concentration. To determine whether the red cluster is thermodynamically less stable or instead kinetically hindered, we combine explicit-solvent configurational sampling using a fine-tuned foundation machine-learned interatomic potential with density functional theory calculations of the Gibbs free energies of formation. Simulated annealing identifies configurations approximately 1 eV lower in energy than those obtained by direct relaxation of the crystallographic structures. Despite requiring more forcing synthetic conditions, Ce ^III ₂ Ti ₄ is predicted to be 4.48 eV more stable than Ce ^IV ₄ Ti ₂ . Comparison with a hypothetical Ce ^IV ₂ Ti ₄ cluster separates this difference into a 2.86 eV stabilization associated with the Ce ^III oxidation state and a further 1.62 eV stabilization associated with the Ti-rich composition and corresponding cluster structure. The preference for CeIII is also found for the isolated solvated Ce ions, while the sampled Ce ^III ₂ Ti ₄ structures show reduced repulsion between capping ligands and a less distorted metal core. The calculations therefore identify Ce ^III ₂ Ti ₄ as the thermodynamic product, while its formation only under more forcing conditions is consistent with kinetic limitation. The results show that predicting the thermodynamic product in solution requires configurational sampling beyond direct optimization of experimentally determined structures.

Over the past decade, the Python-based Simulations of Chemistry Framework (PySCF) has developed into a widely used open-source platform for electronic-structure theory and quantum chemical method development. This article reviews the major advances since the previous overview in 2020, covering new modules and methodology, infrastructure changes, and performance benchmarks.

A machine-learned interatomic potential combined with enhanced sampling elucidates how guests distort Zr-MOF-808 node-linker bonds. Adsorbate size, node binding, hydrogen bonding, and temperature govern the mechanisms and thermodynamics.

Lanthanide molecular magnets are promising candidates for quantum information technologies, but their discovery is limited by the computational cost of accurately predicting their electronic and magnetic properties. Multireference methods provide the required accuracy, yet their application at scale has been hindered by the need to manually select the model space (the states considered in the spin–orbit treatment). We present an automated multireference workflow for single-lanthanide complexes, based on complete active space wave functions followed by state-interaction spin–orbit (SISO) coupling. Its central feature is an iterative protocol for constructing the SISO model space, which enables reliable and reproducible calculations across diverse coordination environments. Benchmark calculations on lanthanide hexachlorides show that including spin–orbit-free states up to approximately 5 eV above the ground state reproduces experimental ligand-field splittings with mean absolute errors of 100–200 cm–1 across the lanthanide series. We further examine how the model-space size affects magnetic anisotropy and g-tensors in representative dysprosium- and erbium-based single-ion magnets and in the [Ln(DOTA)(H2O)]− family. Finally, we apply the protocol to 299 lanthanide complexes to generate a consistent data set of ligand-field splittings, g-tensors, magnetic axes, and approximate barriers to magnetization reversal. This work establishes a practical framework for high-throughput multireference calculations and data generation for lanthanide molecular magnets.

Electrocatalytic hydrogenation (e -H) provides a sustainable route for converting unsaturated organic substrates under mild conditions using renewable electricity as the driving force. Here, we report an MOF-derived cobalt catalyst for the e -H of acetone and pyridine. A new two-dimensional cobalt metal–organic framework, Co-L0-NS, composed of Co(II) nodes and polyaromatic carboxylate linkers, was synthesized as nanosheets and used as a precursor to generate the active catalyst under cathodic bias. Electrochemical pretreatment induces controlled framework reconstruction to form MD-Cat, a highly dispersed, structurally disordered, Co(OH)2-rich nanocluster material. MD-Cat catalyzes the e -H of acetone to isopropanol with nearly quantitative Faradaic efficiency at optimized potentials and promotes pyridine hydrogenation to piperidine with up to 50% Faradaic efficiency. Comparative studies with electrodeposited cobalt, commercial cobalt nanoparticles, and bulk Co(OH)2 show that the MOF-derived catalyst exhibits superior current densities and product selectivity, which we attribute to its nanoscale morphology and hydroxylated cobalt environment. In situ Co K-edge XAS, XPS, PXRD, ATR-SEIRAS, and STEM analyses indicate that Co remains predominantly in the +2 oxidation state during catalysis while undergoing structural reorganization. Tafel analysis supports a PCET-type mechanism for acetone hydrogenation; while DFT calculations suggest that the Co/Co(OH)2 interface suppresses HER by weakening H* binding while preserving organic-substrate activation. These results highlight MOF-templated electrochemical reconstruction as a promising approach for designing selective e -H catalysts, not only by increasing catalyst accessibility through nanostructuring but also by enabling the formation of unique catalytic motifs that would otherwise be difficult to access using traditional methods.

We report an end-to-end computational-experimental workflow for the discovery of metal–organic frameworks (MOFs), demonstrated by the computational design and synthesis of two novel Zn-based frameworks, UCHI-1 and UCHI-2, exhibiting enhanced methane uptake and selectivity at low pressure under ambient conditions (298 K, 1 bar). The workflow enables the rational selection and experimental realization of metal–organic frameworks combining data mining, machine-learning driven adsorption prediction, and structure generation, with experimental synthesis and validation within a closed-loop discovery pipeline. Analysis of existing and newly generated MOFs reveals the structure–property relationships governing low-pressure methane adsorption, identifying an optimal pore size and shape, framework densities, linker functionalities, and framework topologies that maximize dispersive C–H/π and van der Waals interactions. Beyond the specific materials identified herein, the results establish this workflow as a scalable and extensible platform for accelerated MOF discovery, with clear routes toward further optimization and automation while demonstrating practical applicability beyond purely theoretical exploration of hypothetical materials.