Theory of chemical bonds in metalloenzymes XXIV electronic and spin structures of FeMoco and Fe-S clusters by classical and quantum computing

Permutation symmetry in spin-adapted many-body wave functions

In the domain of exchange-coupled polynuclear transition-metal (PNTM) clusters, local emergent symmetries exist which can be exploited to greatly increase the sparsity of the configuration interaction (CI) eigensolutions of such systems. Sparsity of the CI secular problem is revealed by exploring the site permutation space within spin-adapted many-body bases, and highly compressed wave functions may arise by finding optimal site orderings. However, the factorial cost of searching through the permutation space remains a bottleneck for clusters with a large number of metal centers. In this work, we explore ways to reduce the factorial scaling, by combining permutation and point group symmetry arguments, and using commutation relations between cumulative partial spin and the Hamiltonian operators, . Certain site orderings lead to commuting operators, from which more sparse wave functions arise. Two graphical strategies will be discussed, one to rapidly evaluate the commutators of interest, and one in the form of a tree search algorithm to predict how many and which distinct site permutations are to be analyzed, eliminating redundancies in the permutation space. Particularly interesting is the case of the singlet spin states for which an additional reversal symmetry can be utilized to further reduce the number of distinct site permutations.

The Nature of the Chemical Bonds of High-Valent Transition-Metal Oxo (M=O) and Peroxo (MOO) Compounds: A Historical Perspective of the Metal Oxyl-Radical Character by the Classical to Quantum Computations

This review article describes a historical perspective of elucidation of the nature of the chemical bonds of the high-valent transition metal oxo (M=O) and peroxo (M-O-O) compounds in chemistry and biology. The basic concepts and theoretical backgrounds of the broken-symmetry (BS) method are revisited to explain orbital symmetry conservation and orbital symmetry breaking for the theoretical characterization of four different mechanisms of chemical reactions. Beyond BS methods using the natural orbitals (UNO) of the BS solutions, such as UNO CI (CC), are also revisited for the elucidation of the scope and applicability of the BS methods. Several chemical indices have been derived as the conceptual bridges between the BS and beyond BS methods. The BS molecular orbital models have been employed to explain the metal oxyl-radical character of the M=O and M-O-O bonds, which respond to their radical reactivity. The isolobal and isospin analogy between carbonyl oxide R2C-O-O and metal peroxide LFe-O-O has been applied to understand and explain the chameleonic chemical reactivity of these compounds. The isolobal and isospin analogy among Fe=O, O=O, and O have also provided the triplet atomic oxygen (3O) model for non-heme Fe(IV)=O species with strong radical reactivity. The chameleonic reactivity of the compounds I (Cpd I) and II (Cpd II) is also explained by this analogy. The early proposals obtained by these theoretical models have been examined based on recent computational results by hybrid DFT (UHDFT), DLPNO CCSD(T0), CASPT2, and UNO CI (CC) methods and quantum computing (QC).

Molybdenum-Sulfur Bond: Electronic Structure of Low-Lying States of MoS

The molybdenum-sulfur bond plays an important role in many processes such as nitrogen-fixation, and it is found as a building block in layered materials such as MoS₂, known for its various shapes and morphologies. Here, we present an accurate theoretical and experimental investigation of the chemical bonding and the electronic structure of 20 low-lying states of the MoS molecule. Multireference and coupled cluster methodologies, namely, MRCISD, MRCISD + Q, RCCSD(T), and RCCSD[T], were employed in conjunction with basis sets up to aug-cc-pwCV5Z-PP/aug-cc-pwCV5Z for the study of these states. We note the significance of including the inner 4s²4p⁶ electrons of Mo and 2s²2p⁶ of S in the correlated space to obtain accurate results. Experimentally, the predissociation threshold of MoS was measured using resonant two-photon ionization spectroscopy, allowing for a precise measurement of the bond dissociation energy. Our extrapolated computational D₀ value for the ground state is 3.936 eV, in excellent agreement with our experimental measurement of 3.932 ± 0.004 eV. The largest calculated adiabatic D₀ (5.74 eV) and the largest dipole moment (6.50 D) were found for the ⁵Σ⁺ state, where a triple bond is formed. Finally, the connection of the chemical bonding of the isolated MoS species to the relevant solid, MoS₂, is emphasized. The low-lying septet states of the diatomic molecule are involved in the material as a building block, explaining the stability and the variety of the shapes and morphologies of the material.

Resolution of Low-Energy States in Spin-Exchange Transition-Metal Clusters: Case Study of Singlet States in [Fe(III)4S4] Cubanes

Polynuclear transition-metal (PNTM) clusters owe their catalytic activity to numerous energetically low-lying spin states and stable oxidation states. The characterization of their electronic structure represents one of the greatest challenges of modern chemistry. We propose a theoretical framework that enables the resolution of targeted electronic states with ease and apply it to two [Fe(III)₄S₄] cubanes. Through direct access to their many-body wave functions, we identify important correlation mechanisms and their interplay with the geometrical distortions observed in these clusters, which are core properties in understanding their catalytic activity. The simulated magnetic coupling constants predicted by our strategy allow us to make qualitative connections between spin interactions and geometrical distortions, demonstrating its predictive power. Moreover, despite its simplicity, the strategy provides magnetic coupling constants in good agreement with the available experimental ones. The complexes are intrinsically frustrated anti-ferromagnets, and the obtained spin structures together with the geometrical distortions represent two possible ways to release spin frustration (spin-driven Jahn–Teller distortion). Our paradigm provides a simple, yet rigorous, route to uncover the electronic structure of PNTM clusters and may be applied to a wide variety of such clusters.