Magnetic Interactions in a [Co(II)₃Er(III)(OR)₄] Model Cubane through Forefront Multiconfigurational Methods

Abstract

Strong electron correlation effects are one of the major challenges in modern quantum chemistry. Polynuclear transition metal clusters are peculiar examples of systems featuring such forms of electron correlation. Multireference strategies, often based on but not limited to the concept of complete active space, are adopted to accurately account for strong electron correlation and to resolve their complex electronic structures. However, transition metal clusters already containing four magnetic centers with multiple unpaired electrons make conventional active space based strategies prohibitively expensive, due to their unfavorable scaling with the size of the active space. In this work, forefront techniques, such as density matrix renormalization group (DMRG), full configuration interaction quantum Monte Carlo (FCIQMC), and multiconfiguration pair-density functional theory (MCPDFT), are employed to overcome the computational limitation of conventional multireference approaches and to accurately investigate the magnetic interactions taking place in a [Co(II)3Er(III)(OR)4] (chemical formula [Co(II)3Er(III)(hmp)4(μ2-OAc)2(OH)3(H2O)], hmp = 2-(hydroxymethyl)-pyridine) model cubane water oxidation catalyst. Complete active spaces with up to 56 electrons in 56 orbitals have been constructed for the seven energetically lowest different spin states. Relative energies, local spin, and spin–spin correlation values are reported and provide crucial insights on the spin interactions for this model system, pivotal in the rationalization of the catalytic activity of this system in the water-splitting reaction. A ferromagnetic ground state is found with a very small, ∼50 cm–1, highest-to-lowest spin gap. Moreover, for the energetically lowest states, S = 3–6, the three Co(II) sites exhibit parallel aligned spins, and for the lower states, S = 0–2, two Co(II) sites retain strong parallel spin alignment.

Exploiting Locality in Full Configuration Interaction Quantum Monte Carlo for Fast Excitation Generation

“…This will be the subject of a future publication. In a series of recent works, − ,,− we have shown that by simple orbital localizations and reorderings, it is possible to obtain CI Hamiltonian matrices with a unique and unprecedented block diagonal structure. As a consequence, extremely compact wave functions (to the limit of near-single-reference) are obtained for ground and excited states of exchange-coupled polynuclear transition metal clusters.…”

“…The full configuration interaction quantum Monte Carlo (FCIQMC) method is a sparse and highly parallelizable CI eigensolver in quantum chemistry. , Relying on the sparsity of the CI Hamiltonian and its eigensolutions, FCIQMC is in general not limited by the active space sizes, − in contrast to conventional CI methods, , which are limited to at most 18 electrons and 18 orbitals . Due to the nearly linear parallelization of the algorithm, FCIQMC takes full advantage of modern computer architectures and allows a large number of electrons and orbitals to be explicitly correlated; active spaces containing up to 96 electrons in 159 orbitals have been reported to date .…”

“…Thus, the development of efficient sampling schemes for single excitations becomes particularly relevant for localized orbital bases. These orbital bases play a crucial role in our recently discovered compression of spin-adapted wave functions of ground and excited states of exchange coupled polynuclear transition metal clusters. − ,,− …”

Toward a Stochastic Complete Active Space Second-Order Perturbation Theory

“…Provided that the perturbation would not cause a significant adjustment of the |ψ (0) ⟩ amplitudes, reducing the dimensionality of the FOIS does not affect the energy correction substantially; however, if the zeroth-order description is flawed, this approximation breaks down. Practical examples include the V -state of ethene or many instances of transition-metal clusters. ,,,, …”

“…The size of the virtual space also limits the naive application of the uncontracted perturbation theory that uses a perturber space whose size is directly proportional to the length of the reference expansion. The effective Hamiltonian formalism based on Löwdin’s partitioning technique allows to describe the influence of a perturbation on a model space without changing the dimension of the zeroth-order problem, transferring the computational burden on the calculation of the transfer matrix. , Through the model space Quantum Monte Carlo method, this cost can be greatly reduced. − Other approaches such as MC-PDFT , or transcorrelation − promise to alleviate the dependence on the orbital expansion by describing dynamic correlation based on the on-top pair density or Jastrow factors, respectively.…”