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The present paper reports an original computational strategy for the computation of the isotropic hyperfine coupling constants (hcc). The algorithm proposed here is based on an approach recently introduced by some of the authors, namely, the first-order breathing orbital self-consistent field (FOBO-SCF). The approach is an almost parameter-free wave function method capable to accurately treat the spin delocalization together with the spin polarization effects while staying in a restricted formalism and avoiding spin contamination. The efficiency of the method is tested on a series of small radicals, among which four nitroxide radicals and the comparison with high-level ab initio methods show very encouraging results. On the basis of these results, the method is then applied to compute the hcc of a challenging system, namely, the DEPMPO-OOH radical in various conformations. The reference values obtained on such a large system allows us to validate a cheap computational method based on density functional theory (DFT). Another interesting feature of the model applied here is that it allows for the rationalization of the results according to a relatively simple scheme based on a two-step mechanism. More precisely, the results are analyzed in terms of two separated contributions: first the spin delocalization and then the spin polarization.

RESUMEN

The impact of the antisymmetrization is often addressed as a local property of the many-electron wave function, namely that the wave function should vanish when two electrons with parallel spins are in the same position in space. In this paper, we emphasize that this presentation is unduly restrictive: we illustrate the strong non-local character of the antisymmetrization principle, together with the fact that it is a matter of spin symmetry rather than spin parallelism. To this aim, we focus our attention on the simplest representation of various states of two-electron systems, both in atomic (helium atom) and molecular (H2 and the π system of the ethylene molecule) cases. We discuss the non-local property of the nodal structure of some two-electron wave functions, both using analytical derivations and graphical representations of cuttings of the nodal hypersurfaces. The attention is then focussed on the impact of the antisymmetrization on the maxima of the two-body density, and we show that it introduces strong correlation effects (radial and/or angular) with a non-local character. These correlation effects are analyzed in terms of inflation and depletion zones, which are easily identifiable, thanks to the nodes of the orbitals composing the wave function. Also, we show that the correlation effects induced by the antisymmetrization occur also for anti-parallel spins since all Ms components of a given spin state have the same N-body densities. Finally, we illustrate that these correlation effects occur also for the singlet states, but they have strictly opposite impacts: the inflation zones in the triplet become depletion zones in the singlet and vice versa.

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A new strategy based on orthogonal valence-bond analysis of the wave function combined with intermediate Hamiltonian theory has been applied to the evaluation of the magnetic coupling constants in two AF systems. This approach provides both a quantitative estimate of the J value and a detailed analysis of the main physical mechanisms controlling the coupling, using a combined perturbative + variational scheme. The procedure requires a selection of the dominant excitations to be treated variationally. Two methods have been employed: a brute-force selection, using a logic similar to that of the CIPSI approach, or entanglement measures, which identify the most interacting orbitals in the system. Once a reduced set of excitations (about 300 determinants) is established, the interaction matrix is dressed at the second-order of perturbation by the remaining excitations of the CI space. The diagonalization of the dressed matrix provides J values in good agreement with experimental ones, at a very low-cost. This approach demonstrates the key role of d → d* excitations in the quantitative description of the magnetic coupling, as well as the importance of using an extended active space, including the bridging ligand orbitals, for the binuclear model of the intermediates of multicopper oxidases. The method is a promising tool for dealing with complex systems containing several active centers, as an alternative to both pure variational and DFT approaches.

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RESUMEN

The bond nature in beryllium dimer has been theoretically investigated using high-level ab initio methods. A series of ANO basis sets of increasing quality, going from sp to spdf ghi contractions, has been employed, combined with HF, CAS-SCF, CISD, and MRCI calculations with several different active spaces. The quality of these calculations has been checked by comparing the results with valence Full-CI calculations, performed with the same basis sets. It is shown that two quasi-degenerated partly occupied orbitals play a crucial role to give a qualitatively correct description of the bond. Their nature is similar to that of the edge orbitals that give rise to the quasi-degenerated singlet-triplet states in longer beryllium chains.

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