Projected Unrestricted Hartree−Fock Calculations and the Magnetism of Large Nickel Clusters

Abstract

The study of the multiplicity (M) of transition metal clusters of different sizes has been motivated by its importance in relation to the reactivity of the structures. For this reason, the accuracy and utility of restricted and unrestricted HF methodologies have been extensively analyzed. We compare rather time-consuming restricted open-shell Hartree-Fock calculations followed by multireference CI (ROHF/MRCI) with fully projected unrestricted Hartree-Fock (PUHF) methodologies for the evaluation of the M of small Ni n clusters (n ) 4, 6, 8, 13) using the intermediate neglect of differential overlap model Hamiltonian (INDO). Different geometry and lattice parameters are considered, searching for the best way of dealing with the open-shell electronic distributions that are strongly related to reactivity. We examine both the optimized, most stable structures, and those associated with the observed interatomic bulk distance. Our results are compared with those obtained from density functional and ab initio calculations, as well as with experimental data, when available. On the basis of the results of this comparison, the PUHF model is applied to the study of trilayer and bilayer surface-slab Ni clusters of 20 and 51 atoms, respectively.

INDO calculations of small copper clusters and CO adsorbed on copper(100) surfaces

“…The values found in Table I are consistent with recent studies on nickel clusters (to Ni 72 ), 11 which require an Ni β s value decrease from −1.0 eV to −1.8 eV. The large change in β d value in Table I is partially caused by the very small value of the overlap S between Cu d-orbitals.…”

Is there a bridging ligand in metal‐substituted zinc β‐lactamases? A spectroscopic and theoretical answer

“…A semiempirical quantum chemical spin‐restricted open‐shell method (ZINDO/SROHF) was used, at the multireference configuration interaction (MRCI) level for all the calculations of the electronic structure and spectra. The INDO/S model has been used extensively by us and many others 29–34, 36–43. A review of the underlying model Hamiltonian has been furnished in Ref.…”

“…The spectroscopic version of the intermediate neglect of differential overlap model (INDO/S), as implemented in the ZINDO computer program package 27, has been initially parameterized at the single excited configuration interaction level (CIS) to reproduce the spectra of simple chromophores 28. It is, at present, one of the most reliable methodologies to deal both with close‐ and open‐shell transition metals (TM) 29–35 and lanthanide systems 36, 37, and has been successfully applied to study several biological processes: electron transfer and optical properties of the photosynthetic reaction center 38, 39, magnetic properties of heme species (CYP450s) 35, 40, transient peroxide intermediates of peroxidases 41, and the nitrogen fixation mechanism by nitrogenases 42, 43.…”

On the graphical analysis of the electronic structure of ferromagnetic clusters of medium size

“…The x one was built-up by using M ZINDO (Zerner's Intermediate Neglect of Differential Overlap) [9] atomic basis functions. An M by M ZINDO Hückel (tight binding) h 3 matrix was formed and diagonalized by a c one.…”

“…Such a determinant is automatically an eigen-function of the S 2 , S z spin operators, and has the largest multiplicity (for a given number of unpaired electrons), which, usually, is related with the lowest Energy. Although it is true that several methods have been proposed for studying open-shell molecular systems [9,11,12], the present approach is, probably, the only one able to obtain an SO representation for systems having a large number (more than 1000) of unpaired electrons.…”