Theoretical study of the electronic states of Nb4, Nb5 clusters and their anions (Nb4−,Nb5−)

Dressed jeff-1/2 objects in mixed-valence lacunar spinel molybdates

The lacunar-spinel chalcogenides exhibit magnetic centers in the form of transition-metal tetrahedra. On the basis of density-functional computations, the electronic ground state of an Mo₄¹³⁺ tetrahedron has been postulated as single-configuration a₁² e⁴ t₂⁵, where a₁, e, and t₂ are symmetry-adapted linear combinations of single-site Mo t_2g atomic orbitals. Here we unveil the many-body tetramer wave-function: we show that sizable correlations yield a weight of only 62% for the a₁² e⁴ t₂⁵ configuration. While spin-orbit coupling within the peculiar valence orbital manifold is still effective, the expectation value of the spin-orbit operator and the g factors deviate from figures describing nominal t⁵ j_eff = 1/2 moments. As such, our data documents the dressing of a spin-orbit j_eff = 1/2 object with intra-tetramer excitations. Our results on the internal degrees of freedom of these magnetic moments provide a solid theoretical starting point in addressing the intriguing phase transitions observed at low temperatures in these materials.

How Correlations and Spin-Orbit Coupling Work within Extended Orbitals of Transition-Metal Tetrahedra of 4d/5d Lacunar Spinels

Spin-orbit quartet ground states are associated with rich phenomenology, ranging from multipolar phases in f¹ rare-earth borides to magnetism emerging through covalency and vibronic couplings in d¹ transition-metal compounds. The latter effect has been studied since the 1960s on t_2g¹ octahedral ML₆ units in both molecular complexes and extended solid-state lattices. Here we analyze the J_eff = 3/2 quartet ground state of larger cubane-like M₄L₄ entities in lacunar spinels, composed of transition-metal (M) tetrahedra caged by chalcogenide ligands (L). These represent a unique platform where spin-orbit coupling acts on molecular-like, delocalized t₂ orbitals. Using quantum chemical methods, we pin down the interplay of spin-orbit couplings in such a setting and many-body physics related to other molecular-like single-electron levels, both below and above the reference t₂¹. We provide a different interpretation of resonant inelastic X-ray scattering data on GaTa₄Se₈ and, by comparing magnetic susceptibility data with calculated g factors, valuable insights into the important role of vibronic couplings.

Structural, electronic and magnetic effects of Al-doped niobium clusters: a density functional theory study

The application of the ab initio stochastic search procedure with Saunders "kick" method has been carried out for the elucidation of global minimum structures of a series of Al-doped clusters, Nb(n)Al (1 ≤ n ≤ 10). We have studied the structural characters, growth behaviors, electronic and magnetic properties of Nb(n)Al by the density functional theory calculations. Unlike the previous literature reported on Al-doped systems where ground state structures undergo a structural transition from the Al-capped frame to Al-encapsulated structure, we found that Al atom always occupies the surface of Nb(n)Al clusters and structural transition does not take place until n = 10. Note that the fragmentation proceeds preferably by the ejection of an aluminum atom other than niobium atom. According to the natural population analysis, charges always transfer from aluminum to niobium atoms. Furthermore, the magnetic moments of the Nb(n)Al clusters are mainly located on the 4d orbital of niobium atoms, and aluminum atom possesses very small magnetic moments.

Electronic structures, vibrational and thermochemical properties of neutral and charged niobium clusters Nb(n), n = 7-12

Geometric and electronic structures, vibrational properties, and relative stabilities of niobium clusters Nb(n), n = 7-12, are studied using both DFT (BPW91 and M06 functionals) and CCSD(T) calculations with the cc-pVnZ-PP basis set. In each cluster, various lower-lying states are very close in energy in such a way that the ground state cannot be unambiguously established by DFT computations. Nb clusters tend to prefer the lowest possible spin state as the ground state, except for Nb(12) ((3)A(g)). The optimal structure of the cluster at a certain size does not simply grow from that of the smaller one by adding an atom randomly. Instead, the Nb clusters prefer a close-packed growth behavior. Nb(10) has a spherically aromatic character, high chemical hardness and large HOMO-LUMO gap. Electron affinities, ionization energies, binding energy per atom, and the stepwise dissociation energies are evaluated. Energetic properties exhibit odd-even oscillations. Comparison with experimental values shows that both BPW91 and M06 functionals are reliable in predicting the EA and IE values, but the BPW91 is deficient in predicting the binding and dissociation energies. We re-examine in particular the experimental far IR spectra previously recorded using the IR-MPD and free electron laser spectrometric techniques and propose novel assignments for Nb(7) and Nb(9) systems. The IR spectra of the anions are also predicted.

Computational Study of CO Reactivity with Nb3X Heteronuclear Clusters

Density functional calculations were performed to determine the equilibrium structures, ionization potentials, and electron affinities of Nb3X clusters (X = Na, Al, Sc, Sr, Y, Zr, Nb, Mo, Tc, Ru, Rh, Pd, Ag, Cd). Pseudo-tetrahedral geometries were preferred for all Nb3X clusters except Nb3Cd. The equilibrium structures and binding energies of the associatively and dissociatively bound products of the Nb3X + CO reaction were calculated at the same level of theory. All clusters were found to thermodynamically dissociate CO. Only Nb3Al and Nb3Cd reduced the enthalpy of dissociation relative to Nb4, whereas all other heteroatoms increased it.

Octahedral and Tetrahedral Coinage Metal Clusters: Is Three-Dimensional d-Orbital Aromaticity Viable?

The first quantitative evidence for the viability of three-dimensional aromatic clusters involving d-orbitals in pseudo-octahedral coinage metal cages M(6)Li(2) (M = Cu, Ag, Au) as well as in tetrahedral coinage metal cages M'(4)Li(4) (M' = Cu, Ag) was obtained computationally. These cages exhibit many features similar to those of their square planar M(4)Li(2) analogues. The large negative nucleus-independent chemical shifts (NICS) at the cage centers indicate three-dimensional delocalization. This diatropic character arises mostly from d-orbital delocalization combined with substantial contributions from the lowest-valence orbitals. The bonding molecular orbitals of the pseudo-octahedral clusters M(6)Li(2) (M = Cu, Ag, Au) are analogous to those in similar octahedral clusters involving p-orbital delocalization (e.g., B(6)H(6)(2-)). The M'(4)Li(4) clusters exhibit two isomeric forms: metal tetrahedral cages tetracapped by lithium cations on the outside [(M'(4)).4Li] and lithium tetrahedra on the inside capped by coinage metal atoms on each of the four faces [(Li(4)).4M]. Whereas the (M'(4)).4Li type structure is preferred for copper, gold and silver favor the (Li(4)).4M arrangement. NBO-NICS analysis shows that the large diatropic character in (M'(4)).4Li structures is due to the favorable contribution from both s- and d-orbitals, whereas the small NICS values in the center of (Li(4)).4M are due only to the diatropic contributions from the s-orbitals.

Structure and stability of binary transition-metal clusters (NbCo)n (n⩽5): A relativistic density-functional study

Equilibrium geometries and electronic properties of binary transition-metal clusters, (NbCo)n (n < or = 5), have been investigated by means of the relativistic density-functional approach. The metal-metal bonding and stability aspects of these clusters have been analyzed on the basis of calculations. Present results show that these clusters exhibit rich structural varieties on the potential-energy surfaces. The most stable structures have a compact conformation in relatively high symmetry, in which the Nb atoms prefer to form an inner core and Co atoms are capped to the facets of the core. Such building features in clustering of the Nb/Co system are related to the order of bond strength: Nb-Nb>Nb-Co>Co-Co. As the binary cluster size increases, the Nb-Co bond may become stronger than the Nb-Nb bond in the inner niobium core, which results in a remarkable increment of the Nb-Nb bond length. Amongst these binary transition-metal clusters, the singlet (NbCo)4 in T(d) symmetry has a striking high stability due to the presence of the spherical aromaticity and electronic shell closure. The size dependence of the bond length and stability of the cluster has been explored.

Theoretical characterization of the low-lying electronic states of NbC

We have studied the potential-energy curves and the spectroscopic constants of the ground and low-lying excited states of NbC by employing the complete active space self-consistent field method with relativistic effective core potentials followed by multireference configuration-interaction calculations. We have identified 23 low-lying electronic states of NbC with different spin multiplicities and spatial symmetries within 40,000 cm(-1). At the multireference single and double configuration interaction level of theory the 2sigma+ and 2delta states are nearly degenerated, with the 2delta state located 187 cm(-1) lower than the 2sigma+ state. The estimated spin-orbit splitting for the 2delta state results in a 2delta(3/2) ground state and A 2sigma+ which is placed 650 cm(-1) above the ground state, in reasonable agreement with the experimental result, 831 cm(-1). Our computed spectroscopic constants are in good agreement with experimental values although our results differ from those of a previous density-functional investigation of the excited states of NbC, mainly due to the strong multiconfigurational character of NbC. In the present work we have not only suggested assignments for the observed states but also computed more electronic states that are yet to be observed experimentally.