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

Abstract

Geometries and energy separations of the various low-lying electronic states of Nb(n) and Nb(n) (-) (n=4,5) clusters with various structural arrangements have been investigated. The complete active space multiconfiguration self-consistent field method followed by multireference singles and doubles configuration interaction (MRSDCI) calculations that included up to 52x10(6) configuration spin functions have been used to compute several electronic states of these clusters. The ground states of both Nb(4) ((1)A('), pyramidal) and Nb(4) (-) ((2)B(3g), rhombus) are low-spin states at the MRSDCI level. The ground state of Nb(5) cluster is a doublet with a distorted trigonal bipyramid (DTB) structure. The anionic cluster of Nb(5) has two competitive ground states with singlet and triplet multiplicities (DTB). The low-lying electronic states of these clusters have been found to be distorted due to Jahn-Teller effect. On the basis of the energy separations of our computed electronic states of Nb(4) and Nb(5), we have assigned the observed photoelectron spectrum of Nb(n) (-) (n=4,5) clusters. We have also compared our MRSDCI results with density functional calculations. The electron affinity, ionization potential, dissociation and atomization energies of Nb(4) and Nb(5) have been calculated and the results have been found to be in excellent agreement with the experiment.

Onset of carbon–carbon bonding in the Nb5Cy(y = 0–6) clusters: a threshold photo-ionisation and density functional theory study

“…30,31 For the DFT method a distorted trigonal bipyramid geometry was found for Nb 5 [ 2 A 2 , C 2v ], whereas for Nb 5 + a distorted trigonal bipyramid of high spin multiplicity [ 3 A 1 , C 2v ] was found. In this study the lowest energy structure of Nb 5 is also found to be a distorted prolate trigonal bipyramid, I A [ 2 B 1 , C 2v ].…”

The far-infrared spectra of neutral and cationic niobium clusters: Nb5∕+ to Nb9∕+

“…The initial geometries in the optimizations are the ones that have been previously discussed in the literature. [39][40][41][42][43][44] Often these geometries are very similar to the ones of the corresponding vanadium clusters and, therefore, we tested, in particular, all the structures that have also been considered by us in our previous work on vanadium. 10 In all calculations the atomic positions were completely relaxed.…”

“…39,40,42,44 Ionization has been found to lead only to minor structural changes under slight expansion. 39 Finally, the assigned structures of 5A and 5 + A perfectly match the 2 B 1 and 3 A 1 ground states of Nb 5 and Nb 5 + , respectively, identified by Majumdar and Balasubramanian.…”

“…Mainly the density-functional theory has been employed to study their geometric and electronic structures with the aim to find correlations with experimental observations, e.g., on the size dependence of reactivities, electron binding energies, or bond dissociation energies. 17,[39][40][41][42][43][44][45][46][47][48][49][50] The multireference character of the wavefunctions of small niobium clusters containing three to five atoms has been taken into account by using the complete active space multiconfiguration self-consistent field method followed by the multireference singles plus doubles configuration interaction. [43][44][45] This approach generally gives similar ground state structures compared to DFT, although it is expected that explicit treatment of the interaction of different electronic configurations leads to a better description of the various low-lying electronic states.…”

Electronic Structure of Transition Metal Clusters, Actinide Complexes and Their Reactivities

“…This is 13 followed by back donation of electronic charge from the Au(5d π) orbital back into the 1σ u antibonding orbital of H 2 . The dissociation in the excited state is assisted by the dative mechanism of electron transfer from the gold atom to the hydrogens and back transfer from the H 2 1σ u to Au (d π ) and (p π).…”