Electronic Structures of Niobium Carbides:  NbC_n (n = 3−8)

Abstract

The low-lying electronic states of NbC n with five different geometries, namely, ring (R), linear (L), kite (K), Nb-terminally bound to a C n ring (T), and a structure with C−Nb−C bridge fused with a C n ring (A) (n > 3) are considered for n = 3−8. Three different levels of theoretical techniques, viz., complete active space multiconfiguration self-consistent field, multireference singles + doubles configuration interaction, and density functional theory were considered. We compute the equilibrium geometries, energy separations of the low-lying electronic states, Gibbs free energies, and heat capacity functions as a function of temperatures. For smaller clusters such as NbC3, NbC4, and NbC5, we find the ring structure to be lower with the linear structure as the first excited structure. Larger clusters exhibit odd−even alternation in that for even n the linear and ring structures are very close, whereas the clusters with odd n exhibit lower ring structures analogous to the smaller clusters. NbC6 was found to be unusual in having a linear ground state.

Multiple isomers in the photoelectron spectra of small mono-niobium carbide clusters

“…The neutral clusters were previously determined by Dai and collaborators, 21 and our results are mostly in agreement with theirs. Since these are fairly small clusters we manually search for metastable configurations by varying the initial positions of the atoms and optimizing towards any locally metastable state.…”

Competition between linear and cyclic structures in monochromium carbide clusters CrCn− and CrCn (n=2–8): A photoelectron spectroscopy and density functional study

“…Numerous theoretical studies have been performed on the monometal carbide M C n series, [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25] revealing the competition between M -C and C-C interactions in governing the structural evolution of the monometal carbide species. Based on the results of Hartree-Fock ͑HF͒, second-order manybody perturbation theory ͑MBPT͓2͔͒, and density functional theory ͑DFT͒ calculations, it has been concluded that YC 2 , YC 3 , YC 4 , and YC 6 may possess C 2v , kite, fan, and linear ground-state configurations, respectively.…”

“…12,13 For NbC n (nϭ2 -8), extensive calculations concluded that cyclic structures are most stable, except for NbC 6 , which favors a linear ground state. 14,15 Several computations performed for NiC n showed that the relative energies of different geometrical configurations depend strongly on the level of theory applied. 16 -19 Recently, DFT calculations were reported on FeC n (nϭ1 -4), concluding that all the clusters have the fanlike ground-state configurations.…”

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

“…The niobium carbides, Nb n C m , have been the topic of extensive theoretical and experimental research. [14][15][16] Earlier theoretical studies of small niobium clusters (neutral and anionic) have been focussed mainly at the density functional (DFT) level. Fowler and co-workers 17 have studied the neutral Nb 3 and Nb 4 clusters at the DFT level.…”