Spectroscopic constants and potential energy curves of gallium nitride (GaN) and ions: GaN+ and GaN−

Ligand-stabilized heteronuclear diatomics of group 13 and 15

A theoretical investigation of ligand-stabilized MX diatomics (M = group 13, X = group 15 element) with N-heterocyclic carbene (NHC) ligands has been carried out to assess bonding and electronic structure. Binding of two ligands in the form L-MX-L is generally preferred over binding of a single ligand as L-MX or MX-L. Binding of carbene donor ligands is predicted to be thermodynamically favorable for all the systems, and is very favorable for the lighter group 15 systems (nitrogen and phosphorus). Detailed analysis of the bonding in these complexes has been carried out with energy decomposition analysis (EDA). In all cases, the carbene to boron and carbene to nitrogen bonding is described as an electron-sharing double bond with both σ and π bonding interactions. For the heavier elements, bonding to C (except for PC interactions) is best described as a donor-acceptor σ single bond.

Different eyes on the same prize: implications of entry timing heterogeneity and incentives for contestant effort in innovation tournament

Purpose

This paper examines an apparent contrast in organizing innovation tournaments; seekers offer contestant-agnostic incentives to elicit greater effort from a heterogeneous pool of contestants. Specifically, the study tests whether and how such incentives and the underlying heterogeneity in the contestant pool, assessed in terms of contestants' entry timing, are jointly associated with contestant effort. Thus, the study contributes to the prior literature that has looked at behavioral consequences of entry timing as well as incentives in innovation tournaments.

Design/methodology/approach

For hypothesis testing, the study uses a panel dataset of submission activity of over 60,000 contestants observed in nearly 200 innovation tournaments. The estimation employs multi-way fixed effects, accounting for unobserved heterogeneity across contestants, tournaments and submission week. The findings remain stable across a range of robustness checks.

Findings

The study finds that, on average, late entrant tends to exert less effort than an early entrant (H1). Results further show that the effort gap widens in tournaments that offer higher incentives. In particular, the effort gap between late and early entrants is significantly wider in tournaments that have attracted superior solutions from several contestants (H2), offer gain in status (H3, marginally significant) or offer a higher monetary reward (H4).

Originality/value

The study's findings counter conventional wisdom, which suggests that incentives have a positive effect on contestant behavior, including effort. In contrast, the study indicates that incentives may have divergent implications for contestant behavior, contingent on contestants' entry timing. As the study discusses, these findings have several implications for research and practice of managing innovation tournaments.

Ab initio study of the electronic structure and bonding of aluminum nitride

For the diatomic aluminum nitride (AlN), we have constructed potential energy curves for 45 states employing multi-reference variational methods and quantitative basis sets. Thirty-six states are relatively strongly bound, five present local minima, and four are of repulsive nature. Almost all states are of intense multi-reference character rendering their calculation and interpretation quite problematic. Our tentative assignment of the ground state is 3Pi, while a 3Sigma- state is above by less than 1 kcal/mol. Our best estimate for the binding energy of the X3Pi state is D0 = 56.0 +/- 0.5 kcal/mol at re = 1.783 A, in good agreement with the experimental values of D = 66 +/- 9 kcal/mol and re = 1.7864 A. The binding energy of the A3Sigma- state is very similar to the X state because they both correlate to the ground-state atoms, but the bond distance of the former is 0.13 A longer. The first seven states can be tagged as follows: X3Pi, A3Sigma-, a1Sigma+, b1Pi, c1Delta, B3Sigma+, and d1Sigma+, a rather definitive order with the exception of X and A states.

Theoretical Investigation on the Electronic and Geometric Structure of GaN2+ and GaN4+

The electronic and geometric structures of gallium dinitride cation, GaN2+ and gallium tetranitride cation, GaN4+ were systematically studied by employing density functional theory (DFT-B3LYP) and perturbation theory (MP2, MP4) in conjunction with large basis sets, (aug-)cc-pVxZ, x = T, Q. A total of 7 structures for GaN2+ and 24 for GaN4+ were identified, corresponding to minima, transition states, and saddle points. We report geometries and dissociation energies for all the above structures as well as potential energy profiles, potential energy surfaces, and bonding mechanisms for some low-lying electronic states. The calculated dissociation energy (De) of the ground state of GaN2+, X1Sigma+, is 5.6 kcal/mol with respect to Ga+(1S) + N2(X1Sigmag+) and that of the excited state, ã3Pi, is 24.8 kcal/mol with respect to Ga+(3P) + N2(X1Sigmag+). The ground state and the first excited minimum of GaN4+ are of 1A1(C2v) and 3B1(C2v) symmetry with corresponding De of 11.0 and 43.7 kcal/mol with respect to Ga+(1S) + 2N2(X1Sigmag+) for X1A1 and Ga+(3P) + 2N2(X1Sigmag+) for 3B1.