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A new density functional for the total kinetic energy in the generalized gradient approximation is developed through an enhancement factor that leads to the correct behavior in the limits when the reduced density gradient tends to 0 and to infinity and by making use of the conjoint conjecture for the interpolation between these two limits, through the incorporation, in the intermediate region of constraints that are associated with the exchange energy functional. The resulting functional leads to a reasonable description of the kinetic energies of atoms and molecules when it is used in combination with Hartree–Fock densities. Additionally, in order to improve the behavior of the kinetic energy density, a new enhancement factor for the Pauli kinetic energy is proposed by incorporating the correct behavior into the limits when the reduced density gradient tends to 0 and to infinity, together with the positivity condition, and imposing through the interpolation function that the sum of its integral over the whole space and the Weiszacker energy must be equal to the value obtained with the enhancement factor developed for the total kinetic energy.

The catalytic conversion of nitrous oxide (N 2 O) is of crucial environmental relevance because this chemical compound is a greenhouse gas with an important contribution to climate change, even larger than CO 2, depleting the ozone layer. Recently, reduction of N 2 O catalyzed by rhodium subnanoclusters has been the subject of intensive research, both experimental and theoretical, finding dependencies of reaction rate on the size and geometry and electronic structure of the cluster. In this work, the catalytic reduction mechanism of N 2 O by Rh 6 − and Rh 6 + ionic clusters has been studied by means of density functional theory calculations within the zeroorder-regular approximation (ZORA), which explicitly includes relativistic effects. The N 2 O + Rh 6 − and N 2 O + Rh 6 + reaction pathways were approached starting from a comprehensive search of different stable adsorption modes; transition states were determined as well. We have obtained that the Rh 6 − anions present the lowest activation barriers without spin selectivity. The N 2 O reduction pathway on the Rh 6 − anion was more favorable that the simple desorption channel, whereas on Rh 6 + both channels are in competition, as was experimentally observed. The N 2 O reduction on Rh 6 − and Rh 6 + is sensitive to the charge; it seems to be independent of geometry.

Nitrous oxide (N2O) is a by-product of exhaust pipe gases treatment produced by motor vehicles. Therefore, the N2O reduction to N2 is necessary to meet the actual environmental legislation. The N2O adsorption and dissociation assisted by the square-based pyramidal Rh5 cluster was investigated using the density functional theory and the zero-order regular approximation (ZORA). The Rh5 sextet ground state is the most active in N2O dissociation, though the quartet and octet states are also active because they are degenerate. The Rh5 cluster spontaneously activates the N2─O cleavage, and the reaction is highly exothermic ca. -75 kcal mol(-1). The N2─O breaking is obtained for the geometrical arrangement that maximizes the overlap and electron transfers between the N2O and Rh5 frontier orbitals. The Rh5 high activity is due to the Rh 3d orbitals are located between the N2O HOMO and LUMO orbitals, which makes possible the interactions between them. In particular, the O 2p states strongly interact with Rh 3d orbitals, which finally weaken the N2─O bond. The electron transfer is from the Rh5 HOMO orbital to the N2O antibonding orbital.

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