On the evaluation of the non-interacting kinetic energy in density functional theory

The utility of both an orbital-free and a single-orbital expression for computing the non-interacting kinetic energy in density functional theory is investigated for simple atomic systems. The accuracy of both expressions is governed by the extent to which the Kohn-Sham equation is solved for the given exchange-correlation functional and so special attention is paid to the influence of finite Gaussian basis sets. The orbital-free expression is a statement of the virial theorem and its accuracy is quantified. The accuracy of the single-orbital expression is sensitive to the choice of Kohn-Sham orbital. The use of particularly compact orbitals is problematic because the failure to solve the Kohn-Sham equation exactly in regions where the orbital has decayed to near-zero leads to unphysical behaviour in regions that contribute to the kinetic energy, rendering it inaccurate. This problem is particularly severe for core orbitals, which would otherwise appear attractive due to their formally nodeless nature. The most accurate results from the single-orbital expression are obtained using the relatively diffuse, highest occupied orbitals, although special care is required at orbital nodes.     

Exchange methods in Kohn-Sham theory

Differences between exchange methods in exchange-only Kohn-Sham theory are highlighted by calculations of diatomic molecule total energies, uncoupled isotropic NMR shieldings, and HOMO-LUMO eigenvalue differences. Optimised effective potential (OEP) and Wu-Yang (WY) results are very similar. Localised Hartree-Fock (LHF) and Krieger-Li-Iafrate (KLI) results are close to one another, but are different to OEP and WY. Becke 1988 exchange (B88X) is different again. Shieldings reduce from OEP/WY to LHF/KLI to B88X, which is consistent with an observed reduction in HOMO-LUMO gaps. LHF, KLI, and B88X shieldings and HOMO-LUMO gaps are closer to near-exact, correlated values, than are the OEP values. These variations arise entirely due to differences in the one-electron exchange potentials, which is clearly evident in potential difference plots, relative to OEP, for the N2 molecule. Density difference plots are also presented, which exhibit a spatial correlation with the potential differences. HOMO and LUMO probability density difference plots show a contraction of the LUMO relative to OEP, which is consistent with the NMR and HOMO-LUMO findings. Plots are also presented for near-exact, correlated Kohn-Sham calculations. The features are qualitatively similar to those observed in the LHF, KLI, and B88X plots, highlighting correlated character in these approximate exchange-only calculations.     

Hydrogenation of

The course of the hydrogenation of [5]- and [6]metacyclophane (1b and 1c) and their thermochemistry is described. Both compounds are hydrogenated rapidly (within 10 s) to furnish the bridgehead olefins 13b and 12c. The accompanying hydrogenation enthalpies are -220 and -141 kJmol(-1), respectively. Strain energies (SE) and olefinic strains (OS) of a number of bridgehead olefins have been evaluated by DFT calculations; it was concluded that 13b belongs to the class of hyperstable olefins which correlates nicely with its reluctance to undergo hydrogenation. By combining experimental hydrogenation enthalpies and DFT calculations, SE of 187 and 121 kJmol(-1) were derived for 1b and 1c.     

Computation of the hardness and the problem of negative electron affinities in density functional theory

The absolute hardness in density functional theory (DFT) is discussed, emphasizing the charge-transfer excitation interpretation. Direct evaluation from the computed ionization potential and electron affinity is intrinsically problematic when the affinity is negative; the calculated affinity exhibits a strong basis set dependence, becoming near zero as diffuse functions are added. An alternative Koopmans-based approximation using local functional eigenvalues uniformly and significantly underestimates the hardness. A simple correction to the Koopmans expression is highlighted on the basis of a consideration of the integer discontinuity. The resulting hardness expression does not require the explicit computation of the affinity and has a straightforward interpretation in terms of the electronegativity. The correction eliminates the underestimation and gives hardness values that do not degrade as the electron affinity becomes more negative. For systems with large negative affinities, the values are an improvement over those from the other approaches. The success can be traced to an implicit, unconventional approximation for the electron affinity, which outperforms the standard approach when the affinity is significantly negative and which does not break down as the basis set becomes more diffuse.     

Using 15N to determine a budget for effluent-derived nitrogen applied to forest

Using stable N isotopes, the fate of effluent-derived N has been determined within a land based municipal effluent irrigation scheme. Over 900 metric tonnes(t) of effluent-derived N have been applied to 192 ha of production conifer forest near Rotorua (NZ) over the past 11 years. The effluent N has a natural isotopic signal, generated by the treatment process, allowing it to be traced into various components of the system. Using this isotopic signal, a realistic approximation of storage capacity of various components of the system has been generated, including a calculation of the contribution of effluent N exiting the catchment via stream flow.Forest storage accounts for 50% of the applied N with a considerable proportion of that immobilized in wood and soil. The wetland, although not intensively sampled, retains 115 t, (13%) of the applied N. Denitrification, including that occurring within the wetland, accounts for 23 t (3%). Nitrogen isotope data confirm that the rise in NO3 concentrations is directly attributable to effluent N. Currently 88% of NO3-N in the stream is effluent-derived. Using current N isotope values for the stream and extrapolating over the discharge period, export of effluent N via the stream is estimated as 263 t (29%) of the applied N. Overall the forest and wetland ecosystem has intercepted or denitrified 65% of applied N, with 29% lost to the stream, and 50 t (5%) unaccounted for.The forest ecosystem is currently over-supplied with N and a number of management implications flows from these findings. In the long term the continued application of effluent N to the current irrigation area is not sustainable.