On the required shape corrections to the local density and generalized gradient approximations to the Kohn-Sham potentials for molecular response calculations of (hyper)polarizabilities and excitation energies

It is well known that shape corrections have to be applied to the local-density (LDA) and generalized gradient (GGA) approximations to the Kohn-Sham exchange-correlation potential in order to obtain reliable response properties in time dependent density functional theory calculations. Here we demonstrate that it is an oversimplified view that these shape corrections concern primarily the asymptotic part of the potential, and that they affect only Rydberg type transitions. The performance is assessed of two shape-corrected Kohn-Sham potentials, the gradient-regulated asymptotic connection procedure applied to the Becke-Perdew potential (BP-GRAC) and the statistical averaging of (model) orbital potentials (SAOP), versus LDA and GGA potentials, in molecular response calculations of the static average polarizability alpha, the Cauchy coefficient S-4, and the static average hyperpolarizability beta. The nature of the distortions of the LDA/GGA potentials is highlighted and it is shown that they introduce many spurious excited states at too low energy which may mix with valence excited states, resulting in wrong excited state compositions. They also lead to wrong oscillator strengths and thus to a wrong spectral structure of properties like the polarizability. LDA, Becke-Lee-Yang-Parr (BLYP), and Becke-Perdew (BP) characteristically underestimate contributions to alpha and S-4 from bound Rydberg-type states and overestimate those from the continuum. Cancellation of the errors in these contributions occasionally produces fortuitously good results. The distortions of the LDA, BLYP, and BP spectra are related to the deficiencies of the LDA/GGA potentials in both the bulk and outer molecular regions. In contrast, both SAOP and BP-GRAC potentials produce high quality polarizabilities for 21 molecules and also reliable Cauchy moments and hyperpolarizabilities for the selected molecules. The analysis for the N-2 molecule shows, that both SAOP and BP-GRAC yield reliable energies omega(i) and oscillator strengths f(i) of individual excitations, so that they reproduce well the spectral structure of alpha and S-4.(C) 2002 American Institute of Physics.

The failure of generalized gradient approximations (GGAs) and meta-GGAs for the two-center three-electron bonds in He-2(+), (H2O)(2)(+), and (NH3)(2)(+)

The radical cations He-2(+) (H2O)(2)(+), and (NH3)(2)(+) with two-center three-electron A-A bonds are investigated at the configuration interaction (CI), accurate Kohn-Sham (KS), generalized gradient approximation (GGA), and meta-GGA levels. Assessment of seven different GGA and six meta-GGA methods shows that the A(2)(+) systems remain a difficult case for density functional theory (DFT). All methods tested consistently overestimate the stability of A(2)(+): the corresponding D-e errors decrease for more diffuse valence densities in the series He-2(+) > (H2O)(2)(+) > (NH3)(2)(+). Upon comparison to the energy terms of the accurate Kohn-Sham solutions, the approximate exchange functionals are found to be responsible for the errors of GGA-type methods, which characteristically overestimate the exchange in A(2)(+). These so-called exchange functionals implicitly use localized holes. Such localized holes do occur if there is left-right correlation, i.e., the exchange functionals then also describe nondynamical correlation. However, in the hemibonded A(2)(+) systems the typical molecular (left-right, nondynamical) correlation of the two-electron pair bond is absent. The nondynamical correlation built into the exchange functionals is then spurious and yields too low energies.

A generalized functional response for predators that switch between multiple prey species

We develop a theory for the food intake of a predator that can switch between multiple prey species. The theory addresses empirical observations of prey switching and is based on the behavioural assumption that a predator tends to continue feeding on prey that are similar to the prey it has consumed last, in terms of, e.g., their morphology, defences, location, habitat choice, or behaviour. From a predator's dietary history and the assumed similarity relationship among prey species, we derive a general closed-form multi-species functional response for describing predators switching between multiple prey species. Our theory includes the Holling type II functional response as a special case and makes consistent predictions when populations of equivalent prey are aggregated or split. An analysis of the derived functional response enables us to highlight the following five main findings. (1) Prey switching leads to an approximate power-law relationship between ratios of prey abundance and prey intake, consistent with experimental data. (2) In agreement with empirical observations, the theory predicts an upper limit of 2 for the exponent of such power laws. (3) Our theory predicts deviations from power-law switching at very low and very high prey-abundance ratios. (4) The theory can predict the diet composition of a predator feeding on multiple prey species from diet observations for predators feeding only on pairs of prey species. (5) Predators foraging on more prey species will show less pronounced prey switching than predators foraging on fewer prey species, thus providing a natural explanation for the known difficulties of observing prey switching in the field. (C) 2013 Elsevier Ltd. All rights reserved.

Time-dependent R-matrix theory applied to two-photon double ionization of He

We introduce a time-dependent R-matrix theory generalized to describe double-ionization processes. The method is used to investigate two-photon double ionization of He by intense XUV laser radiation. We combine a detailed B-spline-based wave-function description in an extended inner region with a single-electron outer region containing channels representing both single ionization and double ionization. A comparison of wave-function densities for different box sizes demonstrates that the flow between the two regions is described with excellent accuracy. The obtained two-photon double-ionization cross sections are in excellent agreement with other cross sections available. Compared to calculations fully contained within a finite inner region, the present calculations can be propagated over the time it takes the slowest electron to reach the boundary.

A density functional theory study of CO oxidation on Ru(0001) at low coverage

We have performed ab initio density functional theory calculations with the generalized gradient approximation to investigate CO oxidation on Ru(0001). Several reaction pathways and transition states are identified. A much higher reaction barrier compared to that on Pt(111) is determined, confirming that the Ru is very inactive for CO oxidation under UHV conditions. The origin of the reaction barrier was analyzed. It is found that in the transition state the chemisorbed O atom sits in an unfavorable bonding site and a significant competition for bonding with the same substrate atoms occurs between the CO and the chemisorbed O, resulting in the high barrier. Ab initio molecular dynamics calculations show that the activation of the chemisorbed O atom from the initial hcp hollow site (the most stable site) to the bridge site is the crucial step for the reaction. The CO oxidation on Ru(0001) via the Eley-Rideal mechanism has also been investigated. A comparison with previous theoretical work has been made. (C) 2000 American Institute of Physics. [S0021-9606(00)31223-5].