The shortcomings of semi-local and hybrid functionals: what we can learn from surface science studies

A study of the adsorption of CO on late 4d and $5d$ transition metal (111) surfaces (Ru, Rh, Pd, Ag, Os, Ir, and Pt) considering atop and hollow site adsorption is presented. The applied functionals include the gradient corrected PBE and BLYP functional, and the corresponding hybrid Hartree-Fock density functionals HSE and B3LYP. We find that PBE based hybrid functionals (specifically HSE) yield, with the exception of Pt, the correct site order on all considered metals, but they also considerably overestimate the adsorption energies compared to experiment. On the other hand, the semi-local BLYP functional and the corresponding hybrid functional B3LYP yield very satisfactory adsorption energies and the correct adsorption site for all surfaces. We are thus faced with a Procrustean problem: the B3LYP and BLYP functionals seem to be the overall best choice for describing adsorption on metal surfaces, but they simultaneously fail to account well for the properties of the metal, vastly overestimating the equilibrium volume and underestimating the atomization energies. Setting out from these observations, general conclusions are drawn on the relative merits and drawbacks of various semi-local and hybrid functionals. The discussion includes a revised version of the PBE functional specifically optimized for bulk properties and surface energies (PBEsol), a revised version of the PBE functional specifically optimized to predict accurate adsorption energies (rPBE), as well as the aforementioned BLYP functional. We conclude that no semi-local functional is capable to describe all aspects properly, and including non-local exchange also only improves some, but worsens other properties.Comment: 12 pages, 6 figures; to be published in New Journal of Physic

Why is a noble metal catalytically active? The role of the O-Ag interaction in the function of silver as an oxidation catalyst

Extensive density-functional theory calculations, and taking into account temperature and pressure, affords a comprehensive picture of the behavior and interaction of oxygen and Ag(111), and provides valuable insight into the function of silver as an oxidation catalyst. The obtained phase-diagram reveals the most stable species present in a given environment and thus identifies (and excludes) possibly active oxygen species. In particular, for the conditions of ethylene epoxidation, a thin oxide-like structure is most stable, suggesting that such atomic O species are actuating the catalysis, in contrast to hitherto proposed molecular-like species.Comment: 4 pages including 3 figures, Related publications can be found at http://www.fhi-berlin.mpg.de/th/paper.htm

Covalent effects in molecule-surface charge exchange: oxygen on silver(111)

The formation of neg. charged ions (O2-, O-) in the scattering of oxygen from silver surfaces is difficult to explain with the Brako-Newns scheme. Extended-Hueckel tight-binding calcns. are performed on model Ag(111) slabs, placing O2 adsorbates at various sites and mol. orientations. As the survival probability of a neg. charged ion leaving the surface is detd. by the back-tunneling frequency, the mol. ion survival probably should increase as the O2-Ag interaction decreases, and vice versa. On the other hand, the dissocn. probability will increase with increasing interaction strength. The strength of the O2-Ag interaction can be gaged by the dispersion found in the projected d. of states of the O2 affinity level 1pg. The second moment serves as a measure of relative dispersion, and in addn., can be related to the tunneling frequency. The bridging and hollow sites have the strongest O2-Ag interaction, thus the lowest survival probability of neg. ions and the highest degree of dissocn. The interaction at top sites is much less. These results can be used to explain the higher O-/(O- + O2-) ratio obsd. at more grazing incident beam angle

Covalent effects in molecule-surface charge exchange: oxygen on silver(111)

The formation of neg. charged ions (O2-, O-) in the scattering of oxygen from silver surfaces is difficult to explain with the Brako-Newns scheme. Extended-Hueckel tight-binding calcns. are performed on model Ag(111) slabs, placing O2 adsorbates at various sites and mol. orientations. As the survival probability of a neg. charged ion leaving the surface is detd. by the back-tunneling frequency, the mol. ion survival probably should increase as the O2-Ag interaction decreases, and vice versa. On the other hand, the dissocn. probability will increase with increasing interaction strength. The strength of the O2-Ag interaction can be gaged by the dispersion found in the projected d. of states of the O2 affinity level 1pg. The second moment serves as a measure of relative dispersion, and in addn., can be related to the tunneling frequency. The bridging and hollow sites have the strongest O2-Ag interaction, thus the lowest survival probability of neg. ions and the highest degree of dissocn. The interaction at top sites is much less. These results can be used to explain the higher O-/(O- + O2-) ratio obsd. at more grazing incident beam angle

Phase diagram for Ca_{1-x}Y_xMnO_3 type crystals

We present a simple model to study the electron doped manganese perovskites. The model considers the competition between double exchange mechanism for itinerant electrons and antiferromagnetic superexchange interaction for localized electrons. It represents each Mn^{4+} ion by a spin 1/2, on which an electron can be added to produce Mn^{3+}; we include a hopping energy t, a strong intratomic interaction exchange J (in the limit J/t>>1), and an interatomic antiferromagnetic interaction K between the local spins. Using the Renormalized Perturbation Expansion and a Mean Field Approximation on the hopping terms and on the superexchange interaction we calculate the free energy. From it, the stability of the antiferromagnetic, canted, ferromagnetic, and novel spin glass phases can be determined as functions of the parameters characterizing the system. The model results can be expressed in terms of t and K for each value of the doping x in phase diagrams. The magnetization m and canting angle can also be calculated as fuctions of temperature for fixed values of doping and model parameters.Comment: 4 figure

Forage Allowance and Daily Gain Relationships on Rye-Ryegrass Pastures at Different Stocking Rates With Continuous and Rotational Stocking

‘Maton’ cereal rye (Secale cereale L.) and ‘TAM-90’ annual ryegrass (Lolium multiflorum Lam.) are used for winter annual pastures to background stocker cattle in the southeastern US. Rye and ryegrass were sod-seeded into bermudagrass [Cynodon dactylon (L.) Pers.] pastures and fixed-stocked at different rates under continuous and 8-paddock rotation methods during each of 7 years to: 1) compare stocking methods for daily gain per animal (ADG) and gain/ha; and 2) quantify relationships of ADG with forage mass and forage allowance. Each of 3 levels of stocking rate, 4.9, 6.4, and 8.6 hd/ha, significantly affected ADG at 1.24, 1.04, and 0.74 kg/d, and gain/ha at 821, 991, and 794 kg/ha, respectively. There were no effects of stocking method on ADG at 1 kg/ha or gain/ha at 870 kg/ha. There was a 2-stage linear relationship for ADG and forage mass with the join point for maximum gain at 1850 kg/ha forage mass and 16 cm forage height. The 2-stage join point for forage allowance was 1.0 forage dry matter : animal body weight. The primary management strategy for rye + annual ryegrass pastures is that of stocking rate. During this 7-year period, stocker ADG ranged from 0.33 kg/d to 1.38 kg/d with gain/ha ranging from 388 kg/ha to 1291 kg/ha. Stocking strategies must be flexible with climatic changes to obtain optimum economic returns per unit land area. Rotational stocking method becomes a management choice to adjust forage mass options without expectations for increased ADG or gain/ha