Scalable properties of metal clusters: A comparative study of modern exchange-correlation functionals

Abstract

The performance of eight generalized gradient approximation exchange-correlation (xc) functionals is assessed by a series of scalar relativistic all-electron calculations on octahedral palladium model clusters Pd(n) with n = 13, 19, 38, 55, 79, 147 and the analogous clusters Au(n) (for n up through 79). For these model systems, we determined the cohesive energies and average bond lengths of the optimized octahedral structures. We extrapolate these values to the bulk limits and compare with the corresponding experimental values. While the well-established functionals BP, PBE, and PW91 are the most accurate at predicting energies, the more recent forms PBEsol, VMTsol, and VT{84}sol significantly improve the accuracy of geometries. The observed trends are largely similar for both Pd and Au. In the same spirit, we also studied the scalability of the ionization potentials and electron affinities of the Pd clusters, and extrapolated those quantities to estimates of the work function. Overall, the xc functionals can be classified into four distinct groups according to the accuracy of the computed parameters. These results allow a judicious selection of xc approximations for treating transition metal clusters.

Size-dependent properties of transition metal clusters: from molecules to crystals and surfaces – computational studies with the program ParaGauss

“…6,[15][16][17] The economical relevance 18 of industrial applications represents an especially strong driving force for scientific research aiming at a detailed understanding of the properties of TM clusters and NPs. 3,[38][39][40][41][42][43][44][45][46][47][48][49][50][51] Indeed, the physical and chemical properties of such systems follow scaling laws as they slowly approach their corresponding bulk limits. 16,[19][20][21][22][23][24] In such combined studies the experimentally examined systems need to be as close as possible to the models used in the corresponding computational studies.…”

“…Often enough, synergy effects resulting from joint experimental and computational studies turn out to be essential for gaining insights at the atomic level. 3,[39][40][41][42][43][44][45][46][47][48][49][50][51] The onset of this latter scaling behavior, hence the beginning of the so-called scalable regime, is smooth and the cluster sizes at which it occurs depend on the atomic element of the particles at hand and the property under study. With regard to nanocatalysis 6,[25][26][27] this requirement can impose considerable problems as the catalytically active species employed in industrial processes often are significantly larger than the computational models for which accurate calculations are feasible, 24,25 e.g., by means of Kohn-Sham (KS) density functional theory (DFT).…”

“…With regard to nanocatalysis 6,[25][26][27] this requirement can impose considerable problems as the catalytically active species employed in industrial processes often are significantly larger than the computational models for which accurate calculations are feasible, 24,25 e.g., by means of Kohn-Sham (KS) density functional theory (DFT). [39][40][41][42][43][44][45][46][47][48][49][50][51] From results for a series of such medium-sized clusters, scaling laws (Section 2.1) then can be invoked to extrapolate the properties of much larger NPs. 9,24 Modern cluster sources based on sputtering, 29 laser vaporization, 30,31 pulsed microplasma, 32 or discharge techniques 33 can generate particles in a wide range of sizes, but specific mass-selection is only guaranteed for species consisting of a few atoms.…”

“…9,24 Modern cluster sources based on sputtering, 29 laser vaporization, 30,31 pulsed microplasma, 32 or discharge techniques 33 can generate particles in a wide range of sizes, but specific mass-selection is only guaranteed for species consisting of a few atoms. 3,[39][40][41][42]44,45,[48][49][50][51] As those latter systems often are better defined in experiments than are individual clusters (see above), such comparisons are very advantageous for methodological assessments. 9,24 The properties of smaller clusters often change dramatically [3][4][5][6]14,16,17,24,34 upon addition of a single atom, hence approaches such as the ''superatom'' concept [35][36][37] are more suitable for their description.…”

“…9,24 Thus, even under laboratory conditions, larger clusters inevitably are produced with certain size distributions. [48][49][50] Probably the biggest advantage of the cluster scaling approach is that results computed for medium-size clusters suffice to derive properties of much larger systems. Fortunately, the behavior of larger TM nanoparticles is more predictable.…”