Cr2 in density-functional theory: approximate spin projection

Edgecombe, Kenneth E.; Becke, Axel D.

doi:10.1016/0009-2614(95)00945-z

Cited by 79 publications

(64 citation statements)

References 22 publications

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“…23 A large literature has developed on this and related broken-symmetry approaches. [24][25][26][27][28][29][30][31][32][33] Broken-symmetry solutions have also been studied in other contexts, and it has often been found that it is important to allow the orbitals to break symmetry in order to get a qualitatively correct description of the system. [33][34][35][36][37][38][39][40][41][42] The energies of the broken-symmetry states are often used without correcting for their spin character.…”

Section: Introductionmentioning

confidence: 99%

“…[24][25][26][27][28][29][30][31][32][33] Broken-symmetry solutions have also been studied in other contexts, and it has often been found that it is important to allow the orbitals to break symmetry in order to get a qualitatively correct description of the system. [33][34][35][36][37][38][39][40][41][42] The energies of the broken-symmetry states are often used without correcting for their spin character. [34][35][36][37][38][39][40][41][42] In fact, it has been argued on theoretical grounds that the fully self-consistent brokensymmetry single Slater determinant of lowest total energy is the correct solution to the problem.…”

Section: Introductionmentioning

confidence: 99%

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Density Functional Theory in Transition-Metal Chemistry: Relative Energies of Low-Lying States of Iron Compounds and the Effect of Spatial Symmetry Breaking

Sorkin

Iron

Truhlar

2008

J. Chem. Theory Comput.

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Abstract:The ground and lower excited states of Fe 2 , Fe 2 -, and FeO + were studied using a number of density functional theory (DFT) methods. Specific attention was paid to the relative state energies, the internuclear distances (r e ), and the harmonic vibrational frequencies (ω e ). A number of factors influencing the calculated values of these properties were examined. These include basis sets, the nature of the density functional chosen, the percentage of HartreeFock exchange in the density functional, and constraints on orbital symmetry. A number of different types of generalized gradient approximation (GGA) density functionals (straight GGA, hybrid GGA, meta-GGA, and hybrid meta-GGA) were examined, and it was found that the best results were obtained with hybrid GGA or hybrid meta-GGA functionals that contain nonzero fractions of HF exchange; specifically, the best overall results were obtained with B3LYP, M05, and M06, closely followed by B1LYP. One significant observation was the effect of enforcing symmetry on the orbitals. When a degenerate orbital (π or δ) is partially occupied in the 4 Φ excited state of FeO + , reducing the enforced symmetry (from C 6v to C 4v to C 2v ) results in a lower energy since these degenerate orbitals are split in the lower symmetries. The results obtained were compared to higher level ab initio results from the literature and to recent PBE+U plane wave results by Kulik et al. (Phys. Rev. Lett. 2006, 97, 103001). It was found that some of the improvements that were afforded by the semiempirical +U correction can also be accomplished by improving the form of the DFT functional and, in one case, by not enforcing high symmetry on the orbitals.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Density Functional Theory in Transition-Metal Chemistry: Relative Energies of Low-Lying States of Iron Compounds and the Effect of Spatial Symmetry Breaking

Sorkin

Iron

Truhlar

2008

J. Chem. Theory Comput.

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“…[1] another cluster isomer is shown based on a direct optimization of the Pd 6 Ru 6 (CO) 24 bimetallic core using its intrinsic D 3d -symmetry. This isomer is found to be higher in energy than the C 2h -symmetric structure reported herein.…”

Section: Computational Detailsmentioning

confidence: 99%

“…Although studies strongly suggest far less SC in DFT Kohn-Sham wavefunctions than in the corresponding UHF wavefunctions [18,19], the magnitude of the effects of SC on DFT-predicted TM cluster properties is generally uncertain. For some TM systems, spin projection [20] can be applied to the DFT results, which can yield more accurate, pure mutiplet energies [21,22], although it overcorrects in other cases [23,24]. The starting point for spin-projection methods is the use of BS-DFT calculations.…”

Section: Introduction Ementioning

confidence: 98%

“…An alternative source of TM clusters is molecular crystals, whereby complex well-defined heterometallic clusters can be simply derived from organometallic cluster precursors. In this way, as each naked TM cluster is derived from a separate identical precursor, for example, Pd 6 Ru 6 from [Pd 6 Ru 6 (CO) 24 ] 2Ϫ [1], each is thus known to be of identical composition. The theoretical study of such clusters can also be facilitated by X-ray structural determination of the cluster precursors in the molecular crystal.…”

Section: Introduction Ementioning

confidence: 99%

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Magnetism and energetics of the 4d bimetallic cluster Pd₆Ru₆

Bromley¹,

Catlow²

2002

Int J of Quantum Chemistry

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ABSTRACT:A density functional investigation into the energetics and magnetism of a novel 4d transition metal cluster possessing an equal number of "open-shell" Ru atoms and "closed-shell" Pd atoms is presented. The two atom types give rise to a potentially rich spectrum of low-energy geometric cluster structures and corresponding cluster wavefunctions. The cluster's structure is based on experimental data for a denuded highly symmetric (D 3d ) organometallic cluster and then optimized, allowing for energy-lowering structural symmetry breaking, to a C 2h configuration. The cluster wavefunction is then is calculated for high and low multiplicities with and without employing the natural structural symmetry of the cluster. Of particular interest is the magnetism of the cluster and the extent of 4d spin polarization of the Pd atoms by the Ru atoms in the cluster. We find that the energetically favored state of the cluster has high multiplicity with significant spin density carried by the Pd atoms.

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