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Journal ArticleDOI

Stable structural and magnetic isomers of small transition-metal clusters from the Ni group: an ab initio density-functional study

25 Oct 2006-Journal of Physics: Condensed Matter (IOP Publishing)-Vol. 18, Iss: 42, pp 9703-9748
TL;DR: Futschek et al. as discussed by the authors presented ab initio density-functional studies of structural and magnetic isomers of NiN and PtN clusters with up to 13 atoms based on fixed-moment calculations within a spin-polarized generalized gradient approximation and on static as well as dynamical optimizations of the cluster-structure.
Abstract: We present ab initio density-functional studies of structural and magnetic isomers of NiN and PtN clusters with up to 13 atoms. Our investigations are based on fixed-moment calculations within a spin-polarized generalized gradient approximation and on static as well as dynamical optimizations of the cluster-structure, using quantum-mechanical many-body forces calculated via the Hellmann?Feynman theorem. Together with our earlier paper on PdN clusters (Futschek et al 2005 J.?Phys.:?Condens.?Matter 17 5927?63) the present work completes a comprehensive investigation of small clusters formed by metals of the Pt group of the periodic table. We discuss the trends in structure, binding energy and magnetic moments as a function of cluster size and through the 3d?4d?5d series. We demonstrate that the transition from the more localized 3d to the more extended 5d orbitals influences not only the magnetic ground state, but also the geometric structure of the clusters. The difference is most pronounced for the largest clusters in this series (N = 11,12,13) where the Ni clusters adopt a polytetrahedral arrangement converging to the Ni13 icosahedron, whereas the structures of Pd clusters and Pt clusters are based on octahedral motifs closely resembling fragments of the face-centred cubic structure of the bulk metals.
Citations
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Journal ArticleDOI
TL;DR: The implementation of various DFT functionals and many‐body techniques within highly efficient, stable, and versatile computer codes, which allow to exploit the potential of modern computer architectures are discussed.
Abstract: During the past decade, computer simulations based on a quantum-mechanical description of the interactions between electrons and between electrons and atomic nuclei have developed an increasingly important impact on solid-state physics and chemistry and on materials science—promoting not only a deeper understanding, but also the possibility to contribute significantly to materials design for future technologies. This development is based on two important columns: (i) The improved description of electronic many-body effects within density-functional theory (DFT) and the upcoming post-DFT methods. (ii) The implementation of the new functionals and many-body techniques within highly efficient, stable, and versatile computer codes, which allow to exploit the potential of modern computer architectures. In this review, I discuss the implementation of various DFT functionals [local-density approximation (LDA), generalized gradient approximation (GGA), meta-GGA, hybrid functional mixing DFT, and exact (Hartree-Fock) exchange] and post-DFT approaches [DFT + U for strong electronic correlations in narrow bands, many-body perturbation theory (GW) for quasiparticle spectra, dynamical correlation effects via the adiabatic-connection fluctuation-dissipation theorem (AC-FDT)] in the Vienna ab initio simulation package VASP. VASP is a plane-wave all-electron code using the projector-augmented wave method to describe the electron-core interaction. The code uses fast iterative techniques for the diagonalization of the DFT Hamiltonian and allows to perform total-energy calculations and structural optimizations for systems with thousands of atoms and ab initio molecular dynamics simulations for ensembles with a few hundred atoms extending over several tens of ps. Applications in many different areas (structure and phase stability, mechanical and dynamical properties, liquids, glasses and quasicrystals, magnetism and magnetic nanostructures, semiconductors and insulators, surfaces, interfaces and thin films, chemical reactions, and catalysis) are reviewed. © 2008 Wiley Periodicals, Inc. J Comput Chem, 2008

2,364 citations

Journal ArticleDOI
TL;DR: In this paper, a density functional theory study of the atomic structure, binding energies, effective coordination numbers, average bond lengths, and magnetic properties of the $3d, $4d, and $5d$ metal (30 elements) clusters containing 13 atoms was performed.
Abstract: The knowledge of the atomic structure of clusters composed by few atoms is a basic prerequisite to obtain insights into the mechanisms that determine their chemical and physical properties as a function of diameter, shape, surface termination, as well as to understand the mechanism of bulk formation. Due to the wide use of metal systems in our modern life, the accurate determination of the properties of $3d$, $4d$, and $5d$ metal clusters poses a huge problem for nanoscience. In this work, we report a density functional theory study of the atomic structure, binding energies, effective coordination numbers, average bond lengths, and magnetic properties of the $3d$, $4d$, and $5d$ metal (30 elements) clusters containing 13 atoms, ${M}_{13}$. First, a set of lowest-energy local minimum structures (as supported by vibrational analysis) were obtained by combining high-temperature first-principles molecular-dynamics simulation, structure crossover, and the selection of five well-known ${M}_{13}$ structures. Several new lower energy configurations were identified, e.g., ${\text{Pd}}_{13}$, ${\text{W}}_{13}$, ${\text{Pt}}_{13}$, etc., and previous known structures were confirmed by our calculations. Furthermore, the following trends were identified: (i) compact icosahedral-like forms at the beginning of each metal series, more opened structures such as hexagonal bilayerlike and double simple-cubic layers at the middle of each metal series, and structures with an increasing effective coordination number occur for large $d$ states occupation. (ii) For ${\text{Au}}_{13}$, we found that spin-orbit coupling favors the three-dimensional (3D) structures, i.e., a 3D structure is about 0.10 eV lower in energy than the lowest energy known two-dimensional configuration. (iii) The magnetic exchange interactions play an important role for particular systems such as Fe, Cr, and Mn. (iv) The analysis of the binding energy and average bond lengths show a paraboliclike shape as a function of the occupation of the $d$ states and hence, most of the properties can be explained by the chemistry picture of occupation of the bonding and antibonding states.

194 citations

Journal ArticleDOI
TL;DR: In this article, the structural trends of late-transition-metal 13-atom clusters using density functional theory within the generalized gradient approximation to exchange-correlation functional were studied.
Abstract: Because reactivity increases as particle size decreases and competition between numerous structures are possible, which affects catalytic and magnetic properties, we study the structural trends of late-transition-metal 13-atom clusters using density functional theory within the generalized gradient approximation to exchange-correlation functional. We consider open structural motifs, such as bilayer and cubic (recently found to have lower energy), and find new bilayer candidates that are even lower in energy. To study the influence of $d$-orbital filling on structural trends, we focus on Pt, Pd, and Rh clusters and find several new, low-energy structures for ${\mathrm{Pt}}_{13}$ and ${\mathrm{Pd}}_{13}$ from searches using a first-principle molecular dynamics high-temperature annealing. We find that 13-atom clusters prefer less square-cubic order as the $d$-orbitals gradually fill in the order of Rh, Pt, and Pd, and generally, low symmetry, open structures are preferred to high symmetry, compact ones, a trend explained from their electronic structures. For completeness, we briefly comment on improved exchange-correlation functionals affects on cluster morphology.

120 citations

Journal ArticleDOI
TL;DR: In this article, the magnetic anisotropy energy of transition-metal atoms from groups 8 to 10 of the Periodic Table was investigated using a noncollinear implementation of spin-density functional theory.
Abstract: We present ab initio density functional calculations of the magnetic anisotropy of dimers of the transition-metal atoms from groups 8 to 10 of the Periodic Table. Our calculations are based on a noncollinear implementation of spin-density functional theory (DFT) where spin-orbit coupling (SOC) is included self-consistently. The physical mechanism determining the sign and magnitude of the magnetic anisotropy energy (MAE) is elucidated via an analysis of the influence of SOC on the spectrum of the Kohn-Sham eigenvalues of the dimers. The possible influence of orbital-dependent electron-electron interactions has been investigated by performing calculation with a hybrid functional (mixing Hartree-Fock and DFT exchanges) and with a $\text{DFT}+U$ Hamiltonian introducing an orbital-dependent on-site Coulomb repulsion $U$. The results demonstrate that the MAE is stable with respect to the addition of such orbital-dependent interactions.

112 citations

References
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Journal ArticleDOI
TL;DR: An efficient scheme for calculating the Kohn-Sham ground state of metallic systems using pseudopotentials and a plane-wave basis set is presented and the application of Pulay's DIIS method to the iterative diagonalization of large matrices will be discussed.
Abstract: We present an efficient scheme for calculating the Kohn-Sham ground state of metallic systems using pseudopotentials and a plane-wave basis set. In the first part the application of Pulay's DIIS method (direct inversion in the iterative subspace) to the iterative diagonalization of large matrices will be discussed. Our approach is stable, reliable, and minimizes the number of order ${\mathit{N}}_{\mathrm{atoms}}^{3}$ operations. In the second part, we will discuss an efficient mixing scheme also based on Pulay's scheme. A special ``metric'' and a special ``preconditioning'' optimized for a plane-wave basis set will be introduced. Scaling of the method will be discussed in detail for non-self-consistent and self-consistent calculations. It will be shown that the number of iterations required to obtain a specific precision is almost independent of the system size. Altogether an order ${\mathit{N}}_{\mathrm{atoms}}^{2}$ scaling is found for systems containing up to 1000 electrons. If we take into account that the number of k points can be decreased linearly with the system size, the overall scaling can approach ${\mathit{N}}_{\mathrm{atoms}}$. We have implemented these algorithms within a powerful package called VASP (Vienna ab initio simulation package). The program and the techniques have been used successfully for a large number of different systems (liquid and amorphous semiconductors, liquid simple and transition metals, metallic and semiconducting surfaces, phonons in simple metals, transition metals, and semiconductors) and turned out to be very reliable. \textcopyright{} 1996 The American Physical Society.

81,985 citations

Journal ArticleDOI
Peter E. Blöchl1
TL;DR: An approach for electronic structure calculations is described that generalizes both the pseudopotential method and the linear augmented-plane-wave (LAPW) method in a natural way and can be used to treat first-row and transition-metal elements with affordable effort and provides access to the full wave function.
Abstract: An approach for electronic structure calculations is described that generalizes both the pseudopotential method and the linear augmented-plane-wave (LAPW) method in a natural way. The method allows high-quality first-principles molecular-dynamics calculations to be performed using the original fictitious Lagrangian approach of Car and Parrinello. Like the LAPW method it can be used to treat first-row and transition-metal elements with affordable effort and provides access to the full wave function. The augmentation procedure is generalized in that partial-wave expansions are not determined by the value and the derivative of the envelope function at some muffin-tin radius, but rather by the overlap with localized projector functions. The pseudopotential approach based on generalized separable pseudopotentials can be regained by a simple approximation.

61,450 citations

Journal ArticleDOI
TL;DR: In this paper, the formal relationship between US Vanderbilt-type pseudopotentials and Blochl's projector augmented wave (PAW) method is derived and the Hamilton operator, the forces, and the stress tensor are derived for this modified PAW functional.
Abstract: The formal relationship between ultrasoft (US) Vanderbilt-type pseudopotentials and Bl\"ochl's projector augmented wave (PAW) method is derived. It is shown that the total energy functional for US pseudopotentials can be obtained by linearization of two terms in a slightly modified PAW total energy functional. The Hamilton operator, the forces, and the stress tensor are derived for this modified PAW functional. A simple way to implement the PAW method in existing plane-wave codes supporting US pseudopotentials is pointed out. In addition, critical tests are presented to compare the accuracy and efficiency of the PAW and the US pseudopotential method with relaxed core all electron methods. These tests include small molecules $({\mathrm{H}}_{2}{,\mathrm{}\mathrm{H}}_{2}{\mathrm{O},\mathrm{}\mathrm{Li}}_{2}{,\mathrm{}\mathrm{N}}_{2}{,\mathrm{}\mathrm{F}}_{2}{,\mathrm{}\mathrm{BF}}_{3}{,\mathrm{}\mathrm{SiF}}_{4})$ and several bulk systems (diamond, Si, V, Li, Ca, ${\mathrm{CaF}}_{2},$ Fe, Co, Ni). Particular attention is paid to the bulk properties and magnetic energies of Fe, Co, and Ni.

57,691 citations

Journal ArticleDOI
TL;DR: A detailed description and comparison of algorithms for performing ab-initio quantum-mechanical calculations using pseudopotentials and a plane-wave basis set is presented in this article. But this is not a comparison of our algorithm with the one presented in this paper.

47,666 citations

Journal ArticleDOI
TL;DR: In this paper, the authors present an ab initio quantum-mechanical molecular-dynamics calculations based on the calculation of the electronic ground state and of the Hellmann-Feynman forces in the local density approximation.
Abstract: We present ab initio quantum-mechanical molecular-dynamics calculations based on the calculation of the electronic ground state and of the Hellmann-Feynman forces in the local-density approximation at each molecular-dynamics step. This is possible using conjugate-gradient techniques for energy minimization, and predicting the wave functions for new ionic positions using subspace alignment. This approach avoids the instabilities inherent in quantum-mechanical molecular-dynamics calculations for metals based on the use of a fictitious Newtonian dynamics for the electronic degrees of freedom. This method gives perfect control of the adiabaticity and allows us to perform simulations over several picoseconds.

32,798 citations