A fast and robust algorithm for Bader decomposition of charge density
TL;DR: In this article, an algorithm for decomposition of electronic charge density into atomic contributions is presented. But instead of explicitly finding and representing the dividing surfaces, which is a challenging task, the algorithm assigns each point on a regular (x,y,z) grid to one of the regions by following a steepest ascent path on the grid.
About: This article is published in Computational Materials Science.The article was published on 2006-06-01. It has received 7231 citations till now. The article focuses on the topics: Charge density & Atoms in molecules.
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TL;DR: This paper describes how accurate off-lattice ascent paths can be represented with respect to the grid points, and maintains the efficient linear scaling of an earlier version of the algorithm, and eliminates a tendency for the Bader surfaces to be aligned along the grid directions.
Abstract: A computational method for partitioning a charge density grid into Bader volumes is presented which is efficient, robust, and scales linearly with the number of grid points. The partitioning algorithm follows the steepest ascent paths along the charge density gradient from grid point to grid point until a charge density maximum is reached. In this paper, we describe how accurate off-lattice ascent paths can be represented with respect to the grid points. This improvement maintains the efficient linear scaling of an earlier version of the algorithm, and eliminates a tendency for the Bader surfaces to be aligned along the grid directions. As the algorithm assigns grid points to charge density maxima, subsequent paths are terminated when they reach previously assigned grid points. It is this grid-based approach which gives the algorithm its efficiency, and allows for the analysis of the large grids generated from plane-wave-based density functional theory calculations.
5,417 citations
Cites background or methods from "A fast and robust algorithm for Bad..."
...A strength of the on-grid method is that there is a fixed computational effort per charge density grid point, and therefore the total computational time scales linearly with the number of grid points [18]....
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...The Bader analysis algorithm presented here removes the lattice bias of a constrained grid-based algorithm [18] allowing convergence in the limit of a fine charge density grid....
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...The algorithm described in this work is an improvement upon such a grid-based method [18]....
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...Additional details are provided in [18]....
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...This method for finding Bader volumes without lattice bias is an improvement to an earlier grid-based method [18]....
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TL;DR: An improvement to the grid‐based algorithm of Henkelman et al. for the calculation of Bader volumes is suggested, which more accurately calculates atomic properties as predicted by the theory of Atoms in Molecules, resulting in a more robust method of partitioning charge density among atoms in the system.
Abstract: An improvement to the grid-based algorithm of Henkelman et al. for the calculation of Bader volumes is suggested, which more accurately calculates atomic properties as predicted by the theory of Atoms in Molecules. The CPU time required by the improved algorithm to perform the Bader analysis scales linearly with the number of interatomic surfaces in the system. The new algorithm corrects systematic deviations from the true Bader surface, calculated by the original method and also does not require explicit representation of the interatomic surfaces, resulting in a more robust method of partitioning charge density among atoms in the system. Applications of the method to some small systems are given and it is further demonstrated how the method can be used to define an energy per atom in ab initio calculations.
2,999 citations
TL;DR: In this paper, the elastic constants of 2D honeycomb structures from the strain energy and calculate the Poisson's ratio as well as in-plane stiffness values were revealed, and the properties of these honeycomb materials were compared to those of three-dimensional Group IV and Group III-V compounds.
Abstract: Using first-principles plane wave calculations, we investigate two dimensional honeycomb structure of Group IV elements and their binary compounds, as well as the compounds of Group III-V elements. Based on structure optimization and phonon mode calculations, we determine that 22 different honeycomb materials are stable and correspond to local minima on the Born-Oppenheimer surface. We also find that all the binary compounds containing one of the first row elements, B, C or N have planar stable structures. On the other hand, in the honeycomb structures of Si, Ge and other binary compounds the alternating atoms of hexagons are buckled, since the stability is maintained by puckering. For those honeycomb materials which were found stable, we calculated optimized structures, cohesive energies, phonon modes, electronic band structures, effective cation and anion charges, and some elastic constants. The band gaps calculated within Density Functional Theory using Local Density Approximation are corrected by GW0 method. Si and Ge in honeycomb structure are semimetal and have linear band crossing at the Fermi level which attributes massless Fermion character to charge carriers as in graphene. However, all binary compounds are found to be semiconductor with band gaps depending on the constituent atoms. We present a method to reveal elastic constants of 2D honeycomb structures from the strain energy and calculate the Poisson’s ratio as well as in-plane stiffness values. Preliminary results show that the nearly lattice matched heterostructures of these compounds can offer new alternatives for nanoscale electronic devices. Similar to those of the three-dimensional Group IV and Group III-V compound semiconductors, one deduces interesting correlations among the calculated properties of present honeycomb structures. PACS numbers: 73.22.-f, 61.48.De, 63.22.-m, 62.23.Kn
1,686 citations
TL;DR: This Review discusses the recent progress from the viewpoint of theory and computations, with connections to relevant experiments in the understanding of the molecular structure of the gold-sulfur interface in these systems.
Abstract: Thiolate-protected gold surfaces and interfaces, relevant for self-assembled monolayers of organic molecules on gold, for passivated gold nanoclusters and for molecule-gold junctions, are archetypal systems in various fields of current nanoscience research, materials science, inorganic chemistry and surface science. Understanding this interface at the nanometre scale is essential for a wide range of potential applications for site-specific bioconjugate labelling and sensing, drug delivery and medical therapy, functionalization of gold surfaces for sensing, molecular recognition and molecular electronics, and gold nanoparticle catalysis. During the past five years, considerable experimental and theoretical advances have furthered our understanding of the molecular structure of the gold-sulfur interface in these systems. This Review discusses the recent progress from the viewpoint of theory and computations, with connections to relevant experiments.
1,408 citations
TL;DR: A practical synthesis method to produce isolated single platinum atoms and clusters using the atomic layer deposition technique and indicates that the partially unoccupied density of states of the platinum atoms' 5d orbitals on the nitrogen-doped graphene are responsible for the excellent performance.
Abstract: Platinum-based catalysts have been considered the most effective electrocatalysts for the hydrogen evolution reaction in water splitting. However, platinum utilization in these electrocatalysts is extremely low, as the active sites are only located on the surface of the catalyst particles. Downsizing catalyst nanoparticles to single atoms is highly desirable to maximize their efficiency by utilizing nearly all platinum atoms. Here we report on a practical synthesis method to produce isolated single platinum atoms and clusters using the atomic layer deposition technique. The single platinum atom catalysts are investigated for the hydrogen evolution reaction, where they exhibit significantly enhanced catalytic activity (up to 37 times) and high stability in comparison with the state-of-the-art commercial platinum/carbon catalysts. The X-ray absorption fine structure and density functional theory analyses indicate that the partially unoccupied density of states of the platinum atoms’ 5d orbitals on the nitrogen-doped graphene are responsible for the excellent performance. Downsizing platinum based nanocatalysts has the twin advantages of lower platinum usage and increased activity per platinum atom. Here, the authors report an atomic layer deposition technique for single platinum atom catalyst fabrication and assess their hydrogen evolution activity.
1,374 citations
References
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IBM1
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
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
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
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
TL;DR: Novel features are that the pseudopotential itself becomes charge-state dependent, the usual norm-conservation constraint does not apply, and a generalized eigenproblem is introduced.
Abstract: A new approach to the construction of first-principles pseudopotentials is described. The method allows transferability to be improved systematically while holding the cutoff radius fixed, even for large cutoff radii. Novel features are that the pseudopotential itself becomes charge-state dependent, the usual norm-conservation constraint does not apply, and a generalized eigenproblem is introduced. The potentials have a separable form well suited for plane-wave solid-state calculations, and show promise for application to first-row and transition-metal systems.
18,782 citations