From ultrasoft pseudopotentials to the projector augmented-wave method
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.
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TL;DR: In this article, the optical and structural properties of carbon nanotubes have been investigated using the projected augmented wave (POW) method, where the optical dielectric function and second-order optical susceptibility were derived.
Abstract: A systematic ab initio study of the optical as well as structural and electronic properties of the carbon nanotubes within density-functional theory in the local-density approximation has been performed. Highly accurate full-potential projected augmented wave method was used. Specifically, the optical dielectric function $\ensuremath{\varepsilon}$ and second-order optical susceptibility ${\ensuremath{\chi}}^{(2)}$ as well as the band structure of a number of the armchair [(3,3),(5,5),(10,10),(15,15),(20,20)], zigzag [(5,0),(10,0),(15,0),(20,0)] and chiral [(4,2),(6,2),(6,4),(8,4), (10,5)] carbon nanotubes have been calculated. The underlying atomic structure of the carbon nanotubes was determined theoretically. It is found that for the electric field parallel to the nanotube axis $(E\ensuremath{\Vert}\mathrm{z\ifmmode \hat{}\else \^{}\fi{}}),$ the absorptive part ${\ensuremath{\varepsilon}}^{\ensuremath{''}}$ of the optical dielectric function for the small nanotubes (the diameter being smaller than, say, 25 \AA{}) in the low-energy range (0--8 eV) consists of a few distinct peaks. Furthermore, the energy position, the shape, and the number of the peaks depend rather strongly on the diameter and chirality. This suggests that one could use these distinct optical features to characterize the chirality and diameter of the grown nanotubes. In contrast, for the electric field perpendicular to the nanotube axis $(E\ensuremath{\perp}\mathrm{z\ifmmode \hat{}\else \^{}\fi{}}),$ the ${\ensuremath{\varepsilon}}^{\ensuremath{''}}$ spectrum of all the nanotubes studied except the three 4 \AA{} nanotubes in the low-energy region is made up of a broad hump. The bandwidth of the hump increases with the nanotube diameter and the magnitude of the hump is in general about half of that of the ${\ensuremath{\varepsilon}}^{\ensuremath{''}}$ for $E\ensuremath{\Vert}\mathrm{z\ifmmode \hat{}\else \^{}\fi{}}.$ Surprisingly, given their one-dimensional character, the optical anisotropy of the nanotubes is smaller than that of graphite. For the nanotubes with a moderate diameter (say, 30 \AA{}) such as the (20,20) nanotube, the optical anisotropy is not large and the ${\ensuremath{\varepsilon}}^{\ensuremath{''}}$ spectrum for both electric-field polarizations becomes rather similar to that of graphite with electric-field parallel to the graphene layers $(E\ensuremath{\perp}c).$ The calculated static polarizability $\ensuremath{\alpha}(0)$ for the semiconducting nanotubes is rather anisotropic with $\ensuremath{\alpha}(0)$ for $E\ensuremath{\Vert}\mathrm{z\ifmmode \hat{}\else \^{}\fi{}}$ being several times larger than that for $E\ensuremath{\perp}\mathrm{z\ifmmode \hat{}\else \^{}\fi{}}.$ For both electric-field polarizations, $\ensuremath{\alpha}(0)$ is nearly proportional to the square of the tube diameter. The calculated electron energy loss spectra of all the nanotubes studied here for both electric field polarizations are similar to that of $E\ensuremath{\perp}c$ of graphite, being dominated by a broad $(\ensuremath{\pi}+\ensuremath{\sigma})$-electron plasmon peak at near 27 eV and a small $\ensuremath{\pi}$-electron plasmon peak at 5--7 eV. Only the chiral nanotubes would exhibit second-order nonlinear optical behavior. Furthermore, only two tensor elements ${\ensuremath{\chi}}_{\mathrm{xyz}}^{(2)}$ and ${\ensuremath{\chi}}_{\mathrm{yzx}}^{(2)}$ are possibly nonzero with ${\ensuremath{\chi}}_{\mathrm{xyz}}^{(2)}=\ensuremath{-}{\ensuremath{\chi}}_{\mathrm{yzx}}^{(2)}.$ For all the chiral nanotubes studied here, both the real and imaginary parts of ${\ensuremath{\chi}}_{\mathrm{xyz}}^{(2)}(\ensuremath{-}2\ensuremath{\omega},\ensuremath{\omega},\ensuremath{\omega})$ show an oscillatory behavior. The absolute value of ${\ensuremath{\chi}}_{\mathrm{xyz}}^{(2)}(\ensuremath{-}2\ensuremath{\omega},\ensuremath{\omega},\ensuremath{\omega})$ of all the chiral nanotubes in the photon energy range of 0.1--3.0 eV is huge, being up to ten times larger than that of GaAs, suggesting that chiral nanotubes have potential applications in nonlinear optics, e.g., second-harmonic generation and sum-frequency generation. Nevertheless, the static value of both ${\ensuremath{\chi}}_{\mathrm{xyz}}^{(2)}$ and ${\ensuremath{\chi}}_{\mathrm{yzx}}^{(2)}$ is zero.
234 citations
TL;DR: In this article, the atomic and electronic structures and stability of native defects in a single-layer single-atom supercell were investigated based on density-functional theory calculations, and the formation energies of the native defect in neutral and charged states were calculated.
Abstract: The atomic and electronic structures and stability of native defects in a single-layer ${\mathrm{MoS}}_{2}$ are investigated, based on density-functional theory calculations. Native defects such as a S vacancy (${V}_{\mathrm{S}}$), a S interstitial (${\mathrm{S}}_{i}$), a Mo vacancy (${V}_{\mathrm{Mo}}$), and a Mo interstitial (${\mathrm{Mo}}_{i}$) are considered. The ${\mathrm{S}}_{i}$ is found to have S-adatom configuration on top of a host S atom, and the ${\mathrm{Mo}}_{i}$ has Mo-${\mathrm{Mo}}_{i}$ split interstitial configuration along the $c$ direction. The formation energies of the native defects in neutral and charged states are calculated. For the charged states, the artificial electrostatic interactions between image charges in supercells are eliminated by a supercell size scaling scheme and a correction scheme that uses a Gaussian model charge. It is found that the ${V}_{\mathrm{S}}$ has a low formation energy of 1.3--1.5 eV in the Mo-rich limit condition, and the ${\mathrm{S}}_{i}$ has 1.0 eV in the S-rich limit condition. The ${V}_{\mathrm{S}}$ is found to be a deep single acceptor with the (0/$\ensuremath{-}$) transition level at 1.7 eV above the valence-band maximum (VBM). The ${\mathrm{S}}_{i}$ is found to be an electrically neutral defect. The Mo-related native defects of ${V}_{\mathrm{Mo}}$ and ${\mathrm{Mo}}_{i}$ are found to be high in formation energy above 4 eV. The ${V}_{\mathrm{Mo}}$ is a deep single acceptor and the ${\mathrm{Mo}}_{i}$ is a deep single donor, of which the (0/$\ensuremath{-}$) acceptor and (+/0) donor transition levels are found at 1.1 and 0.3 eV above the VBM, respectively.
234 citations
Additional excerpts
...lly associated Re impurities. METHODS We performed DFT calculations as implemented in the Vienna ab initio simulation package (VASP) code [21, 22]. The projector augmented wave (PAW) pseudopotentials [23, 24] and the local density approximation (LDA) [25] for the exchange-correlation energy of electrons were employed. The 8×8 supercell with 192 host atoms with the vacuum region of 18 7 ˚A was used for the...
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01 Oct 2020
TL;DR: In this article, the authors report that copper nanowires with rich surface steps exhibit a remarkably high Faradaic efficiency for C2H4 that can be maintained for over 200 hours.
Abstract: Electrochemical CO2 reduction to value-added chemical feedstocks is of considerable interest for renewable energy storage and renewable source generation while mitigating CO2 emissions from human activity. Copper represents an effective catalyst in reducing CO2 to hydrocarbons or oxygenates, but it is often plagued by a low product selectivity and limited long-term stability. Here we report that copper nanowires with rich surface steps exhibit a remarkably high Faradaic efficiency for C2H4 that can be maintained for over 200 hours. Computational studies reveal that these steps are thermodynamically favoured compared with Cu(100) surface under the operating conditions and the stepped surface favours C2 products by suppressing the C1 pathway and hydrogen production. The electrochemical reduction of CO2 to value-added fuels and feedstocks has recently received a great deal of attention. Here, Cu nanowires that display rich surface steps are reported to sustain C2H4 production from CO2 with a remarkably high Faradaic efficiency for 200 hours.
234 citations
TL;DR: In this paper, an activity correlation with catalysts, electronic structure, in order to clarify the origin of reactivity for a series of transition metals supported on nitrogen-doped graphene as SACs for hydrogen evolution reaction (HER) by a combination of density functional theory calculations and electrochemical measurements.
Abstract: DOI: 10.1002/aenm.201803689 On the other hand, the limited fossil fuel reserves coupled with sustainable development vision call for the development of new green technologies for energy production.[1] Hydrogen, an abundant, renewable, and highly dense energy source, has been considered as a potential alternative sustainable energy source.[2] The ideal way to produce hydrogen of high purity and in large quantities is by the electrolytic reduction of water via hydrogen evolution reaction (HER). Naturally, HER has a high energy barrier (known as overpotential, ɳ, the minimum potential required to produce hydrogen above its thermodynamic value), which demands effective catalysts to overcome. Amongst all HER catalysts, platinum is the most efficient to date with a small overpotential in acidic solutions. However, the high cost and scarcity of platinum limit its application for industrial production of hydrogen.[3] Thus, the proper choice of an active, efficient, and durable electrocatalyst from earth’s abundant sources remains a major challenge in energy research. In recent years, tremendous effort has been devoted to the invention of new types of heterogeneous electrocatalysts, based on a variety of nonprecious transition metals, including Co, Ni, Mo, Fe, and their derivatives (i.e., nitrides, The proper choice of nonprecious transition metals as single atom catalysts (SACs) remains unclear for designing highly efficient electrocatalysts for hydrogen evolution reaction (HER). Herein, reported is an activity correlation with catalysts, electronic structure, in order to clarify the origin of reactivity for a series of transition metals supported on nitrogen-doped graphene as SACs for HER by a combination of density functional theory calculations and electrochemical measurements. Only few of the transition metals (e.g., Co, Cr, Fe, Rh, and V) as SACs show good catalytic activity toward HER as their Gibbs free energies are varied between the range of –0.20 to 0.30 eV but among which Co-SAC exhibits the highest electrochemical activity at 0.13 eV. Electronic structure studies show that the energy states of active valence dz orbitals and their resulting antibonding state determine the catalytic activity for HER. The fact that the antibonding state orbital is neither completely empty nor fully filled in the case of Co-SAC is the main reason for its ideal hydrogen adsorption energy. Moreover, the electrochemical measurement shows that Co-SAC exhibits a superior hydrogen evolution activity over Ni-SAC and W-SAC, confirming the theoretical calculation. This systematic study gives a fundamental understanding about the design of highly efficient SACs for HER.
233 citations
TL;DR: The high quality of the IrO2 film grown using molecular-beam epitaxy affords the ability to extract the surface oxygen adsorption and its impact on the OER and highlights the importance of the interfacial electrified interaction in electrocatalyst design.
Abstract: A catalyst functions by stabilizing reaction intermediates, usually through surface adsorption. In the oxygen evolution reaction (OER), surface oxygen adsorption plays an indispensable role in the electrocatalysis. The relationship between the adsorption energetics and OER kinetics, however, has not yet been experimentally measured. Herein we report an experimental relationship between the adsorption of surface oxygen and the kinetics of the OER on IrO2(110) epitaxially grown on a TiO2(110) single crystal. The high quality of the IrO2 film grown using molecular-beam epitaxy affords the ability to extract the surface oxygen adsorption and its impact on the OER. By examining a series of electrolytes, we find that the adsorption energy changes linearly with pH, which we attribute to the electrified interfacial water. We support this hypothesis by showing that an electrolyte salt modification can lead to an adsorption energy shift. The dependence of the adsorption energy on pH has implications for the OER kinetics, but it is not the only factor; the dependence of the OER electrocatalysis on pH stipulates two OER mechanisms, one operating in acidic solution and another operating in alkaline solution. Our work points to the subtle adsorption-kinetics relationship in the OER and highlights the importance of the interfacial electrified interaction in electrocatalyst design.
233 citations
References
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Book•
31 Dec 1993
TL;DR: The linearized augmented planewave (LAPW) method has emerged as the standard by which density functional calculations for transition metal and rare-earth containing materials are judged.
Abstract: With its extreme accuracy and reasonable computational efficiency, the linearized augmented planewave (LAPW) method has emerged as the standard by which density functional calculations for transition metal and rare-earth containing materials are judged. This volume presents a thorough and self-conta
1,150 citations