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The Hubbard-U correction and optical properties of d⁰ metal oxide photocatalysts

JOURNAL OF CHEMICAL PHYSICS 2020年第22期153卷 224116页

作者： Brown, Joshua J. Page, Alister J. Univ Newcastle Sch Environm & Life Sci Callaghan NSW 2308 Australia

We report a systematic investigation of individual and multisite Hubbard-U corrections for the electronic, structural, and optical properties of the metal titanate oxide d(0) photocatalysts SrTiO3 and rutile/anatase TiO2. Accurate bandgaps for these materials can be reproduced with local density approximation and generalized gradient approximation exchange-correlation density functionals via a continuous series of empirically derived U-d and U-p combinations, which are relatively insensitive to the choice of functional. On the other hand, lattice parameters are much more sensitive to the choice of U-d and U-p, but in a systematic way that enables the U-d and U-p corrections to be used to qualitatively gauge the extent of self-interaction error in the electron density. Modest U-d corrections (e.g., 4 eV-5 eV) yield the most reliable dielectric response functions for SrTiO3 and are comparable to the range of U-d values derived via linear response approaches. For r-TiO2 and a-TiO2, however, the U-d,U-p corrections that yield accurate bandgaps fail to accurately describe both the parallel and perpendicular components of the dielectric response function. Analysis of individual U-d and U-p corrections on the optical properties of SrTiO3 suggests that the most consequential of the two individual corrections is U-d, as it predominately determines the accuracy of the dominant excitation from O-2p to the Ti-3d t(2g)/e(g) orbitals. U-p, on the other hand, can be used to shift the entire optical response uniformly to higher frequencies. These results will assist high-throughput and machine learning approaches to screening photoactive materials based on d(0) photocatalysts.

关键词： Optical absorption Local density approximations exchange correlation functionals Density functional theory Dielectric properties Dielectric response functions Optical properties Hybrid density functional calculations

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The color center singlet state of oxygen vacancies in TiO2

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JOURNAL OF CHEMICAL PHYSICS 2020年第20期153卷 204704页

作者： Chen, Ji Bogdanov, Nikolay A. Usvyat, Denis Fang, Wei Michaelides, Angelos Alavi, Ali Peking Univ Sch Phys Beijing 100871 Peoples R China Max Planck Inst Solid State Res Heisenbergstr 1 D-70569 Stuttgart Germany Humboldt Univ Inst Chem Brook Taylor St 2 D-12489 Berlin Germany Swiss Fed Inst Technol Lab Phys Chem CH-8093 Zurich Switzerland UCL London Ctr Nanotechnol Thomas Young Ctr Dept Phys & Astron Gower St London WC1E 6BT England Univ Cambridge Dept Chem Lensfield Rd Cambridge CB2 1EW England

Oxygen vacancies are ubiquitous in TiO2 and play key roles in catalysis and magnetism applications. Despite being extensively investigated, the electronic structure of oxygen vacancies in TiO2 remains controversial both experimentally and theoretically. Here, we report a study of a neutral oxygen vacancy in TiO2 using state-of-the-art quantum chemical electronic structure methods. We find that the ground state is a color center singlet state in both the rutile and the anatase phases of TiO2. Specifically, embedded coupled cluster with singles, doubles, and perturbative triples calculations find, for an oxygen vacancy in rutile, that the lowest triplet state energy is 0.6 eV above the singlet state, and in anatase, the triplet state energy is higher by 1.4 eV. Our study provides fresh insights into the electronic structure of the oxygen vacancy in TiO2, clarifying earlier controversies and potentially inspiring future studies of defects with correlated wave function theories.

关键词： 2020 JCP Emerging Investigators Special Collection Topics Local density approximations Electronic structure methods exchange correlation functionals Density functional theory Crystallographic defects Coupled-cluster methods Triplet state Ab initio electronic structure calculations Polarons

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A thermal orbital-free density functional approach

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JOURNAL OF CHEMICAL PHYSICS 2019年第1期151卷 014103-014103页

作者： Nagy, A. Univ Debrecen Dept Theoret Phys H-4002 Debrecen Hungary

A generating function sigma is defined for spherically symmetric systems. Compared to the density, the generating functional has two extra variables and reduces to the density if these variables are equal to zero. It is proved that sigma satisfies a differential equation that contains only the derivatives of sigma and the Kohn-Sham potential. A Schrodinger-like equation for the square root of sigma is also derived. The effective potential of this equation is the sum of the Kohn-Sham potential and a term that is expressed with an integral containing the derivatives of sigma. The noninteracting kinetic energy can be calculated in the knowledge of sigma. The theory is valid in case of zero and nonzero temperatures as well. For nonspherically symmetric systems, the muffin-tin approximation can be applied.

关键词： Density-matrix Kohn-Sham equation Muffin tin approximation Functional equations Entropy Density functional theory exchange correlation functionals Fluid dynamics Harmonic oscillator Statistical thermodynamics

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Simple exchange hole models for long-range-corrected density functionals

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JOURNAL OF CHEMICAL PHYSICS 2019年第9期151卷 094106-094106页

作者： Laikov, Dimitri N. Moscow MV Lomonosov State Univ Chem Dept Moscow 119991 Russia

Density functionals with a range-separated treatment of the exchange energy are known to improve upon their semilocal forerunners and fixed-fraction hybrids. The conversion of a given semilocal functional into its short-range analog is not straightforward, however, and not even unique, because the latter has a higher information content that has to be recovered in some way. Simple models of the spherically averaged exchange hole as an interpolation between the uniform electron gas limit and a few-term Hermite function are developed here for use with generalized-gradient approximations, so that the energy density of the error-function-weighted Coulomb interaction is given by explicit closed-form expressions in terms of elementary and error functions. For comparison, some new nonoscillatory models in the spirit of earlier works are also built and studied;the energy densities from both kinds of models match rather closely (within less than 5%), but the latter slightly mismatches (by about 1%) the exact uniform electron gas limit.

关键词： Generalized gradient approximations Density functional theory exchange correlation functionals

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An alternative derivation of orbital-free density functional theory

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JOURNAL OF CHEMICAL PHYSICS 2019年第20期150卷 204109-204109页

作者： Thompson, Russell B. Univ Waterloo Dept Phys & Astron 200 Univ Ave West Waterloo ON N2L 3G1 Canada Univ Waterloo Waterloo Inst Nanotechnol 200 Univ Ave West Waterloo ON N2L 3G1 Canada

Polymer self-consistent field theory techniques are used to derive quantum density functional theory without the use of the theorems of density functional theory. Instead, a free energy is obtained from a partition function that is constructed directly from a Hamiltonian so that the results are, in principle, valid at finite temperatures. The main governing equations are found to be a set of modified diffusion equations, and the set of self-consistent equations are essentially identical to those of a ring polymer system. The equations are shown to be equivalent to Kohn-Sham density functional theory and to reduce to classical density functional theory, each under appropriate conditions. The obtained noninteracting kinetic energy functional is, in principle, exact but suffers from the usual orbital-free approximation of the Pauli exclusion principle in addition to the exchange-correlation approximation. The equations are solved using the spectral method of polymer self-consistent field theory, which allows the set of modified diffusion equations to be evaluated for the same computational cost as solving a single diffusion equation. A simple exchange-correlation functional is chosen, together with a shell-structure-based Pauli potential, in order to compare the ensemble average electron densities of several isolated atom systems to known literature results. The agreement is excellent, justifying the alternative formalism and numerical method. Some speculation is provided on considering the timelike parameter in the diffusion equations, which is related to temperature, as having dimensional significance, and thus picturing pointlike quantum particles instead as nonlocal, polymerlike, threads in a higher dimensional thermal-space. A consideration of the double-slit experiment from this point of view is speculated to provide results equivalent to the Copenhagen interpretation. Thus, the present formalism may be considered as a type of "pilot-wave," realist, perspective o

关键词： Kohn-Sham density functional theory Electron density Orbital-free density functional theory Polymers Spectral methods exchange correlation functionals Mean field theory Self consistent field methods Quantum mechanical principles Statistical thermodynamics

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Upper bound to the gradient-based kinetic energy density of noninteracting electrons in an external potential

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JOURNAL OF CHEMICAL PHYSICS 2019年第6期151卷 064113-064113页

作者： Witt, William C. Jiang, Kaili Carter, Emily A. Princeton Univ Dept Mech & Aerosp Engn Princeton NJ 08544 USA Princeton Univ Sch Engn & Appl Sci Princeton NJ 08544 USA

We examine a simple upper bound to the gradient-based kinetic energy density (KED) of noninteracting electrons in an external potential: t(r) <= [mu - v(r)]n(r) + 1/4 del(2)n(r), where t(r) is the gradient-based (non-negative) KED, mu is the Fermi energy, v(r) is the external potential, and n(r) is the electron density. The bound emerges naturally from a well-known expression for t(r), leading to an intuitive physical interpretation. For example, t(r) approaches the upper bound in regions where the electron density consists mainly of contributions from states with energies close to the Fermi energy. This upper bound complements the orbital-free lower bound provided by the gradient form of the von Weizsacker (vW) KED, which is also non-negative. Both bounds yield t(r) exactly for single-orbital systems, and accordingly, they merge in single-orbital regions of more general systems. We demonstrate the universality of the two bounds over a wide range of test systems, including model potentials, atoms, diatomic molecules, and pseudopotential approximations of crystals. We also show that the exact t(r) frequently exceeds the sum of the vW and Thomas-Fermi KEDs, rendering that sum unsuitable as a strict upper bound to the gradient-based KED. Published under license by AIP Publishing.

关键词： Electron density Diatomic molecule Local density approximations Generalized gradient approximations Hohenberg Kohn Sham density functional theory Quantum mechanical principles Density of states Schrodinger equations exchange correlation functionals

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Restoring the iso-orbital limit of the kinetic energy density in relativistic density functional theory

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JOURNAL OF CHEMICAL PHYSICS 2019年第17期151卷 174114-174114页

作者： Maier, Toni M. Ikabata, Yasuhiro Nakai, Hiromi Waseda Univ Dept Chem & Biochem Sch Adv Sci & Engn Shinjuku Ku 3-4-1 Okubo Tokyo 1698555 Japan Waseda Univ Waseda Res Inst Sci & Engn Shinjuku Ku 3-4-1 Okubo Tokyo 1698555 Japan Kyoto Univ ESICB Kyoto 6158520 Japan

In contrast to nonrelativistic density functional theory, the ratio between the von Weizsacker and the Kohn-Sham kinetic energy density, commonly used as iso-orbital indicator t within exchange-correlation functionals beyond the generalized-gradient level, violates the exact iso-orbital limit and the appropriate parameter range, 0 <= t <= 1, in relativistic density functional theory. Based on the exact decoupling procedure within the infinite-order two-component method and the Cauchy-Schwarz inequality, we present corrections to the relativistic and the picture-change-transformed nonrelativistic kinetic energy density that restores these exact constraints. We discuss the origin of the new correction terms and illustrate the effectiveness of the current approach for several representative cases. The proposed generalized iso-orbital indicator t(lambda) is expected to be a useful ingredient for the development of relativistic exchange-correlation functionals. (c) 2019 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://***/licenses/by/4.0/).

关键词： Relativistic effects exchange correlation functionals Electronic correlation Hybrid density functional calculations Density functional theory Density-matrix Magnetic fields

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Ensemble first-principles molecular dynamics simulations of water using the SCAN meta-GGA density functional

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JOURNAL OF CHEMICAL PHYSICS 2019年第16期151卷 164101-164101页

作者： LaCount, Michael D. Gygi, Francois Univ Calif Davis Dept Comp Sci Davis CA 95616 USA

We present an ensemble of 16 independent first-principles molecular dynamics simulations of water performed using the Strongly Constrained and Appropriately Normed (SCAN) meta-generalized gradient approximation exchange-correlation functional. These simulations were used to compute the structural and electronic properties of liquid water, as well as polarizabilities, Raman and infrared spectra. Overall, we find that the SCAN functional used at a simulation temperature of 330 K provides an accurate description of the structural and electronic properties of water while incurring a moderate computational cost. The availability of an ensemble of independent simulations provides a quantitative estimate of the uncertainty in computed structural and electronic properties. Results are also compared with a similar dataset generated using the Perdew, Burke, and Ernzerhof exchange-correlation functional at a temperature of 400 K. All simulation data and trajectories are available at http://***. (C) 2019 Author(s).

关键词： Raman spectroscopy exchange correlation functionals Infrared spectroscopy Polarizability Molecular dynamics Density functional theory Computer simulation

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Chemical bonding and band alignment at X2O3/GaN (X = Al, Sc) interfaces

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APPLIED PHYSICS LETTERS 2019年第16期114卷 161601-161601页

作者： Zhang, Zhaofu Guo, Yuzheng Robertson, John Univ Cambridge Dept Engn Cambridge CB2 1PZ England Swansea Univ Coll Engn Swansea SA1 8EN W Glam Wales

The chemical bonding and the band alignment at Al2O3/GaN and Sc2O3/GaN interfaces are studied using density functional supercell calculations. Using bonding models based on the electron counting rule, we have created the insulating interfaces with a small roughness and a clean bandgap. Ga-O bonds dominate the interfacial chemical bonding at both interfaces. The calculated band alignment agrees with the experimental values. For the Al2O3 interface, the calculated valence band offset is 1.17 eV using hybrid functionals, while that for the Sc2O3 interface is 0.81 eV. The conduction band offsets for both are larger than 1 eV, and is as large as similar to 2 eV for the Al2O3 interface. The calculated band alignments indicate that Al2O3 and Sc2O3 are both suitable insulators for GaN-based MOSFET applications. Published under license by AIP Publishing.

关键词： Transistors Band gap Chemical bonding Chemical elements Semiconductors Metal oxides Electronic bandstructure Hybrid density functional calculations Density functional theory exchange correlation functionals

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Co(CO)n/Cu(001): Towards understanding chemical control of the Kondo effect

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JOURNAL OF APPLIED PHYSICS 2019年第14期125卷 142910-142910页

作者： Bahlke, Marc Philipp Wahl, Peter Diekhoner, Lars Herrmann, Carmen Univ Hamburg Inst Anorgan & Angew Chem Martin Luther King Pl 6 D-20146 Hamburg Germany Univ St Andrews Sch Phys & Astron SUPA St Andrews KY16 9SS Fife Scotland Aalborg Univ Dept Mat & Prod Skjernvej 4a DK-9220 Aalborg Denmark

The Kondo effect is a many-body phenomenon, allowing insight into the electronic and atomistic structure of magnetic adsorbates on metal surfaces. Its chemical control is intriguing because it deepens such insight, but the underlying mechanisms are only partly understood. We study the effect of increasing the number of CO ligands attached to a cobalt adatom on copper(001), which correlates with an increase in the Kondo temperature T-K experimentally [Wahl et al., Phys. Rev. Lett. 95, 166601 (2005)], by solving an Anderson impurity model parametrized by the density functional theory. Our results suggest that the orbital responsible for the Kondo effect is d(x)2-(y)2 for the tetracarbonyl and its combination with d(z)2 for the dicarbonyl. The molecular structures depend considerably on the approximate exchange-correlation functional, which may be related to the known difficulty of describing CO binding to metal surfaces. These structural variations strongly affect the Kondo properties, which is not only a concern for predictive studies but also of interest for detecting mechanical deformations and for understanding the effect of tip-adsorbate interactions in the scanning tunneling microscope. Still, by constraining the tetracarbonyl to C-4v symmetry, as suggested by experimental data, we find structures compatible with the experimental trend for T-K (employing BLYP-D3+U). This is not possible for the tricarbonyl despite the range of computational parameters scanned. For the tetra- and dicarbonyl, the increased T-K correlates with a larger hybridization function at the Fermi level, which we trace back to an increased interaction of the Co 3d orbitals with the ligands. Published under license by AIP Publishing.

关键词： Magnetism Adsorption Chemical elements Anderson impurity model Ligands Spintronics Molecular properties Density functional theory Transition metals exchange correlation functionals

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