Semiempirical GGA-type density functional constructed with a long-range dispersion correction.
TL;DR: A new density functional of the generalized gradient approximation (GGA) type for general chemistry applications termed B97‐D is proposed, based on Becke's power‐series ansatz from 1997, and is explicitly parameterized by including damped atom‐pairwise dispersion corrections of the form C6 · R−6.
Abstract: A new density functional (DF) of the generalized gradient approximation (GGA) type for general chemistry applications termed B97-D is proposed. It is based on Becke's power-series ansatz from 1997 and is explicitly parameterized by including damped atom-pairwise dispersion corrections of the form C(6) x R(-6). A general computational scheme for the parameters used in this correction has been established and parameters for elements up to xenon and a scaling factor for the dispersion part for several common density functionals (BLYP, PBE, TPSS, B3LYP) are reported. The new functional is tested in comparison with other GGAs and the B3LYP hybrid functional on standard thermochemical benchmark sets, for 40 noncovalently bound complexes, including large stacked aromatic molecules and group II element clusters, and for the computation of molecular geometries. Further cross-validation tests were performed for organometallic reactions and other difficult problems for standard functionals. In summary, it is found that B97-D belongs to one of the most accurate general purpose GGAs, reaching, for example for the G97/2 set of heat of formations, a mean absolute deviation of only 3.8 kcal mol(-1). The performance for noncovalently bound systems including many pure van der Waals complexes is exceptionally good, reaching on the average CCSD(T) accuracy. The basic strategy in the development to restrict the density functional description to shorter electron correlation lengths scales and to describe situations with medium to large interatomic distances by damped C(6) x R(-6) terms seems to be very successful, as demonstrated for some notoriously difficult reactions. As an example, for the isomerization of larger branched to linear alkanes, B97-D is the only DF available that yields the right sign for the energy difference. From a practical point of view, the new functional seems to be quite robust and it is thus suggested as an efficient and accurate quantum chemical method for large systems where dispersion forces are of general importance.
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University of Udine1, École Polytechnique Fédérale de Lausanne2, University of Lugano3, Leipzig University4, University of Paris5, University of North Texas6, Princeton University7, National Research Council8, International School for Advanced Studies9, Cornell University10, University of Lincoln11, University of Milan12, École Polytechnique13, International Centre for Theoretical Physics14, University of Paderborn15, University of Oxford16, Jožef Stefan Institute17, University of Padua18, Sapienza University of Rome19, Vietnam Academy of Science and Technology20, University of British Columbia21, Centre national de la recherche scientifique22, University of Lorraine23, École Normale Supérieure24, University of Zurich25, Université Paris-Saclay26, Wake Forest University27, Temple University28
TL;DR: Quantum ESPRESSO as discussed by the authors is an integrated suite of open-source computer codes for quantum simulations of materials using state-of-the-art electronic-structure techniques, based on density functional theory, density functional perturbation theory, and many-body perturbations theory, within the plane-wave pseudo-potential and projector-augmented-wave approaches.
Abstract: Quantum ESPRESSO is an integrated suite of open-source computer codes for quantum simulations of materials using state-of-the art electronic-structure techniques, based on density-functional theory, density-functional perturbation theory, and many-body perturbation theory, within the plane-wave pseudo-potential and projector-augmented-wave approaches. Quantum ESPRESSO owes its popularity to the wide variety of properties and processes it allows to simulate, to its performance on an increasingly broad array of hardware architectures, and to a community of researchers that rely on its capabilities as a core open-source development platform to implement theirs ideas. In this paper we describe recent extensions and improvements, covering new methodologies and property calculators, improved parallelization, code modularization, and extended interoperability both within the distribution and with external software.
2,818 citations
TL;DR: A summary of the technical advances that are incorporated in the fourth major release of the Q-Chem quantum chemistry program is provided in this paper, covering approximately the last seven years, including developments in density functional theory and algorithms, nuclear magnetic resonance (NMR) property evaluation, coupled cluster and perturbation theories, methods for electronically excited and open-shell species, tools for treating extended environments, algorithms for walking on potential surfaces, analysis tools, energy and electron transfer modelling, parallel computing capabilities, and graphical user interfaces.
Abstract: A summary of the technical advances that are incorporated in the fourth major release of the Q-Chem quantum chemistry program is provided, covering approximately the last seven years. These include developments in density functional theory methods and algorithms, nuclear magnetic resonance (NMR) property evaluation, coupled cluster and perturbation theories, methods for electronically excited and open-shell species, tools for treating extended environments, algorithms for walking on potential surfaces, analysis tools, energy and electron transfer modelling, parallel computing capabilities, and graphical user interfaces. In addition, a selection of example case studies that illustrate these capabilities is given. These include extensive benchmarks of the comparative accuracy of modern density functionals for bonded and non-bonded interactions, tests of attenuated second order Moller–Plesset (MP2) methods for intermolecular interactions, a variety of parallel performance benchmarks, and tests of the accuracy of implicit solvation models. Some specific chemical examples include calculations on the strongly correlated Cr_2 dimer, exploring zeolite-catalysed ethane dehydrogenation, energy decomposition analysis of a charged ter-molecular complex arising from glycerol photoionisation, and natural transition orbitals for a Frenkel exciton state in a nine-unit model of a self-assembling nanotube.
2,396 citations
TL;DR: Transition metal dichalcogenides sandwiched between two layers of graphene produce an enhanced photoresponse, which allows development of extremely efficient flexible photovoltaic devices with photoresponsivity above 0.1 ampere per watt (corresponding to an external quantum efficiency of above 30%).
Abstract: The isolation of various two-dimensional (2D) materials, and the possibility to combine them in vertical stacks, has created a new paradigm in materials science: heterostructures based on 2D crystals. Such a concept has already proven fruitful for a number of electronic applications in the area of ultrathin and flexible devices. Here, we expand the range of such structures to photoactive ones by using semiconducting transition metal dichalcogenides (TMDCs)/graphene stacks. Van Hove singularities in the electronic density of states of TMDC guarantees enhanced light-matter interactions, leading to enhanced photon absorption and electron-hole creation (which are collected in transparent graphene electrodes). This allows development of extremely efficient flexible photovoltaic devices with photoresponsivity above 0.1 ampere per watt (corresponding to an external quantum efficiency of above 30%).
2,209 citations
TL;DR: In this paper, dispersion corrections to standard Kohn-Sham density functional theory (DFT) are reviewed, focusing on computationally efficient methods for large systems that do not depend on virtual orbitals or rely on separated fragments.
Abstract: Dispersion corrections to standard Kohn–Sham density functional theory (DFT) are reviewed. The focus is on computationally efficient methods for large systems that do not depend on virtual orbitals or rely on separated fragments. The recommended approaches (van der Waals density functional and DFT-D) are asymptotically correct and can be used in combination with standard or slightly modified (short-range) exchange–correlation functionals. The importance of the dispersion energy in intramolecular cases (conformational problems and thermochemistry) is highlighted. © 2011 John Wiley & Sons, Ltd. WIREs Comput Mol Sci 2011 1 211-228 DOI: 10.1002/wcms.30
2,057 citations
Pennsylvania State University1, Rensselaer Polytechnic Institute2, Oak Ridge National Laboratory3, University of Central Florida4, Yale University5, Purdue University6, Carnegie Mellon University7, Massachusetts Institute of Technology8, Lawrence Berkeley National Laboratory9, University of California, Berkeley10, Rice University11, Chinese Academy of Sciences12, University of Texas at Austin13, University of California, Santa Barbara14
TL;DR: Insight is provided into the theoretical modeling and understanding of the van der Waals forces that hold together the 2D layers in bulk solids, as well as their excitonic properties and growth morphologies.
Abstract: The isolation of graphene in 2004 from graphite was a defining moment for the “birth” of a field: two-dimensional (2D) materials In recent years, there has been a rapidly increasing number of papers focusing on non-graphene layered materials, including transition-metal dichalcogenides (TMDs), because of the new properties and applications that emerge upon 2D confinement Here, we review significant recent advances and important new developments in 2D materials “beyond graphene” We provide insight into the theoretical modeling and understanding of the van der Waals (vdW) forces that hold together the 2D layers in bulk solids, as well as their excitonic properties and growth morphologies Additionally, we highlight recent breakthroughs in TMD synthesis and characterization and discuss the newest families of 2D materials, including monoelement 2D materials (ie, silicene, phosphorene, etc) and transition metal carbide- and carbon nitride-based MXenes We then discuss the doping and functionalization of 2
2,036 citations
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TL;DR: A simple derivation of a simple GGA is presented, in which all parameters (other than those in LSD) are fundamental constants, and only general features of the detailed construction underlying the Perdew-Wang 1991 (PW91) GGA are invoked.
Abstract: Generalized gradient approximations (GGA’s) for the exchange-correlation energy improve upon the local spin density (LSD) description of atoms, molecules, and solids. We present a simple derivation of a simple GGA, in which all parameters (other than those in LSD) are fundamental constants. Only general features of the detailed construction underlying the Perdew-Wang 1991 (PW91) GGA are invoked. Improvements over PW91 include an accurate description of the linear response of the uniform electron gas, correct behavior under uniform scaling, and a smoother potential. [S0031-9007(96)01479-2] PACS numbers: 71.15.Mb, 71.45.Gm Kohn-Sham density functional theory [1,2] is widely used for self-consistent-field electronic structure calculations of the ground-state properties of atoms, molecules, and solids. In this theory, only the exchange-correlation energy EXC › EX 1 EC as a functional of the electron spin densities n"srd and n#srd must be approximated. The most popular functionals have a form appropriate for slowly varying densities: the local spin density (LSD) approximation Z d 3 rn e unif
146,533 citations
TL;DR: In this article, a semi-empirical exchange correlation functional with local spin density, gradient, and exact exchange terms was proposed. But this functional performed significantly better than previous functionals with gradient corrections only, and fits experimental atomization energies with an impressively small average absolute deviation of 2.4 kcal/mol.
Abstract: Despite the remarkable thermochemical accuracy of Kohn–Sham density‐functional theories with gradient corrections for exchange‐correlation [see, for example, A. D. Becke, J. Chem. Phys. 96, 2155 (1992)], we believe that further improvements are unlikely unless exact‐exchange information is considered. Arguments to support this view are presented, and a semiempirical exchange‐correlation functional containing local‐spin‐density, gradient, and exact‐exchange terms is tested on 56 atomization energies, 42 ionization potentials, 8 proton affinities, and 10 total atomic energies of first‐ and second‐row systems. This functional performs significantly better than previous functionals with gradient corrections only, and fits experimental atomization energies with an impressively small average absolute deviation of 2.4 kcal/mol.
87,732 citations
TL;DR: Numerical calculations on a number of atoms, positive ions, and molecules, of both open- and closed-shell type, show that density-functional formulas for the correlation energy and correlation potential give correlation energies within a few percent.
Abstract: A correlation-energy formula due to Colle and Salvetti [Theor. Chim. Acta 37, 329 (1975)], in which the correlation energy density is expressed in terms of the electron density and a Laplacian of the second-order Hartree-Fock density matrix, is restated as a formula involving the density and local kinetic-energy density. On insertion of gradient expansions for the local kinetic-energy density, density-functional formulas for the correlation energy and correlation potential are then obtained. Through numerical calculations on a number of atoms, positive ions, and molecules, of both open- and closed-shell type, it is demonstrated that these formulas, like the original Colle-Salvetti formulas, give correlation energies within a few percent.
84,646 citations
TL;DR: In this paper, the Hartree and Hartree-Fock equations are applied to a uniform electron gas, where the exchange and correlation portions of the chemical potential of the gas are used as additional effective potentials.
Abstract: From a theory of Hohenberg and Kohn, approximation methods for treating an inhomogeneous system of interacting electrons are developed. These methods are exact for systems of slowly varying or high density. For the ground state, they lead to self-consistent equations analogous to the Hartree and Hartree-Fock equations, respectively. In these equations the exchange and correlation portions of the chemical potential of a uniform electron gas appear as additional effective potentials. (The exchange portion of our effective potential differs from that due to Slater by a factor of $\frac{2}{3}$.) Electronic systems at finite temperatures and in magnetic fields are also treated by similar methods. An appendix deals with a further correction for systems with short-wavelength density oscillations.
47,477 citations
TL;DR: This work reports a gradient-corrected exchange-energy functional, containing only one parameter, that fits the exact Hartree-Fock exchange energies of a wide variety of atomic systems with remarkable accuracy, surpassing the performance of previous functionals containing two parameters or more.
Abstract: Current gradient-corrected density-functional approximations for the exchange energies of atomic and molecular systems fail to reproduce the correct 1/r asymptotic behavior of the exchange-energy density. Here we report a gradient-corrected exchange-energy functional with the proper asymptotic limit. Our functional, containing only one parameter, fits the exact Hartree-Fock exchange energies of a wide variety of atomic systems with remarkable accuracy, surpassing the performance of previous functionals containing two parameters or more.
45,683 citations