Density-functional exchange-energy approximation with correct asymptotic behavior.
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.
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TL;DR: The new local density functional, called M06-L, is designed to capture the main dependence of the exchange-correlation energy on local spin density, spin density gradient, and spin kinetic energy density, and it is parametrized to satisfy the uniform-electron-gas limit.
Abstract: We present a new local density functional, called M06-L, for main-group and transition element thermochemistry, thermochemical kinetics, and noncovalent interactions. The functional is designed to capture the main dependence of the exchange-correlation energy on local spin density, spin density gradient, and spin kinetic energy density, and it is parametrized to satisfy the uniform-electron-gas limit and to have good performance for both main-group chemistry and transition metal chemistry. The M06-L functional and 14 other functionals have been comparatively assessed against 22 energetic databases. Among the tested functionals, which include the popular B3LYP, BLYP, and BP86 functionals as well as our previous M05 functional, the M06-L functional gives the best overall performance for a combination of main-group thermochemistry, thermochemical kinetics, and organometallic, inorganometallic, biological, and noncovalent interactions. It also does very well for predicting geometries and vibrational frequencies. Because of the computational advantages of local functionals, the present functional should be very useful for many applications in chemistry, especially for simulations on moderate-sized and large systems and when long time scales must be addressed. © 2006 American Institute of Physics. DOI: 10.1063/1.2370993
4,154 citations
Cites background from "Density-functional exchange-energy ..."
...Note that, also discussed by Perdew et al.,20 there are five other empirical parameters in the B2PLYP functional: one is in the Becke88 Ref....
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TL;DR: It is shown how derivatives of the GPW energy functional, namely ionic forces and the Kohn–Sham matrix, can be computed in a consistent way and the computational cost is scaling linearly with the system size, even for condensed phase systems of just a few tens of atoms.
4,047 citations
TL;DR: Only the alternating pattern of single-double carbon bonds within the sp2 carbon ribbons provides a satisfactory explanation for the experimentally observed blue shift of the G band of the Raman spectra relative to graphite.
Abstract: We investigate Raman spectra of graphite oxide and functionalized graphene sheets with epoxy and hydroxyl groups and Stone−Wales and 5−8−5 defects by first-principles calculations to interpret our experimental results. Only the alternating pattern of single−double carbon bonds within the sp2 carbon ribbons provides a satisfactory explanation for the experimentally observed blue shift of the G band of the Raman spectra relative to graphite. To obtain these single−double bonds, it is necessary to have sp3 carbons on the edges of a zigzag carbon ribbon.
4,000 citations
TL;DR: In this paper, the Perdew-Burke-Ernzerhof (PBE) functional was compared with empirical functionals for the atomization energies of the G2 set, and the PBE functional showed systematic errors larger than those of commonly used empirical functions.
Abstract: In order to discriminate between approximations to the exchange-correlation energy EXC[ρ↑,ρ↓], we employ the criterion of whether the functional is fitted to a certain experimental data set or if it is constructed to satisfy physical constraints. We present extensive test calculations for atoms and molecules, with the nonempirical local spin-density (LSD) and the Perdew–Burke–Ernzerhof (PBE) functional and compare our results with results obtained with more empirical functionals. For the atomization energies of the G2 set, we find that the PBE functional shows systematic errors larger than those of commonly used empirical functionals. The PBE ionization potentials, electron affinities, and bond lengths are of accuracy similar to those obtained from empirical functionals. Furthermore, a recently proposed hybrid scheme using exact exchange together with PBE exchange and correlation is investigated. For all properties studied here, the PBE hybrid gives an accuracy comparable to the frequently used empirical ...
3,493 citations
Cites methods from "Density-functional exchange-energy ..."
...46#, BLYP ~Becke88 exchange331Lee–Yang–Parr correlation34!, LSD ~local spin-density approximation1 with the parametrization of the exact correlation energy density of the homogene electron gas by Vosko, Wilk, and Nusair;46 this functional is SVWN5 in GAUSSIAN!, and the recently developed VSX…...
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TL;DR: The M05-2X functional has the best performance for thermochemical kinetics, noncovalent interactions (especially weak interaction, hydrogen bonding, π···π stacking, and interactions energies of nucleobases), and alkyl bond dissociation energies and the best composite results for energetics, excluding metals.
Abstract: We present a new hybrid meta exchange-correlation functional, called M05-2X, for thermochemistry, thermochemical kinetics, and noncovalent interactions. We also provide a full discussion of the new M05 functional, previously presented in a short communication. The M05 functional was parametrized including both metals and nonmetals, whereas M05-2X is a high-nonlocality functional with double the amount of nonlocal exchange (2X) that is parametrized only for nonmetals. In particular, M05 was parametrized against 35 data values, and M05-2X is parametrized against 34 data values. Both functionals, along with 28 other functionals, have been comparatively assessed against 234 data values: the MGAE109/3 main-group atomization energy database, the IP13/3 ionization potential database, the EA13/3 electron affinity database, the HTBH38/4 database of barrier height for hydrogen-transfer reactions, five noncovalent databases, two databases involving metal−metal and metal−ligand bond energies, a dipole moment databas...
3,246 citations