14 research outputs found
Resolution-of-identity approach to Hartree-Fock, hybrid density functionals, RPA, MP2, and \textit{GW} with numeric atom-centered orbital basis functions
Efficient implementations of electronic structure methods are essential for
first-principles modeling of molecules and solids. We here present a
particularly efficient common framework for methods beyond semilocal
density-functional theory, including Hartree-Fock (HF), hybrid density
functionals, random-phase approximation (RPA), second-order M{\o}ller-Plesset
perturbation theory (MP2), and the method. This computational framework
allows us to use compact and accurate numeric atom-centered orbitals (popular
in many implementations of semilocal density-functional theory) as basis
functions. The essence of our framework is to employ the "resolution of
identity (RI)" technique to facilitate the treatment of both the two-electron
Coulomb repulsion integrals (required in all these approaches) as well as the
linear density-response function (required for RPA and ). This is possible
because these quantities can be expressed in terms of products of
single-particle basis functions, which can in turn be expanded in a set of
auxiliary basis functions (ABFs). The construction of ABFs lies at the heart of
the RI technique, and here we propose a simple prescription for constructing
the ABFs which can be applied regardless of whether the underlying radial
functions have a specific analytical shape (e.g., Gaussian) or are numerically
tabulated. We demonstrate the accuracy of our RI implementation for Gaussian
and NAO basis functions, as well as the convergence behavior of our NAO basis
sets for the above-mentioned methods. Benchmark results are presented for the
ionization energies of 50 selected atoms and molecules from the G2 ion test set
as obtained with and MP2 self-energy methods, and the G2-I atomization
energies as well as the S22 molecular interaction energies as obtained with the
RPA method.Comment: 58 pages, 15 figures, and 7 table
Assessment of correlation energies based on the random-phase approximation
The random-phase approximation to the ground state correlation energy (RPA)
in combination with exact exchange (EX) has brought Kohn-Sham (KS) density
functional theory one step closer towards a universal, "general purpose first
principles method". In an effort to systematically assess the influence of
several correlation energy contributions beyond RPA, this work presents
dissociation energies of small molecules and solids, activation energies for
hydrogen transfer and non-hydrogen transfer reactions, as well as reaction
energies for a number of common test sets. We benchmark EX+RPA and several
flavors of energy functionals going beyond it: second-order screened exchange
(SOSEX), single excitation (SE) corrections, renormalized single excitation
(rSE) corrections, as well as their combinations. Both the single excitation
correction as well as the SOSEX contribution to the correlation energy
significantly improve upon the notorious tendency of EX+RPA to underbind.
Surprisingly, activation energies obtained using EX+RPA based on a KS reference
alone are remarkably accurate. RPA+SOSEX+rSE provides an equal level of
accuracy for reaction as well as activation energies and overall gives the most
balanced performance, which makes it applicable to a wide range of systems and
chemical reactions.Comment: 14 pages, 5 figures, full articl
Ab initio study of atomic hydrogen diffusion on the clean and hydrogen-terminated Si(001) surface
Recent experiments have shown an unexpected diffusion behavior of hydrogen on the Si(001) surface at high temperatures and high coverages. To shed some light on this behavior, we have employed densityfunctional theory to investigate H diffusion on the flat Si(001) surface for different coverages with main emphasis on the high-coverage limit of Si(001) monohydride. Three basic diffusion steps, intradimer, intrarow, and interrow have been studied both for isolated H atoms on the clean Si(001) surface, as well as for isolated and paired H vacancies on the Si(001) monohydride surface. The barrier energies depend strongly on the distance between the two Si neighbors of the diffusing H atom in the transition state. We observe that an isolated vacancy is less mobile than an isolated H atom showing that the Si(001) monohydride surface is more rigid than the clean surface. Interestingly, two adjacent vacancies may transfer dangling-bond charge from one to another prior to a transition of one of them, which significantly lowers the transition barrier. We visualize the reaction mechanisms using maximally localized Wannier functions and we discuss hopping rates within the harmonic approximation to transition state theory in comparison with experimental dat
Hybrid functionals for large periodic systems in an all-electron, numeric atom-centered basis framework
We describe a framework to evaluate the Hartree-Fock exchange operator for periodic electronic-structure calculations based on general, localized atom-centered basis functions. The functionality is demonstrated by hybrid-functional calculations of properties for several semiconductors. In our implementation of the Fock operator, the Coulomb potential is treated either in reciprocal space or in real space, where the sparsity of the density matrix can be exploited for computational efficiency. Computational aspects, such as the rigorous avoidance of on-the-fly disk storage, and a load-balanced parallel implementation, are also discussed. We demonstrate linear scaling of our implementation with system size by calculating electronic structure of a bulk semiconductor (GaAs) with up to 1,024 atoms per unit cell without compromising the accuracy
Accurate localized resolution of identity approach for linear-scaling hybrid density functionals and for many-body perturbation theory,
A key component in calculations of exchange and correlation energies is the Coulomb operator, which requires the evaluation of two-electron integrals. For localized basis sets, these four-center integrals are most efficiently evaluated with the resolution of identity (RI) technique, which expands basis-function products in an auxiliary basis. In this work we show the practical applicability of a localized RI-variant ('RI-LVL'), which expands products of basis functions only in the subset of those auxiliary basis functions which are located at the same atoms as the basis functions. We demonstrate the accuracy of RI-LVL for Hartree–Fock calculations, for the PBE0 hybrid density functional, as well as for RPA and MP2 perturbation theory. Molecular test sets used include the S22 set of weakly interacting molecules, the G3 test set, as well as the G2–1 and BH76 test sets, and heavy elements including titanium dioxide, copper and gold clusters. Our RI-LVL implementation paves the way for linear-scaling RI-based hybrid functional calculations for large systems and for all-electron many-body perturbation theory with significantly reduced computational and memory cost.Peer reviewe