Plato: A localised orbital based density functional theory code

Kenny, Steven D.; Horsfield, Andrew P.

doi:10.1016/j.cpc.2009.08.006

Cited by 34 publications

(22 citation statements)

References 51 publications

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“…For Gaussian or plane wave basis sets these integrals are given analytically. For numeric atom-centered orbital [15][16][17][18][19][20][21][22][23] (NAO) basis sets r R i I { ( )} jon the other hand, these integrals with four different atomic positions R I , often called four-center integrals, have to be evaluated by explicit integration.…”

Section: Introductionmentioning

confidence: 99%

Accurate localized resolution of identity approach for linear-scaling hybrid density functionals and for many-body perturbation theory

et al. 2015

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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 basisfunction 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 manybody perturbation theory with significantly reduced computational and memory cost.

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Section: Introductionmentioning

confidence: 99%

Accurate localized resolution of identity approach for linear-scaling hybrid density functionals and for many-body perturbation theory

et al. 2015

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“…For DFT-LDA/GGA, NAOs are well established and can be found in several implementations [64][65][66][67][68][69][70]. This is, however, not the case for HF and the MBPT approaches we are going to address in this paper.…”

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confidence: 99%

Resolution-of-identity approach to Hartree–Fock, hybrid density functionals, RPA, MP2 andGWwith numeric atom-centered orbital basis functions

Ren

Rinke²,

Blüm³

et al. 2012

New J. Phys.

677

1,043

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The efficient implementation of electronic structure methods is essential for first principles modeling of molecules and solids. We present here a particularly efficient common framework for methods beyond semilocal density-functional theory (DFT), including Hartree-Fock (HF), hybrid density functionals, random-phase approximation (RPA), second-order Møller-Plesset perturbation theory (MP2) and the GW method. This computational framework allows us to use compact and accurate numeric atom-centered orbitals (NAOs), popular in many implementations of semilocal DFT, 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) and the linear density-response function (required for RPA and GW ). This is possible because these quantities can be expressed in terms of the 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 we propose here a simple prescription for constructing ABFs which can be applied regardless of whether the underlying radial functions have a specific analytical shape 2 (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 obtained with the GW and MP2 selfenergy methods, and the G2-I atomization energies as well as the S22 molecular interaction energies obtained with the RPA method. 6.2. Benchmark MP2 and RPA results for the G2-I atomization energies . . . . . . 40 6.3. Benchmark MP2 and RPA binding energies for the S22 molecular set . . . . . 42 7. Conclusions and outlook 44 Acknowledgments 44 Appendix A. Matrix elements for numeric atom-centered orbitals 45 Appendix B. Ionization energies of a set of atoms and molecules 48 Appendix C. The modified Gauss-Legendre grid 48 References 50 New Journal of Physics 14 (2012) 053020 (http://www.njp.org/) 3 1. IntroductionAccurate quantum-mechanical predictions of the properties of molecules and materials (solids, surfaces, nano-structures, etc) from first principles play an important role in chemistry and condensed-matter research today. Of particular importance are computational approximations to the many-body Schrödinger or Dirac equations that are tractable and yet retain quantitatively reliable atomic-scale information about the system-if not for all possible materials and properties, then at least for a relevant subset. Density-functional theory (DFT) [1,2] is one such successful avenue. It maps the interacting many-body problem onto an effective single-particle one where the many-body complexity is hidden in the unknown exchange-correlation (XC) term, which has to be approx...

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“…The algorithms for the full set of gaussian integrals have not yet been implemented in the atomic orbital code Plato 38, so self‐consistent DFT calculations were performed using the proposed basis sets and neutral atom potential, together with LDA. Using the basis set for Si described in Fig.…”

Section: Resultsmentioning

confidence: 99%

Where does tight binding go from here?

Horsfield

2011

Physica Status Solidi (b)

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Density functional tight binding (TB) has been successfully applied to a wide range of materials and problems. Here is asked the question: What is the next step for TB theory? One suggestion for a way forward is proposed that makes extensive use of gaussian expansions to ensure all integrals are analytic.1 Introduction In this special edition we celebrate the many contributions Thomas Frauenheim has made to the simulation of materials. Here I want to pick up on his huge contribution to the application of tight binding (TB); he has used it to study a wide spectrum of materials, ranging from carbon [1] to lanthanides [2], using methods for open boundaries [3] and excited states [4] as well as standard total energy calculations. A key contributor to this success was the innovative approach he took (together with Seifert and coworkers) to building TB models, namely density functional based TB (DFTB) [5]. The use of density functional theory (DFT) to build many of the integrals removed at a stroke much of the problem of fitting parameters, and speed was maintained by keeping a minimal basis set, throwing away a number of integrals, and using look-up tables for the remaining integrals. Accuracy is restored by adding a pair potential fitted to binding energy curves. DFT also provided the theoretical framework within which to derive the corrections from spin polarization and charge transfer [5]. Given the success of DFTB, a natural question to ask is: is this the final word in TB, or are new developments called for? The purpose of this paper is to argue that there are situations in which it is desirable to extend DFTB, and one particular way forward is described.To put the project in context it is useful to remind ourselves of the characteristics of TB. The key one is that molecular orbitals are expanded in atomic type orbitals (usually minimal in number), which allows the single particle Hamiltonian to be written as a matrix. The matrix

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Plato: A localised orbital based density functional theory code

Cited by 34 publications

References 51 publications

Accurate localized resolution of identity approach for linear-scaling hybrid density functionals and for many-body perturbation theory

Accurate localized resolution of identity approach for linear-scaling hybrid density functionals and for many-body perturbation theory

Resolution-of-identity approach to Hartree–Fock, hybrid density functionals, RPA, MP2 andGWwith numeric atom-centered orbital basis functions

Where does tight binding go from here?

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