Orbital-free density functional theory for materials research

Witt, William C.; Río, Beatriz González del; Dieterich, Johannes M.; Carter, Emily A.

doi:10.1557/jmr.2017.462

Cited by 137 publications

(151 citation statements)

References 155 publications

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“…This completely bypasses its inherent complexity. Particularly, OF-DFT algorithms are promising because they involve a computational scaling of at most O(N ln N ), where N is a measure of the system size, and a memory requirement of only O(N ) [13-15].Unfortunately, even though OF-DFT has already proven to be successful for simulations of million-atom systems involving crystalline and liquid metals and alloys [15][16][17][18], as well as plasmas and warm dense matter [19][20][21], its applicability has been severely limited by the accuracy of the available Kinetic Energy density functionals (KEDFs). For example, finite systems such as metal clusters and quantum dots have been outside the range of applicability of OF-DFT.In this work, we achieve a breakthrouth by carefully balancing three important aspects defining the KEDFs: asymptotics of the corresponding potential, intrinsic nonlocality, and ability to handle nonhomogeneous systems.…”

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confidence: 99%

Orbital-free density functional theory correctly models quantum dots when asymptotics, nonlocality, and nonhomogeneity are accounted for

Pavanello

2019

Phys. Rev. B

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Million-atom quantum simulations are in principle feasible with Orbital-Free Density Functional Theory (OF-DFT) because the algorithms only require simple functional minimizations with respect to the electron density function. In this context, OF-DFT has been useful for simulations of warm dense matter, plasma, cold metals and alloys. Unfortunately, systems as important as quantum dots and clusters (having highly inhomogeneous electron densities) still fall outside OF-DFT's range of applicability. In this work, we address this century old problem by devising and implementing an accurate, transferable and universal family of nonlocal Kinetic Energy density functionals that feature correct asymptotics and can handle highly inhomogenous electron densities. For the first time to date, we show that OF-DFT achieves close to chemical accuracy for the electronic energy and reproduces the electron density to about 5% of the benchmark for semiconductor quantum dots and metal clusters. Therefore, this work demonstrates that OF-DFT is no longer limited to simulations of systems with nearly homogeneous electron density but it can venture into simulations of clusters and quantum dots with applicability to rational design of novel materials. 1 arXiv:1812.08952v1 [cond-mat.mtrl-sci] 21 Dec 2018 Metal clusters and quantum dots constitute an important class of systems of pivotal importance for materials design particularly in photovoltaics [1], catalysis [2], and even quantum computing [3]. Although these fields are already strongly shaped by computeraided design, the high computational cost of available quantum-mechanical methods such as Kohn-Sham density functional theory (KS-DFT) [4, 5] is hampering futher progress. In this playing field, what is really needed is a breakthrough in techniques alternative to the current standard, and among them [6-12] Orbital-Free Density Functional Theory (OF-DFT) is a promising candidate. OF-DFT is a promising and intriguing alternative because approximate density functionals for the kinetic energy entirely replace the need to solve for a Schrödinger equation. This completely bypasses its inherent complexity. Particularly, OF-DFT algorithms are promising because they involve a computational scaling of at most O(N ln N ), where N is a measure of the system size, and a memory requirement of only O(N ) [13-15].Unfortunately, even though OF-DFT has already proven to be successful for simulations of million-atom systems involving crystalline and liquid metals and alloys [15][16][17][18], as well as plasmas and warm dense matter [19][20][21], its applicability has been severely limited by the accuracy of the available Kinetic Energy density functionals (KEDFs). For example, finite systems such as metal clusters and quantum dots have been outside the range of applicability of OF-DFT.In this work, we achieve a breakthrouth by carefully balancing three important aspects defining the KEDFs: asymptotics of the corresponding potential, intrinsic nonlocality, and ability to handle nonhomogeneous systems. Th...

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confidence: 99%

Orbital-free density functional theory correctly models quantum dots when asymptotics, nonlocality, and nonhomogeneity are accounted for

Pavanello

2019

Phys. Rev. B

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“…It was constrained to satisfy Eqs. (8) and (9) for physical atom densities, i.e., those that obey the Kato cusp condition [25]. VT84F also was constrained to respect lim s→∞ F θ (s)/F W (s) = 0.…”

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confidence: 99%

A simple generalized gradient approximation for the noninteracting kinetic energy density functional

2018

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A simple, novel, non-empirical, constraint-based orbital-free generalized gradient approximation (GGA) non-interacting kinetic energy density functional is presented along with illustrative applications. The innovation is adaptation of constraint-based construction to the essential properties of pseudo-densities from the pseudo-potentials that are essential in plane-wave-basis ab initio molecular dynamics. This contrasts with constraining to the qualitatively different Kato-cusp-condition densities. The single parameter in the new functional is calibrated by satisfying Pauli potential positivity constraints for pseudo-atom densities. In static lattice tests on simple metals and semiconductors, the new LKT functional outperforms the previous best constraint-based GGA functional, VT84F (Phys. Rev. B 88, 161108(R) (2013)), is generally superior to a recently proposed meta-GGA, is reasonably competitive with parametrized two-point functionals, and is substantially faster.

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“…Widespread use of OFDFT in applications beyond light metals is held back by the absence of sufficiently accurate KEFs. The high stakes of the KEF issue are well known [109,110] and will not be repeated here. Recent years witnessed the appearance of several works using ML for KEF construction for systems where previous approximations were not good enough for use in applications (i.e.…”

Section: Kinetic Energy Functionalsmentioning

confidence: 99%

Machine learning for the solution of the Schrödinger equation

Manzhos

2020

Mach. Learn.: Sci. Technol.

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Machine learning (ML) methods have recently been increasingly widely used in quantum chemistry. While ML methods are now accepted as high accuracy approaches to construct interatomic potentials for applications, the use of ML to solve the Schrödinger equation, either vibrational or electronic, while not new, is only now making significant headway towards applications. We survey recent uses of ML techniques to solve the Schrödinger equation, including the vibrational Schrödinger equation, the electronic Schrödinger equation and the related problems of constructing functionals for density functional theory (DFT) as well as potentials which enter semi-empirical approximations to DFT. We highlight similarities and differences and specific difficulties that ML faces in these applications and possibilities for cross-fertilization of ideas.© 2020 The Author(s). Published by IOP Publishing Ltd Mach. Learn.: Sci. Technol. 1 (2020) 013002 S Manzhos approximator properties, with modifications specific to the problem of solving the SE or building functionals, including adapted architectures of ML methods and data selection schemes. It is therefore important to recognize similarities and differences in the requirements that can be addressed via ML among different applications.In this Perspective, we survey recent uses of ML techniques to solve the Schrödinger equation, including the vibrational Schrödinger equation and the electronic problem: the electronic Schrödinger equation and the related problems of constructing exchange-correlation and kinetic energy functionals for Kohn-Sham (KS-) and orbital-free (OF-) density functional theory (DFT) as well as use of ML for semi-empirical approximations used in density functional based approaches such as DFTB (density functional tight binding) and dispersion-corrected DFT (DFT-D). We only consider the use of ML for the solution of the vibrational and electronic SE or the KS equation or the Hohenberg-Kohn (HK) equation and not methods that aim to avoid such solutions (such as those directly mapping the molecular structure to the spectrum or energy or properties without solving for the density or wavefunction [29][30][31][32][33][34][35][36]); we also do not consider uses of ML for other types of quantum mechanical modelling or other types of differential or integral equations [37][38][39][40][41][42].We do not aim to present a comprehensive review but rather a survey allowing similarities and differences of ML uses in all these applications, as well as promising directions for future research, to transpire. This is not a review of ML methods; the key machine learning techniques that found use in quantum chemistry are well reviewed elsewhere [3-5, 43, 44], their description will not be repeated there; the reader is advised to consult the literature for their introduction, such as [45,46] for neural networks, [47,48] for Gaussian process regression (GPR), [49] for kernel ridge regression (KRR; note the similarity in the form of the function representation between GPR and KRR), [50] for...

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Orbital-free density functional theory for materials research

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Cited by 137 publications

References 155 publications

Orbital-free density functional theory correctly models quantum dots when asymptotics, nonlocality, and nonhomogeneity are accounted for

Orbital-free density functional theory correctly models quantum dots when asymptotics, nonlocality, and nonhomogeneity are accounted for

A simple generalized gradient approximation for the noninteracting kinetic energy density functional

Machine learning for the solution of the Schrödinger equation

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