Compressed Representation of Kohn–Sham Orbitals via Selected Columns of the Density Matrix

Damle, Anil; Lin, Lin; Ying, Lexing

doi:10.1021/ct500985f

Cited by 105 publications

(139 citation statements)

References 37 publications

Supporting

Mentioning

139

Contrasting

Order By: Relevance

“…An alternative method for generating localised Wannier functions, known as the selected columns of the density matrix (SCDM) algorithm, has been proposed by Damle, Lin and Ying. 96,97 At its core the scheme exploits the information stored in the real-space representation of the single-particle density matrix, a gaugeinvariant quantity. Localisation of the resulting functions is a direct consequence of the well-known nearsightedness principle 98,99 of electronic structure in extended systems with a gapped Hamiltonian, i.e., insulators and semiconductors.…”

Section: Automatic Wannier Functions: the Scdm Methodsmentioning

confidence: 99%

Wannier90 as a community code: new features and applications

Pizzi

Vitale

Arita

et al. 2020

J. Phys.: Condens. Matter

1,243

692

View full text Add to dashboard Cite

Wannier90 is an open-source computer program for calculating maximally-localised Wannier functions (MLWFs) from a set of Bloch states. It is interfaced to many widely used electronicstructure codes thanks to its independence from the basis sets representing these Bloch states. In the past few years the development of Wannier90 has transitioned to a community-driven model; this has resulted in a number of new developments that have been recently released in Wannier90 v3.0. In this article we describe these new functionalities, that include the implementation of new features for wannierisation and disentanglement (symmetry-adapted Wannier functions, selectivelylocalised Wannier functions, selected columns of the density matrix) and the ability to calculate new properties (shift currents and Berry-curvature dipole, and a new interface to many-body perturbation theory); performance improvements, including parallelisation of the core code; enhancements in functionality (support for spinor-valued Wannier functions, more accurate methods to interpolate quantities in the Brillouin zone); improved usability (improved plotting routines, integration with arXiv:1907.09788v1 [cond-mat.mtrl-sci]

show abstract

Section: Automatic Wannier Functions: the Scdm Methodsmentioning

confidence: 99%

Wannier90 as a community code: new features and applications

Pizzi

Vitale

Arita

et al. 2020

J. Phys.: Condens. Matter

1,243

692

View full text Add to dashboard Cite

show abstract

“…As such, the computational cost of the DD-RSH-CAM can be further reduced, whereas the effect is typically within 0.1 eV for the band gap [34,176,177]. On a more general remark, recent developments have shown that the computational cost of hybrid functionals can be significantly reduced through a compressed representation of the Fock exchange operator [178] or a localized representation of the orbitals [179,180], making the DD-RSH-CAM a feasible method for the purpose of high-throughput materials screening.…”

Section: B Practical Aspectsmentioning

confidence: 99%

Nonempirical dielectric-dependent hybrid functional with range separation for semiconductors and insulators

Chen

Miceli

Rignanese

et al. 2018

Phys. Rev. Materials

145

148

View full text Add to dashboard Cite

We present a general scheme of range-separated hybrid functionals in which the mixing parameters of Fock exchange are fully nonempirical and determined solely from the dielectric function.We showthat the full dielectric dependence leads to an unscreened Fock exchange in the short range, while in the long range the Fock exchange is correctly screened by the macroscopic dielectric constant. The range separation is obtained by fitting to the calculated static dielectric function in the long-wavelength limit. The resulting hybrid functional accurately accounts for electronic and structural properties of various semiconductors and insulators spanning a wide range of band gaps. We present a general scheme of range-separated hybrid functionals in which the mixing parameters of Fock exchange are fully nonempirical and determined solely from the dielectric function. We show that the full dielectric dependence leads to an unscreened Fock exchange in the short range, while in the long range the Fock exchange is correctly screened by the macroscopic dielectric constant. The range separation is obtained by fitting to the calculated static dielectric function in the long-wavelength limit. The resulting hybrid functional accurately accounts for electronic and structural properties of various semiconductors and insulators spanning a wide range of band gaps.

show abstract

“…We further expect that there exists a unitary matrix U ∈ C Ne×Ne , called a gauge matrix, so that each column of the rotated matrix Φ = ΨU is localized, i.e., it concentrates on a small number of elements compared to the size of the vector N . We point out that efficient numerical algorithms have been developed to compute such gauge and the corresponding localized functions (see e.g., [11,29,9]). Once the localized functions are obtained, we may find localized functions associated with the index set for the bath I b denoted by Ψ 0,b .…”

Section: Evaluation Of the Bath Projectormentioning

confidence: 99%

Projection-Based Embedding Theory for Solving Kohn--Sham Density Functional Theory

Lin¹,

Zepeda-Núñez²

2019

Multiscale Model. Simul.

Self Cite

View full text Add to dashboard Cite

Quantum embedding theories are playing an increasingly important role in bridging different levels of approximation to the many-body Schrödinger equation in physics, chemistry and materials science. In this paper, we present a linear algebra perspective of the recently developed projection based embedding theory (PET) [Manby et al, J. Chem. Theory Comput. 8, 2564, 2012, restricted to the context of Kohn-Sham density functional theory. By partitioning the global degrees of freedom into a "system" part and a "bath" part, and by choosing a proper projector from the bath, PET is an in-principle exact formulation to confine the calculation to the system part only, and hence can be performed with reduced computational cost. Viewed from the perspective of domain decomposition methods, one particularly interesting feature of PET is that it does not enforce a boundary condition explicitly, and remains applicable even when the discretized Hamiltonian matrix is dense, such as in the context of the planewave discretization. In practice, the accuracy of PET depends on the accuracy of the bath projector. Based on the linear algebra reformulation, we develop a first order perturbation correction to the projector from the bath to improve its accuracy. Numerical results for real chemical systems indicate that with a proper choice of reference system used to compute the bath projector, the perturbatively corrected PET can be sufficiently accurate even when strong perturbation is applied to very small systems, such as the computation of the ground state energy of a SiH 3 F molecule, using a SiH 4 molecule as the reference system. Since the dimension of Bis a diagonal matrix containing all the eigenvalues of H| B ⊥ 0 ordered non-decreasingly, and Ψ ∈ C N ×(N −N b ) is given by orthogonal columns of an unitary matrix in the subspace 6 7

show abstract

Compressed Representation of Kohn–Sham Orbitals via Selected Columns of the Density Matrix

Cited by 105 publications

References 37 publications

Wannier90 as a community code: new features and applications

Wannier90 as a community code: new features and applications

Nonempirical dielectric-dependent hybrid functional with range separation for semiconductors and insulators

Projection-Based Embedding Theory for Solving Kohn--Sham Density Functional Theory

Contact Info

Product

Resources

About