On the removal of the exchange singularity in extended systems

Aissing, Gerrard; Monkhorst, Hendrik J.

doi:10.1002/qua.560480811

Cited by 17 publications

(15 citation statements)

References 14 publications

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“…The orthonormality of the orbitals implies that ρ ia ( G = 0) = 0 and divergence at G = 0 is thus avoided. 50 Note that the PW auxiliary basis is a natural choice for periodic systems, but it can equally be used for gas phase or surface calculations. Indeed, once the density is specified on a regular grid efficient methods are available for solving the Poisson equation with free (for example cluster or slab) boundary conditions [51][52][53] .…”

Section: The Gaussian and Plane Wave Mpmethodsmentioning

confidence: 99%

Second-Order Møller–Plesset Perturbation Theory in the Condensed Phase: An Efficient and Massively Parallel Gaussian and Plane Waves Approach

Ben

Hutter

VandeVondele

2012

J. Chem. Theory Comput.

130

115

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A novel algorithm, based on a hybrid Gaussian and plane waves (GPW) approach, is developed for the canonical second order Moller-Plesset perturbation energy (MP2) of finite and extended systems. The key aspect of the method is that the electron repulsion integrals (ia vertical bar lambda sigma) are computed by direct integration between the products of Gaussian basis functions lambda sigma and the electrostatic potential arising from a given occupied virtual pair density ia. The electrostatic potential is obtained in a plane waves basis set after solving the Poisson equation in Fourier space. In particular, for condensed phase systems, this scheme is highly efficient. Furthermore, our implementation has low memory requirements and displays excellent parallel scalability up to 100 000 processes. In this way, canonical MP2 calculations for condensed phase systems containing hundreds of atoms or more than 5000 basis functions can be performed within minutes, while systems up to 1000 atoms and 10 000 basis functions remain feasible. Solid LiH has been employed as a benchmark to study basis set and system size convergence. Lattice constants and cohesive energies of various molecular crystals have been studied with MP2 and double-hybrid functionals. Furthermore, our implementation has low memory requirements and displays excellent parallel scalability up to 100 000 processes. In this way, canonical MP2 calculations for condensed phase systems containing hundreds of atoms or more than 5000 basis functions can be performed * To whom correspondence should be addressed † Institute of Physical Chemistry, University of Zürich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland ‡ Department of Materials, ETH Zürich, Wolfgang-Pauli-Strasse 27, CH-8093 Zürich, Switzerland 1 within minutes. Lattice constants and cohesive energies of various molecular crystals have been studied with MP2 and double hybrid functionals.

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Section: The Gaussian and Plane Wave Mpmethodsmentioning

confidence: 99%

Second-Order Møller–Plesset Perturbation Theory in the Condensed Phase: An Efficient and Massively Parallel Gaussian and Plane Waves Approach

Ben

Hutter

VandeVondele

2012

J. Chem. Theory Comput.

130

115

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“…68,69 Therefore, there have been many efforts to characterize the conductive and optical (response) properties of these compounds. 68,69 Specifically, the monomer units of these polymers are the (E)-[2,2 0 -biphospholylidene] 1,1 0 -dioxide and the (E)-[2,2 0 -biphospholylidene] 1,1 0 -disulfide, respectively, henceforth named monomer A and monomer B, respectively, for sake of brevity (cf. Fig.…”

Section: Computational Details Results and Discussionmentioning

confidence: 99%

Implementation of a Parallel Linear-Response Coupled-Cluster-Theory Module in ACES III

Perera

Morales

2016

Concepts of Mathematical Physics in Chemistry: A Tribute to Frank E. Harris - Part B

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“…Excitation energy should be minimized by separate localization transformations of occupied and unoccupied orbitals, which provides a mechanism to reduce Hartree–Fock band gaps. The correlation response kernel has the physical effect of screening the Hartree and exchange terms, as is well‐known from many‐body theory 22. Such direct effects on energy gaps are evident in the TOFT formalism.…”

Section: Excitation Energies and Energy Gapsmentioning

confidence: 88%

“…The inverse operator in this equation is represented explicitly in the GW approximation of solid‐state theory 21. Screened exchange is required for metals to eliminate the singularity due to discontinuity of occupation numbers at the Fermi surface 22. If a screened Coulomb interaction is used in (Φ∣ H scr ∣Φ), (Φ∣ H − H scr ∣Φ) must be added to E c , with parameters chosen to cancel out this singularity.…”

Section: Variational Formalismmentioning

confidence: 99%

Orbital functional theory of linear response and excitation

Nesbet

2001

Int J of Quantum Chemistry

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ABSTRACT:Orbital functional theory (OFT) is based on a rule that determines a single-determinant reference state for any exact N-electron eigenstate . An OFT model postulates an explicit correlation energy functional E c of occupied orbital functions {φ i } and occupation numbers {n i }. The orbital Euler-Lagrange equations are analogous to Kohn-Sham equations, but do not in general contain local potential functions. Time-dependent Hartree-Fock theory is generalized in OFT to a formally exact linear response theory that includes electronic correlation. In the exchange-only limit, the theory reduces to the random-phase approximation of many-body theory. The formalism determines excitation energies.

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On the removal of the exchange singularity in extended systems

Cited by 17 publications

References 14 publications

Second-Order Møller–Plesset Perturbation Theory in the Condensed Phase: An Efficient and Massively Parallel Gaussian and Plane Waves Approach

Second-Order Møller–Plesset Perturbation Theory in the Condensed Phase: An Efficient and Massively Parallel Gaussian and Plane Waves Approach

Implementation of a Parallel Linear-Response Coupled-Cluster-Theory Module in ACES III

Orbital functional theory of linear response and excitation

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