<i>Ab initio</i>approach for many-electron systems without invoking orbitals: An integral formulation of density-functional theory

Yang, Weitao

doi:10.1103/physrevlett.59.1569

Cited by 34 publications

(12 citation statements)

References 17 publications

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“…The core idea is to use a stochastic technique to DFT (SDFT) calculating directly the density from the KS Hamiltonian using a trace formula without computing KS orbitals or density matrices. The use of a stochastic technique combined with DFT has been put forward several decades ago based on path integral Monte Carlo [21][22][23][24], but has not found general use due to algorithmic problems [21]. In contrast, our approach uses a deterministic Chebyshev expansion of the density matrix projection operator and applies it to stochastic orbitals thereby circumventing the pathologies of path integral Monte Carlo.…”

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confidence: 99%

Self-Averaging Stochastic Kohn-Sham Density-Functional Theory

2013

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We formulate the Kohn-Sham density functional theory (KS-DFT) as a statistical theory in which the electron density is determined from an average of correlated stochastic densities in a trace formula. The key idea is that it is sufficient to converge the total energy per electron to within a predefined statistical error in order to obtain reliable estimates of the electronic band structure, the forces on nuclei, the density and its moments, etc. The fluctuations in the total energy per electron are guaranteed to decay to zero as the system size increases. This facilitates "self-averaging" which leads to the first ever report of sublinear scaling KS-DFT electronic structure. The approach sidesteps calculation of the density matrix and thus, is insensitive to its evasive sparseness, as demonstrated here for silicon nanocrystals. The formalism is not only appealing in terms of its promise to far push the limits of application of KS-DFT, but also represents a cognitive change in the way we think of electronic structure calculations as this stochastic theory seamlessly converges to the thermodynamic limit.

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confidence: 99%

Self-Averaging Stochastic Kohn-Sham Density-Functional Theory

2013

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“…where F is the total energy potential, F c the curvature elastic energy [3,29], and φ the general form of the free energy density. H and K are, respectively, the membrane's mean curvature and Gaussian curvature.…”

Section: Description Of Two-component Lipid Bilayer Vesiclesmentioning

confidence: 99%

Equilibrium Theory and Geometrical Constraint Equation for Two-Component Lipid Bilayer Vesicles

Yin

2008

J Biol Phys

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This paper aims at the general mathematical framework for the equilibrium theory of two-component lipid bilayer vesicles. To take into account the influences of the local compositions together with the mean curvature and Gaussian curvature of the membrane surface, a general potential functional is constructed. We introduce two kinds of virtual displacement modes: the normal one and the tangential one. By minimizing the potential functional, the equilibrium differential equations and the boundary conditions of two-component lipid vesicles are derived. Additionally, the geometrical constraint equation and geometrically permissible condition for the two-component lipid vesicles are presented. The physical, mathematical, and biological meanings of the equilibrium differential equations and the geometrical constraint equations are discussed. The influences of physical parameters on the geometrically permissible phase diagrams are predicted. Numerical results can be used to explain recent experiments.

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“…In previous work, it has already appeared the idea of using the PI approach within the framework of DFT,14, 15 but the main aim there was avoiding the use of orbitals within the Kohn–Sham approach where an exchange and correlation functional, E xc [ρ], was predefined. The intention of this work, instead, is that of describing a procedure, rigorous from the conceptual and numerical point of view, to make it possible the numerical calculation of the exact energy density for a given system (external potential), and thus use this information for developing analytic functionals.…”

Section: Practical Utilitymentioning

confidence: 99%

“…Of course, convergence must be proven and intuition suggests to start from some “reasonable” ρ trial . However, beyond the several problems that a “realistic implementation” would imply, this procedure would have at least some conceptual benefits; this is a real space procedure which does not require neither orbitals nor a predefinition of the functional as it is instead the case for the Kohn–Sham approach (as in Refs 14, 15…”

Section: Universal Functionalmentioning

confidence: 99%

Electronic energy functionals: Levy–Lieb principle within the ground state path integral quantum Monte Carlo

Site¹,

Ghiringhelli

Ceperley

2012

Int J of Quantum Chemistry

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We propose a theoretical/computational protocol based on the use of the Ground State Path Integral Quantum Monte Carlo for the calculation of the kinetic and Coulomb energy density for a system of N interacting electrons in an external potential. The idea is based on the derivation of the energy densities via the (N − 1)‐conditional probability density within the framework of the Levy–Lieb constrained search principle. The consequences for the development of energy functionals within the context of density functional theory are discussed. We propose also the possibility of going beyond the energy densities and extend this idea to a computational procedure where the (N − 1)‐conditional probability is an implicit functional of the electron density, independently from the external potential. In principle, such a procedure paves the way for an on‐the‐fly determination of the energy functional for any system. © 2012 Wiley Periodicals, Inc.

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Ab initioapproach for many-electron systems without invoking orbitals: An integral formulation of density-functional theory

Cited by 34 publications

References 17 publications

Self-Averaging Stochastic Kohn-Sham Density-Functional Theory

Self-Averaging Stochastic Kohn-Sham Density-Functional Theory

Equilibrium Theory and Geometrical Constraint Equation for Two-Component Lipid Bilayer Vesicles

Electronic energy functionals: Levy–Lieb principle within the ground state path integral quantum Monte Carlo

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