Broken symmetry in density-functional theory: Analysis and cure

Harju, Ari; Räsänen, E.; Saarikoski, Henri; Puska, Martti J.; Nieminen, Risto M.; Niemelä, K.

doi:10.1103/physrevb.69.153101

Cited by 32 publications

(34 citation statements)

References 11 publications

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“…It is noteworthy that the description of particular systems and phenomena in electronic systems also calls for extensions of the Kohn-Sham implementation of HK-DFT to deal with symmetry-breaking solutions [17,18,19,20]. The latter extensions are still connected to the HK theorem and differ from MR-EDF calculations performed in nuclear physics to restore broken symmetries.…”

Section: General Aspects Of the Nuclear Edf Approachmentioning

confidence: 99%

“…There, hybrid approaches that use a density functional for diagonal kernels and the (sometimes scaled) bare Coulomb force for non-diagonal kernels are used instead [19,20,76,77], an approach that is facilitated by the fact that the correlation and exchange parts of the energy are a mere correction to the direct Coulomb interaction in most Coulomb systems.…”

Section: Edf Approachmentioning

confidence: 99%

“…In the general case, we have expressed the two quasi-particle vacua, Eq. (20), in a common, arbitrary single-particle basis. However, numerical applications often make use of two non-equivalent sets of single-particle states to define the two vacua.…”

Section: No-pairing Casementioning

confidence: 99%

“…Indeed, the nuclear MR-EDF method is outside the scope of existing implementations of the Hohenberg-Kohn theorem, even of those dealing specifically with symmetry breaking issues [17,18,19,20]. As far as motivating MR-EDF calculations based on the GCM, hybrid approaches used in electronic systems that combine a density functional for diagonal energy kernels and (sometimes scaled) matrix elements of the bare Coulomb force for off-diagonal ones [21] have to be ruled out because of the different nature of the nuclear force and the more complex correlations it induces in the nuclear medium.…”

Section: Introductionmentioning

confidence: 99%

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Configuration mixing within the energy density functional formalism: Removing spurious contributions from nondiagonal energy kernels

2009

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Multi-reference calculations along the lines of the Generator Coordinate Method or the restoration of broken symmetries within the nuclear Energy Density Functional (EDF) framework are becoming a standard tool in nuclear structure physics. These calculations rely on the extension of a singlereference energy functional, of the Gogny or the Skyrme types, to non-diagonal energy kernels. There is no rigorous constructive framework for this extension so far. The commonly accepted way proceeds by formal analogy with the expressions obtained when applying the generalized Wick theorem to the non-diagonal matrix element of a Hamilton operator between two product states. It is pointed out that this procedure is ill-defined when extended to EDF calculations as the generalized Wick theorem is taken outside of its range of applicability. In particular, such a procedure is responsible for the appearance of spurious divergences and steps in multi-reference EDF energies, as was recently observed in calculations restoring particle number or angular momentum. In the present work, we give a formal analysis of the origin of this problem for calculations with and without pairing, i.e. constructing the density matrices from either Slater determinants or quasi-particle vacua. We propose a method to regularize non-diagonal energy kernels such that divergences and steps are removed from multi-reference EDF energies. Such a removal is a priori quasi-particle-basis dependent. A special feature of the method we use to proceed to the actual regularization is that it singles out one basis among all possible ones. The regularization method is applicable to calculations based on any symmetry restoration or generator coordinate but is limited to EDFs depending only on integer powers of the normal and anomalous density matrices. Eventually, the method is formally illustrated for particle number restoration and is specified to configuration mixing calculations based on Slater determinants.

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Section: General Aspects Of the Nuclear Edf Approachmentioning

confidence: 99%

Section: Edf Approachmentioning

confidence: 99%

Section: No-pairing Casementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Configuration mixing within the energy density functional formalism: Removing spurious contributions from nondiagonal energy kernels

2009

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“…9 For Coulomb-interacting fermions, the density-functional approach suffers from the relatively crude approximations for the exchange-correlation energy, as well as from the problems in using a single-configuration wave function. 10 The mean-field approach is, however, indispensable since analytic solutions are out of reach for N ജ 3, and a numerically accurate direct diagonalization is also typically restricted to fairly small particle numbers.…”

Section: Introductionmentioning

confidence: 99%

Stability of vortex structures in quantum dots

Saarikoski

Reimann²,

Räsänen

et al. 2005

Phys. Rev. B

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We study the stability and structure of vortices emerging in two-dimensional quantum dots in high magnetic fields. Our results obtained with exact diagonalization and density-functional calculations show that vortex structures can be found in various confining potentials. In nonsymmetric external potentials we find offelectron vortices that are localized giving rise to charge deficiency or holes in the electron density with rotating currents around them. We discuss the role of quantum fluctuations and show that vortex formation is observable in the energetics of the system. Our findings suggest that vortices can be used to characterize the solutions in high magnetic fields, giving insight into the underlying internal structure of the electronic wave function.

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Best‐Practice DFT Protocols for Basic Molecular Computational Chemistry**

et al. 2022

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Nowadays, many chemical investigations are supported by routine calculations of molecular structures, reaction energies, barrier heights, and spectroscopic properties. The lion's share of these quantumchemical calculations applies density functional theory (DFT) evaluated in atomic-orbital basis sets. This work provides best-practice guidance on the numerous methodological and technical aspects of DFT calculations in three parts: Firstly, we set the stage and introduce a step-by-step decision tree to choose a computational protocol that models the experiment as closely as possible. Secondly, we present a recommendation matrix to guide the choice of functional and basis set depending on the task at hand. A particular focus is on achieving an optimal balance between accuracy, robustness, and efficiency through multi-level approaches. Finally, we discuss selected representative examples to illustrate the recommended protocols and the effect of methodological choices.

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Broken symmetry in density-functional theory: Analysis and cure

Cited by 32 publications

References 11 publications

Configuration mixing within the energy density functional formalism: Removing spurious contributions from nondiagonal energy kernels

Configuration mixing within the energy density functional formalism: Removing spurious contributions from nondiagonal energy kernels

Stability of vortex structures in quantum dots

Best‐Practice DFT Protocols for Basic Molecular Computational Chemistry**

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