Geometric potential of the exact electron factorization: Meaning, significance, and application

Kocák, Jakub; Kraisler, Eli; Schild, Axel

doi:10.1103/physrevresearch.5.013016

Cited by 4 publications

(4 citation statements)

References 67 publications

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“…Note that, among the scalar potentials, the geometric potential v G appears. This is defined as [30,33]…”

Section: A Equation For the Marginal Amplitudementioning

confidence: 99%

“…The application of this formalism in a purely electronic framework, sometimes referred to as exact electron factorization, to distinguish it from its electro-nuclear counterpart, sits well within the scope of density-functional theory (DFT), both in its pure Hohenberg-Kohn version [15] and in its more popular Kohn-Sham (KS) one [16]. In this context, the exact factorization has been adopted to gain physical insight in the effective potentials that map the many-body (electronic) problem into a one-body problem [17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33]. There are stark features of the Kohn-Sham potential as well as of the effective potential in orbital-free DFT [34,35], in the form of peaks and steps, that are extremely hard to model [19,28,36,37] but have been shown to be paramount for the proper description of phenomena such as molecular dissociation [38] or Mott-Hubbard transitions [39].…”

Section: Introductionmentioning

confidence: 99%

“…This restriction can be imposed with no loss of generality for ground states but it is limiting in the study of excited states where complex wavefunctions may occur. For complex wavefunctions, extra terms, in addition to the well-studied local potentials, are expected to appear, notably a vector potential [30][31][32][33].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Electronic vector potential from the exact factorization of a complex wavefunction

Giarrusso,

Gori-Giorgi,

Agostini

2024

Preprint

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We generalize the definitions of local scalar potentials named vkin and vN−1, which are relevant to properly describe phenomena such as molecular dissociation with density-functional theory, to the case in which the electronic wavefunction corresponds to a complex current-carrying state. In such a case, an extra term in the form of a vector potential appears which cannot be gauged away. Both scalar and vector potentials are introduced via the exact factorization formalism which allows to expand the given Schrödinger equation in two coupled equations, one for the marginal and one for the conditional amplitude. The electronic vector potential is directly related to the paramagnetic current density carried by the total wavefunction and to the diamagnetic current density in the equation for the marginal amplitude. An explicit example of this vector potential in a triplet state of two non-interacting electrons is showcased together with its associated circulation, giving rise to a non-vanishing geometric phase. Some connections with the exact factorization for the full molecular wavefunction beyond the Born-Oppenheimer approximation are also discussed.

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“…Note that, among the scalar potentials, the geometric potential v G appears. This is defined as [30,33]…”

Section: A Equation For the Marginal Amplitudementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Electronic vector potential from the exact factorization of a complex wavefunction

Giarrusso,

Gori-Giorgi,

Agostini

2024

Preprint

View full text Add to dashboard Cite

show abstract

“…but with detailed contributions directly from the N e -electron wave function and N e − 1 conditional factor. Equivalent routes have been explored 334,335 in specific applications of the exact factorization approach. 336 A different way to exploit the decomposition is to do a Levy−Lieb constrained search on the conditional factor f(r 2 ...r Nd e ∥r 1 ) via Monte Carlo calculations.…”

Section: Two-point Functionalsmentioning

confidence: 99%

Orbital-Free Density Functional Theory: An Attractive Electronic Structure Method for Large-Scale First-Principles Simulations

Mi,

Luo,

Trickey

et al. 2023

Chem. Rev.

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Kohn−Sham Density Functional Theory (KSDFT) is the most widely used electronic structure method in chemistry, physics, and materials science, with thousands of calculations cited annually. This ubiquity is rooted in the favorable accuracy vs cost balance of KSDFT. Nonetheless, the ambitions and expectations of researchers for use of KSDFT in predictive simulations of large, complicated molecular systems are confronted with an intrinsic computational cost-scaling challenge. Particularly evident in the context of firstprinciples molecular dynamics, the challenge is the high cost-scaling associated with the computation of the Kohn−Sham orbitals. Orbital-free DFT (OFDFT), as the name suggests, circumvents entirely the explicit use of those orbitals. Without them, the structural and algorithmic complexity of KSDFT simplifies dramatically and near-linear scaling with system size irrespective of system state is achievable. Thus, much larger system sizes and longer simulation time scales (compared to conventional KSDFT) become accessible; hence, new chemical phenomena and new materials can be explored. In this review, we introduce the historical contexts of OFDFT, its theoretical basis, and the challenge of realizing its promise via approximate kinetic energy density functionals (KEDFs). We review recent progress on that challenge for an array of KEDFs, such as one-point, twopoint, and machine-learnt, as well as some less explored forms. We emphasize use of exact constraints and the inevitability of design choices. Then, we survey the associated numerical techniques and implemented algorithms specific to OFDFT. We conclude with an illustrative sample of applications to showcase the power of OFDFT in materials science, chemistry, and physics.

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Electronic Vector Potential from the Exact Factorization of a Complex Wavefunction

Giarrusso,

Gori‐Giorgi,

Agostini

2024

ChemPhysChem

View full text Add to dashboard Cite

We generalize the definitions of local scalar potentials named vkin and vN−1, which are relevant to properly describe phenomena such as molecular dissociation with density‐functional theory, to the case in which the electronic wavefunction corresponds to a complex current‐carrying state. In such a case, an extra term in the form of a vector potential appears which cannot be gauged away. Both scalar and vector potentials are introduced via the exact factorization formalism which allows us to express the given Schrödinger equation as two coupled equations, one for the marginal and one for the conditional amplitude. The electronic vector potential is directly related to the paramagnetic current density carried by the total wavefunction and to the diamagnetic current density in the equation for the marginal amplitude. An explicit example of this vector potential in a triplet state of two non‐interacting electrons is showcased together with its associated circulation, giving rise to a non‐vanishing geometric phase. Some connections with the exact factorization for the full molecular wavefunction beyond the Born‐Oppenheimer approximation are also discussed.

show abstract

Geometric potential of the exact electron factorization: Meaning, significance, and application

Cited by 4 publications

References 67 publications

Electronic vector potential from the exact factorization of a complex wavefunction

Electronic vector potential from the exact factorization of a complex wavefunction

Orbital-Free Density Functional Theory: An Attractive Electronic Structure Method for Large-Scale First-Principles Simulations

Electronic Vector Potential from the Exact Factorization of a Complex Wavefunction

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