Quantal density-functional theory in the presence of a magnetic field

Yang, Tao; Pan, Xiao-Yin; Sahni, Viraht

doi:10.1103/physreva.83.042518

Cited by 37 publications

(54 citation statements)

References 34 publications

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“…This feature has made it a testing ground for a wide variety of methods. [59][60][61][62] The Hooke's atom consists of two electrons in a parabolic potential. The Hamiltonian of that system can be written asĤ…”

Section: Calculations and Results Of Benchmark Systemsmentioning

confidence: 99%

Variational solution of the congruently transformed Hamiltonian for many-electron systems using a full-configuration-interaction calculation

2012

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The congruent transformation of the electronic Hamiltonian is developed to address the electron correlation problem in many-electron systems. The central strategy presented in this method is to perform transformation on the electronic Hamiltonian for approximate removal of the Coulomb singularity. The principle difference between the present method and the transcorrelated method of Handy and Boys is that the congruent transformation preserves the Hermitian property of the Hamiltonian. The congruent transformation is carried out using explicitly correlated functions and the optimum correlated transform Hamiltonian is obtained by performing a search over a set of transformation functions. The ansatz of the transformation functions are selected to facilitate analytical evaluation of all the resulting integrals. The ground state energy is obtained variationally by performing a full configuration interaction (FCI) calculation on the congruent transformed Hamiltonian. Computed results on well-studied benchmark systems show that for the identical basis functions, the energy from the congruent transformed Hamiltonian is significantly lower than the conventional FCI calculations. Since the number of configuration state functions in the FCI calculation increases rapidly with the size of the 1-particle basis set, the results indicate that the congruent transformed Hamiltonian provides a viable alternative to obtain FCI quality energy using a smaller underlying 1-particle basis set.

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Section: Calculations and Results Of Benchmark Systemsmentioning

confidence: 99%

Variational solution of the congruently transformed Hamiltonian for many-electron systems using a full-configuration-interaction calculation

2012

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“…Such a unique mapping from the interacting to a model noninteracting particle system is possible only for the correct basic variables. In prior work [31], in which the interaction of the magnetic field with only the orbital angular momentum was considered [1,2] and for which case the basic variables are also {ρ(r), j(r)}, we have demonstrated such a mapping via quantal density functional theory (QDFT). There we mapped a ground state of the Hooke's atom in a magnetic field [14] to one of noninteracting fermions also in their ground state reproducing the same {ρ(r), j(r)}.…”

Section: Discussionmentioning

confidence: 99%

Hohenberg-Kohn theorem including electron spin

Pan

Sahni

2012

Phys. Rev. A

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The Hohenberg-Kohn theorem is generalized to the case of a finite system of N electrons in external electrostatic E(r) = −∇v(r) and magnetostatic B(r) = ∇ × A(r) fields in which the interaction of the latter with both the orbital and spin angular momentum is considered. For a nondegenerate ground state a bijective relationship is proved between the gauge invariant density ρ(r) and physical current density j(r) and the potentials {v(r), A(r)}. The possible many-to-one relationship between the potentials {v(r), A(r)} and the wave function is explicitly accounted for in the proof. With the knowledge that the basic variables are {ρ(r), j(r)}, and explicitly employing the bijectivity between {ρ(r), j(r)} and {v(r), A(r)}, the further extension to N -representable densities and degenerate states is achieved via a Percus-Levy-Lieb constrained-search proof. A {ρ(r), j(r)} -functional theory is developed. Finally, a Slater determinant of equidensity orbitals which reproduces a given {ρ(r), j(r)} is constructed.

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“…The "Quantal Newtonian" first law for each electron for the above interacting system states that the sum of the external F ext (r) and internal F int (r) fields experienced by each electron vanish [13,15]:…”

Section: Case Of External Static Electromagnetic Fieldmentioning

confidence: 99%

“…The components of the total energy E-the kinetic, electron-interaction, internal magnetic, and external-can each be expressed in integral virial form in terms of the respective fields [13].…”

Section: Case Of External Static Electromagnetic Fieldmentioning

confidence: 99%

“…Here, we focus on the correlations within the corresponding LEPT). A QDFT [13] can be formulated in the traditional manner, i.e., via the construction of both an effective scalar v s (r) and vector A s (r) potential for the model S system. The correlations that must be accounted for in this LEPT are those due to the Pauli exclusion principle, Coulomb repulsion, and Correlation-Kinetic effects.…”

Section: Introductionmentioning

confidence: 99%

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Electron Correlations in Local Effective Potential Theory

2016

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Local effective potential theory, both stationary-state and time-dependent, constitutes the mapping from a system of electrons in an external field to one of the noninteracting fermions possessing the same basic variable such as the density, thereby enabling the determination of the energy and other properties of the electronic system. This paper is a description via Quantal Density Functional Theory (QDFT) of the electron correlations that must be accounted for in such a mapping. It is proved through QDFT that independent of the form of external field, (a) it is possible to map to a model system possessing all the basic variables; and that (b) with the requirement that the model fermions are subject to the same external fields, the only correlations that must be considered are those due to the Pauli exclusion principle, Coulomb repulsion, and Correlation-Kinetic effects. The cases of both a static and time-dependent electromagnetic field, for which the basic variables are the density and physical current density, are considered. The examples of solely an external electrostatic or time-dependent electric field constitute special cases. An efficacious unification in terms of electron correlations, independent of the type of external field, is thereby achieved. The mapping is explicated for the example of a quantum dot in a magnetostatic field, and for a quantum dot in a magnetostatic and time-dependent electric field.

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Quantal density-functional theory in the presence of a magnetic field

Cited by 37 publications

References 34 publications

Variational solution of the congruently transformed Hamiltonian for many-electron systems using a full-configuration-interaction calculation

Variational solution of the congruently transformed Hamiltonian for many-electron systems using a full-configuration-interaction calculation

Hohenberg-Kohn theorem including electron spin

Electron Correlations in Local Effective Potential Theory

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