Diagonalisation of the Dirac Hamiltonian as a basis for a relativistic many-body procedure

Heully, Jean‐Louis; Lindgren, Ingvar; Lindroth, Eva; Lundqvist, S.; Pendrill, Ann-Marie

doi:10.1088/0022-3700/19/18/011

Cited by 388 publications

(219 citation statements)

References 21 publications

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“…These effects are normally introduced only at first order in the Pauli expansion. The regular zeroth order Hamiltonian turns out to be identical to the Hamiltonian derived earlier by Chang et al 12 and Heully et al 11 Recently, Wang et al and Peng et al proposed a time-dependent density-functional formalism which makes use of the two-component zeroth order regular approximation and a noncollinear exchange-correlation functional to calculate the excitation energies in molecules. [13][14][15][16] They showed that this relativistic time-dependent densityfunctional theory ͑TDDFT͒ formalism has the correct nonrelativistic limit, reproduces the correct threefold degeneracy of the triplet excitations, and yields excitation energies with errors comparable to nonrelativitic TDDFT calculations on light elements.…”

Section: Introductionmentioning

confidence: 67%

Relativistic two-component formulation of time-dependent current-density functional theory: Application to the linear response of solids

Boeij

2007

The Journal of Chemical Physics

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In this paper we derive the relativistic two-component formulation of time-dependent current-density-functional theory. To arrive at a two-component current-density formulation we apply a Foldy-Wouthuysen-type transformation to the time-dependent four-component Dirac-Kohn-Sham equations of relativistic density-functional theory. The two-component Hamiltonian is obtained as a regular expansion which is gauge invariant at each order of approximation, and to zeroth order it represents the time-dependent version of the relativistic zeroth order regular Hamiltonian obtained by van Lenthe et al., for the ground state [J. Chem. Phys.99, 4597 (1993)]. The corresponding zeroth order regular expression for the density is unchanged, whereas the current-density operator now comprises a paramagnetic, a diamagnetic, and a spin contribution, similar to the Gordon decomposition of the Dirac four current. The zeroth order current density is directly related to the mean velocity corresponding to the zeroth order Hamiltonian. These density and current density operators satisfy the continuity equation. This zeroth order approximation is therefore consistent and physically realistic. By combining this formalism with the formulation of the linear response of solids within time-dependent current-density functional theory [Romaniello and de Boeij, Phys. Rev. B71, 155108 (2005)], we derive a method that can treat orbital and spin contributions to the response in a unified way. The effect of spin-orbit coupling can now be taken into account. As first test we apply the method to calculate the relativistic effects in the linear response of several metals and nonmetals to a macroscopic electric field. Treatment of spin-orbit coupling yields visible changes in the spectra: a smooth onset of the interband transitions in the absorption spectrum of Au, a sharp onset with peak at about 0.46eV in the absorption spectrum of W, and a low-frequency doublet structure in the absorption spectra of ZnTe, CdTe, and HgTe in agreement with experimental results.

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Section: Introductionmentioning

confidence: 67%

Relativistic two-component formulation of time-dependent current-density functional theory: Application to the linear response of solids

Boeij

2007

The Journal of Chemical Physics

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“…18,32,38 The relativistic effects are taken into account at the all-electron level with the zero-orderregular approximation (ZORA) approach. [39][40][41][42][43][44] The molecular orbitals (MOs) were expanded in an uncontracted set of Slater-type orbitals (STO), based on a basis set study. This computational approach has been successful to describe the Pt/C and Co/C interactions.…”

Section: Computational Detailsmentioning

confidence: 99%

Influence of Carbon Support on Electronic Structure and Catalytic Activity of Pt Catalysts: Binding to the CO Molecule

2016

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Single-atom catalysts, especially with single Pt atoms, exhibit potentially improved catalytic activity as compared to metal clusters and metal surfaces. Here, the atop and bridged bondings of the CO molecule on the Pt/C system are studied. Vibrational frequencies, Mulliken populations, charge transfer, charge density differences and density of states are examined to determine the influence of the carbon support on electronic properties and catalytic activity of the Pt adatom and dimer. Comparing orbital populations and the amount of electron transfer to/from the CO molecule show that the net amount of electron transfer to the anti-bonding 2π * orbitals of the CO molecule is higher for the supported Pt dimer than for the substrate-free Pt dimer which leads to a lower vibrational frequency and a larger C−O bond distance. The hybridization between the π orbitals of the polycyclic aromatic hydrocarbons surface and the d orbitals of the Pt adatoms is responsible for enhancing the back donation of electrons to the 2π * orbitals of the CO molecule which results in a larger peak below the Fermi level for the 2π * states of the CO molecule in the corresponding density of state analysis. Therefore, it can be concluded that the carbon support significantly enhances the catalytic activity of the Pt atoms in contact with the surface for activating the CO molecule. The calculated C−O vibrational stretching frequencies provide valuable guidance for experiments considering the use of atom-type catalyst as building blocks for designing new catalysts.

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“…The FW transformation U can then be written as a product of a decoupling step U d and a renormalization step U N , as [5,47,48]…”

Section: From Four To Two Componentsmentioning

confidence: 99%

Relativistic calculations of magnetic resonance parameters: background and some recent developments

Autschbach

2014

Phil. Trans. R. Soc. A.

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This article outlines some basic concepts of relativistic quantum chemistry and recent developments of relativistic methods for the calculation of the molecular properties that define the basic parameters of magnetic resonance spectroscopic techniques, i.e. nuclear magnetic resonance shielding, indirect nuclear spin-spin coupling and electric field gradients (nuclear quadrupole coupling), as well as with electron paramagnetic resonance g-factors and electron-nucleus hyperfine coupling. Density functional theory (DFT) has been very successful in molecular property calculations, despite a number of problems related to approximations in the functionals. In particular, for heavy-element systems, the large electron count and the need for a relativistic treatment often render the application of correlated wave function ab initio methods impracticable. Selected applications of DFT in relativistic calculation of magnetic resonance parameters are reviewed.

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Diagonalisation of the Dirac Hamiltonian as a basis for a relativistic many-body procedure

Cited by 388 publications

References 21 publications

Relativistic two-component formulation of time-dependent current-density functional theory: Application to the linear response of solids

Relativistic two-component formulation of time-dependent current-density functional theory: Application to the linear response of solids

Influence of Carbon Support on Electronic Structure and Catalytic Activity of Pt Catalysts: Binding to the CO Molecule

Relativistic calculations of magnetic resonance parameters: background and some recent developments

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