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Eberhard Engel

Publications and source records attributed to Eberhard Engel.

7 recordsLinked to original sources
arXiv2026

Reply to Comment on "Efficient implementation of the superposition of atomic potentials initial guess for electronic structure calculations in Gaussian basis sets"

We reply to the Comment by Surjuse, Deng, Asadchev, and Valeev [arXiv:2603.16989] on our article "Efficient implementation of the superposition of atomic potentials initial guess for electronic structure calculations in Gaussian basis sets" [J. Chem. Phys. 152, 144105 (2020)]. We do not disagree with their work, but point out that they appear to have misinterpreted a statement in our original abstract: our suggestion to evaluate the matrix elements of the superposition of atomic potentials (SAP) using two-electron integral code was made on grounds of portability rather than as a recommendation against a dedicated one-electron implementation. Such an implementation is in fact already available in existing codes - in Dirac, for example, where a Gaussian SAP potential is formally indistinguishable from a Gaussian finite-nucleus model at the level of the nuclear attraction integral routine. We further note that both routes reduce to the same three-Gaussian overlap kernel through the Obara-Saika Laplace transform, and that SAP itself enjoys a rigorous theoretical justification through Theophilou's theorem on spherical densities and its extensions by Nagy.

physics.chem-ph↗
arXiv2020

Efficient implementation of the superposition of atomic potentials initial guess for electronic structure calculations in Gaussian basis sets

The superposition of atomic potentials (SAP) approach has recently been shown to be a simple and efficient way to initialize electronic structure calculations [S. Lehtola, J. Chem. Theory Comput. 15, 1593 (2019)]. Here, we study the differences between effective potentials from fully numerical density functional and optimized effective potential calculations for fixed configurations. We find that the differences are small, overall, and choose exchange-only potentials at the local density approximation level of theory computed on top of Hartree-Fock densities as a good compromise. The differences between potentials arising from different atomic configurations are also found to be small at this level of theory. Furthermore, we discuss the efficient Gaussian-basis implementation of SAP via error function fits to fully numerical atomic radial potentials. The guess obtained from the fitted potentials can be easily implemented in any Gaussian-basis quantum chemistry code in terms of two-electron integrals. Fits covering the whole periodic table from H to Og are reported for non-relativistic as well as fully relativistic four-component calculations that have been carried out with fully numerical approaches.

physics.comp-ph↗
arXiv2007

Random-phase-approximation-based correlation energy functionals: Benchmark results for atoms

The random phase approximation (RPA) for the correlation energy functional of density functional theory has recently attracted renewed interest. Formulated in terms of the Kohn-Sham (KS) orbitals and eigenvalues, it promises to resolve some of the fundamental limitations of the local density and generalized gradient approximations, as for instance their inability to account for dispersion forces. First results for atoms, however, indicate that the RPA overestimates correlation effects as much as the orbital-dependent functional obtained by a second order perturbation expansion on the basis of the KS Hamiltonian. In this contribution, three simple extensions of the RPA are examined, (a) its augmentation by an LDA for short-range correlation, (b) its combination with the second order exchange term, and (c) its combination with a partial resummation of the perturbation series including the second order exchange. It is found that the ground state and correlation energies as well as the ionization potentials resulting from the extensions (a) and (c) for closed sub-shell atoms are clearly superior to those obtained with the unmodified RPA. Quite some effort is made to ensure highly converged RPA data, so that the results may serve as benchmark data. The numerical techniques developed in this context, in particular for the inherent frequency integration, should also be useful for applications of RPA-type functionals to more complex systems.

cond-mat.other↗
arXiv2007

Time-dependent Density Functional calculation of e-H scattering

Phase shifts for single-channel elastic electron-atom scattering are derived from time-dependent density functional theory. The H$^-$ ion is placed in a spherical box, its discrete spectrum found, and phase shifts deduced. Exact-exchange yields an excellent approximation to the ground-state Kohn-Sham potential, while the adiabatic local density approximation yields good singlet and triplet phase shifts.

cond-mat.mtrl-sci↗
arXiv2006

Exact-Exchange Kohn-Sham formalism applied to one-dimensional periodic electronic systems

The Exact-Exchange (EXX) Kohn-Sham formalism, which treats exchange interactions exactly within density-functional theory, is applied to one-dimensional periodic systems. The underlying implementation does not rely on specific symmetries of the considered system and can be applied to any kind of periodic structure in one to three dimensions. As a test system, $trans$-polyacetylene, both in form of an isolated chain and in the bulk geometry has been investigated. Within the EXX scheme, bandstructures and independent particle response functions are calculated and compared to experimental data as well as to data calculated by several other methods. Compared to results from the local-density approximation, the EXX method leads to an increased value for the band gap, in line with similar observations for three-dimensional semiconductors. An inclusion of correlation potentials within the local density approximation or generalized gradient approximations leads to only negligible effects in the bandstructure. The EXX band gaps are in good agreement with experimental data for bulk $trans$-polyacetylene. Packing effects of the chains in bulk $trans$-polyacetylene are found to lower the band gap by about 0.5 eV.

cond-mat.mtrl-sci↗
arXiv1999

Total energy density as an interpretative tool

We present an unambiguous formulation for the total energy density within density-functional theory. We propose that it be used as a tool for the interpretation of computed energy and electronic structure changes during structural transformations and chemical reactions, augmenting the present use of electron density changes and changes in the Kohn-Sham local density of states and Kohn-Sham energy density.

cond-mat.mtrl-sci↗