Modellierung der elektronischen Struktur mit dem strikt-korrelierten Elektronen-Dichtefunktional
Theoretische Chemie: Moleküle, Materialien, Oberflächen
Zusammenfassung der Projektergebnisse
Fundamental study of the strictly correlated electrons functional in the time domain in one dimension: Approximate density functionals do commonly fail for the description of charge-transfer processes in the adiabatic time-dependent Kohn-Sham framework. First applications of the strictly correlated electrons (SCE) functional to a one-dimensional model system of a stretched H2 molecule, however, have shown excitation resonances close to the accurately computed charge-transfer resonance of the Schrödinger equation. As the SCE functional possesses an approximate derivative discontinuity – a formal property any density functional should have in order to capture charge-transfer resonances – an in-depth study was undertaken to understand if the observed SCE resonance can indeed be attributed to the charge-transfer resonance. It turned out that the appearance of the SCE resonance close to the predicted charge-transfer wavelength of the H2 model is barely accidental and that the SCE resonance can be attributed to a Hydrogenic excitation from the atomic ground state to the third excited state. To understand the failure in the charge-transfer description of the SCE functional with its approximate derivative discontinuity we did then study the SCE kernel. A model density was constructed where a fraction of an electron is shifted from one Hydrogen fragment to the other and we did find that the SCE charge-transfer frequency decays to 0 with increased bond length. This is similar to traditional density functional approximations, but with the SCE functional 1/R 2 decay of the frequency is obtained in contrast to the usual exponential decay. The SCE functional can thus compensate for the exponentially vanishing overlap of the Hydrogen-fragment densities, but the next order contribution does still not lead to the correct charge-transfer frequency. SCE extension and efficient algorithmic implementations for three-dimensional systems: For an accurate computation of the SCE functional the numerical procedures for its step-wise solution have been revised and examined on their reliability in one- and three-dimensional systems. Starting from the one-dimensional case an increase in the numerical performance was achieved whenever a Fourier transform could be used for integration and spectral accuracy was obtained for this steps. The transition from one- to three dimensions for this integration steps is straight forward. More involved is the case where integrals on bounded intervals are computed that are used subsequently to compute the co-motion functions. A rounding error occurs that is propagated such that, e.g., for the dynamics of the one-dimensional H 2 prototype self-consistency in the solution of the Kohn-Sham equation can barely be achieved or that the computed excitation frequencies in the absorption spectra are dependent on the integration method of choice. We were not able to control this rounding error sufficiently and no general purpose routine could be devised for the use in electronic structure programs.
