A number of significant theoretical advances were made which represent general tools to interpret and exploit dynamical processes. Those do not refer to any specific milestones (or rather refer to several milestones simultaneously). Specifically, the excitation spectra of zero-dimensional systems have been studied at the Modena node: a novel scheme for a solid-state implementation of quantum information processing was proposed, where the qubit is identified with the long-lived spin degrees of freedom of the electrons confined in coupled quantum dots, and optically manipulated on the ps timescale by means of coherent-carrier control techniques [EX-1, EX-3]. Within this approach the required qubit-qubit coupling is provided by the Coulomb interactions between the confined carriers [M8], which is selectively switched on and off by optical means.
At the Berlin node, a time-dependent generalization of the electron localization function (ELF) was developed [B3]. The static ELF represents a tool to visualize the degree of localization of the electron distribution and, thereby, gives rise to a classification of chemical bonds. The time-dependent generalization of the ELF contains an additional term arising from the phases of the time-dependent Kohn-Sham orbitals. Movies of the time-dependent ELF allow the time-resolved observation of the formation, the modulation, and the breaking of chemical bonds, and can thus provide a visual understanding of complex reactions involving the dynamics of excited electrons.
The following results refer to specific milestones:
Significant progress was made in understanding whether, and under which conditions, the Kohn-Sham oscillator strengths of finite systems yield good approximations for the true oscillator strengths [B1]. Consequences are currently being explored to construct improved exchange-correlation (xc) kernels. Two review articles on the present status of TDDFT were published [B2, B8]. In nonlinear optical processes, the nuclear motion often plays an important role. While some phenomena, such as the generation of high harmonics, are well described by classically moving nuclei, other processes involve a splitting of the nuclear wave packet and hence cannot be dealt with by treating the nuclei as classical objects. This typically happens in chemical reactions when a given set of reactants can end up in several reaction channels. In such situations, a quantum mechanical treatment of the nuclei is essential. To achieve this, the Berlin node developed a multi-component TDDFT which treats both the nuclei and the electrons quantum mechanically [B6, B12].
A variety of exchange-correlation kernels (the exchange-only kernel of Petersilka, Gossmann and Gross, the hybrid-kernel of Burke, Petersilka and Gross, and the energy-optimized kernels of Dobson and Wang) have been critically assessed and compared by the Louvain group [L3]. All these kernels are now implemented in the ABINIT code. Another route to assess the quality of exchange-correlation kernels was followed by the Berlin node: In X-ray absorption spectra of 3d transition metals where the response function is dominated by only two poles (corresponding to L2 and L3 absorption), the diagonal matrix elements of exchange-correlation kernels can be directly compared with experimental data, thus providing a stringent test of the approximations made for the exchange-correlation functional [B9].
The formalism for implementing the GW method within the LAPW method has been worked out. In this context, a GW treatment of hot electron lifetimes in metals has been developed within the LAPW method. This approach can generally be extended with respect to the real part of the self energy allowing for a correction of the band gaps which are usually underestimated by conventional DFT calculations. For this part of the project a collaboration with Ricardo Gómez-Abal and Matthias Scheffler (Nanophase network) has been established. For other developments concerning the GW approximation, see also Milestone 8.
The calculation of the dielectric function for semiconductors requires the solution of a two-particle Hamiltonian allowing for bound electron-hole pairs. In this context, the formalisms for solving the Bethe-Salpeter equation have been developed for the pseudopotential method and the LAPW method in Modena and Graz, respectively. In both groups the corresponding computer codes already exist and have been successfully applied (see Milestones 9 and 16).
The ab-initio description of excitonic effects in polymers reinforces the applicability of this formalism to further one-dimensional systems such as nanotubes that represent one of the major recent breakthroughs in materials science. The nature of their optical excitations has yet to be clarified. In order to make the calculation of excitonic properties computationally feasible for carbon and boron-nitride nanotubes, the Modena group has developed a theoretical-computational scheme, where the peculiar symmetry properties of these systems are fully exploited through the choice of an appropriate basis set.
Several orbital functionals for the xc energy to improve ground-state DFT calculations were explored. In particular, a crucial link between the Exact Exchange (EXX) + Adiabatic Connection Framework and the linear-response Sham-Schlüter equation has been established by the Louvain node. It was shown that the self-consistent xc potentials resulting from a second-order energy functional are perfectly well-behaved. Hence, recent results obtained by Facco Bonetti et al., Phys. Rev. Lett. 86, 2241 (2001), claiming asymptotic divergences of such potentials were demonstrated to be wrong [L1, L2].
Within this framework, the corresponding potentials and ground-state energies were obtained. In particular, the reasons of the spurious bump in the non-self-consistent dissociation energy curve of the hydrogen and nitrogen dimers have been studied. Three possible reasons for the bump have been identified:
The Berlin node investigated the performance of the EXX functional for large-bandgap insulators. Previous calculations had revealed that the EXX method (combined with LDA for correlations) yields bandgaps in excellent agreement with experiment for essentially all semiconductors. The new calculations showed that the EXX method gives far less satisfactory results for ionic as well as van-der-Waals-bonded insulators. Although there is a significant improvement over the LDA, the EXX-Kohn-Sham gaps are typically still 20% smaller than the experimental optical gaps for these solids [B4, B5].
The WIENNCM code (see Milestone M13) was used to examine the magnetic structure of uranium dioxide taking into account spin-orbit coupling, strong Coulomb correlations (using the LDA+U approach) and non-collinear magnetism. The collinear 1-k antiferromagnetic type-I structure and the non-collinear anti-ferromagnetic 2-k and 3-k orderings were examined. The two first-mentioned structures could be excluded on the basis of a comparison of calculated and experimentally observed electrical field gradients (EFGs). The 3-k structure is energetically favored if a certain O-displacement is assumed, and in that case there is also good agreement with observed EFGs, orbital- and spin magnetic moments as well as hyperfine fields [A1]. (This work is also relevant to the Psi-k RTN network f-electron materials).
Optical spectra of simple fcc metals have been studied by the Graz group [G11, G12] within the random phase approximation taking the Kohn-Sham energies and orbitals as a first approximation for the quasiparticle states. It turned out that when performing highly precise calculations this procedure is a very good starting point leading to good agreement with experimental spectra. In this context further investigations have been started in collaboration with experimentalists.
The nodes of Modena and Graz are currently comparing their approaches to treat the screening in the BSE formalism. A first example, i.e. anthracene, highlights the importance to include the full dielectric matrix [G7] in order to correctly describe the exciton binding energies. Systematic tests of both groups will lead to a better understanding in which case an approximation can be made.
The comparison of TDDFT results with the GW approach has been prepared at the Louvain node.