POSITION OPERATOR r IN EXTENDED SYSTEMS WITHIN DFT AND HF
CECAM, Lyon, France, September 29th - October 1st, 2003
Sponsors:
- ESF Ψ-k Programme "Towards Atomistic Materials Design"
- Centre Europeen de Calcul Atomique et Moleculaire (CECAM)
Organisers:
- Michael Springborg, Physical Chemistry, University of Saarland, Saarbrucken, Germany
- Raffaele Resta, INFM DEMOCRITOS National Simulation Center, Trieste, Italy and Dipartimento di Fisica Teorica, Universita di Trieste, Italy
Report
The quantum-mechanical operator r (i.e., the electronic position) is the key quantity for dealing with electric polarization in atomic, molecular, and solid-state physics. Whenever the electronic system is microscopic (i.e., an atom, a molecule, a cluster, ...) the treatment of r is a relatively trivial matter: its integral over the ground-state density provides by definition the dipole of the system, possible in the presence of a given external perturbation. However, even in this case, if the external perturbation is due to an externally applied electric field problems may occur: there is no bound state but instead resonances with shorter or longer lifetimes exist.
For extended systems (e.g., polymers and solids) the treatment of r has been a challenging issue over the years that has been addressed both by physicists (with the main emphasis on the calculation of polarization of solids in the absence or presence of an external electrostatic field) and by chemists (focusing mainly on linear and non-linear responses of polymers to external AC or DC fields). Each community has developed useful concepts and methods, and in order to improve the interaction between the two communities, Michael Springborg (Physical Chemistry, University of Saarland, Germany) and Raffaele Resta (Theoretical Physics, University of Trieste, Italy) organized a three-days workshop at CECAM, Lyon, France.
The workshop was attended by 32 scientists and contained 24 oral presentations. No poster presentation was organized; instead ample time was devoted to discussions (15 min. per presentation), which turned out to be extremely useful. Although there was a slight asymmetry between the number of chemists and that of physicists and despite the slightly different notations and concepts, it was clear that both communities could and did learn from each other. In some cases very similar concepts had been developed independently by the two communities, whereas in others the concepts of one community could be taken over by the other. Thus, in total the workshop did fulfil its purpose of bridging the gap between theoretical chemistry and theoretical physics.
The workshop opened with two overview lectures by the organizers on solids (Raffele Resta) and polymers (Michael Springborg) which was aimed at giving the non-expert an introduction to the two fields. Raffaele Resta emphasized the role of currents in defining a polarization and showed how the concept of Berry phases leads to an elegant way of calculating the polarization of an extended system. Michael Springborg discussed methods and results for the calculation of polarizabilities and hyperpolarizabilities of conjugated polymers, emphasizing that extrapolation of finite-chain results to the infinite chain may be problematic.
Subsequently, in 22 contributions different aspects of treating Fin current research projects were reported. In some of those (Ivo Souza, Feliciano Giustino, Paolo Umari) the properties of crystalline materials exposed to an external electrostatic field were treated. The effects of the external field were included via an extra term in the Hamiltonian E - P, where the polarization P was calculated using the Berryphase approach. Since the calculation of the polarization can be done using Wannier functions, several presentations (Roberto Dovesi, Daniel Sebastiani, Ricardo Nunes, Marek Veithen) discussed how to construct Wannier functions, in some cases also in the presence of an external field.
One of the ultimate goal of theoretical calculations is to extend and explain experimental studies and, therefore, the calculation of experimentally accessible quantities (e.g., spectra) is of great importance. Several contributions at the workshop (Mebarek Alouani, Alberto Debernardi, Alfredo Pasquarello, Michele Lazzeri) emphasized this and in particular the calculation of Raman spectra (not only position but also intensities of the peaks) was found to be a considerable challenge since the calculation of the intensities in effect involves the calculation of non-linear responses of the system to external perturbations (electric fields and vibrations).
Other presentations focused on the role of electric currents either in approximate density functionals (Paul L. de Boeij, Oleg V. Gritsenko) where in particular extended quasi-one-dimensional systems pose a problems for presently applied approximate density functionals, or in the calculation of transport through a nanojunction (Andrea Dal Corso). Two different approaches for studying polymers in external fields were presented (Bernie Kirtman, Feng Long Gu); in one truly infinite, but periodic chains were studied, whereas in the other finite, not necessarily periodic chains were treated.
Several contributions focused on fundamental aspects of treating extended systems in external fields. In one (John E. Sipe) a formalism based on polarization and magnetization in contrast to electron density and current was presented, although it still is in its infancy, so that no applications could be presented. Alternatively, Michele Lazzeri presented a a method based on the density matrix that allowed for the direct inclusion of external fields. This method, as well as the method based on the 2n + 1 theorem, presented by Marek Veithen, allow for the calculation both of polarization and polarizabilities as well as of hyperpolarizabilities, i.e., of non-linear responses.
Michel Rerat presented results of calculations using the CRYSTAL programs where an external electrostatic field was directly included by approximating it with a saw-tooth curve. Richard F. W. Bader emphasized that systems exposed to external fields are open systems and, therefore, that surface effects are important. He showed how any system, molecule or solid, could be decomposed into atoms and how, e.g., polarization could be written as contributions .from the individual atoms when taking the surface terms (i.e., currents) into account. Finally, Fred Nastos discussed how some semiconductors respond nonlinearly by inducing a polarization when been exposed to strong and short laser pulses.
The wealth of the issues that were discussed shows that the treatment of r for extended systems is of central importance for many questions. Not only for the calculation of linear and non-linear responses of polymers and solids to external static or dynamic electric fields a proper treatment of r is required, but also in developing new and more accurate density functionals within density-functional theory and in characterizing materials, to name just two examples, problems related to the treatment of r occur. It shall therefore not surprise that how to treat r for extended systems is been discussed in many areas of physics and chemistry. Therefore, the workshop, where representatives from many different communities, each with their motivation for dealing with r, were brought together was highly informative and productive for all participants.
Raffaele Resta
Michael Springborg
More details may be found in newsletter 60 from page 72