The main research activity of our group is to develop new methods to describe the continuum states of atoms and molecules, to implement the methods on computer codes and to apply such codes to investigate recent problems concerning electron spectroscopy, in order to understand the physics of the phenomenon and to rationalize the experimental findings. From the continuum wave-function an important deal of information can be extracted: for example the cross section (the intensity of the emitted photoelectrons per photon unit flux as a function of the energy of the incident radiation) and the asymmetry parameter (the angular distribution of the photoelectrons as a function of the energy of the incident radiation)

Methods

Our methods for the continuum have the peculiar characteristic to be L2 approaches which employ a basis set of B-spline functions to solve the Schrödinger equation for the continuum electronic spectrum. B-spline functions have proven a very powerful choice, because are particularly suited to tackle with the boundary conditions obeyed by the continuum (unbound) wave-function. Such wave-function does not decay at large distances, but rather oscillates with well defined asymptotic behavior, and this cannot be described with canonical basis sets consisting of Gaussian or Slater orbitals.

According to the basis set, two different approaches have been considered in our group:

About the Hamiltonian, we have chosen the formalism of the Density Functional Theory (DFT), which represents a realistic compromise between accuracy and computational economy. In particular, two levels of theory have been considered:

The KS approach is, in general, a rather accurate and realistic description of the photoionization, however the agreement with the experiment is not usually quantitative. On the other hand the TDDFT formalism is much more accurate: a quantitative agreement with the measurements is often obtained, though the computational effort is definitely larger with respect to the KS approach. Within the TDDFT the coupling among different ionization channels is actually allowed, this is the reason not only for its better performances but also for its ability to describe properly autoionization (Feshbach) resonances, an effect completely missed at the KS level.

Recently we have explored also the possibility to extend such methods in order to include relativistic effects. In particular we have developed and implemented with success a KS and TDDFT atomic method based on the 4-components Dirac equation.

Implementation

The computer codes which solve the continuum problem have been totally implemented in our group. We only employ an interface to get the electron density (which is necessary to build the KS Hamiltonian and the TDDFT equations in our B-spline basis set) from a standard quantum chemical DFT calculation, taken from a conventional run of the ADF program.

Our group has started to develop the codes at the beginning of the nineties, and they are all written in FORTRAN language. A particular care has been devoted to the numerical stability and the efficiency of the algorithms, which are very important to have robust methods with wide range of applicability.

Apart the development of new algorithms, we are spending considerable efforts to paralleize our codes. We employ standard Message Passing Interface (MPI) libraries, and we have at the moment the OCE-KS code parallelized, while the LCAO-KS is on the way. We run our codes on the IBM SP4 supercomputer at CINECA (Bologna – Italy), and we currently employ 128 or 256 CPU for the largest calculation.

Application

The range of applications of our methods is quite wide, and is growing continuously. Our recent publications are the most meaningful descriptions of our current research, so we refer the reader to the publication list for an exhaustive description.

More precisely, we can identify some areas in which we have focused our efforts:

  1. Accurate calculations on small systems (comparison with ab-initio, sysmmetry resolved core states, accurate comparison with recent Synchrotron Radiation experiments)
  2. Fullerene (C60) and endohedral compounds (M@C60 ): valence and core photoionization, high energy oscillations, shape resonance analysis.
  3. Transition Metal Compounds: cross section and branching ratios analysis, connections between electronic structure (i.e. metal 3d contributions) and spectral patterns, shape resonance analysis.
  4. Oriented molecule photoionization: description and interpretations of Photo Electron Photo Ion COincidence (PEPICO) experiments.
  5. Calculation of accurate bound – unbound dipole integrals for the description of time resolved photoelectron imaging.

Acknowledgement

All this would have not been possible without the efforts of our former members of the group (PhD students, undergraduate and postgraduate students):

Michela Brosolo
Marco Venuti
Sara Furlan
Paula Colavita

Our research is supported by:

MIUR, INSTM, Democritos, CINECA, CNR.