# Computational Physics

**Electronic structure calculations**

Computational materials science represents a relatively recent discipline dealing with the study of materials at any level of aggregation, from atoms to molecules and solids, by using computer simulations at different level of accuracy. In our group, we routinely use a variety of state-of the-the-art ab-initio, atomistic and multiscale techniques for investigating electronic, optical, mechanical and thermodynamical properties of materials, notably carbon-based nanostructures such as graphene, fullerenes and carbon nanotubes. We model materials by using both mean field approaches, such as Hartree-Fock and Density Functional Theory, and beyond mean-field, such as many-body perturbation theory, multi-configurational methods, and quantum Monte-Carlo. We are able to investigate phenomena as different as the growth of materials, ultra-cold Fermi gases at unitarity, BCS superconductivity, hydrogen adsorption and optical band-gap in insulators and semiconductors.

**Spectroscopy**

A powerful tool to probe the basics properties of materials is given by perturbing the system, from surface to bulk, with photons and electrons causing electronic excitations. Within the framework of the formal theory of scattering, we investigate matter in its interaction with external fields, following the Fano’s formulation of the continuum-discrete interaction. We have recently developed a quantum-mechanical method (SURPRISES) that allows the calculation of the continuum wavefunction including the main correlation effects with a computational effort comparable to that required for atoms. We are able to interpret electron spectra for the characterization of materials detected in resonance-affected photo-ionization and Auger processes.

**Stellar nucleosynthesis**

Important issues concerning the origin of the elements depend on our knowledge of weak interactions. A widely known problem in this field concerns the 7Li abundance, which in stars receives contributions from electron captures on 7Be, but whose uncertain origin and fate link together Big-Bang nucleosynthesis and the nuclear processes in stars. We develop a theoretical method going beyond the Debye-Hϋckel approximation to electric screening, frequently used to study the temperature and density dependence of electron-capture decays in hot plasmas. Our procedure is based on a mean-field adiabatic approximation of the scattering process, reminiscent of the Born-Oppenheimer approach ubiquitously used in quantum chemistry.

**Molecular Dynamics**

Beyond a thousand atoms, a calculation from first principles rapidly becomes unfeasible, due to extremely large computational requirements. In order to overcome this limitation, approximate methods are required. Generally, the interaction between atoms is cast in the form of an effective potential, described by a relatively small number of parameters, so that the dynamics of the system under investigation can be efficiently simulated by the direct solution of Newton’s equations. In this way, properties of relatively large molecules can be calculated, such as proteins or artificial polymers.

This approach, however, is restricted to the sampling of configuration space around local potential minima, as the crossing of free energy barriers is exponentially suppressed. Even most powerful supercomputers are not able to overcome this bottleneck. More efficient methods are thus needed to sample thermally activated phenomena. For this purpose we developed the Variational Dynamics method, which makes it possible to simulate rare events for biologically significant macromolecules, such as for instance serpins.

**Monte Carlo Methods**

Monte Carlo methods ingenuously use random numbers to solve many kind of physical problems.

The standard application of this method is the calculation of thermodynamic quantities from a microscopic description of the systems of interest. At LISC we use Monte Carlo simulations to investigate the efficiency of microporous materials to adsorb hydrogen or other gases or to calculate with unprecedented precision the equation of state of non-degenerate quantum gases.

Additionally, Monte Carlo methods are used to investigate the motion of fast (keV) electrons into organic and inorganic materials, in order to rationalise the results of experiments where the scattering of electrons is used to gain information on the surface and bulk properties.