Combining Statistical Physics and Quantum Mechanics for Studying Atomic and Molecular Systems along the Phase Diagram.

The combination of quantum and statistical mechanics allows inclusion of the thermodynamic condition and hence studying atomic and molecular systems in different locations of the phase diagram. In recent years the studies in the liquid phase have advanced the knowledge of spectral properties of molecules in solution, a situation that is germane in Chemistry and of enormous importance in Biology [1]. More recently, our attention has been devoted to the condition of supercritical fluids analyzing the structure, spectra and properties of molecules in a supercritical environment, [2,3] thus beyond the critical point. Theoretical studies of the critical behavior of fluids have been conducted mostly by universal scaling functions and renormalization theories. We now focus on the electronic properties of homogeneous fluids close to the critical point and have given the first explicitly calculated values of the dielectric constant in the close vicinity of the critical point (T = Tc + 2K). Thus, the behavior of the dielectric constant, only slightly above the critical point, is determined using first-principle quantum mechanical calculations. The multi-scale results [4] obtained by combining statistical and quantum mechanics indicate that the dielectric constant of Ar slightly above Tc and around the critical isochoric (0.531 g/cm$^3$) becomes density-independent. Further aspects can be explored and our progress will be reported in this presentation.\\ \\
References\\

$[1]$ S. Canuto, Ed., Solvation Effects on Molecules and Biomolecules. Computational Methods and Applications. Springer (2008).\\
$[2]$ B. J. C. Cabral, R. Rivelino, K. Coutinho and S. Canuto, J. Chem. Phys. 142, 024504 (2015).\\
$[3]$ T. L. Fonseca, H. C. Georg, K. Coutinho and S. Canuto J. Phys. Chem. A 113, 5112 (2009).\\
$[4]$ M. Hidalgo, K. Coutinho and S. Canuto, Phys. Rev. E. 91, 032115 (2015).\\