Quantum mechanics meets scaling theory near the critical point

The critical point is believed to be not amenable to quantum mechanical calculations because the correlation length goes to infinity, the density is largely inhomogeneous and some thermodynamic properties diverge. For these reasons, until very recently all theoretical information of the critical point has been obtained by statistical physics and nothing was known about the electronic structure. Employing a sequential quantum mechanical/molecular mechanical (S-QM/MM) approach for a nonpolar atomic fluid, we study the behavior of the dielectric constant at different temperatures, ranging from dense fluid to supercritical condition. Our primary focus lies on the vicinity of the critical point. By using quantum mechanical calculations with thermodynamic condition, we perfectly reproduce the behavior found previously for classical monoatomic fluid by using scaling functions and renormalization theory that in the vicinity of the critical point the dielectric constant shares the critical behavior of the internal energy and, although the dielectric constant remains finite, its variation with temperature diverges. This perfect agreement leads credence to multiscale QM/MM methods and suggests the possibility of obtaining theoretical information about the electronic structure of a fluid near the critical point.