## A new 3rd-rung electron correlation energy functional based on Quantum Continuum Mechanics

John F. Dobson and Tim Gould

Queensland Micro and Nano Technology Centre, Griffith University, Nathan, Queensland, Australie.

Vendredi 24 Mai 2013, 16^{h}00

Barre 15-25, 1er étage, salle 02

Recently Tokatly and co-workers introduced [1] a novel approach to the motion of quantum mechanical many-particle systems. A linearized version of this theory [2] will here be termed "quantum continuum mechanics" (QCM). It takes a hydrodynamic form, but is nevertheless exact for the linear response of any one-particle quantum system, and is asymptotically exact at high frequencies for many-particle quantum systems. There are many possible applications, but here we will emphasize the use of the linear density-density response from QCM to calculate the groundstate correlation energy of many-electrons systems via the adiabatic connection and fluctuation-dissipation theorems. The result is a correlation energy functional that is "third rung" functional in the sense of Perdew, namely one that uses for its input the groundstate electron number density n(r) plus a "new density" T0(r), the kinetic stress tensor obtained from the occupied one-electron orbitals of the Kohn-Sham description of the system. The new functional [3,4] has been used to evaluate successfully the long ranged correlation energy (van der Waals energy) of some test many-electron systems. The theory promises to be efficient for calculation of such long-ranged correlation physics in general, provided that one can overcome some mathematical difficulties that will be mentioned here.

[1] I. V. Tokatly, Phys. Rev. B **71** 165105 (2005); **75** 125105 (2007)

[2] J. Tao, X. Gao, G. Vignale, and I. V. Tokatly, Phys. Rev. Lett. **103** 086401 (2009); X. Gao, J. Tao, G. Vignale, and I. V. Tokatly, Phys. Rev. B **81** 195106 (2010)

[3] T. Gould and J. F. Dobson, Phys. Rev. B **84** 241108(R) (2011)

[4] T. Gould, G. Jansen, I. V. Tokatly and J. F. Dobson, J. Chem. Phys. **136** 204115 (2012)