Alternative Representations of the Correlation Energy in Density-Functional Theory: A Kinetic-Energy Based Adiabatic Connection

The adiabatic-connection framework has been widely used to explore the properties of the correlation energy in density-functional theory. The integrand in this formula may be expressed in terms of the electron-electron interactions directly, involving intrinsically two-particle expectation values. Alternatively, it may be expressed in terms of the kinetic energy, involving only one-particle quantities. In this work, we explore this alternative representation for the correlation energy and highlight some of its potential for the construction of new density functional approximations. The kinetic-energy based integrand is effective in concentrating static correlation effects to the low interaction strength regime and approaches zero asymptotically, offering interesting new possibilities for modeling the correlation energy in density-functional theory