Range-dependent adiabatic connections

Recently, we have implemented a scheme for the calculation of the adiabatic connection linking the Kohn–Sham system to the physical, interacting system. This scheme uses a generalized Lieb functional, in which the electronic-interaction strength is varied in a simple linear fashion, keeping the potential or the density fixed in the process. In the present work, we generalize this scheme further to accommodate arbitrary two-electron operators, allowing the calculation of adiabatic connections following alternative paths as outlined by Yang [J. Chem. Phys. 109, 10107 (1998)]. Specifically, we examine the error-function and Gaussian-attenuated error-function adiabatic connections. We explore the high-density and strong staticcorrelation regimes for two-electron systems. The resulting adiabatic connections give an alternative view of the exchange– correlation problem and their utility for the development of new exchange–correlation functionals in Kohn–Sham and rangeseparated hybrid schemes is discussed.