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 static-correlation 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.

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