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. It is shown that while the error-function connection displays some promising features, making it amenable to the possible development of new exchange-correlation functionals by modeling the adiabatic connection integrand, the Gaussian-attenuated error-function connection is less promising. We explore the high-density and strong static correlation regimes for two-electron systems. Implications of this work for the utility of range-separated schemes are discussed.