A generalized adiabatic connection is developed for density functional theory. The method extends the well-known adiabatic connection formula and provides a general link between the Kohn-Sham and the physical system. When the complimentary error function is used as a special case, the expression for the exchange-correlation functional does not have the 1/r(12) Coulomb component. The exact contributions from the physical system and the noninteracting system are established: The physical system limit has a dominant contribution, while the noninteracting system limit has no contribution.