  An alternative nonunitary transcorrelation, inspired by the F12 ansatz, is
investigated. In contrast to the Jastrow transcorrelation of Boys-Handy, the
effective Hamiltonian of this projective transcorrelation features: 1. a series
terminating formally at four-body interactions. 2. no spin-contamination within
the non-relativistic framework. 3. simultaneous satisfaction of the singlet and
triplet first-order cusp conditions. 4. arbitrary choices of pairs for
correlation including frozen core approximations. We discuss the connection
between the projective transcorrelation and F12 theory with applications to
small molecules, to show that the cusp conditions play an important role to
reduce the uncertainty arising from the nonunitary transformation.
