  We describe the implementation of the frozen-orbital and downfolding
approximations in the auxiliary-field quantum Monte Carlo (AFQMC) method. These
approaches can provide significant computational savings compared to fully
correlating all the electrons. While the many-body wave function is never
explicit in AFQMC, its random walkers are Slater determinants, whose orbitals
may be expressed in terms of any one-particle orbital basis. It is therefore
straightforward to partition the full N-particle Hilbert space into active and
inactive parts to implement the frozen-orbital method. In the frozen-core
approximation, for example, the core electrons can be eliminated in the
correlated part of the calculations, greatly increasing the computational
efficiency, especially for heavy atoms. Scalar relativistic effects are easily
included using the Douglas-Kroll-Hess theory. Using this method, we obtain a
way to effectively eliminate the error due to single-projector, norm-conserving
pseudopotentials in AFQMC. We also illustrate a generalization of the
frozen-orbital approach that downfolds high-energy basis states to a physically
relevant low-energy sector, which allows a systematic approach to produce
realistic model Hamiltonians to further increase efficiency for extended
systems.
