  We discuss the multispecies time-dependent restricted-active-space
self-consistent-field theory, an \textit{ab initio} wavefunction-based theory
for mixtures of ultracold atomic and molecular gases. We present the general
theory, based on the time-dependent variational principle, and derive the
equations of motion. The theory captures in a time-dependent setting, via the
specification of the restricted-active-space scheme, different levels of
approximation from the mean-field to the full configuration interaction
approach. To assess its accuracy and to illustrate its ability to identify
correlation effects at successive approximation levels, we apply the theory to
compute the ground state energy of a Bose-Bose mixture interacting through a
harmonic potential, for which the exact ground state energy is known
analytically. We focus on the case of an ideal Bose gas interacting with a few
impurities. The intra-species interaction between the impurities is relatively
strong compared to the inter-species interaction between the impurities and the
ideal noninteracting Bose gas. For this system, we find that an accurate
description of the ground state necessitates the possibility of the theory to
account for few-particle excitations out of the condensed phase; a situation
well accounted for by the present restricted-active-space theory for mixtures;
and not within reach for approaches not incorporating orbital-restriction
schemes.
