Embedded (emb-) correlated wavefunction (CW) theory enables accurate assessments of both ground- and excited-state reaction mechanisms involved in heterogeneous catalysis. Embedded multireference second-order perturbation theory (emb-MRPT2) based on reference wavefunctions generated via embedded complete active space self-consistent field (emb-CASSCF) theory is currently state-of-the-art. However, the factorial scaling of CASSCF limits the size of active space and the complexity of systems that can be studied. In this work, we assess the efficacy of an alternative CW method, adaptive sampling configuration interaction (ASCI)?which enables large active spaces to be used?for studying surface reactions. We couple ASCI with density functional embedding theory (DFET) and benchmark its performance for two reactions: H<
sub>
2<
/sub>
desorption from and CH<
sub>
4<
/sub>
dissociation on the Cu(111) surface. Unlike embedded complete active space second-order perturbation theory (emb-CASPT2) that accurately reproduces a measured H<
sub>
2<
/sub>
desorption barrier, embedded ASCI, using a very large active space (though one that still comprises a small portion of the full set of orbitals) fails to do so. Adding an extra correlation term from embedded M�ller?Plesset second-order perturbation theory (emb-MP2) improves the desorption barrier and endothermicity predictions. Thus, the inaccuracy of embedded ASCI comes from the missing dynamic correlation from the many other electrons and orbitals not included in the active space. For CH<
sub>
4<
/sub>
dissociation, again embedded ASCI overestimates the dissociation barrier compared to emb-CASPT2 predictions. Adding dynamic correlation from emb-MP2 helps correct the barrier. However, this composite approach suffers from double counting of correlation within embedded ASCI followed by emb-MP2 calculations. We therefore conclude that the state-of-the-art emb-MRPT2 based on reference wavefunctions generated via emb-CASSCF remains the method of choice for studying surface reactions. emb-ASCI is useful when large active spaces beyond the limit of emb-CASSCF are essential, such as to study complex surface reactions with significant multiconfigurational character (static correlation) but weak dynamic correlation.