  A comprehensive theoretical understanding of electron-photon correlation is
essential for describing the reshaping of molecular orbitals in quantum
electrodynamics (QED) environments. The strong coupling QED Hartree-Fock
(SC-QED-HF) theory tackles these aspects by providing consistent molecular
orbitals in the strong coupling regime. The previous implementation, however,
has significant convergence issues that limit the applicability. In this work
we introduce two second-order algorithms that significantly reduce the
computational requirements, thereby enhancing the modeling of large molecular
systems in QED environments. Furthermore, the implementation will enable the
development of correlated methods based on a reliable molecular orbital
framework.
