  The ever-growing intersection of quantum electrodynamics (QED) and molecular
processes has shown remarkable and unanticipated advancements in altering
molecular properties and reactivity by exploiting light-matter couplings. In
recent years, multiple ab initio methods have been developed to compute the
eigenstates of molecular systems strongly coupled to cavities, ranging from the
mean-field to quantum many-body methods. The quantum many-body methods, such as
coupled-cluster theories, usually rely on the quality of mean-field reference
wavefunctions. Hence, developing efficient and physically reliable mean-filed
approaches for molecular quantum electrodynamics problems is crucial. The
current widely used methods, such as QED Hartree-Fock and the self-consistent
counterpart, are limited to specific coupling regimes. In this work, we
developed a variational transformation-based molecular quantum electrodynamics
mean-field method, namely VT-QEDHF, for light-matter interaction at arbitrary
coupling strength. The numerical benchmark demonstrates that the VT-QEDHF
method naturally connects both QEDHF and self-consistent QEDHF methods at the
two limits, showcasing the advantage of VT-QEHDF across all coupling strengths.
