We use the quantum mechanical description of the molecule-cavity hybrid system using the Pauli-Fierz Hamiltonian in the dipole gauge, as shown in the following Eq. 1, to investiagte how cavity vacuum fluctuations induce modifications to the ground state. ĤPF = Ĥel + Ĥph + ω c A 0 μ • ê(â † + â) + ω c A 2 0 ( μ • ê) (1) Ĥel is the electronic Hamiltonian under the Born-Oppenheimer approximation, which is without the nuclear kinetic energy operator, Ĥph = ω c â † â is the Hamiltonian of the cavity field, â † and â are the raising and lowering operators of the cavity field, ê is a unit vector indicating the field polarization direction, and μ is the dipole operator of the molecule. The last two terms are the direct light-matter coupling Ĥel-ph and the dipoleself energy (DSE) ĤDSE , respectively. Moreover, the light-matter coupling strength is expressed as