Strong Coupling Møller-Plesset Perturbation Theory

Abstract

Perturbative approaches are methods to efficiently tackle many-body problems, offering both intuitive insights and analysis of correlation effects. However, their application to systems where light and matter are strongly coupled is nontrivial. Specifically, the definition of suitable orbitals for the zeroth-order Hamiltonian represents a significant theoretical challenge. While reviewing previously investigated orbital choices, this work presents an alternative polaritonic orbital basis suitable for the strong coupling regime. We develop a quantum electrodynamical (QED) Møller-Plesset perturbation theory using orbitals obtained from the strong coupling QED Hartree-Fock. We assess the strengths and limitations of the different approaches with emphasis on frequency and coupling strength dispersions, intermolecular interactions and polarization orientational effects. The results show the essential role of using a consistent molecular orbital framework in order to achieve an accurate description of cavity-induced electron-photon correlation effects.

Figure 1

Coupling dispersions for an ammonia molecule. The cavity frequency is set to ω = 8.16 eV, while the polarization ϵ is along the C₃ axis. For realistic coupling values, λ ≤ 0.05 a.u., all the methods show the same increasing trend. For SC-QED-MP2, the inclusion of electron-photon correlation at the mean-field level becomes important for larger couplings.

Figure 2

Frequency dispersions for an ammonia molecule. The cavity light-matter coupling is set to λ = 0.05 a.u., while the polarization ϵ is along the C₃ axis. The SC-QED-MP2 approach reproduces well the QED-CCSD trend for the whole range of ω.

Figure 3

Dissociation curves for two H₂ molecules in an optical cavity with frequency and light-matter coupling set to ω = 27.2 eV and λ = 0.01 a.u. On the left the polarization ϵ is orthogonal to the displacement direction, while on the right it has a component . When the polarization has a component along the displacement direction the QED-MP2 method displays an unphysical behavior in the long-range regime.

Figure 4

Dissociation curves for two water molecules in a hydrogen bonding geometry inside a cavity. The frequency is set to ω = 8.16 eV, while the polarization ϵ is along to the displacement direction. The light-matter coupling is set to λ = 0.005 a.u. on the left and λ = 0.01 a.u. on the right. The unphysical behavior displayed by QED-MP2 is enhanced at higher couplings.

Figure 5

Dissociation curves inside a cavity for a benzene and a water molecule in two different geometries. For both cases the frequency is set to ω = 2.27 eV, while light-matter the coupling is set to λ = 0.005 a.u. The polarization ϵ is along to the displacement direction. The unphysical behavior displayed by QED-MP2 changes an unbounded intermolecular interaction into a bounded one (see plot on right).

Figure 6

Comparison between SC-QED-MP2 and LF-MP2 dissociation curves for two H₂ molecules in an optical cavity with frequency and light-matter coupling set to ω = 2.72 eV and λ = 0.01 a.u. The polarization ϵ is along the displacement direction. The LF-MP2 method displays the same unphysical behavior as QED-MP2.

Figure 7

Field polarization ϵ orientational effects on chloroethylene (a) and water (b) inside an optical cavity with frequency and the light-matter coupling set to ω = 2.72 eV and λ = 0.01 a.u. For both molecules, two orthogonal rotations of the field polarization are shown.