Unraveling a Cavity-Induced Molecular Polarization Mechanism from Collective Vibrational Strong Coupling

Do Molecular Geometries Change Under Vibrational Strong Coupling?

“…The corresponding normal modes clearly show a hybridization of the vibrational transition and the cavity photon mode with the polarization axis e 1 . As λ m increases, the Rabi splitting between the LP and UP transitions increases and becomes more asymmetric, consistent with our previous work. , At the same time, a third weaker peak between the LP and UP transitions becomes visible. Similarly to the single-mode case, this peak is due to the coupling between a specific rotational degree of freedom and the photon mode with the polarization axis e 2 .…”

“…In this work, we use the cavity Born–Oppenheimer Hartree–Fock (CBO-HF) ansatz together with analytical gradients to optimize H 2 O and H 2 O 2 resonantly coupled to one and two cavity photon modes. The CBO-HF ansatz is capable of describing the electronic ground state of single molecules, as well as an ensemble of molecules coupled to an optical cavity under VSCs conditions. ,, By optimizing the geometries in the laboratory frame together with the polarization vectors of the cavity, we are able to study both the orientation and the relaxation of the internal coordinates of the molecules induced by the interaction with the cavity photon modes. Furthermore, we compute vibro-polaritonic IR spectra within the harmonic approximation, which allow us to verify the structures found as real minima and to analyze in detail the polaritonic states formed.…”

“…Starting from the nonrelativistic Pauli–Fierz Hamiltonian in the length gauge representation, − we apply the cavity Born–Oppenheimer approximation (CBOA) − to simulate molecules interacting with the confined electromagnetic field in an optical cavity under VSC conditions. By making use of a generalized Born–Huang expansion , the cavity modes are grouped with the nuclei and the resulting electronic subsystem can be solved in an ab initio manner. ,, Atomic units ( ℏ = 4πε 0 = m e = 1) are used in the following unless otherwise noted, and bold symbols denote vectors. The electronic CBOA Hamiltonian for multiple cavity modes takes the form of Ĥ CBO = Ĥ el + ∑ m N M 1 2 ω m 2 q m 2 − ω m q m ( λ m · μ̂ ) + 1 2 ( λ m · μ̂ ) 2 where μ ̂ represents the molecular dipole operator, which is defined by the operators of the N el electron coordinates r ̂ and the classic coordinates R of the N Nuc nuclei.…”

“…Interestingly, the energy change is much larger for the single-mode case (green line) compared to the two-mode case (orange line), although the change in α is comparable. To explain this, we have to consider that the total DSE contribution can be separated into a one-electron and two-electron part. ,, The behavior of the one-electron contribution, which is usually the larger part, can be estimated by the polarizability, while the two-electron contribution is defined by the product of the dipole moment with itself. Since in the single-mode case H 2 O 2 planarizes with increasing coupling strength, its dipole moment decreases and is minimal in the fully planar trans configuration.…”