Spin-Flip Configuration Interaction for Strong Static Correlation in Quantum Electrodynamics

Abstract

In computational chemistry of molecular materials, strong static correlation effects appear when electronic states, often involving the ground state, become quasi-degenerate, as occurs, for example, in bond-breaking processes. Such situations present significant challenges for accurate theoretical treatment. In these regimes, many-body methods involving a single-determinant description, such as Hartree-Fock theory and its time-dependent extension, fail to reproduce the correct topology of the ground and excited state potential energy surfaces (e.g., near conical intersections). When strongly correlated electronic systems are further strongly coupled to a quantized radiation field within the framework of non-relativistic cavity quantum electrodynamics, an additional photonic degree of freedom introduces both new complexity and new opportunities to control. Excited cavity photons can modify bond-breaking processes and enable tunability of geometrical and spin-phase transitions, for instance, in organometallic complexes. To overcome this bottleneck, in this work, we extend the well-studied spin-flip configuration interaction singles (SF-CIS) approach to explicitly include quantized cavity photons leading to QED-SF-CIS method. We derive the spin-flip Hamiltonian and find that the double excitation subspace of the system (single with respect to electronic excitation) must be included in the configurations to properly describe singlet electronic states interacting with cavity photons. We then illustrate, through representative molecular examples, how cavity coupling can provide additional tunability in bond-breaking processes. We finally generalize this approach to include higher numbers of photonic excitations, which are required in the strong coupling regime.

Figures (6)

• Figure 1: Singlet and triplet potential energy surfaces of the (a) H$_2$ dissociation coordinate $R_\mathrm{HH}$ and (b) ethylene dihedral angle $\phi_\mathrm{HCCH}$ at various levels of theory.
• Figure 2: Potential energy surfaces of the four lowest-energy singlet polaritonic states S$_0$, S$_1$, S$_2$, and S$_3$ of the polaritonic system with $\omega_\mathrm{c} = 0.10$ a.u. (2.71 eV) for light-matter coupling strengths $\lambda$ = (a) 0.00, (b) 0.02, and (c) 0.04 a.u. The colorbar indicates the average photon character, $N_i = \langle \mathrm{S}_i |\hat{a}^\dagger \hat{a} | \mathrm{S}_i \rangle$ for each polaritonic state. At $\lambda = 0.0$ a.u., the non-interacting configurations are shown at $\phi_\mathrm{HCCH} = 0\degree$. Note that the character of the adiabatic states changes with nuclear configuration, $\phi_\mathrm{HCCH}$.
• Figure 3: (a) Rabi splitting $\Omega_\mathrm{R} (\lambda,\phi_\mathrm{r}) = E_2(\lambda,\phi_\mathrm{r}) - E_1(\lambda, \phi_\mathrm{r})$ as a function of the light-matter coupling strength $\lambda$ for the dihedral which satisfies the resonance condition $\phi_\mathrm{r}$ ($E_2(\lambda = 0,\phi_\mathrm{r}) - E_1(\lambda = 0,\phi_\mathrm{r}) = 0$ at $\lambda = 0$ a.u.).. (b) Singlet-triplet ground state gap, $\Delta E_\mathrm{ST}(\lambda) = E^\mathrm{T}_0(\lambda,\phi_\mathrm{HCCH} = 90\degree) - E^\mathrm{S}_0(\lambda,\phi_\mathrm{HCCH} = 90\degree)$ The cavity frequency was set to $\omega_\mathrm{c} = 0.10$ a.u. (2.71 eV).
• Figure 4: Potential energy surfaces of the singlet polaritonic ground state $S_0$ and the triplet ground state $T_1$ as functions of the dihedral angle $\phi_\mathrm{HCCH}$ of ethylene for a set of light-matter coupling strengths $\lambda$ = 0.00 (black), 0.10 (red), 0.20 (blue), 0.30 (green), 0.40 (orange), 0.50 (purple) with $\omega_\mathrm{c} = 0.10$ a.u. (2.71 eV). The linear fit (red) indicates the power of 1.9823 (nearly quadratic) for $\lambda < 0.05$ a.u.
• Figure 5: Potential energy surfaces along the ethylene dihedral twist angle $\phi_\mathrm{HCCH}$ at varying number of Fock states $N_\mathrm{Fock}$ = 2 (blue), 3 (red), and 4 (grey). Four values of light-matter coupling strength are shown: $\lambda$ = (a) 0.00, (b) 0.01, (c) 0.02, and (d) 0.05 a.u. At $\lambda = 0.0$ a.u., the non-interacting configurations are shown at $\phi_\mathrm{HCCH} = 0\degree$. Note that the character of the adiabatic states changes with nuclear configuration, $\phi_\mathrm{HCCH}$.