Analytic Nuclear Gradients and Derivative Couplings for SA-QED-CASSCF
Abstract
Exploring the potential energy surfaces of molecules in optical cavities requires analytical derivatives. We present analytical nuclear gradients and nonadiabatic derivative couplings for state-averaged quantum-electrodynamics complete-active-space self-consistent field theory (SA-QED-CASSCF) forthe coherent-state Pauli–Fierz Hamiltonian, including the coupledperturbed response of the QED-Hartree–Fock reference and the photon contribution to the coupling that arises because the coherent-state displacement depends on the geometry. The derivatives agree with finite differences to within 10−6 atomic units (5×10−6 for the state of smallest weight in an unequal average) for equal, unequal and zero-weight state averaging, and with independent codes without the cavity. With them we locate a polariton-induced conical intersection in LiH, where the cavity makes the molecular orientation a second coordinate and a reflection combined with photon parity makes the crossing symmetry-allowed. In ethylene, the S0/S1 conical intersection persists under coupling and keeps its twisted–pyramidalized geometry, and it becomes more accessible from the Franck–Condon point, because the dipole self-energy raises the diffuse π → 3s state more than the crossing pair. Capturing the partial return of this penalty through the bilinear coupling requires the polarization-axis partner orbital in the active space, a rule for polaritonic CASSCF in general.
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BibTeX
@misc{vu2026analytic,
title = {{Analytic Nuclear Gradients and Derivative Couplings for SA-QED-CASSCF}},
author = {Nam Vu and Jonathan J. Foley},
howpublished = {ChemRxiv},
year = {2026},
month = oct,
doi = {10.26434/chemrxiv.15009951/v1},
url = {https://chemrxiv.org/doi/full/10.26434/chemrxiv.15009951/v1},
note = {CC BY},
}
RIS
TY - UNPB
TI - Analytic Nuclear Gradients and Derivative Couplings for SA-QED-CASSCF
AU - Nam Vu
AU - Jonathan J. Foley
PY - 2026
DA - 2026/10/05
PB - ChemRxiv
DO - 10.26434/chemrxiv.15009951/v1
UR - https://chemrxiv.org/doi/full/10.26434/chemrxiv.15009951/v1
AB - Exploring the potential energy surfaces of molecules in optical cavities requires analytical derivatives. We present analytical nuclear gradients and nonadiabatic derivative couplings for state-averaged quantum-electrodynamics complete-active-space self-consistent field theory (SA-QED-CASSCF) forthe coherent-state Pauli–Fierz Hamiltonian, including the coupledperturbed response of the QED-Hartree–Fock reference and the photon contribution to the coupling that arises because the coherent-state displacement depends on the geometry. The derivatives agree with finite differences to within 10−6 atomic units (5×10−6 for the state of smallest weight in an unequal average) for equal, unequal and zero-weight state averaging, and with independent codes without the cavity. With them we locate a polariton-induced conical intersection in LiH, where the cavity makes the molecular orientation a second coordinate and a reflection combined with photon parity makes the crossing symmetry-allowed. In ethylene, the S0/S1 conical intersection persists under coupling and keeps its twisted–pyramidalized geometry, and it becomes more accessible from the Franck–Condon point, because the dipole self-energy raises the diffuse π → 3s state more than the crossing pair. Capturing the partial return of this penalty through the bilinear coupling requires the polarization-axis partner orbital in the active space, a rule for polaritonic CASSCF in general.
ER -