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Like adiabatic time-dependent density-functional theory (TD-DFT), theBethe-Salpeter equation (BSE) formalism of many-body perturbation theory, inits static approximation, is "blind" to double (and higher) excitations, whichare ubiquitous, for example, in conjugated molecules like polyenes. Here, weapply the spin-flip \textit{ansatz} (which considers the lowest triplet stateas the reference configuration instead of the singlet ground state) to the BSEformalism in order to access, in particular, double excitations. The presentscheme is based on a spin-unrestricted version of the $GW$ approximationemployed to compute the charged excitations and screened Coulomb potentialrequired for the BSE calculations. Dynamical corrections to the static BSEoptical excitations are taken into account via an unrestricted generalizationof our recently developed (renormalized) perturbative treatment. Theperformance of the present spin-flip BSE formalism is illustrated by computingexcited-state energies of the beryllium atom, the hydrogen molecule at variousbond lengths, and cyclobutadiene in its rectangular and square-planargeometries.

Spin-Conserved and Spin-Flip Optical Excitations From the Bethe-Salpeter Equation Formalism