where 𝜔 is the frequency of the incident photons, 𝛼 is the fine structure constant, 𝑐 is the speed of light, 𝑎 0 is the Bohr radius, 𝑔 is the broadening function (typically Lorentzian or Gaussian, depending on the broadening mechanism ) and 𝛿 TPA is the orientationally-averaged two-photon transition strength, which can be determined based on electronic-structure theories (see below). Despite significant developments, an accurate theoretical estimation of 𝜎 TPA in molecules remains challenging due to the necessity of using advanced quantum chemistry methods, including electron correlation effects and relying on a large basis set. Many efforts have been made to find efficient methods capable of computing TPA in a cost-effective manner. Validation of the results of new computational methodologies can be approached in two ways: by comparisons with experimental data, or by comparison with benchmark values. The former approach presents several challenges, as reproducing experimental 𝜎 TPA requires consideration of multiple factors such as solvent effects and vibrational couplings. Moreover, 𝜎 TPA depends on 𝜔 2 and 𝛿 TPA , each introducing distinct sources of error in the computations, potentially leading to misleading interpretations. The choice of an appropriate broadening function and the proper selection of constants in Eq. 1 are also subjects of debate. For these reasons, direct comparison of 𝛿 TPA with more accurate (albeit expensive) wavefunction methods is generally preferred to establish the accuracy of computational methods. In the case of a linearly polarized light, for an excited state 𝑖, the general formulation of 𝛿 TPA standing for both Hermitian and non-Hermitian theories is: