S, T, f: Excited state properties

Closed-shell molecules exists in stable, singlet ground states (\(S_{0}\)) where all of their electrons are paired in the occupied orbitals. Excitation refers to the promotion of an electron into higher-energy orbitals, typically with the absorption of a photon, transitioning the molecule from its ground state to an excited state: singlets (\(S_{n}\)) for electrons remaining in anti-parallel spin alignment after excitation and triplets (\(T_{n}\)) for parallel-spin electrons.

Radiative decay from singlet states is known as fluorescence. Most fluorescent molecules decay from their \(S_{1}\) state due to rapid internal conversion from higher singlet states - this is known as Kasha’s rule. Direct radiative decay from \(T_{n}\) is phosphorescence, although this is less efficient due to being a spin-forbidden process.

In general, absorption corresponds to the vertical \(S_{0}\) → \(S_{n}\) transition where the molecule’s geometry has not yet relaxed to the minimum of the excited state’s potential energy surface. Emission corresponds to the vertical \(S_{n}\) → \(S_{0}\) transition.

Oscillator strengths correspond to the propensity for the transition to occur and are related to the intensity of a transition. Excitations from \(S_{0}\) → \(T_{n}\) are formally forbidden and have zero oscillator strengths.

In the DiaDEM database, single-molecule, vacuum vertical excitation energies related to absorption are provided, in units of eV, as precomputed properties and are estimated using the Calibrated TDDFT protocol. These are calibrated to experimental values. Oscillator strength values are also provided.

  1. \(E(S_{1})\): \(S_{0}\) → \(S_{1}\) vertical transition energy

  2. \(f(S_{1})\): oscillator strength for the \(S_{0}\) → \(S_{1}\) transition

  3. \(E(S_{2})\): \(S_{0}\) → \(S_{2}\) vertical transition energy

  4. \(f(S_{2})\): oscillator strength for the \(S_{0}\) → \(S_{2}\) transition

  5. \(E(S_{3})\): \(S_{0}\) → \(S_{3}\) vertical transition energy

  6. \(f(S_{3})\): oscillator strength for the \(S_{0}\) → \(S_{3}\) transition

  7. \(E(S_{4})\): \(S_{0}\) → \(S_{4}\) vertical transition energy

  8. \(f(S_{4})\): oscillator strength for the \(S_{0}\) → \(S_{4}\) transition

  9. \(E(T_{1})\): \(S_{0}\) → \(T_{1}\) vertical transition energy

  10. \(E(T_{2})\): \(S_{0}\) → \(T_{2}\) vertical transition energy