Theoretical Considerations Concerning the Intramolecular Heavy-Atom Effect on the Phosphorescence Process: C2v Symmetric Dihalonaphthalene

Interactions leading to the observed intramolecular heavy‐atom effect on the phosphorescence process of C_2v dihalonaphthalenes have been examined. Using one electron operator, the observed heavy‐atom effects in these molecules are found to be due to: (1) Mixing between the P_π orbitals of the halogen and the π system of the aromatic hydrocarbon. (2) First‐order spin—orbit interaction between the lowest π, π^* triplet state and σ, π^* (or π, σ^*) singlet states (this explains Subspectrum I). (3) Second‐order spin—orbit—vibronic interaction between the lowest π, π^* triplet state and π, π^* (or σ, σ^*) singlet states (this accounts for the appearance of Subspectrum II). These mechanisms are found to give rise to one‐center spin—orbit terms on the halogen atom (as well as halogen—carbon two‐ and higher‐center terms). First‐order spin—orbit interaction between singlet and triplet π, π^* states is found to have vanishing one‐ and two‐center terms involving the halogen orbitals. Direct spin—orbit interaction between π, π^* states in haloaromatics does not give rise to intramolecular heavy‐atom effect. Mechanisms involving the first‐order spin—vibronic terms of the total Hamiltonian are found to give predictions inconsistent with the observed results and thus seem to be unimportant. The S.O. matrix elements for the ${}^1{A}_1{\mathrm{(\sigma ,\sigma }}^{*}\hspace{0.17em}\mathrm{or}{\mathrm{\hspace{0.17em}\pi ,\pi }}^{*}{\mathrm{)\leftrightarrow }}^3{B}_1{\mathrm{(\sigma ,\pi }}^{*}\hspace{0.17em}\mathrm{or}{\mathrm{\hspace{0.17em}\pi ,\sigma }}^{*})$ is found to vanish for 1,4‐ but not for the 2,3‐dihalonaphthalene. This result, together with the fact that the ¹A₁ (σ,σ^*)←¹A₁ transition has zero moment for 1,4‐dihalonaphthalene but not for the 2,3 derivative, leads to the conclusion that for the 1,4 compound, only the ¹B₂ (σ,σ^* or σ,σ^*) (short axis polarized) is an important perturbing singlet state while both the ¹B₂ and the ¹A₁ are perturbing the emitting triplet state in the 2,3 derivative. This is found to be in agreement with the observed fact in glasses at 77°K that in the 1,4 derivative, Subspectrum II is highly polarized and parallel to the ¹L_a←¹A₁ transition (short axis polarized) whereas in the 2,3 derivative, Subspectrum II is almost depolarized with respect to ¹L_a excitation. Using the proposed mechanism it is shown, in agreement with observation, that the relative importance of Mechanism I (giving rise to Subspectrum I) to that of II is practically independent of the atomic number of the halogen. The fact that Mechanisms I and II are comparably important even though Mechanism I involves a first‐order interaction whereas II involves a second‐order interaction is shown to result from the great difference in the values of the oscillator strength of the perturbing singlet states involved in the two mechanisms.