sEDA, pEDA, and cSAR descriptors of the substituent effect were determined for >30 monosubstituted benzenes in the first excited singlet S state at the LC-ωB97XD/aug-cc-pVTZ level. It was found that in the S state, the σ- and π-valence electrons are a bit less and a bit more affected, respectively, than in the S state, but basically, the effect in both states remains the same. In the S and S states, the d(C-X) distances to the substituent's first atom and the ring perimeter correlate with the sEDA and pEDA in the appropriate states, respectively. The energies and the gap of the frontier orbitals in the two states are linearly correlated and for the HOMO(S), LUMO(S), and HOMO(S)-LUMO(S) gap correlate also with the pEDA(S) and cSAR(S) descriptors. In all studied correlations, three similar groups of substituents can be distinguished, for which correlations (i) are very good, (ii) deviate slightly, and (iii) deviate significantly. Comparison of the shape of the HOMO(S) and HOMO(S) orbitals shows that for case (i) HOMO orbitals exhibit almost perfect antisymmetry against the benzene plane, for case (ii) the antisymmetry of HOMO in one of the states is either perturbed or changed, and for case (iii) one HOMO state has σ-character.
The structure of
30 monosubstituted benzenes
in the first excited triplet T1 state
was optimized with both unrestricted (U) and restricted open shell
(RO) approximations combined with the ωB97XD/aug-cc-pVTZ basis
method. The substituents exhibited diverse σ- and π-electron-donating
and/or -withdrawing groups. Two different positions of the substituents
are observed in the studied compounds in the T1 state:
one distorted from the plane and the other coplanar with a quinoidal
ring. The majority of the substituents are π-electron donating
in the first group while π-electron withdrawing in the second
one. Basically, U- and RO-ωB97XD approximations yield concordant
results except for the B-substituents and a few of the planar groups.
In the T1 state, the studied molecules are not aromatic,
yet aromaticity estimated using the HOMA (harmonic oscillator model
of aromaticity) index increases from ca. −0.2 to ca. 0.4 with
substituent distortion, while in the S1 state, they are
only slightly less aromatic than in the ground state (HOMA ≈0.8
vs ≈1.0, respectively). Unexpectedly, the sEDA(T1) and pEDA(T1) substituent effect descriptors do not correlate
with analogous parameters for the ground and first excited singlet
states. This is because in the T1 state, the geometry of
the ring changes dramatically and the sEDA(T1) and pEDA(T1) descriptors do not characterize only the functional group
but the entire molecule. Thus, they cannot provide useful scales for
the substituents in the T1 states. We found that the spin
density in the T1 states is accumulated at the Cipso and Cp atoms, and with the substituent deformation angle,
it nonlinearly increases at the former while decreases at the latter.
It appeared that the gap between singly unoccupied molecular orbital
and singly occupied molecular orbital (SUMO-SOMO) is determined by
the change of the SOMO energy because the former is essentially constant.
For the nonplanar structures, SOMO correlates with the torsion angle
of the substituent and the ground-state pEDA(S0) descriptor
of the π-electron-donating substituents ranging from 0.02 to
0.2 e. Finally, shapes of the SOMO-1 instead of SOMO
frontier orbitals in the T1 state somehow resemble the
highest occupied molecular orbital ones of the S0 and S1 states. For several planar systems, the shape of the U- and
RO-density functional theory-calculated SOMO-1 orbitals differs substantially.
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