Are Multicentre Bond Indices and Related Quantities Reliable Predictors of Excited-State Aromaticity?

Abstract

Systematic scrutiny is carried out of the ability of multicentre bond indices and the NOEL-based similarity index dAB to serve as excited-state aromaticity criteria. These indices were calculated using state-optimized complete active-space self-consistent field wavefunctions for several low-lying singlet and triplet states of the paradigmatic molecules of benzene and square cyclobutadiene and the inorganic ring S2N2. The comparison of the excited-state indices with aromaticity trends for individual excited states suggested by the values of magnetic aromaticity criteria show that whereas the indices work well for aromaticity reversals between the ground singlet and first triplet electronic states, addressed by Baird’s rule, there are no straightforward parallels between the two sets of data for singlet excited states. The problems experienced while applying multicentre bond indices and dAB to singlet excited states are explained by the loss of the information inherently present in wavefunctions and/or pair densities when calculating the first-order density matrix.

Excited-State Aromaticity Reversals in Möbius Annulenes

“…Relaxation of the D 9h geometry along one of the normal modes associated with this imaginary frequency, followed by re-optimization at the same level, produced a non-planar local minimum of C s symmetry, corresponding to "folding" of the D 9h geometry along one of the C 0 2 symmetry axes. This result is not entirely unexpected, because the next annulene ring, [10]annulene, a Hückel 4n C 2 conjugated system which should be aromatic in its ground state, is well-known to have several local minimum conformers of similar energies, none of which is planar. 60,61 Similarly, the potential energy surfaces for the T 1 and S 1 electronic states of C 9 H C 9 can be expected to include various local mimima, the theoretical studies of which may become of interest when and if more experimental information about these states becomes available.…”

“…A more detailed analysis carried out by Baird led to the formulation of Baird’s rule, which states that Hückel’s 4 n + 2 and 4 n criteria for electronic ground-state (S 0 ) aromaticity in cyclic conjugated hydrocarbons are switched in the lowest triplet state (T 1 ): Rings with 4 n π electrons become aromatic while those with 4 n + 2 π electrons end up as antiaromatic. Similar changes in aromaticity have been shown to take place in the lowest singlet excited state (S 1 ). − Excited-state aromaticity reversals in molecules with Hückel aromatic or antiaromatic electronic ground states have been attracting considerable theoretical and experimental interest. − Understanding this type of molecular behavior can help in the design of molecular photoswitches , and molecular motors − and explain experimental evidence for photochemical reactions such as excited-state intramolecular proton transfers. , Theoretical studies suggest that excited-state aromaticity reversals are not limited to cyclic conjugated hydrocarbons but can also occur in inorganic rings, such as disulfur dinitride (S 2 N 2 ); S 0 –T 1 aromaticity reversals have been predicted for several all-metal systems …”

“…Similar changes in aromaticity have been shown to take place in the lowest singlet excited state (S 1 ). [5][6][7][8][9][10] Excited-state aromaticity reversals in molecules with Hückel aromatic or antiaromatic electronic ground states have been attracting considerable theoretical and experimental interest. [11][12][13][14][15] Understanding this type of molecular behavior can help in the design of molecular photoswitches 15,16 and molecular motors, [17][18][19] and explain experimental evidence for photochemical reactions such as excited-state intramolecular proton transfers.…”

Investigating István Mayer's “improved” definitions of bond orders and free valence for correlated singlet‐state wave functions

“…The underlying problem remains after the inclusion of these correction terms, namely the reliance on one‐electron density matrices (and thus occupation numbers). Such density matrices do of course reflect the multi‐reference character but they can, as has been shown previously [17], nonetheless obscure important details that are apparent in the CASSCF wave functions, such as the degree of partial diradical character.…”

“…As our final group of examples, we now use correlated wave functions for ground and excited singlet states of benzene, S 2 N 2 and square (D 4 h ) cyclobutadiene to investigate “improved” definitions of multicenter indices ( k > 3) for such aromatic and antiaromatic systems. Instead of considering the C 4 H 4 and C 6 H 6 rings in terms of separate C and H atoms, as was done in our recent study [17], we have chosen here to perform the analysis in terms of merged CH domains. We find that the values of the free valence index F CH for these hydrocarbon rings all lie in the range 2.81–2.98, with no sign of any link to whether a given state is aromatic or antiaromatic.…”