The electronic structure of benzene from a tiling of the correlated 126-dimensional wavefunction

Abstract

The electronic structure of benzene is a battleground for competing viewpoints of electronic structure, with valence bond theory localising electrons within superimposed resonance structures, and molecular orbital theory describing delocalised electrons. But, the interpretation of electronic structure in terms of orbitals ignores that the wavefunction is anti-symmetric upon interchange of like-spins. Furthermore, molecular orbitals do not provide an intuitive description of electron correlation. Here we show that the 126-dimensional electronic wavefunction of benzene can be partitioned into tiles related by permutation of like-spins. Employing correlated wavefunctions, these tiles are projected onto the three dimensions of each electron to reveal the superposition of Kekulé structures. But, opposing spins favour the occupancy of alternate Kekulé structures. This result succinctly describes the principal effect of electron correlation in benzene and underlines that electrons will not be spatially paired when it is energetically advantageous to avoid one another.

The Ground State Electronic Energy of Benzene

“…Popularly ascribed to a vivid dream of a serpent biting its own tail, the original conjugated structure was soon nuanced in favour of a more balanced, D 6h -symmetric resonance picture of benzene. 3,4 However, studies of the finer details of its electronic structure continue to be in vogue to this day, [5][6][7][8][9][10][11][12] and an account of its intra-as well as intermolecular physical effects remains a key constraint on a great number of ab initio simulations in the field of computational (bio-)chemistry. [13][14][15][16][17][18][19][20][21][22] Even more so, benzene-alongside, for instance, water-may easily be named among the members of an exclusive subset of molecules which are identifiable by wider parts of the public.…”

Hybrid Boron-Carbon Chemistry

“…Benzene is a colorless liquid, with a characteristic odor, volatile, very flammable and carcinogenic. This molecule is the paradigm of Hückel theory [ 1 ] and the concept of aromaticity itself, with a very interesting debate reaching our days on the role of its correlation energy and the π electron spin-pairing [ 27 ]. As opposed to the previous example, the singlet-triplet energy gaps for benzene and cyclic hexaborane(12) B 6 H 12 are quite similar, 8 kJ·mol −1 larger in benzene, due to the aromatic nature of the latter.…”

Synchronizing chemistry, quantum mechanics and radioactivity in a revolutionary renewed atom model. Part 1: the elements whereZis 1–10 (H, He, Li, Be, B, C, N, O, F, Ne)

“…Or in other words, a resonance system is created that answers the famous Kekulé benzene-structure problem from 1865. 29, 30 Other examples of P * N À T P resonance, namely between C and O, will be dealt with in paragraph 2.4.…”