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

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 Kekule structures. But, opposing spins favour the occupancy of alternate Kekule 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 electronic structure of benzene has been a test bed for competing theories along the years. Here the authors show via quantum chemistry calculations that the wavefunction of benzene can be partitioned into tiles which show that the two electron spins exhibit staggered Kekule structures.