The symmetry-broken formalism applied to the electronic structure of an iminosemiquinone copper(II) catalyst: a key to the qualitative understanding of its reactivity.

A concise outline of the known derivation of the singlet-triplet energy-gap equations within the symmetry-broken wavefunction framework is given. They allow a computation of the singlet-triplet energy gap for molecules that exhibit a weak antiferromagnetic coupling of electrons. The accuracy of the equations is assessed by computation of the singlet-triplet gaps in model Na2 molecules. Various antiferromagnetic coupling strengths are simulated by the use of different Na-Na bond lengths in the computations. The singlet-triplet energy gaps obtained with the different equations are compared with the gaps computed with the more accurate coupled-cluster methods. Subsequently, the equations are applied to an iminosemiquinone copper(II) complex found previously to have remarkable catalytic properties. The application is performed by employing wave-function equations but with quantities computed within the density functional framework. The electronic ground state of this complex is computed to be a singlet state, which is also the experimental finding. Moreover, the experimental geometry and the singlet-triplet gap are reasonably reproduced by the computation. A straightforward method to determine the magnetic orbitals is suggested and applied. We illustrate that the form of the magnetic orbitals indicates in a qualitative manner that hydrogen-atom abstraction should be a major reaction pathway of the iminosemiquinone copper(II) complex. Hydrogen-atom abstraction has been suggested previously to be the rate-determining step in a catalytic process initiated by the iminosemiquinone copper(II) complex. The results support the notion that the form of the magnetic orbitals might be a qualitative indicator for the reactivity of molecules that exhibit weak antiferromagnetic coupling.

The photochemistry of 1,3-butadiene rationalized by means of theoretical resonance structures and their weights

A complete active-space self-consistent-field wave function for the pi-electron part of s-trans-1,3-butadiene has been expanded into a set of localized bonding schemes and their weights. These bonding schemes are close to the resonance structures used in organic chemistry. The expansion technique has been applied to both the electronic ground state and the electronically first-excited singlet and triplet pi,pi* states. The manifolds of large-weight bonding schemes represent approximate resonance hybrids for the ground and the singlet and triplet pi,pi* states of s-trans-1,3-butadiene. These resonance hybrids, obtained by theory alone, permit a qualitative rationalization of a significant part of the known singlet and triplet photochemistry.