Magnetic Properties of Conjugated Hydrocarbons from Topological Hamiltonians

On Entangled Singlet Pure Diradicals

This work addresses a class of conjugated hydrocarbons that are expected to be singlet diradicals according to the topological Hückel Hamiltonian while possibly satisfying full on-bond electron pairing. These systems possess two degenerate singly occupied molecular orbitals (SOMOs), but aromaticity brought by properly positioned six-membered rings does prevent Jahn-Teller distortions. Density functional theory (DFT) calculations performed on two emblematic examples confirm the strong bond-length alternation in the closed-shell solutions and the clear spatial symmetry in the open-shell spin-unrestricted determinants, the latter solution always being found to have significantly lower energy. Since the SOMOs are here of different symmetry, the wave function is free from ionic valence-bond component, and spin decontamination of the unrestricted DFT solutions and wave function calculations at the CASSCF-plus-second-order-perturbation level confirm the expected pure diradical character of such molecules. In contrast to disjoint diradicals, the SOMOs of present systems have large amplitudes on neighbor atoms, and we propose to name them entangled pure diradicals, further providing some prescription rules for their design. Additional calculations point out the qualitative contrast between these molecules and the related diradicaloids.

Difficulty of the evaluation of the barrier height of an open-shell transition state between closed shell minima: The case of small C4n rings

C_4n cyclacenes exhibit strong bond-alternation in their equilibrium geometry. In the two equivalent geometries, the system keeps an essentially closed-shell character. The two energy minima are separated by a transition state suppressing the bond-alternation, where the wave function is strongly diradical. This paper discusses the physical factors involved in this energy difference and possible evaluations of the barrier height. The barrier given as the energy difference between the restricted density functional theory (DFT)/B3LYP for the equilibrium and the broken symmetry DFT/B3LYP of the transition state is either negative or small, in contradiction with the most reliable Wave Function Theory calculations. The minimal (two electrons in two molecular orbitals) Complete Active Space self-consistent field (CASSCF) overestimates the barrier, and the subsequent second-order perturbation cancels it. Due to the collective character of the spin-polarization effect, it is necessary to perform a full π CASSCF + second-order perturbation to reach a reasonable value of the barrier, but this type of treatment cannot be applied to large molecules. DFT procedures treating on an equal foot the closed-shell and open-shell geometries have been explored, such as Mixed-Reference Spin-Flip Time-dependent-DFT and a new spin-decontamination proposal, namely, DFT-dressed configuration interaction, but the results still depend on the density functional. M06-2X without or with spin-decontamination gives the best agreement with the accurate wave function results.

Assessing the Calculation of Exchange Coupling Constants and Spin Crossover Gaps Using the Approximate Projection Model To Improve Density Functional Calculations

This work evaluates the quality of exchange coupling constant and spin crossover gap calculations using density functional theory corrected by the approximate projection model. Results show that improvements using the approximate projection model range from modest to significant. This study demonstrates that, at least for the class of systems examined here, spin projection generally improves the quality of density functional theory calculations of J-coupling constants and spin crossover gaps. Furthermore, it is shown that spin projection can be important for both geometry optimization and energy evaluations. The approximate projection model provides an affordable and practical approach for effectively correcting spin-contamination errors in such calculations.

Communication: Proper use of broken-symmetry calculations in antiferromagnetic polyradicals

The present comment formulates some recommendations regarding the use of broken-symmetry Unrestricted Density Functional Theory (UDFT) solutions in those polyradical architectures predicted to be of ground-state singlet character according to Ovchinnikov's rule. It proposes a procedure to identify the number of open shells, to reach the relevant Ms = 0 solution, and to estimate the low-energy spectrum of the states which keeps this number of open shells.