Metaphenylene-Based Nitroxide Diradicals: A Protocol To Calculate Intermolecular Coupling Constant in a One-Dimensional Chain

Abstract

Intramolecular magnetic exchange coupling constants are determined for seven isolated metaphenylene-based dinitroxide diradicals by unrestricted density functional methodology (UDFT) using a number of hybrid functionals such as B3LYP, B3LYP-D3, M06-2X, HSE, and LC-ωPBE. Geometry optimizations for both triplet and broken symmetry solutions are performed with the 6-311G(d,p) basis set for all the molecules. In all cases, B3LYP somewhat overestimates the coupling constant, and M06-2X produces a more realistic value. The range-separated HSE and LC-ωPBE functional yield large deviations from experiment. The nature of spin coupling agrees with the spin alternation rule and the calculated spin densities, in conjunction with the McConnell rule. It can also be explained in terms of the nondisjoint Single Occupied Molecular Orbital effect. Furthermore, it correlates with the calculated NICS(1) isotropic and zz and hyperfine coupling constants. We also put forward a method for the determination of the intramolecular (J) and intermolecular (J') coupling constants from quantum chemical calculations on a one-dimensional chain of weakly bound diradicals. Two expressions are derived for the energies of different spin states in terms of J and J'. Exemplary UDFT computations are done on the N-mers (N = 2-6) of two diradicals for which the crystal coordinates are available. The intramolecular and intermolecular coupling constants are determined from the calculated UDFT energies. These are indeed in general agreement with the measured coupling constants.

Intriguing diaza effects on magnetic coupling characteristics in diaza‐benzo[k]tetraphene‐bridged nitroxide diradicals

“…As listed in Table , the calculated NICS(0) and NICS(1) are negative for different 6‐membered rings within parent diradical, indicating that all five rings are aromatic. However, the aromaticity is generally unfavorable to the diradical character and blocks the spin exchange couplings . Nevertheless, after diaza‐functionalization the conversion in the aromaticity of the coupler from parent diradical occurs for 1 .…”

“…A large basis set 6‐311++G(3df,2p) was employed for single‐point calculations to further confirm the rationality of the computational results using B3LYP function. Moreover, we also adopted a more modern M06‐2X functional to verify the calculated results once again, which could perform better than the B3LYP functional in describing the electronic structure and properties of open‐shell systems . To understand the effect of the aromaticity on the magnetic couplings, we calculated the nucleus‐independent chemical shifts (NICS) at the center or at a point 1 Å above the different six membered ring centers (Scheme ) in each coupler for all diradicals with the more stable states (ground states) at the B3LYP/6‐311++G(d,p) level using the GIAO methodology.…”

“…In general, the DFT-based methods including B3LYP tend to overestimate the J values, [14,16,[51][52][53][54] which might well be attributed to the fact that DFT-based functionals fail to correct the inherent self-interaction errors, leading to an artificial stronger delocalization of the unpaired electrons. [52,53] The use of hybrid functional can reduce the self-interaction errors to some extent and the B3LYP functional has been broadly accepted to evaluate the J values of many organic diradical systems, providing relatively good accordance with experimental values.…”

“…[7,9,52,53] To yield more reliable J values of these diradicals, more polarization and diffuse functions are generally added to the basis sets demonstrated by Datta et al and other researchers. [7][8][9][14][15][16]18,38,39,[52][53][54] In consideration of these, we selected the B3LYP functional with an adequately large basis set 6-311++G(d,p) to evaluate the J values for the newly designed diradicals in this study. It is feasible to observe the convergence in calculations of three possible low-lying states including the closed-shell (CS) singlet state, BS open-shell singlet state and triplet (T) state.…”

Tuning the Spin Coupling Interactions in the Nitroxide‐Based Bisphenol‐Like Diradicals

“…Besides, the B3LYP functional is known to often overestimate the J value. Hence, a more modern M06‐2X function is also taken into consideration to estimate the J values using a 6‐311++G(d,p) basis set . Also, single‐point calculations were done at the CASSCF(10,10)/6‐311++G(d,p) level including 5 highest occupied molecular orbitals (HOMOs) and 5 lowest unoccupied molecular orbitals (LUMO) as the active space to predict the diradical character of all the open‐shell BS states through calculating the occupation numbers of their LUMOs, and to obtain the singlet‐triplet energy differences of some representative molecules, proving the reasonableness of our results.…”