Diradicalar Character and Ring Stability of Mesoionic Heterocyclic Oxazoles and Thiazoles by Ab Initio Mono and Multi-Reference Methods

Mesoionics are neutral compounds that cannot be represented by a fully covalent or purely ionic structure. Among the possible mesomeric structures of these compounds are the diradical electronic configurations. Theoretical and experimental studies indicate that some mesoionic rings are unstable, which may be related to a significant diradical character, that until then is not quantified. In this work, we investigated the diradical character of four heterocycles: 1,3-oxazol-5-one, 1,3-oxazol-5-thione, 1,3-thiazole-5-one, and 1,3-thiazole-5-thione. The oxazoles are known to be significatively less stable than thiazoles. DFT and ab initio single (B3LYP, MP2, CCSD, and QCISD) and ab initio multi-reference (MR-CISD) methods with three basis sets (6-311+G(d), aug-cc-pVDZ, and aug-cc-pVTZ) were employed to assess the diradical character of the investigated systems, in gas phase and DMSO solvent, from three criteria: (i) HOMO-LUMO energy gap, (ii) determination of energy difference between singlet and triplet wave functions, and (iii) quantification of the most significant diradical character (y₀, determined in the unrestricted formalism). All of the results showed that the diradical character of the investigated systems is very small. However, the calculated electronic structures made it possible to identify the possible origin of the oxazoles instability, which can help the design of mesoionic systems with the desired properties.

Partition of optical properties into orbital contributions

A new tool to analyze the response property through the partition of nonlinear optical properties in terms of orbital contributions (PNOC), valuable in the assessment of the electronic structure methods in the NLOPs computations, is presented.

Approximate Spin-Projected Density-Based Romberg Differentiation Procedure to Evaluate the Second-Hyperpolarizability of p-Quinodimethane and Twisted Ethylene and Their Diradical Character Dependence

The evaluation of the static second hyperpolarizability (γ) of diradical species is a challenging task due to the use of spin-unrestricted methods, which may suffer from spin contamination. Here, we present the methodological aspect of a density-based differentiation procedure to evaluate static polarizability and hyperpolarizabilities. The finite-field calculations are done on the spin-projected electron density to remove the spin contamination, and the automatized Romberg's differentiation procedure is used to improve the numerical accuracy in the finite-field method. This implementation is tested in the present report for the challenging case of the evaluation of the second hyperpolarizability of the singlet ground state of p-quinodimethane (PQM) for the equilibrium geometry as well as for a stretched geometry where the diradical character of PQM is increased, and for twisted ethylene models where the diradical character changes with the dihedral angle. The application of the approximate spin-projected (ASP) scheme leads to a major improvement of the density functional theory calculations. In particular, for PQM models, BHandHLYP functional reproduces the UCCSD(T) values when the diradical character is below 0.5. The visualization of the γ-densities shows that (i) when increasing the diradical character, the amount of γ-density increases on the -CH2(•) extremities, and (ii) the ASP scheme decreases the amount of "p-like" γ-density for diradical character below 0.4, and increases it for larger diradical character. For twisted ethylene model, we show that the UCCSD(T) reference values can be reproduced by the ASP-UB3LYP method for y < 0.4 and by the ASP-UBHandHLYP method for y > 0.6. To best reproduce the UCCSD(T) reference calculations, the amount of exact exchange in hybrid functionals needs to be tuned along the range of diradical characters.