[Al₂O₄]⁻, a Benchmark Gas-Phase Class II Mixed-Valence Radical Anion for the Evaluation of Quantum-Chemical Methods

Abstract

The radical anion [Al2O4](-) has been identified as a rare example of a small gas-phase mixed-valence system with partially localized, weakly coupled class II character in the Robin/Day classification. It exhibits a low-lying C2v minimum with one terminal oxyl radical ligand and a high-lying D2h minimum at about 70 kJ/mol relative energy with predominantly bridge-localized-hole character. Two identical C2v minima and the D2h minimum are connected by two C2v-symmetrical transition states, which are only ca. 6-10 kJ/mol above the D2h local minimum. The small size of the system and the absence of environmental effects has for the first time enabled the computation of accurate ab initio benchmark energies, at the CCSDT(Q)/CBS level using W3-F12 theory, for a class-II mixed-valence system. These energies have been used to evaluate wave function-based methods [CCSD(T), CCSD, SCS-MP2, MP2, UHF] and density functionals ranging from semilocal (e.g., BLYP, PBE, M06L, M11L, N12) via global hybrids (B3LYP, PBE0, BLYP35, BMK, M06, M062X, M06HF, PW6B95) and range-separated hybrids (CAM-B3LYP, ωB97, ωB97X-D, LC-BLYP, LC-ωPBE, M11, N12SX), the B2PLYP double hybrid, and some local hybrid functionals. Global hybrids with about 35-43% exact-exchange (EXX) admixture (e.g., BLYP35, BMK), several range hybrids (CAM-B3LYP, ωB97X-D, ω-B97), and a local hybrid provide good to excellent agreement with benchmark energetics. In contrast, too low EXX admixture leads to an incorrect delocalized class III picture, while too large EXX overlocalizes and gives too large energy differences. These results provide support for previous method choices for mixed-valence systems in solution and for the treatment of oxyl defect sites in alumosilicates and SiO2. Vibrational gas-phase spectra at various computational levels have been compared directly to experiment and to CCSD(T)/aug-cc-pV(T+d)Z data.

Iron versus Ruthenium: Clarifying the Electronic Differences between Prototypical Mixed-Valence Organometallic Butadiyndiyl Bridged Molecular Wires

“…In order to provide a better description of the spin-density distribution, and in particular better electronic excitation spectra in TDDFT calculations (see below), single point calculations using the local hybrid functional Lh-SsirPW92-D3 44 were performed (with D3-type dispersion corrections), using a recent efficient implementation. [45][46] Related local hybrids, which in contrast to BLYP35 or B3LYP exhibit position-dependent rather than constant exact-exchange admixture, have recently been shown to provide a good description of both localized and delocalized mixed-valence systems, 47 while reducing the spin contamination compared to "global" hybrids with high exact exchange, such as BLYP35. The structures were not optimized with local hybrids, as the higher computational demand of the current gradient implementation for local hybrids was not warranted by the expected small structural improvements.…”

“…44 The local hybrid functional is constructed according to where the constant admixture parameter a (global hybrid functional, e.g. 0.35 for BLYP35, 0.2 for B3LYP) has been replaced by a real-space dependent local mixing function a(r): a(r) = 0.646 τ W /τ , where τ W and τ are the von Weizsäcker and the Kohn-Sham kinetic-energy densities, respectively.This and closely related local hybrids have not only been found to perform extremely well in TDDFT calculations of a wide range of excitation classes,70 but such functionals also have interesting properties regarding the treatment of mixed-valence systems,47 thus extending our general computational protocol. The calculations used the recent efficient semi-numerical implementation of local hybrids into TURBOMOLE 7.161…”

Electronic Structures of Divinylchalcogenophene‐Bridged Biruthenium Complexes: Exploring Trends from O to Te

“…To gain further insight concerning the influence of the chalcogenide on the electronic structures of 4a – 4d , DFT calculations were performed by using the BLYP35 functional [LANL2DZ for Ru, Se and Te, 6‐31G** for all other atoms, COSMO(CH 2 Cl 2 )] , , . The 35 % direct exchange contribution in the BLYP35 global hybrid functional proved to be well‐suited to the study of both localised and delocalised organic and organometallic mixed‐valence complexes . Structures were optimised without constraints and shown to be true minima by frequency analysis.…”

“…[8,111,112] The 35 % direct exchange contribution in the BLYP35 global hybrid functional proved to be well-suited to the study of both localised and delocalised organic and organometallic mixed-valence complexes. [113][114][115][116][117][118][119] Structures were optimised without constraints and shown to be true minima by frequency analysis. The geometry optimisation consistently returned the all-trans-4-s-cis structures determined crystallographically for 4b-4d, but no minimum structure corresponding to the all-trans-2-s-trans-4-s-cis conformation in the crystal structure of 4a could be identified.…”

Highly Accurate CCSDT(Q)/CBS Reaction Barrier Heights for a Diverse Set of Transition Structures: Basis Set Convergence and Cost-Effective Approaches for Estimating Post-CCSD(T) Contributions

“…1,2,3,4,5 In particular, the CCSD(T) method (i.e., CC with single, double, and quasiperturbative triple excitations) 6,78 has been extensively used for obtaining reaction barrier heights in a wide range of chemical systems (for a few recent examples see refs. 9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24). With the increase in available computational power and efficiency of quantum chemical codes, the calculation of reaction barrier heights with higher-order CC methods (normally up to CCSDT(Q)) has become more prevalent over the past decade.…”