A Spectroscopic and Computationally Minimal Approach to the Analysis of Charge-Transfer Processes in Conformationally Fluxional Mixed-Valence and Heterobimetallic Complexes

The Marcus dimension: identifying the nuclear coordinate for electron transfer from ab initio calculations

The Marcus model forms the foundation for all modern discussion of electron transfer (ET). In this model, ET results in a change in diabatic potential energy surfaces, separated along an ET nuclear coordinate. This coordinate accounts for all nuclear motion that promotes electron transfer. It is usually assumed to be dominated by a collective asymmetric vibrational motion of the redox sites involved in the ET. However, this coordinate is rarely quantitatively specified. Instead, it remains a nebulous concept, rather than a tool for gaining true insight into the ET pathway. Herein, we describe an ab initio approach for quantifying the ET coordinate and demonstrate it for a series of dinitroradical anions. Using sampling methods at finite temperature combined with density functional theory calculations, we find that the electron transfer can be followed using the energy separation between potential energy surfaces and the extent of electron localization. The precise nuclear motion that leads to electron transfer is then obtained as a linear combination of normal modes. Once the coordinate is identified, we find that evolution along it results in a change in diabatic state and optical excitation energy, as predicted by the Marcus model. Thus, we conclude that a single dimension of the electron transfer described in Marcus-Hush theory can be described as a well-defined nuclear motion. Importantly, our approach allows the separation of the intrinsic electron transfer coordinate from other structural relaxations and environmental influences. Furthermore, the barrier separating the adiabatic minima was found to be sufficiently thin to enable heavy-atom tunneling in the ET process.

Quantum Interference in Mixed-Valence Complexes: Tuning Electronic Coupling Through Substituent Effects

Whilst 2- or 5-OMe groups on the bridging phenylene ring in [{Cp*(dppe)RuC≡C}₂ (μ-1,3-C₆ H₄ )]⁺ have little influence on the electronic structure of this weakly coupled mixed-valence complex, a 4-OMe substituent enhances ground state electron delocalization, and increases the intensity of the IVCT transition. Vibrational frequency and TDDFT calculations (LH20t-D3(BJ), def2-SVP, COSMO (CH₂ Cl₂ )) on ([{Cp*(dppe)RuC≡C}₂ (μ-1,3-C₆ H₃ -n-OMe)]⁺ (n=2, 4, 5) models are in excellent agreement with the experimental results. The stronger ground state coupling is attributed to the change in composition of the β-HOSO brought about by the 4-OMe group, which is ortho or para to each of the metal fragments. The intensity of the IVCT transition increases with the greater overlap of the β-HOSO and β-LUSO, whilst the relative phases of the β-HOSO and β-LUSO in the 4-OMe substituted complex are consistent with predictions of constructive quantum interference from molecular circuit rules.

Reliable TDDFT Protocol Based on a Local Hybrid Functional for the Prediction of Vibronic Phosphorescence Spectra Applied to Tris(2,2'-bipyridine)-Metal Complexes

An efficient computational protocol for the prediction of vibrationally resolved phosphorescence spectra is developed and validated for five tris(2,2'-bipyridine)-metal complexes ([M(bpy)₃]ⁿ⁺, where M = Zn, Ru, Rh, Os, Ir). The outstanding feature of this protocol is the use of full linear-response time-dependent density functional theory (TDDFT) for the excited-state triplet calculation, i.e., the commonly seen strategies employing the Tamm-Dancoff approximation (TDA) or unrestricted density functional theory (DFT) calculations for the T₁ state are not needed. This is achieved by the use of a local hybrid functional (LH12ct-SsirPW92) that features a real-space dependent admixture of exact exchange governed by a local mixing function. The excellent performance of this LH for triplet excitation energies known from previous studies transfers to a remarkable mean absolute error of 0.06 eV for the phosphorescence 0-0 energies investigated herein, while the popular B3PW91 functional gives an error of 0.27 eV in TDDFT and 0.09 eV in unrestricted DFT calculations, respectively. The advantages of the local hybrid are particularly apparent for excited states with a mixed-valence character. The influence of spin-orbit coupling was found to be significant for [Os(bpy)₃]²⁺ red-shifting the 0-0 energy for phosphorescence by 0.17 eV, while the effect is negligible for the other complexes (<0.03 eV). The influence of the basis-set and integration-grid sizes is evaluated, and a computationally lighter protocol is validated that leads to drastic savings in computation time with negligible loss in accuracy.

Iron vs. ruthenium: syntheses, structures and IR spectroelectrochemical characterisation of half-sandwich Group 8 acetylide complexes

A synthetic ‘trick’ affording complexes [M(CCR)(dppe)Cp′] (M = Fe, Ru) in high purity directly from the reaction vessel is described.

Metal/Metal Redox Isomerism Governed by Configuration

A pair of diastereomeric dinuclear complexes, [Tp′(CO)BrW{μ‐η²‐C,C′‐κ²‐S,P‐C₂(PPh₂)S}Ru(η⁵‐C₅H₅)(PPh₃)], in which W and Ru are bridged by a phosphinyl(thiolato)alkyne in a side‐on carbon P,S‐chelate coordination mode, were synthesized, separated and fully characterized. Even though the isomers are similar in their spectroscopic properties and redox potentials, the like‐isomer is oxidized at W while the unlike‐isomer is oxidized at Ru, which is proven by IR, NIR and EPR‐spectroscopy supported by spectro‐electrochemistry and computational methods. The second oxidation of the complexes was shown to take place at the metal left unaffected in the first redox step. Finally, the tipping point could be realized in the unlike isomer of the electronically tuned thiophenolate congener [Tp′(CO)(PhS)W{μ‐η²‐C,C′‐κ²‐S,P‐C₂(PPh₂)S}Ru(η⁵‐C₅H₅)‐(PPh₃)], in which valence trapped W^III/Ru^II and W^II/Ru^III cationic species are at equilibrium.

TURBOMOLE: Modular program suite for ab initio quantum-chemical and condensed-matter simulations

TURBOMOLE is a collaborative, multi-national software development project aiming to provide highly efficient and stable computational tools for quantum chemical simulations of molecules, clusters, periodic systems, and solutions. The TURBOMOLE software suite is optimized for widely available, inexpensive, and resource-efficient hardware such as multi-core workstations and small computer clusters. TURBOMOLE specializes in electronic structure methods with outstanding accuracy-cost ratio, such as density functional theory including local hybrids and the random phase approximation (RPA), GW-Bethe-Salpeter methods, second-order Møller-Plesset theory, and explicitly correlated coupled-cluster methods. TURBOMOLE is based on Gaussian basis sets and has been pivotal for the development of many fast and low-scaling algorithms in the past three decades, such as integral-direct methods, fast multipole methods, the resolution-of-the-identity approximation, imaginary frequency integration, Laplace transform, and pair natural orbital methods. This review focuses on recent additions to TURBOMOLE's functionality, including excited-state methods, RPA and Green's function methods, relativistic approaches, high-order molecular properties, solvation effects, and periodic systems. A variety of illustrative applications along with accuracy and timing data are discussed. Moreover, available interfaces to users as well as other software are summarized. TURBOMOLE's current licensing, distribution, and support model are discussed, and an overview of TURBOMOLE's development workflow is provided. Challenges such as communication and outreach, software infrastructure, and funding are highlighted.