Theoretical Determination of the Excited States and of g-Factors of the Creutz−Taube Ion, [(NH3)5−Ru−pyrazine−Ru−(NH3)5]5+

Symmetric Electron Transfer Coordinates are Intrinsic to Bridged Systems: An ab Initio Treatment of the Creutz-Taube Ion

A long-standing question in electron transfer research concerns the number and identity of collective nuclear motions that drive electron transfer or localisation. It is well established that these nuclear motions are commonly gathered into a so-called electron transfer coordinate. In this theoretical study, we demonstrate that both anti-symmetric and symmetric vibrational motions are intrinsic to bridged systems, and that both are required to explain the characteristic shape of their intervalence charge transfer bands. Using the properties of a two-state Marcus-Hush model, we identify and quantify these two coordinates as linear combinations of normal modes from ab initio calculations. This quantification gives access to the potential coupling, reorganization energy and curvature of the potential energy surfaces involved in electron transfer, independent of any prior assumptions about the system of interest. We showcase these claims with the Creutz-Taube ion, a prototypical Class III mixed valence complex. We find that the symmetric dimension is responsible for the asymmetric band shape, and trace this back to the offset of the ground and excited state potentials in this dimension. The significance of the symmetric dimension originates from geometry dependent coupling, which in turn is a natural consequence of the well-established superexchange mechanism. The conceptual connection between the symmetric and anti-symmetric motions and the superexchange mechanism appears as a general result for bridged systems.

Pyrazine-Coordinated Dinuclear and Mononuclear Ruthenium Complexes Formed via the Conversion of the Triply Chlorido-Bridged Diruthenium(II) Complex

The pyrazine-coordinated dinuclear and mononuclear ruthenium complexes were synthesized through the framework conversion reactions of the triply chlorido-bridged diruthenium(II) complex [{RuII,II(bbpma)}2(μ-Cl)3]+ (bbpma; benzylbis(2-pyridylmethyl)amine, [1]+) in the presence of pyrazine, which could function as the simple molecular multinucleation ligand of metal compounds. A reduction reaction of fac-[RuIIICl3(bbpma)] with zinc in the presence of hydrochloric acid afforded [1]+ in solution, and the following addition of pyrazine (1 equiv) in the solution led to the formation of a singly pyrazine (pz)-bridged diruthenium complex, [{RuII,II(μ-Cl2ZnCl2)(bbpma)}2(μ-pz)] ([2(II,II)(ZnCl2)2]). The stoichiometric two-electron oxidation of [2(II,II)(ZnCl2)2] was successfully proceeded, and a Ru(III)-Ru(III) species, [{RuIII,IIICl2(bbpma)}2(μ-pz)](PF6)2 ([III,III](PF6)2), was isolated. The reaction of [1]+ with excess amounts of pyrazine without hydrochloric acid afforded mononuclear Ru(III) and Ru(II) complexes containing one or two pyrazine, fac-[RuClm(pz)3-m(bbpma)]+ (m = 2; [3]+; m = 1; [4]+). The details of the electrochemical and spectroscopic properties of [1]+-[4]+ in organic and aqueous solutions were discussed.

Vibrational Coherences of the Photoinduced Mixed-Valent Creutz-Taube Ion Revealed by Excited State Dynamics

A recent study of photoinduced mixed-valency in the one-electron reduced form (μ-pz)[RuII(NH3)5]24+ of the Creutz-Taube ion used transient absorption spectroscopy with vis-NIR broadband detection to uncover a mixed-valent excited state with a typical intervalence charge transfer band and a nanosecond lifetime [Pieslinger et al. Angew. Chem., Int. Ed. 2022, 61, e202211747]. Herein, we use excited state dynamics simulations with implicit solvation to elucidate the electronic and vibrational evolution in the first 10 ps after the optical excitation. A manifold of excited states with weak interaction between the metal centers is populated already at time zero due to the breakdown of the Condon approximation and dominates the population of electronic states at short time scales (<0.5 ps). A long-lived vibrational wave packet mostly confined to oscillations of the metal center-bridge distances is observed. The oscillations are traced to the electronic structure properties of states with weak metal-metal coupling. The long-lived mixed-valent excited state of the Creutz-Taube ion analogue is formed vibrationally cold and has a more compact geometry. While experimentally, intersystem crossing and vibrational relaxation were deduced to be completed within 1 ps, our analysis indicates that both processes might persist at longer times.

Going beyond the Electric-Dipole Approximation in the Calculation of Absorption and (Magnetic) Circular Dichroism Spectra including Scalar Relativistic and Spin-Orbit Coupling Effects

In this work, a time-dependent density functional theory (TD-DFT) scheme for computing optical spectroscopic properties in the framework of linearly and circularly polarized light is presented. The scheme is based on a previously formulated theory for predicting optical absorption and magnetic circular dichroism (MCD) spectra. The scheme operates in the framework of the full semi-classical field-matter interaction operator, thus generating a powerful and general computational scheme capable of computing the absorption (ABS), circular dichroism (CD), and MCD spectra. In addition, our implementation includes the treatment of relativistic effects in the framework of quasidegenerate perturbation theory, which accounts for scalar relativistic effects (in the self-consistent field step) and spin-orbit coupling (in the TD-DFT step), as well as external magnetic field perturbations. Hence, this formalism is also able to probe spin-forbidden transitions. The random orientations of molecules are taken into account by a semi-numerical approach involving a Lebedev numerical quadrature alongside analytical integration. It is demonstrated the numerical quadrature requires as few as 14 points for satisfactory converged results thus leading to a highly efficient scheme, while the calculation of the exact transition moments creates no computational bottlenecks. It is demonstrated that at zero magnetic field, the CD spectrum is recovered while the sum of left and right circularly polarized light contributions provides the linear absorption spectrum. The virtues of this efficient and general protocol are demonstrated on a selected set of organic molecules where the various contributions to the spectral intensities have been analyzed in detail.

Magnetic circular dichroism spectra of transition metal complexes calculated from restricted active space wavefunctions

Multiconfigurational restricted active space (RAS) self-consistent field (SCF) or configuration interaction (CI) approaches, augmented with a treatment of spin–orbit coupling by state interaction, were used to calculate the magnetic circular dichroism , , and/or for closed- and open-shell transition metal complexes.

Magnetic circular dichroism of UCl6− in the ligand-to-metal charge-transfer spectral region

We present a combined ab initio theoretical and experimental study of the magnetic circular dichroism (MCD) spectrum of the octahedral UCl₆⁻ complex ion in the UV-Vis spectral region.

Magnetic Circular Dichroism Evidence for an Unusual Electronic Structure of a Tetracarbene-Oxoiron(IV) Complex

In biology, high valent oxo-iron(IV) species have been shown to be pivotal intermediates for functionalization of C-H bonds in the catalytic cycles of a range of O₂-activating iron enzymes. This work details an electronic-structure investigation of [Fe^IV(O)(L^NHC)(NCMe)]²⁺ (L^NHC = 3,9,14,20-tetraaza-1,6,12,17-tetraazoniapenta-cyclohexacosane-1(23),4,6(26),10,12(25),15,17(24),21-octaene, complex 1) using helium tagging infrared photodissociation (IRPD), absorption, and magnetic circular dichroism (MCD) spectroscopy, coupled with DFT and highly correlated wave function based multireference calculations. The IRPD spectrum of complex 1 reveals the Fe-O stretching vibration at 832 ± 3 cm^-1. By analyzing the Franck-Condon progression, we can determine the same vibration occurring at 616 ± 10 cm^-1 in the E(d_xy → d_xz,yz) excited state. Both values are similar to those measured for [Fe^IV(O)(TMC)(NCMe)]²⁺ (TMC = 1,4,8,11-tetramethyl-1,4,8,11-tetraazacyclotetradecane). The low-temperature MCD spectra of complex 1 exhibit three pseudo A-term signals around 12 500, 17 000, and 24 300 cm^-1. We can unequivocally assign them to the ligand field transitions of d_xy → d_xz,yz, d_xz,yz → d_z2, and d_xz,yz → d_x2-y2, respectively, through direct calculations of MCD spectra and independent determination of the MCD C-term signs from the corresponding electron donating and accepting orbitals. In comparison with the corresponding transitions observed for [Fe^IV(O) (SR-TPA)(NCMe)]²⁺ (SR-TPA = tris(3,5-dimethyl-4-methoxypyridyl-2-methy)amine), the excitations within the (FeO)²⁺ core of complex 1 have similar transition energies, whereas the excitation energy for d_xz,yz → d_x2-y2 is significantly higher (∼12 000 cm^-1 for [Fe^IV(O)(SR-TPA)(NCMe)]²⁺). Our results thus substantiate that the tetracarbene ligand (L^NHC) of complex 1 does not significantly affect the bonding in the (FeO)²⁺ unit but strongly destabilizes the d_x2-y2 orbital to eventually lift it above d_z2. As a consequence, this unusual electron configuration leads to an unprecedentedly larger quintet-triplet energy separation for complex 1, which largely rules out the possibility that the H atom transfer reaction may take place on the quintet surface and hence quenches two-state reactivity. The resulting mechanistic implications are discussed.

Orbital reconstruction in nonpolar tetravalent transition-metal oxide layers

A promising route to tailoring the electronic properties of quantum materials and devices rests on the idea of orbital engineering in multilayered oxide heterostructures. Here we show that the interplay of interlayer charge imbalance and ligand distortions provides a knob for tuning the sequence of electronic levels even in intrinsically stacked oxides. We resolve in this regard the d-level structure of layered Sr₂IrO₄ by electron spin resonance. While canonical ligand-field theory predicts g_||-factors less than 2 for positive tetragonal distortions as present in Sr₂IrO₄, the experiment indicates g_|| is greater than 2. This implies that the iridium d levels are inverted with respect to their normal ordering. State-of-the-art electronic-structure calculations confirm the level switching in Sr₂IrO₄, whereas we find them in Ba₂IrO₄ to be instead normally ordered. Given the nonpolar character of the metal-oxygen layers, our findings highlight the tetravalent transition-metal 214 oxides as ideal platforms to explore d-orbital reconstruction in the context of oxide electronics.

The iridate compounds display interesting physical properties, including quasi-two-dimensional behaviour similar to cuprates. Bogdanov et al. explore the d-level structure of Sr₂IrO₄ using electron spin resonance measurements and detailed calculations and find it is inverted compared to its normal ordering

Magnetic circular dichroism and computational study of mononuclear and dinuclear iron(IV) complexes

High-valent iron(IV)-oxo species are key intermediates in the catalytic cycles of a range of O2-activating iron enzymes. This work presents a detailed study of the electronic structures of mononuclear ([FeIV(O)(L)(NCMe)]2+, 1, L = tris(3,5-dimethyl-4-methoxylpyridyl-2-methyl)amine) and dinuclear ([(L)FeIV(O)(μ-O)FeIV(OH)(L)]3+, 2) iron(IV) complexes using absorption (ABS), magnetic circular dichroism (MCD) spectroscopy and wave-function-based quantum chemical calculations. For complex 1, the experimental MCD spectra at 2-10 K are dominated by a broad positive C-term band between 12000 and 18000 cm-1. As the temperature increases up to ~20 K, this feature is gradually replaced by a derivative-shaped signal. The computed MCD spectra are in excellent agreement with experiment, which reproduce not only the excitation energies and the MCD signs of key transitions but also their temperature-dependent intensity variations. To further corroborate the assignments suggested by the calculations, the individual MCD sign for each transition is independently determined from the corresponding electron donating and accepting orbitals. Thus, unambiguous assignments can be made for the observed transitions in 1. The ABS/MCD data of complex 2 exhibit ten features that are assigned as ligand-field transitions or oxo- or hydroxo-to-metal charge transfer bands, based on MCD/ABS intensity ratios, calculated excitation energies, polarizations, and MCD signs. In comparison with complex 1, the electronic structure of the FeIV=O site is not significantly perturbed by the binding to another iron(IV) center. This may explain the experimental finding that complexes 1 and 2 have similar reactivities toward C-H bond activation and O-atom transfer.

Charge transfer in strongly correlated systems: an exact diagonalization approach to model Hamiltonians

We study charge transfer in bridged di- and triruthenium complexes from a theoretical and computational point of view. Ab initio computations are interpreted from the perspective of a simple empirical Hamiltonian, a chemically specific Mott-Hubbard model of the complexes' π electron systems. This Hamiltonian is coupled to classical harmonic oscillators mimicking a polarizable dielectric environment. The model can be solved without further approximations in a valence bond picture using the method of exact diagonalization and permits the computation of charge transfer reaction rates in the framework of Marcus' theory. In comparison to the exact solution, the Hartree-Fock mean field theory overestimates both the activation barrier and the magnitude of charge-transfer excitations significantly. For triruthenium complexes, we are able to directly access the interruthenium antiferromagnetic coupling strengths.

Quantum-chemical insights into mixed-valence systems: within and beyond the Robin–Day scheme

The application of quantum-chemical methods to both organic and transition-metal mixed-valence systems is reviewed, with particular emphasis on how to describe correctly delocalisation vs. localisation near the borderline between Robin–Day classes II and III.

Multireference ab initio studies of zero-field splitting and magnetic circular dichroism spectra of tetrahedral Co(II) complexes

A newly developed multireference (MR) ab initio method for the calculation of magnetic circular dichroism (MCD) spectra was calibrated through the calculation of the ground- and excited state properties of seven high-spin (S = 3/2) Co(II) complexes. The MCD spectra were computed by the explicit treatment of spin-orbit coupled (SOC) and spin-spin coupled (SSC) N-electron states. For the complexes studied in this work, we found that the SOC is more important than the SSC for determining the ground state zero field splitting (ZFS). Our computed ZFS parameter D for the [Co(PPh(3))(2)Cl(2)] model complex is -17.6 cm(-1), which is reasonably close to the experimental value of -14.8 cm(-1). Generally, the computed absorption and MCD spectra are in fair agreement with experiment for all investigated complexes. Thus, reliable electronic structure and spectroscopic predictions for medium sized transition metal complexes are feasible on the basis of this methodology. This characterizes the presented method as a promising tool for MCD spectra interpretations of transition metal complexes in a variety of areas of chemistry and biology.

Calculation of EPR g Tensors for Transition-Metal Complexes Based on Multiconfigurational Perturbation Theory (CASPT2)

The computation of the electronic g tensor by two multireference methods is presented and applied to a selection of molecules including CN, BO, AlO, GaO, InO, ZnH, ZnF, O(2), H(2)O(+), O(3) (-), and H(2)CO(+) (group A) as well as TiF(3), CuCl(4) (2-), Cu(NH(3))(4) (2+), and a series of d(1)-MOX(4) (n-) compounds, with M=V, Cr, Mo, Tc, W, Re and X=F, Cl, Br (group B). Two approaches are considered, namely, one in which spin-orbit coupling and the Zeeman effect are included using second-order perturbation theory and another one in which the Zeeman effect is added through first-order degenerate perturbation theory within the ground-state Kramers doublet. The two methods have been implemented into the MOLCAS quantum chemistry software package. The results obtained for the molecules in group A are in good agreement with experiment and with previously reported calculated g values. The results for the molecules in group B vary. While the g values for the d(1) systems are superior to previous theoretical results, those obtained for the d(9) systems are too large compared to the experimental values.

Contrasts in the 77 K Emission Spectra, Structures, and Dynamics of Metal-to-Metal and Metal-to-Ligand Charge-Transfer Excited States

The 77 K emission spectrum of trans-[(ms-Me6[14]aneN4)Cr(CNRu(NH3)5)2]5+ has components characteristic of ligand field (LF) and metal-to-metal charge transfer (MMCT) excited states (ms-Me6[14]aneN4=5,12-meso-5,7,7,12,14,14-hexamethyl-1,4,8,11-tetraazacyclotetradecane). The LF component of the emission is best resolved for irradiations at appreciably higher energies than the MMCT absorption band, while only the MMCT emission is observed for irradiations on the low-energy side of the MMCT absorption band. The LF emission component from this complex has vibronic structure that is very similar to that of the trans-[(ms-Me6[14]aneN4)Cr(CN)2]+ parent, but it is red-shifted by 560 cm-1 and the bandwidths are much larger. The red shift and the larger bandwidths of the ruthenated complex are attributed to configurational mixing between the LF and MMCT excited states, and the inferred mixing parameters are shown to be consistent with the known electron-transfer properties of the Ru(NH3)5 moieties. The MMCT excited-state lifetime is about 1 micros at 77 K and am(m)ine perdeuteration of this complex leads to an isotope effect of kNH/kND approximately 15-20. However, the contribution of the N-H stretching vibration to the emission sideband is too weak for a single vibrational mode model to be consistent with the observed lifetimes or the isotope effect. These features are very similar to those reported previously (J. Phys. Chem. A 2004, 108, 5041) for the MMCT emission of trans-[([14]aneN4)Cr{CNRu(NH3)5}2]5+ ([14]aneN4=1,4,8,11-tetraazacyclotetradecane), with the exception that the higher energy LF emission was not well resolved in the earlier work. The energies of the charge transfer absorption and emission maxima of both of these Cr(CN)Ru complexes are very similar to those of [Ru(NH3)4bpy]2+, but the latter has a 50-fold shorter 77 K excited-state lifetime, a 10-fold smaller NH/ND isotope effect, and a very different structure of its vibronic sidebands. Thus, the vibronic sidebands imply that the dominant excited-state distortions are in the metal-ligand vibrational modes for the Cr(CN)Ru complexes and in the bipyridine vibrational modes for the [Ru(NH3)4bpy]2+ complex. While an "equivalent" single vibrational mode model based on the frequencies and amplitudes of the dominant distortion modes is not consistent the observed lifetimes, such models do appear to be a good basis for qualitatively distinguishing different classes of excited-state dynamic behavior. A multimode, multichannel model may be necessary to adequately describe the excited-state dynamics of these simple electron-transfer systems.