Electronic Transitions in Different Redox States of Trinuclear 5,6,11,12,17,18‐Hexaazatrinaphthylene‐Bridged Titanium Complexes: Spectroelectrochemistry and Quantum Chemistry

Abstract Multinuclear transition metal complexes bridged by ligands with extended π‐electronic systems show a variety of complex electronic transitions and electron transfer reactions. While a systematic understanding of the photochemistry and electrochemistry has been attained for binuclear complexes, much less is known about trinuclear complexes such as hexaphenyl‐5,6,11,12,17,18‐hexaazatrinaphthylene‐tristitanocene [(Cp2Ti)3HATN(Ph)6]. The voltammogram of [(Cp2Ti)3HATN(Ph)6] shows six oxidation and three reduction waves. Solution spectra of [(Cp2Ti)3HATN(Ph)6] and of the electrochemically formed oxidation products show electronic transitions in the UV, visible and the NIR ranges. Density functional theory (DFT) and linear response time‐dependent DFT show that the three formally titanium(II) centers transfer an electron to the HATN ligand in the ground state. The optically excited transitions occur exclusively between ligand‐centered orbitals. The charged titanium centers only provide an electrostatic frame to the extended π‐electronic system. Complete active self‐consistent field (CASSCF) calculation on a structurally simplified model compound, which considers the multi‐reference character imposed by the three titanium centers, can provide an interpretation of the experimentally observed temperature‐dependent magnetic behavior of the different redox states of the title compound in full consistency with the interpretation of the electronic spectra.


SI-1 Instrumentation
NIR spectra were measured with a fiber-coupled Matrix-F FT-NIR spectrometer (Bruker Optik GmbH, Ettlingen, Germany) equipped with a halogen lamp as NIR source and an InGaAs detector. Spectra were taken in the range from 12000 to 4000 cm -1 with a resolution of 8 cm -1 . For each measurement 16 scans were accumulated. UV-Vis spectra were taken with a GetSpec 2048 CCD array spectrometer (GetSpec, Sofia, Bulgaria). The device configuration allowed a resolution of 2.4 nm in the range of 200 to 1000 nm. For the measurements, an integration time of 100 ms was used. Both spectrometers were coupled to a spectroelectrochemical cell (ALS Co., LTD, Tokyo, Japan) located inside an Ar-filled glove box ( Figure S1) using 600 µmdiameter N227 quartz fibers (Bruker Optik GmbH).

SI-2 Attempted interpretation of the electronic spectra within single electron model Attempted orbital model and assignment of transitions
Despite very coarse assumptions required and their known severe limitations, [1] we attempted an assignment of all transitions in an experimentally derived single electron (orbital) picture for all redox states using the formal potential E°' of the electron transfer reactions from Table  1 and the energies of the electronic transitions in Figure 4. This attempt is documented here. Despite its the perceived inner consistency, this assignment could not be reproduced by quantum chemical calculations due to the inherent limitations of the MO model discussed in 2.2 and the consequences of the coarse assumptions required.
The correlation between the spectroscopic and electrochemical data in a semi-quantitative approach involved i) Definition of a ground state configuration using experimental solid-state magnetic data ii) The definition of a Fermi energy for dispersed molecular systems iii) Interpretation of observed electronic transitions within a single electron picture, i.e. equating the spectroscopically observed energy of the electronic transition as the difference between two orbital energies iv) Definition of a "Fermi energy" of molecular systems as the mean between HOMO and LUMO or to the value of a SOMO. This energy is equated with the Fermi energy from ii) v) Recalculation of the electrochemical data to the vacuum level Definition of the ground state configuration (i). The general MO scheme is derived from common textbook MO schemes, where metal orbitals and ligand orbitals form MOs, in which the metal-centered d-type orbitals are the frontier orbitals (2 eg and 3 tg orbitals for tetrahedral complexes). [2] The highest occupied ligand  orbital (referred to as HOMO in the following schemes) is the first orbital below the d-eg set and the lowest unoccupied * orbital of the ligand (referred to as LUMO) represents the first orbital above the d t2 set. Note that the MO-scheme of the HATN-ligand as represented schematically in Figure 5 has already been simplified in this approach. For the neutral complex it is known from magnetic susceptibility measurements that this compound is not a closed shell system in respect to the ligand. [3] At least one electron has to be transferred from one Ti(II) center to a ligand orbital, forming a Ti(III) center and one ligandcentered SOMO. Based on the irreversibility of the reduction of HATN -, the transfer of only one electron has been assumed, although a transfer of more than one electron would be an option. Ground states of other redox states were derived from this ground state by subsequent addition or removal of electrons. Note that theoretical calculations in section 2.3-2.5 of the main manuscript showed that actually all metal centers of the neutral complex are Ti(III).

Definition of Fermi levels for dispersed molecules (ii).
In case two redox forms of one molecular system are dissolved in an electrolyte, the "Fermi level of electrons" can be set to the Nernst-Potential of an inert electrode in this solution [4] and recalculated to the vacuum level (vi). In our case, one redox form of a complex with total charge z+ is dissolved in an electrolyte solution. This metal complex can undergo a one-electron oxidation with a formal potential E°´(X +z /X +(z+1) ). The complex can also undergo a one-electron reduction with a formal potential E°´(X +(z-1) /X +z ). The Fermi energy of the redox state X +n on the electrochemical potential scale is than taken as midterm potential Em = ½[ E°´(X +(z-1) /X +z ) + E°´(X +z /X +(z+1) )] between two adjacent one-electron oxidation and one-electron reduction in the cyclic voltammogram. At the potential Em, there is an equal probability that the complex accepts an electron from an inert electrode or transfers an electron to the electrode. The concentrations of the adjacent redox states are exactly equal, provided the oxidation and reduction is kinetically fast, which is the case in our system. Equating the energy of the spectroscopy transition to the difference of orbital energies (iii). This is a consequence of assuming a single electron picture for the interpretation of the spectroscopic transitions. In that picture transitions can be interpreted as electron transitions between discrete orbitals. The starting point for assignment of transitions between ligand orbitals is the energy spacing between HOMO, LUMO and if applicable SOMO. The energetic position of the SOMO within the MO scheme is fixed by the -*, - r and  r -* transitions. Typically, those electronic transition can be identified in the experimental spectra due to their characteristic shape. The index r marks transitions involving single occupied (radical) orbitals because these show special spin selection rules. Please, note that the SOMO may be filled or emptied in other redox states. The transitions which could not be assigned to this set of  orbitals were assumed to be charge transfer transitions between ligand and metal centers. The energies of the d-type orbitals are then derived from these assumed charge transfer bands. However, this empirical approach does not guarantee for correctness of the assumption as the quantum chemical calculations illustrate for [(Cp2Ti)3HATN(Ph)6].
Definition of a "Fermi energy" of molecular systems as the mean between HOMO and LUMO (iv). The "Fermi energy" is taken as the mid-value between HOMO and LUMO, or as the energy of the SOMO. This value is equated to the value derived in ii) from electrochemical data and is used to place energy levels of different redox states on an absolute scale.
Recalculation of the electrochemical data to the absolute energy scale (v). The assessment of the spectroscopic data provides the relative orbital energies for one oxidation state, whereas the electrochemical data show the relative shift of the orbital sets if one compound is reduced or oxidized. To provide a complete picture for comparison of all redox states, the relative energies are referred to the vacuum level. The electrode potentials are measured against the ferrocene/ferrocenium (Fc/Fc + ) redox couple, which is referenced to the standard hydrogen electrode by E°'(Fc/Fc + ) = (0.400  0.005) V vs. SHE. [5] (S1) The electrode potentials against the SHE are than recalculated against the SHE scale according to the IUPAC recommendation [6] Evac = -e  ESHE -(4.440.02) eV.

Assignment of transitions for each charge state
Below the qualitative assignment is detailed, which is summarized in Figure S2. The codes for the transitions are from Figure 4. . Transitions involving single occupied ligand orbital are marked with  r (radical). As spins are parallel within one Ti center but may be antiparallel between different Ti centers, d electron spins are indicated as II.

Construction of an Energy Diagram
From the assignments in Figure S2 and the spectra ( Figure 4 of the main manuscript) one can construct the "orbital diagram" in an energy scale [7] (Figure S3). For this purpose, the data from the electrochemical experiments are transformed to the absolute energy scale by Eq. (S3). From the assignments Figure S3, it is evident that the positions of Ti-centered orbitals are not affected if an electron is removed from the SOMO (HOMO', LUMO') orbital, which seems to be purely ligand-centered. However, if electrons are instead removed from the Ti centers the energetic position of all orbitals in the complex is affected indicating an interaction of the d-orbitals with the ligand.
When the complex is oxidized from -3 to -2 charge state, an electron is removed from antibonding t orbital (because of simplicity all t2 orbitals are denoted in the text as t orbitals), and this influences all orbitals by shift of -0.5 eV. In the next oxidation (from -2 to -1), the electron is removed from the π-system (HOMO' becomes SOMO). The Ti-centered orbitals do not change energy because these orbitals are not interacting with the HOMO' (now SOMO). In next oxidation, an electron is removed from the Ti-centered orbital and, because of π-back bonding, all orbitals are shifted by about -0.5 eV. In the ground state the complex is in the triplet state because of electron paring of two single occupied orbitals (Ti(III)(e) and SOMO). When the titanium complex is oxidized from 0 to +1, removing an electron from the SOMO orbital (now LUMO') and again the titanium centered orbitals do not change energy. The energy difference between LUMO and LUMO' becomes smaller because one unpaired electron is removed from the SOMO orbital, and the complex is again in the doublet state. In oxidation from +1 to +2 charge state, an electron is removed from a Ti-centered orbital and because of π-back bonding, all orbitals are shifted by -0.5 eV to lower energies.
Calculation of orbital diagrams. The midterm potential (Em) is taken as the arithmetic mean of two neighboring redox potentials determined from DPV measurement (vs. Fc/Fc + ), ( Figure  2 of main manuscript). It indicates a potential at which a certain charge state of the complex is stable, i.e. an oxidation to the next higher or a reduction to a lower charge state are equally likely. In the absence of a SOMO orbital in a certain charge state of the complex, this value is taken to be equal to the mean value of the LUMO and the HOMO in that charge state. In the presence of a SOMO orbital, this value corresponds to the energy of SOMO orbital. After this assignment which places the different charge states relatively to each other, the remaining orbital positions were constructed using transition energies from absorption spectra. Orbitals which do not contribute to an electronic transition were omitted from orbital diagrams.
The orbitals of Ti(III) centers have lower energies than those of Ti(II) because removing further electrons from the same metal center becomes increasingly difficult when electrons have already been removed before. The energetic difference between the Ti(III) and the Ti(II) orbitals is always the same and calculated to be 0.16 eV from the optical transition of the neutral complex. The energetic difference between the Ti(t) and the Ti(e) was taken to be 1.65 eV. This value was calculated from data of the neutral complex.

Charge state 0.
The Em was determined to be -1.34 V vs. Fc/Fc + or 3.50 eV vs. Vac according to Eq. (S3). This is the energy of the SOMO. The Em was determined to be -0.315 V vs. Fc/Fc + or -4.52 vs. Vac according to Eq. (S3). The value of -4.52 eV corresponds to the mean value between the lowest unoccupied (LUMO') and the highest occupied level (Ti(II)(e)).
Calculation from absorption spectra The transition between LUMO and the Ti(II)(e) is the MLCT. Since the exact values of the MLCTs are not known for this state, approximation was made that the MLCT has the same value as in +1 charge state, this laces the Ti(II)(e) (-4.97 eV) and the LUMO' (-4.07 eV). Calculation from absorption spectra The transition between Ti(II)(t) and HOMO' is the LMCT. Energy of this transition is lower than 0.5 eV (in this case it was taken the approximation that this transition is at 0.4 eV). From this information the energy of the HOMO' (-2.60 eV) and the Ti(II)(t) (-2.20 eV) was calculated. For this charge state it was approximated that the Em was -2.97 V vs. Fc/Fc + or -1.87 eV vs. Vac according to Eq. (S3). This approximation is based on the observation that the potential difference between the E°´ values of the 0/-1, -1/-2, -2/-3 redox pair is very similar. This differences were averaged and half of that difference was subtracted from E°'(-2/-3) to arrive at an estimation of Em for the -3 charge state. The value of -1.87 eV corresponds to the middle value between the lowest unoccupied (Ti(II)(t)) and the highest occupied level (HOMO').
Calculation from absorption spectra. The transition between these two levels is the LMCT which energy is lower than 0.5 eV (in this case it was taken the approximation that this transition is at 0.3 eV). From this information the energy of the HOMO' (-2.02 eV) and the Ti(II)(t) (-1.72 eV) was calculated.   The energy is referenced to the vacuum level on the left ordinate and to the formal potential of the Fc/Fc + redox couple on the right ordinate. As spins are parallel within one Ti center but may be antiparallel between different Ti centers, d electron spins are indicated as II.
The orbital picture discussed above is not a good approximation of the ground state of [(Cp2Ti)3HATN(Ph)6]. Although the susceptibility measurements showed the electron transfer to the ligand, the number of transferred electrons cannot be ascertained from the solid-state measurements. In connection with the electrochemical stability of the Ti-free ligand, the transfer of only one electron was assumed in a first assessment. This was also in line with the necessity of a SOMO for explaining the NIR - transitions.
Concerning the NIR CT transitions, the MO model discussed above could not explain the disappearance of CT bands for the charge state +2. For assessing the contradictions between experimental results and the MO based assignment, DFT calculations were conducted. At this point the limitations of a such simple model became obvious: The arising multiconfigurational problem as evident from DFT calculation needs to be solved by high level quantum calculations. Afterwards, this can be translated back to "partially occupied (single particle) orbitals". However, in such a situation it becomes impossible to describe an electronic transition as a transition between two orbitals. Rather it should be considered as a transition between two N-electron wave functions. Furthermore, our quantum chemical calculations demonstrate, that the MO-diagram of the ligand in the experimental approach was oversimplified and the electronic configuration with the assumption of a transfer of only one electron to the ligand was not justified. In conclusion, the attempt to derive "orbital diagrams" from experimental data alone should be regarded with great caution, since experimental data simply do not allow for an unambiguous assignment of spectral transitions and a subsequent "construction" of "orbital diagrams" due to a lack of atomistic information.

SI-4 XYZ files of calculated structures
The atom positions in the different calculations are given below.