Quantum Chemical Study of the Inter Ligand Electron Transfer in Ru

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Quantum Chemical Study of the Inter Ligand Electron Transfer in Ru Polypyridyl Complexes Gerard Alcover-Fortuny, Jianfang Wu, Rosa Caballol, and Coen de Graaf J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.7b11422 • Publication Date (Web): 22 Dec 2017 Downloaded from http://pubs.acs.org on December 23, 2017

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The Journal of Physical Chemistry

Quantum Chemical Study of the Inter-ligand Electron Transfer in Ru Polypyridyl Complexes Gerard Alcover-Fortuny,† Jianfang Wu,† Rosa Caballol,∗,† and Coen de Graaf†,‡ †Departament de Qu´ımica F´ısica i Inorgànica, Universitat Rovira i Virgili, Marcel·l´ı Domingo s/n, 43007 Tarragona, Spain ‡ICREA, Pg. Lluis Companys 23, 08010 Barcelona, Spain. E-mail: [email protected]

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ACS Paragon Plus Environment

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Abstract Quantum chemical calculations have been performed to study the photocycle of [Ru(bpy)3 ]2+ , a complex that is extensively used as electron donor in photocatalytic reactions. After the initial spin-allowed excitation from the non-magnetic ground state to a singlet state of metal-to-ligand charge transfer character, the system undergoes a rapid intersystem crossing to a triplet state of equal character. The calculations indicate a life time of 10 fs, in good agreement with experimental estimates. Important factors for this extremely fast intersystem crossing are the large spin-orbit coupling and the large vibrational overlap of the states involved. Both MLCT states are delocalized over the three bipyridine ligands, but the delocalized electron can easily increase its degree of localization. The hopping parameters have been calculated and found to be large for the localization on two ligands and subsequently on one. The combination of localization and geometry relaxation creates a rather long-lived trapped triplet MLCT state with a calculated life time of 9 µs. The addition of methyl groups on the bipyridine ligands decrease the ligand field and consequently lower the metal centered triplet states. This could eventually lead to the opening of a fast deactivation channel of the 3 MLCT

states to the initial non magnetic states via the triplet ligand field states as

occurs in the corresponding Fe(II) complex.

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Introduction

Ru(II) polypyridyl complexes have attracted a lot of interest because of their role in photoinduced electron or energy transfer reactions in supramolecular systems that are used to convert sunlight in chemical energy. These Ru complexes are easily reduced in the excited state and the released electron can be captured by an acceptor group and used in secondary reactions. The excited states are typically accessible upon light irradiation including solar energy, coining the basis of the extensive use of Ru(II) polypyridyl complexes. 1–4 Consequently, these systems are not only extensively studied in the lab, but have also been subject of many theoretical studies, 5–13 especially the prototype complex [Ru(bpy)3 ]2+ (bpy = 2,2’-bipyridine), depicted in Fig. 1. The ground state of this complex is a singlet (S0 ) with the six d-electrons of the Ru(II) ion paired in the 4d(t2g ) orbitals. The photochemistry of the complex is dominated by three types of electronically excited states depending on which orbitals are involved in the excitation. In the first place, there are the metal-centered (MC) states involving transitions from the basically non-bonding t2g to the anti-bonding eg Ru-4d orbitals. Because of the quasi octahedral coordination sphere of Ru, these transitions are only weakly allowed and the MC states are normally not directly populated from the ground state. Secondly, the metal-to-ligand charge transfer (MLCT) states have transition energies similar to or slightly smaller than the MC states. Since they are in general not dipole forbidden, these transitions are responsible for the absorption of (part of) the incident light. The transitions involve electron replacements from the Ru-4d(t2g ) orbitals to antibonding π orbitals (π ∗ ) on the bipyridine ligands. Finally, at slightly higher energies, we can find the ligand-centered (LC) excitations involving π and π ∗ orbitals of the ligands. The absorption band formed by these excitations starts at the edge between visible and UV-light. During the 1970s and 1980s, the photochemistry of [Ru(bpy)3 ]2+ was intensively studied (see references in 14 ). The absorption spectrum of the complex presents two intense bands centered at 4.3 eV (285 nm) and 2.7 eV (455 nm), respectively. 15 The 455 nm absorption 3



Figure 1: Ball and stick representation of the [Ru(bpy)3 ]2+ complex. Large yellow sphere is Ru; smaller blue spheres are N; dark and light grey spheres represent C and H atoms, respectively

band corresponds to a spin allowed transition to the 1 MLCT excited state which rapidly converts by intersystem crossing (ISC) to the 3 MLCT triplet, which is the lowest excited state (as schematically represented in Fig. 2). 16,17 The ISC efficiency is close to 1 and the relatively long life time of the 3 MLCT state makes the complex very suitable for charge transfer processes to other acceptor molecules. 18 Otherwise, the 3 MLCT state decays to the ground state emitting light of 2.0 eV (610 nm). 19 Despite the very long history of the study of the electronic states of [Ru(bpy)3 ]2+ , the family of Ru-polypyridyl complexes is still attracting a lot of attention. Apart from being used as photosensitizer, it is also used in photocatalytic reactions 20,21 and as anti-cancer drug, 22 among other applications. One of the central issues of the electronic structure of the Ru(II) polypyridyl complexes is the character of the MLCT excited states. Whether the excited electron in the singlet and triplet excited states is localized on a single ligand or delocalized over several ligands may determine the electron transfer rate if the acceptor molecule interacts with the Ru com-

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Figure 2: Schematic representation of the most relevant photochemical processes in [Ru(bpy)3 ]2+ .

plex. 23 On one hand, experimental evidences point to an initial photoinduced delocalized MLCT state followed by localization to a single ligand. 24 This process is known as interligand electron transfer (ILET) and from a mixed time-dependent quantum-classical dynamics computational method is predicted to take place in the range of hundreds of femtoseconds depending on the solvent. 25 On the other hand, several TD-DFT results stress that the electron is delocalized over the three bipyridine ligands and therefore no ILET is expected. 26–28 Finally, a quantum mechanics/molecular mechanics (QM/MM) molecular dynamics study indicates delocalized MLCT states in gas phase and localization on two ligands when the effects of the solvent are included. 29 Another aspect to be considered is the description of the deactivation from the vertically excited 1 MLCT state via ISC to the relaxed 3 MLCT. This process is supposed to take place on a very short timescale and depending on the spectroscopic technique, estimates have been obtained in the range of 100-300 fs, 30,31 40 ± 15 fs 32 or 15 ± 10 fs. 33 The ISC rate is determined to a large extent by the spin-orbit coupling between singlet and triplet states, but it has been shown that this is not the only determining factor 34 and structural features are also expected to play an important role. 5



The lowest triplet MC states of the [Ru(bpy)3 ]2+ prototype complex lie approximately 0.5 eV higher in energy than the 3 MLCT emitting state. They are not expected to play a role in the deactivation of the initially excited 1 MLCT state but have been invoked to explain the thermally assisted quenching of the luminescence. 35 Addition of methyl groups on the outside of the bipyridine ligands has been shown to affect the ligand field exerted by the ligands in such a way that the 3 MC states become more stable than the 3 MLCT state. 9 This completely eliminates the luminescence signal ascribed to a fast 3 MLCT to 3 MC internal conversion followed by an ISC with the initial closed-shell 4d6 singlet. We present here a computational study of [Ru(bpy)3 ]2+ and some methyl substituted variants, in which we focus on different aspects of the photocycle of these complexes. After analysing the absorption spectrum and the character of the vertically excited states, we discuss the effect of geometry relaxation on the singlet and triplet MLCT states. We pay special attention to the delocalized/localized nature of the excited electron and estimate the localization rates through the hopping parameters. Finally, the kinetics of the intersystem crossing and the emission are also analyzed.

2 2.1

Results Geometries and absorption spectrum

The calculation of the vertical excitation energies starts with the optimization of the geometry of the closed-shell 4d6 singlet state S0 of the [Ru(bpy)3 ]2+ complex and six different methyl substituted complexes. The substitutions are made on the bipyridine ligands with 1 methyl group on the 5 or 6 position, with 2 methyl groups on the 5, 5’ or 6, 6’ positions, and with 4 methyl groups on the 3,3’,5,5’ or 4,4’,6,6’ positions, as illustrated in Fig. 3. Table 1 overviews the results of the geometry optimizations and it can be seen that the combination of the PBE0 hybrid functional with a triple-zeta + polarization basis and taking into account the dispersion interactions with the D3 correction reproduces accurately the Ru–N 6


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distances of the [Ru(bpy)3 ]2+ complex. A more complete comparison with experiment is given in the supporting information, where it is shown that the N–Ru–N angles and other distances are also close to experiment. The geometry optimization of the parent complex without dispersion correction leads to slightly larger Ru-N distances (2.0668 ˚ A) in agreement with those calculated in previous studies. 9 For three of the substituted complexes, experimental structures are available in the Cambridge Structural Database. In all these cases, the agreement with experiment is satisfactory and given the similarity of the complexes, we expect the calculated geometries of the other systems also to be rather precise.

Figure 3: Enumeration of the substitution sites of the bipyridine ligand

The methyl substitution on the 6 position leads to important steric hindrance and causes an expansion of the first coordination sphere of the Ru ion. In the 6-Me complex the bipyridine ligands stay nearly flat but in the 6,6’-Me and 4,4’6,6,6’-Me the expansion is accompanied by a significant rotation of the two pyridine rings around the central C–C bond. The two rings have a dihedral angle of approximately 21◦ . The substitutions on the 5 position do not cause important changes in the geometry, except for the 3,3’5,5’-Me case. The closeness of the methyl groups on the 3 and 3’ position induce large distortions of the two pyridine rings to release the steric hindrance; the dihedral angles along the C–C bond that connects the two rings is 25◦ for NCCN and 38◦ for CCCC. The absorption spectrum of [Ru(bpy)3 ]2+ is dominated by two peaks with their maximum at 2.75 and 4.35 eV, respectively. The first peak is attributed to arise from metal-to-ligand 7



Table 1: PBE0/def2-TZVP optimized average Ru–N distances, N–Ru–N angles and maxima of the two absorption bands for [Ru(bpy)3 ]2+ and the methyl substituted complexes. complex [Ru(bpy)3 ]2+ 5-Me 5,5’-Me 3,3’,5,5’-Me 6-Me

Ru–N distance [˚ A]a 2.0584 (2.056) 2.0576 (2.059) 2.0571 2.0627 2.0997 (2.091)

6,6’-Me 4,4’,6,6’-Me

2.1365 2.1352

(2.117)

N–Ru–N angles [degrees] absorption bands [eV] 78.68 88.19 96.73 173.59 3.0 / 4.1 78.72 88.25 96.67 173.65 3.0 / 4.2 78.76 88.29 96.63 173.65 3.0 / 4.2 78.74 89.39 96.18 172.33 2.8 / 3.9 78.38 85.37 93.14 172.17 2.9 / 4.2 103.19 79.46 80.66 99.94 179.44 3.0 / 4.3 79.28 80.87 100.02 178.98 2.9 / 4.1

a. experimental average Ru–N distance is given in parenthesis

charge transfer (MLCT) transitions, while the peak at higher energy is generally understood to involve excitations among the bipyridine π-orbitals. Figure 4 compares the experimental spectrum (in red) with those constructed using the calculated transition energies and oscillator strengths (in blue and green). Each transition is represented with a gaussian function with a full width at half height of 0.5 eV and the height is proportional to the oscillator strength. The curves in the Figure are the sum of the separate gaussians of each of the 200 transitions considered in the TD-DFT calculation (see section 3 for the computational details). The overall shape of the experimental spectrum is nicely reproduced in the gas phase calculation (green curve). Taking into the effect of the solvent (acetonitrile) with the COSMO model (blue curve) does not have a large effect on the transition energies but improves the relative intensities of the two main peaks. As can be seen in Table 1, methyl substitution does not lead to radical changes in the absorption spectra of the different complexes. The simulated spectra of all compounds can be found in the supporting information. For a more detailed inspection of the excited states that play a role in the photochemistry of the Ru polypyridyl complexes we will now focus on the relative energies of the lowest singlet and triplet states of MLCT and MC character and compare them in the different compounds. The first columns of Table 2 list the TDDFT estimates of the lowest transition energies. It is clear that the excitations into the MLCT states are not affected by the substitutions on the

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Figure 4: Comparison of the experimental absorption spectrum of [Ru(bpy)3 ]2+ (red dotted line) with the TDDFT ones in gas phase (green) and in acetonitrile solution (blue).

bipyridines. On the other hand, when the addition of methyl groups causes an enlargement of the Ru–N bond distance (substitution on the 6,6’ position), a significant lowering of the MC excitation energies is observed induced by the weaker ligand field, making it less unfavorable to transfer electrons from the non-bonding t2g to the anti-bonding eg Ru-4d orbitals. The distorted geometry of the bipyridine groups in the 3,3’-5,5’-Me complex leads to small changes in the relative energies of all excited states. Despite the lowering of the relative energies of the MC states by approximately 0.5 eV when the bipyridine is substituted at the 6,6’ position, the MLCT transition stays lowest in energy when TDDFT is applied. The use of DFT optimized geometries does in general not lead to the most accurate estimates of the

1,3

MC excitation energies with CASPT2. Because of the occupation of an

anti-bonding Ru-4d(eg ) orbital, small changes in the RuN6 geometry can lead to important changes in the relative energies of these states, and therefore, we have reoptimized the Ru-N distance by exploring the CASPT2 potential energy surface along the symmetric breathing

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Table 2: TDDFT and CASPT2 excitation energies (in eV) of the lowest MC and MLCT states. TDDFT (PBE0/def2-TZVP) MC 3 MC 1 MLCT 3 MLCT 4.20 3.55 2.73 2.56 4.20 3.56 2.74 2.56 4.21 3.56 2.75 2.56 4.24 3.88 2.65 2.44 3.63 3.01 2.69 2.48 3.59 3.08 2.73 2.46 3.56 3.10 2.76 2.48

1

[Ru(bpy)3 ]2+ 5-Me 5,5’-Me 3,3’-5,5’-Me 6-Me 6,6’-Me 4,4’-6,6’-Me

CASSCF(10,10)/CASPT2 MC 3 MC 1 MLCT 3 MLCT 4.32 3.76 2.82 2.92 4.30 3.76 2.81 2.91 4.36 3.80 2.82 2.92 4.29 3.85 2.67 2.62 4.07 3.48 2.88 2.85 3.61 2.54 2.59 2.89 3.51 2.42 2.47 2.74

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coordinate of the RuN6 unit, using the computational set-up described in section 3. The MLCT states are less sensitive to Ru-N distance, as the anti-bonding Ru-4d orbitals are not involved in these excitations. Seven different points were generated by restricted geometry optimizations applying DFT and the subsequent single-point CASPT2 calculations enabled us to determine the optimal distance. The parent compound [Ru(bpy)3 ]2+ and the complexes with a methyl group on the 5,5’ positions suffer a shortening of 0.033 ˚ A of the Ru-N bond, while the 6,6’ substituted complexes undergo a slightly larger contraction of 0.048 ˚ A. These shorter bond lengths increase the relative energy of the MC states by approximately 0.4 eV in comparison to the ones calculated at the DFT optimized geometry, while the MLCT relative energies are practically unchanged. Comparing the different complexes, the singlet states behave similarly as observed in the DFT calculations. The 6,6’ substitution lowers the DFT estimate of the relative energy of the 1 MC states by 0.3-0.5 eV, reducing the gap with the 1 MLCT states without becoming more stable. On the other hand, the CASPT2 results seem to indicate that the triplet MC states are largely stabilized and even lie lower in energy when the complex is methyl-substituted on the 6-6’ positions. However, a closer inspection of the character of the excited states reveals that there is a substantial mixing between the MLCT and MC states and, hence, it becomes difficult to label the states. This has been quantified in three different ways: (i) by calculating the overlap of the CASSCF wave functions with a model wave function that represent a pure MC state;

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(ii) by inspection of the Mulliken spin population on Ru; and (iii) by the determination of the weight of the d5 L1 configuration in an orthogonal Valence Bond analysis of the CASSCF wave function. The model wave function was constructed by superimposing the electron densities of two fragments: a triplet Ru2+ ion and a closed-shell (bpy)3 . Except for very small orthogonalization tails, the orbitals of the superimposed fragments remain fully localized after combining the two fragments. The overlaps with the d6 L model wave function listed in Table 3 allow us to discern very clearly the MC states from the MLCT states in the case of the unsubstituted Ru complex. The lowest 9 triplets have a very small overlap (< 0.1) while it reaches ∼0.5 for the last three states. In the substituted complex, the overlap of the lowest three triplets and the roots 10-12 is similar, indicating that these six states have significant MC character. The Mulliken spin population on Ru confirms this picture (note that the total Mulliken charges are not distinctive at all, they vary by less than 0.3 e- in all cases). The unsubstituted complex has approximately one unpaired electron on Ru in the lower nine states, compatible with a large MLCT character, while the population close to two of the next three triplet states is a sign of MC character. The spin populations of the 4,4’-6,6’Me complex approach 1.5 e- in all states (but root 7-9), revealing a significant MC/MLCT mixing. Finally, we have performed an orthogonal Valence Bond analysis of the CASSCF wave functions. This is done by localizing the orbitals on Ru or the bipyridine ligands following the projection method described in Ref. 36 and re-expressing the wave functions in this new set of orbitals. Since there is no Ru-ligand mixing in the localized orbitals, the configurations in the CI expansion of the CASSCF wave function can be rigorously identified as d6 L, d5 L1 , d4 L2 , etc., which is more inexact when (strongly) delocalized orbitals are used. Summing-up the weights of all the different d5 L1 configurations, we see that the first nine triplet roots in the parent compound have a weight of 0.8 or larger and that this drops to 0.5 for the states that we have identified as MC. Using these values as reference, we see that the labeling of the states as MLCT or MC in the substituted complex is difficult, the weight of the d5 L1 varies less than in the unsubstituted case. Based on these three

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indicators, we conclude that the lowest triplet states in the complexes with methyl groups on the 6,6’ positions are strongly mixed with important contributions from both MC and MLCT electron distributions. One final remark on the relative energies of the singlet and triplet states. From a simple Hund’s rule reasoning one would expect the triplet to be slightly lower in energy than the singlet. This is indeed observed in the PBE0 and CASPT2 results for the MC states. Both methods predict a singlet-triplet gap of approximately 0.6 eV. For the MLCT states the situation is less clear. PBE0 predicts a slightly more stable triplet state, whereas CASPT2 results show, somewhat surprisingly, a lower 1 MLCT state. The small singlet-triplet splitting in the MLCT manifold is expected since the inter-atomic exchange interaction is weaker than the intra-atomic exchange acting in the MC states. Extending the reasoning beyond this simple Hund’s rule picture is rather complicated, since it involves all kind of electron correlation mechanisms, but the most important conclusion from this part is that the singlet and triplet MLCT states are close in energy, favoring a fast intersystem crossing. 41

2.2

Character of the vertically excited MLCT states

Both TD-DFT and CASPT2 calculations indicate a rather large density of states starting at the onset of the MLCT band around 2.5 eV. The presence of singlet and triplet MLCT states in the same energy window triggers the need for including spin-orbit coupling in the description of the electronic structure to reach an accurate representation of the excited states. Table 4 summarizes some of the characteristics of the electronic states after taking into account the spin-orbit interaction in the multiconfigurational wave function calculations. In addition to the relative energy, the Table also makes reference to the composition in terms of singlet and triplet contributions and gives the oscillator strength for the transition from the ground state. The spin-orbit interaction hardly affects the relative energies of the low-lying MLCT states as can be seen by comparing the energies without spin-orbit coupling listed in Table 12


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Table 3: Character of the lowest twelve triplet states of the unsubstituted [Ru(bpy)3 ]2+ and the 4,4’-6,6’-Me substituted complex by overlap with model wave functions for a pure MC state, S(d6 L); Ru Mulliken spin population, µ(Ru); and weight of the Ru-4d5 L-π ∗1 configuration in the orthogonal valence bond analysis,ωM LCT . State 1 2 3 4 5 6 7 8 9 10 11 12

[Ru(bpy)3 ]2+ S(d6 L) µ(Ru) ωM LCT 0.01 1.00 0.80 0.08 1.07 0.82 0.08 1.07 0.82 0.00 1.01 0.85 0.03 1.00 0.84 0.03 1.00 0.84 0.03 1.01 0.88 0.03 1.01 0.88 0.01 1.01 0.95 0.49 1.85 0.50 0.48 1.85 0.50 0.48 1.78 0.41

4,4’-6,6’-Me S(d L) µ(Ru) ωM LCT 0.57 1.65 0.45 0.56 1.65 0.45 0.49 1.68 0.40 0.17 1.48 0.49 0.18 1.48 0.49 0.04 1.40 0.53 0.07 1.01 0.63 0.04 1.01 0.65 0.04 1.01 0.65 0.30 1.28 0.65 0.31 1.28 0.65 0.32 1.18 0.69 6

Table 4: CASPT2-SO relative energies (in eV), oscillator strengths and singlet/triplet fraction of the lowest spin-orbit states of [Ru(bpy)3 ]2+ SO state 1 2 3 4 5 6 7 8 9 10

∆E osc. strength singlet triplet 0.00 – 0.99 – −3 2.81 4.7·10 0.90 0.09 2.88 2.4·10−2 0.15 0.84 2.89 1.8·10−2 0.13 0.86 −7 2.89 9.6·10 – 0.99 2.90 4.1·10−4 0.85 0.12 −4 2.91 1.8·10 0.84 0.13 −4 2.94 3.4·10 0.10 0.90 2.96 2.4·10−5 – 0.98 2.96 5.4·10−4 – 0.96

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2 (2.82 and 2.92 eV) to those of the lowest states dominated by singlet (2.81 eV) and triplet (2.88 eV) contributions. The admixture of 10 to 15% singlet character to the 3 MLCT states causes that the oscillator strength of the transition to these states becomes rather large and as can be anticipated from the data in the table, the lower part of the absorption band will be dominated by the transitions into the states with mostly triplet character. The states with the largest oscillator strength lie at somewhat higher energy (not shown in the Table) and are dominated by singlet contributions. In comparison to experiment, the calculated band is shifted to higher energy by approximately 0.2 eV as previously found in [Fe(bpy)3 ]2+ . 37 Figure 5a shows the ligand π* Kohn-Sham orbital that is occupied in the lowest transition to the 1 MLCT state that has significant oscillator strength and, hence, likely to be populated in the initial stages of the photochemical process. This orbital (and in fact all other low-lying π* as well) is delocalized over the three bipyridine ligands and gives support to the understanding that the electron transferred from Ru to the ligand has a delocalized character at the early stages of the process. The same conclusion can be extracted from the multiconfigurational calculations. In this case, the wave function of the MLCT state with significant oscillator strength has major contributions from Slater determinants in which one of the three orbitals shown in Figure 5(b-d) is occupied. The overall effect of this multiconfigurational description of the electronic structure is also a fully delocalized electron in the vertically excited 1 MLCT state. The same holds for the 3 MLCT states.

Figure 5: (a) Kohn-Sham orbital occupied in the 1 MLCT state; (b-d) CASSCF optimized orbitals that are singly occupied in the Slater determinants that give the largest contribution to the multiconfigurational wave function of the MLCT states.

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2.3

Excited state relaxations

The geometries of the lowest 1 MLCT and 3 MLCT states have been optimized with TD-DFT and DFT, respectively. While in the S0 ground state geometry all six Ru-N distances are identical, 2.058 ˚ A, the RuN6 core of the complex suffers small distortions in the singlet and triplet MLCT states. The average Ru-N distance is very close to the one calculated for the ground state but in both states we observe two longer, two intermediate and two shorter distances, see Table 5. This has two possible explanations. In the first place, the Ru3d(t2g )5 configuration is Jahn-Teller active and induces in principle a spontaneous distortion of the geometry to lower the energy. In the second place, there is a tendency of the excited electron to localize on one of the bipyridine ligands. This localization is accompanied by a distortion of the geometry that traps the electron. To quantify the importance of the Jahn-Teller distortion we have optimized the geometry of the ionized system [Ru(bpy)3 ]3+ , corresponding to a Ru3+ ion with a 3d(t2g )5 electronic configuration. The resulting geometry shows a nearly octahedral RuN6 core with a difference between the long and the short Ru-N distance of less than 0.01 ˚ A, too small to explain the distortion observed in the optimized MLCT geometries of the di-cation. Hence, electron localization is the leading mechanism for the geometry distortion and indeed both singlet and triplet MLCT states have the electron localized on one of the bipyridines. The dipole moment of the 3 MLCT is 6.23 D, to be compared with the 3.77 D in the undistorted geometry. 38 The ligand with the extra electron has the shortest Ru-N distances, while the opposite Ru-N bonds are enlarged as schematically shown in Figure 6. The geometry relaxation causes a stabilization of the lowest MLCT states by approximately 0.2 eV. Consistently with experimental observations, DFT/TD-DFT results predict the relaxed 3

MLCT to be more stable than 1 MLCT. Both states have the same electronic configuration

and the main difference in the energy is the lack of intersite exchange interaction in the singlet. CASSCF and CASPT2 also predict a slightly more stable 3 MLCT state and the excited electron localized on one of the ligands. To check the effect of the solvent on the 15



Figure 6: Left: Schematic representation of the geometric distortion upon relaxation of the MLCT state. Right: Total spin density of the relaxed 3 MLCT state showing how the excited electron localizes on one of the bipyridine ligands.

excited state relaxation, we have repeated the geometry optimization of the ground state and the 3 MLCT state in a COSMO representation of acetonitrile. This leads to very similar results, the geometry is slightly less distorted (∼0.01 ˚ A), but the dipole is further increased to 9.81 D as a result of the solvent stabilization of the excited electron that slightly increases the charge separation. Table 5: PBE0 optimized Ru-N distances and relative energies for the S0 , MLCT and 3 MLCT states.

1

Ru-N distance [˚ A] bpy1 bpy2 bpy3 S0 2.058 2.058 2.058 2.058 2.058 2.058 1 MLCT 2.046 2.046 2.051 2.068 2.051 2.068 3 MLCT 2.020 2.021 2.058 2.088 2.062 2.085

∆E [eV] (a) PBE0 CASPT2 (a) Adiabatic 0.00 0.00 2.55 2.61 2.21 2.56

energy difference, PBE0 optimized geometries for S0 and MLCT states

Despite multiple intents, we have not been able to optimize the geometry for the 3 MC states in the 6,6’ substituted complexes; the complexes with the lowest vertical excitation energy of the MC states and, hence, the best candidates to find a metastable 3 MC state. Even if we use starting geometries with enlarged Ru-N distances that artificially make the MC 16


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state the ground state, the geometry optimization always ended up in the optimal geometry of the 3 MLCT state. Hence, the smaller energy difference between MLCT and MC states induced by the methyl substitution may indeed activate the thermal population of the MC state and the subsequent lower fluorescence efficiency, but more actions need to be taken to invert the relative stability of MC and MLCT states in order to profoundly change the photochemical behaviour of the Ru complex.

2.4

Intersystem crossing, ligand hopping and emission

In the study of the photocycle of Fe-trisbipyridine, the time-dependent formulation of Fermi’s golden rule 39,40 was applied to calculate the intersystem crossing rates (κISC ) relevant to the light-induced spin crossover of this compound. 41 Despite the fact that this way of calculating κISC lacks certain quantum effects as tunneling, interference effects or decoherence, 42,43 the calculated values were in good agreement with available experimental data. A similar coincidence was observed for the case of spin crossover in Fe(III) complexes. 44 We use the same approach to estimate κISC in [Ru(bpy)3 ]2+ for the singlet to triplet transition in the initial stage of the deactivation of the excited electron (see Fig 2). The magnitude of the intersystem crossing rate depends on the size of the spin-orbit coupling, the vibrational overlap of initial and final state (Franck-Condon factors) and the energy difference. The presence of Ru in the complex makes the spin-orbit coupling between the two states rather large, 540 cm−1 . Moreover, the total vibrational contribution also adds up to an important number, 3.49×108 cm−2 ·s−1 due to the similar optimal geometry of the 1 MLCT and 3 MLCT states, which leads to a large vibrational overlap. In combination with the CASPT2 energy difference listed in Table 5, we estimate the intersystem crossing rate to be 1.01×1014 s−1 , which hints at an ultrafast process with a lifetime of the 1 MLCT on the order of 10 fs, in good agreement with the 15±10 fs previously determined from fluorescence-upconversion experiments performed by the group of Chergui. 33 As seen in the previous section, the system evolves from a vertically excited delocalized 17



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MLCT state to a situation in which the electron is localized on one of the bipyridine ligands. The distortion of the geometry that accompanies the localization is likely to cause a trapping of the electron, thus disabling the electron transfer from ligand to ligand. The hopping integral t is one of the central parameters of the Hubbard Hamiltonian often used to rationalize the electronic structure of systems with strong electron correlations. This parameter is a measure of the probability of an electron to move between two adjacent sites. Its value is either derived from experimental information, fitted from the band structure in periodic ˆ f i, where Φi and Φf are the initial and final systems or calculated as the integral hΦi |H|Φ electronic states in the hopping process. Here, we adopt the latter approach to calculate the 1

MLCT hopping integrals for an initially delocalized electron (φd ) to a localized situation

(φ1 , φ2 and φ3 in Fig. 7), and between two electronic states with the electron localized on different ligands.

d

1

2

3

Figure 7: Singly occupied bipyridine orbitals of the 1 MLCT CASSCF wave functions with a delocalized (φd ) or localized (φ1,2,3 ) electron.

The wave functions of the different electronic states have been optimized in separate CASSCF calculations using the ground state geometry with three equivalent ligands. This procedure ensures optimal orbitals for each electronic state but introduces a certain degree of non-orthogonality between the states. The hopping parameter is no longer half the energy difference between two states as it is in centrosymmetric systems but has to be calculated

18


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with a slightly more involved formula v u

1u (Hii − Hff )2 tif = t∆E 2 − 2 2 1 − Sif

(1)

where Hii and Hff are the Hamilton matrix elements of the initial and final non-orthogonal states and Sif the overlap between the two states, which are both calculated in a CAS State Interaction. 45 The results of this calculation are summarized in Table 6, from which it becomes clear immediately that there is a large probability for the localization of the excited electron. The hopping parameter from delocalized to localized is large (∼0.6 eV, about as large as the t that parametrizes the hole mobility in the parent compounds of the cuprate superconductors), whereas the hopping integral for a hypothetical inter-ligand electron transfer is an order of magnitude smaller, only 0.05 eV. Hence, the delocalized electron of the unrelaxed 3 MLCT state has a high probability to localize on one of the ligands and because of the lower probability to hop onto neighboring bipyridines, the complex can relax its geometry as described in the previous section. The excited electron gets even more trapped on a single ligand and will not return to the delocalized situation being significantly higher in energy in the distorted geometry. In addition to this direct localization pathway, we have also calculated the hopping parameters between the fully delocalized and an intermediate MLCT state with the excited electron delocalized over two ligands, and from there to a fully localized solution. The corresponding hopping parameters are of the same order of magnitude and, hence, we cannot exclude this localization pathway in addition to the direct one illustrated above. A full overview of all the hopping parameters can be found in the supporting information. The hopping parameters are practically identical when calculated for the triplet states. It is, therefore, difficult to say whether localization occurs in the singlet or the triplet state based on the information of the hopping parameters only. However, the very high κISC for the 1 MLCT to 3 MLCT process, makes it likely that intersystem crossing precedes electron

19



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Table 6: Hamilton and overlap matrix elements to calculate the hopping integral tif (in eV) between states with (de-)localized excited electron. initial φd φd φd φ1 φ1 φ2

final Hii Hff Sif ∆E φ1 -0.17808 -0.21213 0.547 0.0628 φ2 -0.21421 0.510 0.0633 φ3 -0.21443 0.508 0.0632 φ2 0.052 0.0053 φ3 0.052 0.0054 φ3 0.030 0.0041

tif 0.653 0.644 0.640 0.066 0.067 0.056

Hamilton matrix elements and ∆E in Eh , the former are shifted by 6004 Eh

localization. The final step in the photocycle is the return to the S0 state through the emission of a photon of 610 nm (∆E ≈ 2.0 eV), as schematically illustrated in Fig 2. Table 7 summarizes the relative energies of the 3 MLCT and S0 states calculated with PBE0 and CASPT2 at the relaxed geometry of the 3 MLCT state. The DFT results are closest in agreement with experiment, but it should be noted that these values correspond to the system in vacuum. The inclusion of the environment will lead to further stabilization of the 3 MLCT state and, hence, to slightly larger wave lengths for the emission. The rate of emission can be calculated from the transition dipole moment in the CASPT2 calculation after considering spin-orbit coupling. Again the final electronic states become ∼90:10 mixtures of triplet and singlet, which result in a weakly allowed vertical emission from the 3 MLCT to the S0 state. The calculated lifetime of 9 µs is in good agreement with the experimental estimates of 5 µs. Table 7: PBE0, CASSCF and CASPT2 relative energies (in eV) of the S0 and 3 MLCT state at the relaxed geometry of the triplet state. State S0 3 MLCT vertical emission (nm)

PBE0 CASSCF(10,10) CASPT2 0.28 0.41 0.10 2.21 2.77 2.51 642 525 513

The energy of S0 at the ground state geometry is taken as reference.

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3

Computational information

All (TD-)DFT calculations have been performed with the TurboMole 6.6 package. 46,47 We have used the hybrid PBE0 functional, 48 the def2-TZVP basis set 49,50 to expand the KohnSham orbitals and the m3 integration grid. 51,52 Dispersion interactions were taken into account with the D3 correction of Grimme. 53 The resolution of the identity (RI) approximation was applied in all ground state calculations and solvent effects were represented through the COSMO approach 54 with standard optimized ionic radii (C: 2.00 ˚ A; H: 1.3 ˚ A; N: 1.83 ˚ A; Ru: 2.223 ˚ A) and a dielectric constant of 35.69 to mimic acetonitrile. The excitation energies in the TD-DFT calculations were calculated within the Tamm-Dancoff approximation. 55,56 The multiconfigurational wave function calculations have been performed with the MOLCAS 8 package. 57,58 The molecular orbitals are expanded in the ANO-RCC (atomic natural orbitals optimized for relativistic effects and core-correlation) basis sets with 7s,6p,5d,3f ,1g basis functions for Ru; 4s,3p,1d for N; 3s,2p for C and 2s for H. 59,60 Scalar relativistic effects are considered through the Douglas-Kroll-Hess Hamiltonian 61 and spin-orbit interactions are treated within the AMFI (atomic mean-field integrals) approximation. 62 The computational cost of the two-electron integrals was reduced through the Cholesky decomposition 63,64 using the default threshold of 10−4 . Two different active spaces were used to construct the multiconfigurational wave function in the CASSCF calculations. The first was used to reoptimize the Ru-N distance and the second to calculate relative energies of the different electronic states considered in this study. In both cases, 10 electrons are distributed in all possible ways over 10 orbitals. Seven orbitals are common to both active spaces, these are the five Ru-4d orbitals and two linear combinations of N-2p orbitals directed along the Ru-N bond as shown in Fig. S1 of the supporting information. The first active space also has three Ru-d’ orbitals to account for the double shell effect of the Ru-4d(t2g ) orbitals (see Fig. S2). The Ru-4d(eg ) orbitals are very weakly occupied in the S0 state and no second d-shell can be included for these orbitals. In the second active space, we have replaced the Ru-d’ orbitals for three bipyridine π ∗ orbitals (see Fig. S3). 21



The CASPT2 calculations have been performed using the standard zeroth-order Hamiltonian (IPEA = 0.25) 65,66 and an imaginary level shift of 0.15 Eh to avoid intruder states. 67 All electrons were included in the correlation treatment, except the inner core electrons: Ru-1s2 . . . 3p6 and N,C-1s2 .

4

Summary and Conclusions

We have given a computational description of the photocycle of [Ru(bpy)3 ]2+ . Starting from the initial excitation involving the promotion of an electron from the Ru-4d shell to an antibonding π orbital delocalized over the three bipyridine ligands, the system undergoes a fast intersystem crossing to a slightly lower-lying triplet state, also of metal-to-ligand charge transfer character. The calculated singlet-triplet intersystem crossing rate is in agreement with experimental studies that point at a 1 MLCT lifetime of approximately 15 fs. Given the short time scale it is not expected that geometry relaxation occurs before the intersystem crossing. The minimum energy in the 3 MLCT electronic state corresponds to a lightly distorted geometry leading to a localization of the singly occupied π ∗ orbital on one of the bipyridine ligands. The bipyridine with the localized electron moves in while the opposite Fe–N distances become longer. It was shown that the hopping probability of a delocalized electron to a localized situation is large and can take place directly from a fully delocalized situation to the final state with the electron localized on one ligand, or via an intermediate state where the electron is delocalized on two ligands. The interligand electron transfer from ligand to ligand is calculated to be rather improbable. The combined action of electron localization and geometry relaxation creates a sufficiently deep potential energy well for a long-lived 3 MLCT state, calculated life-time of 9 µs. The present computational description does not include the effect of the thermal motion of the ions. As shown in previous studies on the corresponding Fe(II) complex, it is expected that including this effect will lower the edge of the low energy absorption band by about 0.2

22


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eV, bringing it in slightly better agreement with experiment. A more interesting effect is expected for the degree of localization of the electron in the MLCT state. The disordered thermal motion of the ions in the complex at finite temperatures will most probably lead to a less well-defined potential energy well for the localized electron. Ligand hopping could become more important. Future work will be focusing on the calculation of the inter ligand hopping parameters in a large series of snapshots of a molecular dynamics simulation of the complex in vacuum or solvent. Moreover, it would be very interesting to see how the redox potentials of the complex evolve along these snapshots and whether it is possible to obtain information about the electron hopping to electron acceptor molecules used in secondary reactions.

Supporting information: Comparison of calculated geometrical parameters with experimental data; Graphical representation of the delocalized and projected CASSCF active orbitals; Hopping parameters in the MLCT state for the electron (de)localized over three, two or one ligand(s).

Acknowledgments: Financial support has been provided by the Spanish Administration (Project CTQ2014-51938-P), the Generalitat de Catalunya (Project 2014SGR199) and the European Union (COST Action ECOSTBio CM1305)

23



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Quantum Chemical Study of the Inter Ligand Electron Transfer in Ru

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