Influence of Triplet State Multidimensionality on Excited State Lifetimes

ARTICLE pubs.acs.org/JPCA

Influence of Triplet State Multidimensionality on Excited State Lifetimes of Bis-tridentate RuII Complexes: A Computational Study † € Tomas Osterman, Maria Abrahamsson,‡ Hans-Christian Becker,‡ Leif Hammarstr€om,§ and ,† Petter Persson* †

Chemistry Department, Lund University, Box 124, SE-22100 Lund, Sweden Physical Chemistry, Department of Chemical and Biological Engineering, Chalmers University of Technology, SE-41296 G€oteborg, Sweden § Chemical Physics, Department of Photochemistry and Molecular Science, Uppsala University, Box 532, SE-75120 Uppsala, Sweden ‡

bS Supporting Information ABSTRACT: Calculated triplet excited state potential energy surfaces are presented for a set of three bis-tridentate RuII-polypyridyl dyes covering a wide range of room temperature excited state lifetimes: [RuII(tpy)2]2+, 250 ps; [RuII(bmp)2]2+, 15 ns; and [RuII(dqp)2]2+, 3 μs (tpy is 2,20 :60 ,200 -terpyridine, bmp is 6-(2-picolyl)-2,20 -bipyridine, and dqp is 2,6-di(quinolin-8-yl)pyridine). The computational results provide a multidimensional view of the 3MLCT 3 MC transition for the investigated complexes. Recently reported results of significantly prolonged 3MLCT excited state lifetimes of bis-tridentate RuIIcomplexes, for example [RuII(dqp)2]2+, are found to correlate with substantial differences in their triplet excited state multidimensional potential energy surfaces. In addition to identification of low-energy transition paths for 3MLCT 3 MC conversion associated with simultaneous elongation of two or more RuN bonds for all investigated complexes, the calculations also suggest significant differences in 3MLCT state volume in the multidimensional reaction coordinate space formed from various combinations of RuN bond distance variations. This is proposed to be an important aspect for understanding the large differences in experimentally observed 3MLCT excited state lifetimes. The results demonstrate the advantage of considering multidimensional potential energy surfaces beyond the FranckCondon region in order to predict photophysical and photochemical properties of bis-tridentate RuIIpolypyridyl dyes and related metal complexes.

’ INTRODUCTION Tris-bidentate RuII-polypyridyl complexes, such as [RuII(bpy)3]2+ (bpy is 2,20 -bipyridine), have attracted large interest as sensitizers in photochemical and photobiological electron transfer applications, due to their favorable photophysical properties, including long excited state lifetimes (around 1 μs at ambient temperature for [RuII(bpy)3]2+).16 For the formation of molecular arrays, bis-tridentate RuII-complexes, such as [RuII(tpy)2]2+ (tpy is 2,20 : 60 ,200 -terpyridine), are advantageous compared to tris-bidentate complexes as the former possess a C2 axis allowing for linear assembly. However, a room temperature excited state lifetime of 250 ps makes [RuII(tpy)2]2+ less useful for many photochemical applications.7,8 Interestingly, several new bis-tridentate RuIIcomplexes with ligand bite angles closer to the ideal 180° have recently been presented,9,10 including a new class of complexes based on [RuII(dqp)2]2+ (dqp is 2,6-di(quinolin-8-yl)pyridine), that rival [RuII(bpy)3]2+ in terms of excited state properties and display room temperature 3MLCT excited state lifetimes of several microseconds.1115 Scheme 1 depicts key excited state processes for RuIIpolypyridyl complexes. Initial photoexcitation to a singlet r 2011 American Chemical Society

metal-to-ligand charge transfer (1MLCT) state (not shown in Scheme 1) leads to rapid (typically within 1 ps) intersystem crossing to the lowest triplet MLCT state (3MLCT). The 3 MLCT state can decay directly to the ground state (GS) via radiative or nonradiative pathways, or through thermally activated processes proceeding via either a triplet metal centered state (3MC), or a higher MLCT state (MLCT’) with a larger degree of mixed singlettriplet spin character. It can be noted that Scheme 1 includes a significant stabilization of the relaxed 3MC state relative to the relaxed 3MLCT state in accordance with recent computational results for these complexes.16,17 Experimentally, the temperature dependence of the excited state lifetime can be used to obtain information about the excited state processes involved in excited state decay. Typically, experimental data are analyzed using an Arrhenius-type relationship where the deactivation kinetics is described according to eq 1 Received: July 23, 2011 Revised: November 23, 2011 Published: December 09, 2011 1041

dx.doi.org/10.1021/jp207044a | J. Phys. Chem. A 2012, 116, 1041–1050

The Journal of Physical Chemistry A

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Scheme 1. Schematic Illustration of Deactivation Channels of the 3MLCT State in Typical RuII Complexesa

a The initial photoexcitation process has been omitted for clarity. Decay from the 3MLCT state can proceed either directly to the ground state through radiative or nonradiative processes, or through thermal activation to a state of either metal centered (3MC), or metal-to-ligand charge transfer (MLCT0 ), character.

(for data well above the solvent glass transition temperature): ΔE1 kobs ¼ k0 þ A1 exp ð1Þ RT The first term, k0, corresponds to the intrinsic decay from the emissive state to the ground state, thus including radiative and nonradiative components. The Arrhenius term accounts for an activated decay in which the complex passes from the 3MLCT state to some shorter-lived, upper excited state,18 vide infra. It is striking that although radiative rate constants are fairly similar for most RuII-polypyridyl complexes, the 3MLCT excited state lifetimes vary by more than 3 orders of magnitude at ambient temperature. This reflects significant variations in the nonradiative decay kinetics, in particular involving the thermally activated processes contained in the Arrhenius term. For many bis-tridentate RuII-complexes this occurs through thermal conversion of the 3MLCT state to a 3MC state, from which rapid nonradiative decay to the ground state occurs. The short 3MLCT state lifetime of [RuII(tpy)2]2+ is generally ascribed to a weak ligand field, causing a small energy gap between the 3MLCT state and short-lived 3MC states, which results in efficient thermally activated nonradiative decay. Recent successes to prolong 3 MLCT excited state lifetimes for bis-tridentate RuII-polypyridyl complexes, mentioned above, were based on design of ligands that allow for more octahedral coordination spheres, thus increasing the t2geg gap and consequently increasing the 3 MLCT3MC splitting without concomitant stabilization of the 3MLCT state. An alternative decay pathway, sometimes invoked, is thermal activation to a higher triplet MLCT state often referred to as the “fourth MLCT state” (MLCT0 in Scheme 1), which is more short-lived than the lowest 3MLCT state due to increased singlet character.3,12,19 Furthermore, there are examples of experimental results that have been interpreted as the establishment of an equilibrium between the 3MLCT and the 3MC states.4,20,21

It is desirable to provide a more comprehensive understanding of the factors that govern the excited state kinetics of RuIIcomplexes, and quantum chemical calculations can contribute important insights.22,23 Many calculations of RuII-polypyridyl complexes have been published, including a number of investigations of ground state properties and vertical excitations.24 Such studies have included investigations of environmental effects including, e.g., effects of solvents25,26 and counterions,27 as well as supramolecular28 and heterogeneous interactions.29 It is valuable to calculate triplet state properties beyond the Franck Condon region, including characterization of triplet excited state properties (3MLCT and 3MC states). This has been done for selected RuII-complexes,16,17,3035 as well as for other related transition metal complexes such as IrIII-complexes for OLED applications.36 These calculations have provided support for common beliefs that 3MC states have energy minima that have significantly longer RuN bonds compared to the 3MLCT states of the bis-tridentate RuII-polypyridyl complexes studied here, something which has been difficult to characterize experimentally because of the efficient nonradiative decay of the 3MC states.16,17 To gain further insight into the mechanistic details of 3MLCT 3 MC activated transitions, theoretical information about the reaction profiles would be very useful. However, recent DFT calculations point to the difficulty of identifying formal transition states for the comparatively flat excited state potential energy surfaces using standard transition state searches.17 In this paper, we calculate triplet state potential energy surfaces (PESs), with the aim of providing a more comprehensive picture of multidimensional 3MLCT3MC excited state deactivation pathways. In particular, DFT calculations are here used to provide a continuous adiabatic description of the lowest triplet PES. On this surface, regions corresponding to the 3MLCT and 3 MC states, which are used to describe experimental excited state decay mechanisms from a nonadiabatic perspective as shown in Scheme 1, can be distinguished on the basis of differences in their 1042

dx.doi.org/10.1021/jp207044a |J. Phys. Chem. A 2012, 116, 1041–1050


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Figure 1. Chemical structures of the studied complexes: [RuII(tpy)2]2+ (a), [RuII(bmp)2]2+ (b, bmp is 6-(2-picolyl)-2,20 -bipyridine), and [RuII(dqp)2] 2+ (c).

electronic properties. For this study, we have selected three bistridentate RuII-polypyridyl dyes that cover a wide range of room temperature excited state lifetimes: [RuII(tpy)2]2+, 250 ps; [RuII(bmp)2]2+, 15 ns, and [RuII(dqp)2]2+, 3 μs, Figure 1.

’ COMPUTATIONAL METHODS The ground state and triplet state PESs of three bis-tridentate RuII-polypyridyl complexes have been investigated using density functional theory (DFT) calculations. All quantum chemical calculations have been performed using the Gaussian03 program.37 The calculations comprise DFT calculations using different standard basis sets and effective core potentials for the Ru atom provided in the Gaussian program. In particular, the widely used B3LYP38,39 and PBE1PBE4042 functionals have been used, in conjunction with standard Gaussian type orbital (GTO) basis sets of at least double-ζ quality. The SDD Stuttgart/Dresden effective core potential (ECP) was used to provide an effective core potential for Ru.43 Ground state properties are calculated using the spin-restricted singlet formalism, while spin-unrestricted DFT (UDFT) calculations are performed for the lowest triplet state calculations. This extends previous work using similar methodology to locate stationary points for RuII-complexes.16,17 A comparison of results obtained using different combinations of functionals and basis sets is presented for the experimentally most interesting [RuII(dqp)2]2+ complex, in particular providing information about the method sensitivity for calculated triplet properties. Selected excited state electronic properties have also been investigated for the [RuII(dqp)2]2+ complex using the B3LYP and PBE1PBE functionals, several basis sets, and a PCM solvent description for ethanol (G03 keywords iefpcm and solvent = EtOH). PES scans, with a spacing of 0.02 Å or multiples thereof as judged necessary by the curvature of the investigated state, have been performed for the three investigated complexes with a view to investigate 3MLCT3MC rearrangement pathways. Each point on a given PES is obtained using a full geometry B3LYP/ 6-31G(d,p)-SDD relaxation of all structural parameters except those fixed as the probed coordinates in the PES scan. The resulting PESs are referred to as relaxed PESs. It can be noted that the unrestricted gas phase calculations of the PESs neglect effects from spinorbit coupling,44 and solvent dynamics45 that also play important roles for the excited state dynamics. The accuracy of the PESs in regions where there are nearly degenerate states may furthermore be limited by restrictions imposed by the use of a singledeterminant DFT description. ’ RESULTS Stationary Points for RuII Complexes. First, structural and electronic properties of the ground, 3MLCT, and 3MC states

have been investigated for the [RuII(dqp)2]2+ complex, in order to assess the effect of using different DFT functionals and basis sets. The [RuII(dqp)2]2+ complex was selected for these validations because of its significant potential as chromophore in dyads and triads for vectorial electron transfer.46 It is also beneficial to consider this experimentally interesting complex further because earlier computational work17 has suggested that the excited state energies for the lowest relaxed 3MLCT and 3MC states are close, making a reliable computational assignment of the excited state energy ordering particularly challenging. Complete gas phase geometry optimizations have been performed for the ground, 3MLCT, and 3MC states. Both the hybrid B3LYP functional and the PBE1PBE functional have been tested. All states were optimized with the 6-31G(d,p)-SDD basis set combination, where the 6-31G(d,p) basis set was used for all atoms except Ru for which SDD was employed. Selected structural results are summarized in Table 1 and are presented as three central structural parameters (R-, O-, and S-values), all with an absolute mean deviation representing the calculated variations in the value. The R-value describes the average RuN bond distance, which is relevant since shorter RuN bond distances are generally expected to result in a larger energy gap between the 3MLCT and 3MC states. Furthermore, the 3MC state is expected to display significant elongation of the equatorial RuN bond distances compared to the 3MLCT state. The importance of particular RuN bonds for the excited state properties is analyzed further below in the context of relevant reaction coordinates. The O-value (octahedricity-value) is a measure of the mean absolute deviation of the set of NRuN angles from their “ideal” octahedral values, see also further discussion by Lundqvist.47 Thus, it is a measure of the angular distortion of the complex away from a perfectly octahedral geometry as discussed in standard ligand field theory. As the approach to increase the 3MLCT state lifetime has been based on increasing the ligand field splitting by increased bite angles, the O-value should be one of the key parameters for predicting the 3MLCT state lifetime. Finally, the S-parameter (stackingparameter) measures intramolecular ligandligand interactions in terms of the average interligand distance between the centers of gravity in the benzene and pyridine rings in one quinoline unit and the benzene ring of the other quinoline unit, as previously discussed by Johansson et al.48 The RuN bond lengths for all states are calculated to be ca. 0.03 Å shorter with the PBE1PBE functional compared to the B3LYP functional. This effect is well-known for ground state calculations on similar complexes, where the PBE1PBE functional is typically in somewhat better agreement with experimental observations. The 3MLCT state is found to be very similar to the ground state in terms of its R-, O-, and S-values for 1043



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Table 1. Calculated Structural Properties of [RuII(dqp)2]2+ for the GS (Ground State), 3MLCT, and 3MC Statesa 3

GS method

a

R

3

MLCT

O

S

R

MC

O

S

R

O

S

B3LYP/6-31G(d,p)-SDD

2.11 ( 0.02

0.1 ( 1.6

3.93 ( 0.00

2.10 ( 0.04

0.5 ( 2.3

3.90 ( 0.04

2.25 ( 0.16

1.5 ( 7.9

3.86 ( 0.05

PBE1PBE/6-31G(d,p)-SDD

2.08 ( 0.02

0.1 ( 1.2

3.69 ( 0.00

2.07 ( 0.04

0.4 ( 1.9

3.68 ( 0.02

2.21 ( 0.14

1.4 ( 7.3

3.63 ( 0.05

exptlb

2.03 ( 0.03

0.6 ( 2.0

3.38 ( 0.08

Distances in Å and angles in degrees. Deviations are calculated as σn-values. b Calculated from crystallographic data in ref 11.

Table 2. Calculated Electronic Properties of [RuII(dqp)2]2+ for the 3MLCT and 3MC States using Different DFT Methodsa 3

method optimization B3LYP/6-31G(d,p)-SDD

PBE1PBE/6-31G(d,p)-SDD a

E

property

3

MLCT E

spin density

MC spin density

B3LYP/6-31G(d,p)-SDD

1.99

0.66

1.97

1.73

B3LYP/6-311G(2df,p)-SDD

1.83

0.72

1.81

1.79

B3LYP/6-31G(d,p)-SDD[EtOH]

1.94

0.62

1.92

1.76

B3LYP/6-311G(2df,p)-SDD[EtOH] PBE1PBE/6-31G(d,p)-SDD

1.87 2.01

0.77 0.66

1.89 2.07

1.79 1.80

PBE1PBE/6-31G(d,p)-SDD

1.98

0.73

2.04

1.78

Triplet state energies, E, are given relative to the ground state in eV.

both functionals. The calculations give an indication of a shortening of the average RuN bond distance (by 0.01 Å) and a slightly more distorted octahedral metal coordination (through an increase in the O-value by ca. 0.4°) when going from the ground state to the 3MLCT state. The differences for both the choice of functional and between the ground and 3MLCT states are quite small compared to the typical accuracy of ∼0.02 Å for DFT optimizations. It can be noted that the similarity of the calculated 3MLCT state geometries to the ground state geometries, with a tendency for slightly shorter RuN bonds in the 3 MLCT states, is consistent with, e.g., X-ray absorption spectroscopy measurements for the related [Ru(bpy)3]2+ complex.49 The structural distortions involved in reaching the optimized 3 MC state are more significant. Both DFT functionals show that the 3MC state has significantly longer RuN distances (R-value increases by more than 0.1 Å) and is more distorted (O-value increases from about 0.3 to about 1.5°) compared to the ground state and 3MLCT state geometries. This is also accompanied by significantly increased variations in the R- and O-values, indicative of an overall less regular octahedral structure. Notably, both functionals give very similar differences in RuN distances between the optimized 3MLCT and 3MC states. The shorter RuN bonds with PBE1PBE are accompanied by noticeable reductions in the ligandligand distances for the studied states, as manifested in the S-values. It is noteworthy that the longer RuN bonds for the 3MC state compared to the ground and the 3MLCT states do not lead to increased ligand ligand distances, something that could be due to decreased relevance of the Ru metal center on the ligand geometry as the RuN bonds are weakened. The B3LYP and the PBE1PBE functionals also give similar results for the respective structural properties of the 3MLCT and 3MC states, relative to the ground state geometry. Excited state electronic properties have also been investigated for the [RuII(dqp)2]2+ complex using the B3LYP and PBE1PBE functionals and several basis sets, Table 2. Results from calculations including a PCM solvent description for ethanol for the

Table 3. Summary of Stationary Point (GS (Ground State), 3 MLCT, and 3MC States) Data for the Three Investigated Complexesa [RuII(tpy)2]2+

E (eV)

0.00

2.19

1.91

Q1

2.12

2.11

2.12

Q2

2.12

2.10

2.38

R

2.08 ( 0.05

2.08 ( 0.04

2.21 ( 0.13

O

2.5 ( 12.0

2.8 ( 12.7

3.4 ( 17.3

E (eV) Q1

0.00 2.13

2.09 2.12

1.95 2.25

Q2

2.13

2.12

2.42

R

2.11 ( 0.03

2.10 ( 0.04

2.26 ( 0.13

O

2.2 ( 7.5

2.2 ( 7.7

3.6 ( 15.0

E (eV)

0.00

1.99

1.96

Q1

2.12

2.10

2.15

Q2

2.12

2.13

2.47

R O

2.11 ( 0.02 0.1 ( 1.6

2.10 ( 0.04 0.5 ( 2.3

2.25 ( 0.16 1.5 ( 7.9

[RuII(dqp)2]2+

MLCT

3

quantity

[RuII(bmp)2]2+

GS

3

complex

MC

a

Results from B3LYP/6-31G(d,p)-SDD calculations. Q1 and Q2 are composite reaction coordinates for ligands 1 and 2, respectively. They are calculated as the average of the RuN distances for the two terminal nitrogen atoms of each ligand, respectively. Q1 = [D(RuN1) + D(RuN3)]/2; Q2 = [D(RuN4) + D(RuN6)]/2. R- and O-values as defined above.

electronic structure calculations have been included as well. For all choices of method, the 3MLCT and 3MC states can be clearly distinguished on the basis of the significant change in spin density on the Ru atom. This is consistent with expectations, since 3MC states formally have two unpaired electrons on the Ru metal center, while the 3MLCT states formally have one unpaired electron on the metal center and one on the ligands. Interestingly, the spin density for the [RuII(dqp)2]2+ complex is, in contrast to the other complexes, almost entirely localized on one of 1044



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Figure 2. Single ligand two-dimensional triplet state PES (i.e., 1L-2D-3PES) scans for [RuII(dqp)2]2+ from a 3D-landscape (panel a) and a 2Disosurface (panel b) perspective, respectively. RuN reaction coordinates in Å and energies in eV. The red lines are visual guides that schematically indicate low-energy transition paths between the triplet energy minima.

the ligands (see Supporting Information). Similar to previous findings,17 the difference in energy between the 3MLCT and 3 MC states is less than 0.1 eV with all tested methods. This small energy difference is comparable to typical errors of the method and thus precludes a definite assignment of which relaxed triplet state is lower in energy. It is, however, reassuring that the relative energies of these two triplet states are found to be reasonably insensitive to the choice of DFT functional and basis set. Calculated properties of all three complexes under investigation, using the B3LYP/6-31G(d,p)-SDD standard method, are summarized in Table 3 for the stationary states (GS, 3MLCT, 3 MC). The triplet geometries have been used to identify key structural parameters for 3MLCT3MC conversion pathways discussed below. Particularly noticeable are, as expected, elongations of the equatorial RuN bond distances of one of the ligands, due to population of one antibonding eg orbital. These are here characterized through the introduction of two effective reaction coordinates, Q1 and Q2, describing the elongations for each of the two ligands, respectively. For all three complexes, the geometry of the 3MLCT state is similar to the geometry of the ground state, but the 3MC states have significantly elongated RuN bonds. This is consistent with a stabilization of the 3MC states following a decrease in ligand field splitting. It can be noted that we are limiting our consideration to the most stable of the two calculated 3MC states discussed previously for the [RuII(dqp)2]2+ and [RuII(bmp)2]2+ complexes.17 The calculations of triplet minima for the three complexes provide a coherent view of 3MLCT and 3MC states that are quite close in relaxed energy, but where the 3MC states have structures that include significantly elongated equatorial RuN corresponding to a reduced ligand field splitting of a MC state. These calculated minimum structures provide a starting point for identifying relevant coordinates for calculations, presented in the following, of multidimensional triplet PESs designed to provide more comprehensive information about 3MLCT3MC excited state pathways. Excited State Potential Energy Surfaces. i. [RuII(dqp)2]2+. A relaxed two-dimensional triplet potential energy surface (2D3PES) for the [RuII(dqp)2]2+ complex is presented in Figure 2.

This 2D-3PES comprises the simultaneous scan of two Ru Nquinoline bond distances on a single ligand, i.e., RuN1 and RuN2 according to the labels in Figure 2. We refer to this type of 2D-3PES involving two terminal nitrogen atoms on a single ligand (L) as a 1L-2D-3PES. These scanning dimensions were selected to provide a realistic view of a low-energy activated decay, considering the geometries of the 3MLCT and 3MC states summarized in Table 3. In particular, explicit consideration of the stretching of two terminal RuN bonds from a single ligand provides a comprehensive view of the development of a 3MLCT state minimum region. It can be noted that, not unexpectedly, the calculated triplet energy surface is quite flat over large areas of coordinate space compared to the corresponding ground state surface. This means that, for this complex, as for the subsequently investigated ones, larger areas of coordinate space can be expected to be populated thermally, and it often becomes more meaningful to talk about energy minima regions and transition regions between energy minima regions, rather than definite minima and transition points. The 3MLCT state region allows for significant asymmetric stretching of the two RuN bonds without reaching the 3MLCT3MC crossing region. The asymmetric 3MLCT state minima shown here are consistent with the previous computational findings for the [RuII(dqp)2]2 +3 MLCT state minimum.17 A smooth low-energy activated 3 MLCT3MC transition path is found when both RuN bonds of a single ligand are stretched. This includes a low-energy 3 MLCT3MC transition region located outside the 3MLCT state region, and ranging between two asymmetric transition points located at about (2.10, 2.30) and (2.30, 2.10). The lowest transition points are calculated at this particular level of approximation to be ca. 0.1 eV above the 3MLCT state minimum. ii. [RuII(tpy)2]2+. The 3MLCT3MC transition for [RuII(tpy)2]2+ was first investigated using a similar 1L-2D-3PES scan as described above for [RuII(dqp)2]2+. The resulting PES is shown in Figure 3a, and indicates rapid conversion of the 3MLCT state above the ground state minimum, where all four RuNquinoline bonds are about 2.1 Å, to the 3MC state already through minor stretching (approximately 0.1 Å) of the RuN bonds. Further analysis of the calculated structures shows a discontinuity for the 1045



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Figure 3. 2D-3PES for [RuII(tpy)2]2+. Panel a shows a landscape perspective of a 1L-2D-3PES scan. Panels b and c show landscape and isosurface perspectives, respectively, of a 2 L-2D-3PES scan. RuN reaction coordinates in Å and energies in eV. The red lines are visual guides that schematically indicate low-energy transition paths between the triplet energy minima. 3 MLCT3MC transition at intermediate RuN distances. This is the result of higher dimensional effects due to spontaneous stretching of the RuN bonds of the second ligand once the RuN bonds of the scanned ligand are stretched by a small amount. In order to characterize the 3MLCT3MC conversion better, an alternative 2D-3PES was generated (Figure 3b,c) using Q1 and Q2 as reaction coordinates. Q1 and Q2 correspond to symmetric stretching of the two ligands as described above (giving a 2L-2D-3PES), which can be illustrated for the stationary points as follows. The 3MLCT state is located as a small minimum region around a point near (Q1, Q2) = (2.12, 2.12), i.e., with all four terminal RuN bonds close to 2.12 Å. There are, in contrast, two equivalent 3 MC state minima, at (2.15, 2.38) and (2.38, 2.15). These correspond to one tpy ligand having both terminal RuN bonds stretched to 2.15 Å and the other tpy ligand having both terminal RuN bonds stretched to 2.38 Å, cf., Table 3. Considering the 3MLCT3MC conversion path in the 2L-2D-3PES model, there is no higher dimensional collapse of the PES as seen for the 1L-2D-3PES. Instead, elongation of the RuN bonds of one of the two ligands leads to a low energy 3 MLCT3MC crossing close to the 3MLCT state minimum, which results in a small calculated 3MLCT state region. As a consequence, no significant 3MLCT state region is formed before the crossing region to the 3MC state is reached, and asymmetric stretching effects for a single ligand, captured by the 1L-2D-3PES scan for [RuII(dqp)2]2+, are therefore less important for the [RuII(tpy)2]2+ complex. For the short-lived [RuII(tpy)2]2+ complex, fast regeneration of the ground state, in addition to rapid 3MLCT3MC conversion, requires efficient decay of the 3MC state, which has been suggested to occur nonradiatively via crossing with the ground state at longer RuN bonds for other RuII-polypyridyl complexes.34 To investigate the feasibility of such facile ground state recovery, the 2L-2D-3PES was extended using a coarser grid (step size in each direction 0.08 Å) to longer Q1 and Q2 coordinates. The relaxed PES scan was then augmented by single point singlet ground state calculations at the triplet optimized geometries in a search for low-energy 3MCground state crossing regions. The somewhat unorthodox choice to calculate single point ground state energies at relaxed triplet state points, rather than the other way around, is motivated by the primary interest in the deactivation process, i.e., where the excited state dynamics is expected to follow low energy pathways on the excited state surface until a crossing region with the ground state is encountered. The results for this scan are shown in Figure 4. These calculations

Figure 4. Calculated PES low-energy crossing region between ground (blue) and first triplet (red) states for [RuII(tpy)2]2+. RuN reaction coordinates in Å and energies in eV.

indicate that there is indeed a low-energy crossing seam where the ground state surface rises above that of the 3MC state surface at stretched Q1 and Q2. The lowest energy crossing point, located around (2.12, 2.70), is found about 0.3 eV above the 3MC minimum. A symmetric crossing point is found at around (2.50, 2.50), but is calculated to be higher in energy by more than an additional 0.2 eV. The existence of a low-energy crossing region suggests that, once formed, the 3MC state is indeed likely to undergo fast decay leading to ground state regeneration. iii. [RuII(bmp)2]2+. The [RuII(bmp)2]2+ complex forms mixed 5- and 6-chelate NRuN rings with each ligand and should therefore give a larger ligand bite angle than [RuII(tpy)2]2+, but possibly not as large as for [RuII(dqp)2]2+. [RuII(bmp)2]2+ has been found experimentally to have an excited state lifetime between those of [RuII(tpy)2]2+ and [RuII(dqp)2]2+.10 A 1L-2D3PES scan was therefore performed also for this complex, Figure 5. The PES shows a qualitatively intermediate behavior between [RuII(tpy)2]2+ and [RuII(dqp)2]2+ such that a clearly recognizable 3MLCT state region similar to the [RuII(dqp)2]2+ complex has started to form, but there is an abrupt collapse to the lower 3MC state for stretched RuN bonds similar to what was 1046



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Table 4. Excited State Lifetimes at Room Temperature and Parameters from Arrhenius-Type Analysis of Temperature Dependent Emission Lifetime Data τ/ns

A1/s‑1

0.25

1.9 x1013

1500

[Ru (bmp)2]

15

1.0 1015

3400

[RuII(dqp)2]2+c

3000

1.5 1010

2600

complex [RuII(tpy)2]2+a II

2+b

ΔE1/cm‑1

a

Data from Hecker, C. R.; Gushurst, A. K. I.; McMillin, D. R. Inorg. Chem. 1991, 30, 538541. b Data from ref 10. c Data from ref 52.

Figure 5. Calculated 1L-2D-3PES scan for [RuII(bmp)2]2+. RuN reaction coordinates in Å and energies in eV.

seen for [RuII(tpy)2]2+, owing to the spontaneous relaxation of the second ligand. As this complex is somewhat less interesting from an experimental point of view, attempts to fully characterize the 3MLCT3MC transition path for this complex were not pursued further.

’ DISCUSSION The large variations in observed excited state lifetimes for the here investigated RuII-complexes deserve particular theoretical attention. In phenomenological modeling of the experimental kinetics, these variations mainly manifest themselves as differences in the thermally activated decay, i.e., in the Arrhenius term of eq 1. A kinetic scheme (eqs 2 and 3) is commonly used to describe the activated processes.18 3

ka

MLCT h 3 MC kb

3

kc

MC sf GS

ð2Þ ð3Þ

According to this scheme, the Arrhenius term in eq 1 k1 ¼ A1 expð ΔE1 =RTÞ

ð4Þ

is related to the mechanistic model presented in eqs 2 and 3 such that k1 ¼ ka ðkc =ðkb þ kc ÞÞ

ð5Þ

if steady-state conditions are assumed for the 3MC state.7 Two limiting cases can be identified in this model. When kc . kb, the kinetics simplifies to k1 = ka, corresponding to the process of irreversible surface crossing followed by rapid ground state recovery. If kb . kc, the kinetics is governed by the formation of an equilibrium between the two excited states involved such that k1 = (ka/kb)kc where (ka/kb) is the equilibrium constant K. In this case, the activation energy term, ΔE1, is the free energy difference between the two states involved in the equilibrium plus any activation energy for surface crossing to the ground state, if such a barrier exists.18 Thus, measured activation energies may not always reflect the same properties, but the activated decay rate

k1 is proportional to ka in both limiting cases where kc . kb and kb , kc. Experimentally, the magnitude of the pre-exponential factor for activated decay, A1, is often used to assign a deactivation mechanism. Normally, activated decay is thought to proceed through an irreversible surface crossing from the 3MLCT state to a 3MC state, with a pre-exponential factor corresponding to a typical vibrational frequency, i.e., A1 ≈ 10121014 s1. Preexponential factors in the range 107108 s1 have also been observed, and attributed to decay via a higher MLCT state with more pronounced singlet character (MLCT0 in Scheme 1).20,21,50 In a few cases, A1-values around 1091010 s1 have been reported.12,19,21,5052 These observations have been ascribed either to reversible surface crossings between the 3MLCT state and a 3MC state21,50 or between the 3MLCT state and higher, more short-lived 3MLCT states.12,19,51 In either case A1 equals the decay rate constant of the higher state to the ground state. Experimental data for the herein investigated complexes (Table 4) reveal significantly different pre-exponential factors, and that A1 for [RuII(dqp)2]2+ is significantly less than 10121014 s1.52 The calculated potential energy surfaces provide a theoretical basis for improved understanding of excited state processes. Ideally one should be able to connect phenomenological kinetic models to fundamental kinetic theory, such as transition state theory (TST).53 In TST, the rate of a process is given by eq 654 ! ! kB T ΔS‡ ΔH ‡ k¼k exp exp ð6Þ h R RT where k is the transmission coefficient, kB is the Boltzmann constant, h is Planck’s constant, and ΔS‡ and ΔH‡ are the difference between the reactant state and the transition state in entropy and enthalpy, respectively. A direct comparison between eqs 4 and 6 cannot be done simply from the here calculated PESs, but various aspects of the calculated PES that are relevant for the excited state kinetics are discussed below. Experimentally, it is much harder to estimate energies of 3MC states than of emissive 3MLCT states, but calculations provide measures for both, see Tables 2 and 3. Comparison with previously reported data11,13,16 reveals a slight but consistent overestimation of the 3MLCT state energy, but this can, at least partly, be attributed to the exclusion of solvent effects in the calculations. The lack of experimental values to contrast the calculated 3MC state energies against makes direct comparisons precarious. Therefore, we focus on the relative measures for the investigated series, and examine the 3MLCT3MC ΔE trend to extract information and avoid any systematic errors. The results presented above show that the energy separation between the 3MC and the 3MLCT state is small for all three complexes. 1047



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Scheme 2. Schematic Illustration of the Relation between the Ligand Field Splitting at the GS (Ground State) Geometry (Left) and Thermally Activated 3MLCT3MC Deactivation along an Effective Reaction Coordinate Q (Right)

They also suggest that the 3MC state of [RuII(dqp)2]2+ is destabilized compared to the 3MC states of the other two complexes. This agrees well with experimentally obtained ground state bond lengths and angles where [RuII(dqp)2]2+ is shown to be more octahedral (see Table 3). The prediction of the 3 MLCT3MC ΔE trend also agrees well with the observed trend for excited state lifetimes, see Table 4. The small calculated energy separation between the relaxed 3 MC and 3MLCT states may at first sight appear contrary to standard ligand field theory which suggests that the 3MC state should be significantly destabilized compared to the 3MLCT state for highly octahedral RuII-complexes such as [RuII(dqp)2]2+. However, the calculated triplet PESs (Figures 2, 3, and 5) also corroborate previous calculations17 that the 3MC states are significantly displaced compared to the 3MLCT states. The calculated 3MLCT state minima are characterized by all, or all but one, RuN bond lengths being near those of typical ground state single RuN bond distance, ca. 2.1 Å, while the 3 MC states show significant elongation of the RuN bonds directly involved in the change of electronic state. Thus, while the standard ligand field theory usually refers to vertical excitations from the ground state, the low relaxed 3MC energy is seen to arise from the significant stabilization of the 3MC state at larger Q values (longer RuN bonds). This is illustrated in Scheme 2 for two complexes A and B with similar ground state and 3MLCT state energy surfaces, but with an increased ligand field splitting in complex B corresponding to a higher vertical 3MC state energy (left) compared to that of complex A. The stabilization of 3MC states at larger Q values results in 3MLCT3MC crossing points at intermediate Q values marked A and B for the two complexes, respectively. The PES plots also show that the position of the 3 MC state relative to the 3MLCT state along the effective reaction coordinate is different for the three investigated complexes. A large shift, as in [RuII(dqp)2]2+, is necessary in order to form an extended 3MLCT state region and a large activation barrier for the 3MLCT3MC transition.

The calculated PESs also provide information about the MLCT3MC surface crossings. In particular, an increasingly pronounced 3MLCT3MC transition barrier for the tpy-bmp-dqp series (shown in Figures 2, 3, and 5) qualitatively correlates well with the measured trend of increasing excited state lifetimes, although it can be noted that experimental results show a larger barrier for [RuII(bmp)2]2+ than for [RuII(dqp)2]2+. This apparent discrepancy can be explained by the different kinetic limits of deactivation for these two complexes, as judged from their respective pre-exponential factors A1 (eq 1). Thus, the experimental activation energies do not reflect the same property and cannot be compared directly. In terms of the schematic representation of the 3MLCT3MC decay illustrated in Scheme 2, the increased ligand field splitting in the vertical excitation region, and the shift in energy and position of the relaxed 3MC state minima, together carry over to the 3MLCT3MC crossing point. Using this picture, one can speculate how the ligand field splitting is coupled to the excited state lifetime. Short-lived complexes, such as [RuII(tpy)2]2+, would then have crossing points similar to point A in Scheme 2 with low kinetic barriers for forward 3 MLCT3MC conversion. This would promote a large forward rate ka in eq 2, with an associated high rate for activated decay according to eq 4. In contrast, long-lived complexes, such as [RuII(dqp)2]2+, would have 3MLCT3MC crossing points that are shifted away from the 3MLCT state minimum both in energy and reaction coordinate, Q, similar to crossing point B in Scheme 2, resulting in slower 3MLCT state activated decay (smaller ka and k1 values in eqs 2 and 5, respectively). Thus, the calculated PESs suggest that the relative positions of the 3 MLCT and 3MC states in terms of both energy and location along the effective reaction coordinate have significant influence on the activated decay kinetics,16,35,36 and that neither vertical excitations, nor comparisons of calculated equilibrium state energies, are sufficient by themselves to fully understand the complex excited state decay dynamics of these complexes. The calculations also suggest that the shapes of the multidimensional triplet energy surfaces can influence the activated 3

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The Journal of Physical Chemistry A decay kinetics through entropic factors that have often been neglected.18 The PES calculations indicate that the reaction coordinate volume that is available for molecular motion inside the 3MLCT state minimum region increases significantly from the short-lived [RuII(tpy)2]2+ to the long-lived [RuII(dqp)2]2+ complex. In particular, the calculations indicate the emergence of additional low-energy vibrational modes inside the 3MLCT state region (not directly involved in the 3MLCT3MC conversion) with increasing 3MLCT state volume, such as, e.g., the asymmetric RuN stretch mode for the [RuII(dqp)2]2+ complex shown in Figure 2. This qualitatively indicates that the state’s entropy increases as the conformational space increases, with entropic effects generally influencing rate constants via the preexponential factor, cf., eq 6. Increased 3MLCT state entropy may thus contribute to reduce the forward rate constant ka for 3 MLCT3MC conversions that often determine the overall excited state lifetime, e.g., when k1 = ka in the limit where kc . kb in the kinetic scheme given by eqs 2 and 3. The substantial 3 MLCT state volume for the [RuII(dqp)2]2+ complex could in principle be a contributing factor for reducing the 3MLCT3MC crossing frequency (ka in eq 2). However, within the current analysis of the parameters in eq 1, the experimental data show that the crossing is reversible. Then the relatively large 3MLCT state volume will lower its free energy and therefore shift the equilibrium of eq 2 toward the 3MLCT state. Thus, in both kinetic limits (i.e., with either irreversible or reversible 3MCLT 3 MC crossing) the comparatively large 3MLCT state volume for [RuII(dqp)3]2+ may contribute to reduce the rate of excited state deactivation. Noticeable differences in the shapes of the 3MLCT and 3MC states in the calculated multidimensional PESs for the three investigated complexes are, furthermore, revealed. In contrast to the well-defined 3MLCT states' minima, the 3MC states are calculated to be shallow states where two or more RuN bonds have been significantly elongated, resulting in the presence of much larger 3MC state low-energy regions that extend to large Q. This increases the available reaction coordinate volumes for the 3 MC states compared to the corresponding 3MLCT states in a way that is likely to influence the excited state decay kinetics. Specifically, the 3MC states are likely to be favored statistically over the 3MLCT states for all investigated complexes due to their more shallow nature. Depending on the other kinetic factors involved, this effect will either push the 3MLCT3MC equilibrium toward the 3MC product state, or contribute to making the 3 MLCT3MC forward transition an effectively irreversible process. It is worth noting that the multidimensional energy surface shape effects show up only partially in one-dimensional schematic representations using a single effective reaction coordinate, such as Scheme 2, while they are accentuated in the multidimensional reaction coordinate spaces, since the same effect applies to several RuN bonds. A final observation concerning the shapes of the calculated PES is that the shallow nature of the 3MC state for large Q-values carries over to the prediction of a low-energy 3MC-ground state crossing seam, shown in Figure 4 for the short-lived [RuII(tpy)2]2+ complex. This provides a direct path for ground state recovery, cf., eq 3. The observed singlettriplet crossing for stretched RuN coordinates is, in fact, consistent with typical bond dissociation curves for a wide range of molecular systems where lowenergy triplet states are expected for stretched bonds. The calculated PES provides an improved qualitative understanding of the 3MLCT3MC activated decay pathway and its

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kinetic limitations, but it is not possible to convert the calculated PES properties into accurate quantitative predictions of experimental lifetimes. Computational errors for the calculated absolute energy barriers are likely to be significant, e.g., for the 3 MLCT3MC conversions, considering the small energy barriers involved (∼0.1 eV). Experimentally, kinetic effects such as explicit solvent dynamics can contribute to making direct comparisons with experiments inaccurate. Furthermore, deviations from the simple irreversible 3MLCT3MC surface crossing can complicate the experimental analysis and weaken the quantitative connection between computational and experimental results.

’ CONCLUSIONS First principles quantum chemical calculations have been used to produce multidimensional triplet excited state potential energy surfaces for a set of three bis-tridentate RuII-polypyridyl complexes with very different excited state lifetimes. The calculated PESs indicate clear qualitative differences for the triplet excited state properties of the three investigated bis-tridentate RuII-complexes that survive beyond the FranckCondon region. The presented energy surfaces provide a trend for the 3MLCT 3 MC activation process that qualitatively agrees well with experimentally obtained excited state lifetimes, constituting a significant addition to the understanding of the excited state decay processes. As expected, the 3MLCT states are calculated to have energy minima located close to the ground state geometry. For the 3MC states, the calculated energy surfaces confirm the generally held view that these have minima that are significantly displaced to longer RuN bond lengths. The 3MLCT and 3MC states have significantly different energy profiles, with a shallower 3MC state energy profile relating to the different nature of this electronic state. This makes for significantly larger available low-energy 3 MC state regions in the available coordinate space. The location of the 3MLCT3MC activated crossing regions also has a strong influence on the effective 3MLCT state hypervolume available. Thus, multidimensional energy surfaces help to reconcile experimental information that wide ranges of excited state lifetimes can be observed for complexes with quite similar experimentally observed activation energies. This illustrates the strength of using calculations to investigate multidimensional energy surfaces for light-harvesting complexes that include transient excited state structures that are difficult to fully characterize experimentally, and it will be interesting in future work to build on the insights gained here to improve further on the accuracy of the calculations to see if better quantitative agreement with experimental work can be achieved. Such developments can include both the use of more accurate quantum chemical methods, and the performance of explicitly dynamical simulations. ’ ASSOCIATED CONTENT

bS

Supporting Information. Complete ref 37 and figure of calculated spin densities for the 3MLCT and 3MC states for all three complexes. This material is available free of charge via the Internet at http://pubs.acs.org.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected]. 1049



’ ACKNOWLEDGMENT The Swedish Research Council (VR), the Swedish National Supercomputer Centre (NSC), and the Lund Supercomputer Centre (LUNARC) are gratefully acknowledged for generous support. ’ REFERENCES (1) Gray, H. B.; Winkler, J. R. Annu. Rev. Biochem. 1996, 65, 537–561. (2) Hagfeldt, A.; Gr€atzel, M. Acc. Chem. Res. 2000, 33, 269–277. (3) Alstrum-Acevedo, J. H.; Brennman, M. K.; Meyer, T. J. Inorg. Chem. 2005, 44, 6802–6827. (4) Campagna, S.; Puntoriero, F.; Nastasi, F.; Bergamini, G.; Balzani, V. Top. Curr. Chem. 2007, 280, 117–214. (5) Magnuson, A.; Anderlund, M.; Johansson, O.; Lindblad, P.; Lomoth, R.; Polivka, T.; Ott, S.; Stensj€o, K.; Styring, S.; Sundstr€ om, V.; Hammarstr€om, L. Acc. Chem. Res. 2009, 42, 1899–1909. (6) Wagenknecht, P. S.; Ford, P. C. Coord. Chem. Rev. 2011, 255, 591–616. (7) Sauvage, J.-P.; Collin, J.-P.; Chambron, J.-C.; Guillerez, S.; Coudret, C. Chem. Rev. 1994, 94, 993–1019. (8) Medlycott, E. A.; Hanan, G. S. Coord. Chem. Rev. 2006, 250, 1763–1782. (9) Wolpher, H.; Johansson, O.; Abrahamsson, M.; Kritikos, M.; Sun, L. C.; Åkermark, B. Inorg. Chem. Commun. 2004, 7, 337–340. (10) Abrahamsson, M.; Wolpher, H.; Johansson, O.; Larsson, J.; Kritikos, M.; Eriksson, L.; Norrby, P. O.; Bergquist, J.; Sun, L. C.; Åkermark, B.; Hammarstr€om, L. Inorg. Chem. 2005, 44, 3215–3225. € (11) Abrahamsson, M.; J€ager, M.; Osterman, T.; Eriksson, L.; Persson, P.; Johansson, O.; Becker, H.-C.; Hammarstr€om, L. J. Am. Chem. Soc. 2006, 128, 12616–12617. (12) Abrahamsson, M.; Becker, H.-C.; Hammarstr€om, L.; Bonnefous, C.; Chamchoumis, C.; Thummel, R. P. Inorg. Chem. 2007, 46, 10354–10364. € (13) Abrahamsson, M.; J€ager, M.; Kumar, J.; Osterman, T.; Persson, P.; Becker, H.-C.; Johansson, O.; Hammarstr€om, L. J. Am. Chem. Soc. 2008, 130, 15533–15542. (14) Schramm, F.; Meded, V.; Fliegl, H.; Fink, K.; Fuhr, O.; Qu, Z.; Klopper, W.; Finn, S.; Keyes, T. E.; Ruben, M. Inorg. Chem. 2009, 48, 5677–5684. (15) Hammarstr€om, L.; Johansson, O. Coord. Chem. Rev. 2010, 254, 2546–2559. (16) Abrahamsson, M.; Lundqvist, M. J.; Wolpher, H.; Johansson, O.; Eriksson, L.; Bergquist, J.; Rasmussen, T.; Becker, H.-C.; Hammarstr€om, L.; Norrby, P.-O.; Åkermark, B.; Persson, P. Inorg. Chem. 2008, 47, 3540–3548. (17) Borg, O. A.; Godinho, S. S. M. C.; Lundqvist, M. J.; Lunell, S.; Persson, P. J. Phys. Chem. A 2008, 112, 4470–4476. (18) Juris, A.; Balzani, V.; Barigelletti, F.; Campagna, S.; Belser, P.; von Zelewsky, A. Coord. Chem. Rev. 1988, 84, 85–277. (19) Harriman, A.; Izzet, G. Phys. Chem. Chem. Phys. 2007, 9, 944–948. (20) Barigelletti, F.; Juris, A.; Balzani, V.; Belser, P.; von Zelewsky, A. Inorg. Chem. 1983, 22, 3335–3339. (21) Allen, G. H.; White, R. P.; Rillema, D. P.; Meyer, T. J. J. Am. Chem. Soc. 1984, 106, 2613–2620. (22) Vlcek, A., Jr. Coord. Chem. Rev. 2000, 200202, 933–977. (23) Cramer, C. J.; Truhlar, D. G. Phys. Chem. Chem. Phys. 2009, 11, 10757–10816. (24) Vlcek, A., Jr.; Zalis, S. Coord. Chem. Rev. 2007, 251, 258–287. (25) Guillemoles, J.-F.; Barone, V.; Joubert, L.; Adamo, C. J. Phys. Chem. A 2002, 106, 11354–11360. (26) Fantacci, S.; De Angelis, F.; Selloni, A. J. Am. Chem. Soc. 2003, 125, 4381–4387. (27) Lundqvist, M. J.; Galoppini, E.; Meyer, G. J.; Persson, P. J. Phys. Chem. A 2007, 111, 1487–1497. (28) Meylemans, H. A.; Damrauer, N. H. Inorg. Chem. 2009, 48, 11161–11175.

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(29) Persson, P.; Lundqvist, M. J. J. Phys. Chem. B 2005, 109, 11918–11924. (30) Alary, F.; Heully, J.-L.; Bijeire, L.; Vicendo, P. Inorg. Chem. 2007, 46, 3154–3165. (31) Alary, F.; Boggio-Pasqua, M.; Heully, J.-L.; Marsden, C. J.; Vicendo, P. Inorg. Chem. 2008, 47, 5259–5266. (32) Salassa, L.; Garino, C.; Salassa, G.; Gobetto, R.; Nervi, C. J. Am. Chem. Soc. 2008, 130, 9590–9597. (33) Salassa, L.; Garino, C.; Salassa, G.; Nervi, C.; Gobetto, R.; Lamberti, C.; Gianolio, D.; Bizzarri, R.; Sadler, P. J. Inorg. Chem. 2009, 48, 1469–1481. (34) Heully, J.-L; Alary, F.; Boggio-Pasqua, M. J. Chem. Phys. 2009, 131, 184308. (35) Dixon, I. M.; Alary, F.; Heully, J.-L. Dalton Trans. 2010, 39, 10959–10966. (36) Yang, L.; Okuda, F.; Kobayashi, K.; Nozaki, K.; Tanabe, Y.; Ishii, Y.; Haga, M. Inorg. Chem. 2008, 47, 7154–7165. (37) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, J. A., Jr.; Vreven, T.; Kudin, K. N.; Burant, J. C.; et al. Gaussian 03, revision C.02; Gaussian, Inc.: Wallingford, CT, 2004. (38) Becke, A. D. J. Chem. Phys. 1993, 98, 5648–5652. (39) Lee, C. T.; Yang, W. T.; Parr, R. G. Phys. Rev. B 1988, 37, 785–789. (40) Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys. Rev. Lett. 1996, 77, 3865–3868. (41) Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys. Rev. Lett. 1997, 78, 1396. (42) Adamo, C.; Barone, V. J. Chem. Phys. 1999, 110, 6158–6169. (43) Dolg, M.; Wedig, U.; Stoll, H.; Preuss, H. J. Chem. Phys. 1987, 86, 866–872. (44) Nozaki, K. J. Chin. Chem. Soc. 2006, 53, 101–112. (45) Moret, M.-E.; Tavernelli, I.; Chergui, M.; Rothlisberger, U. Chem.Eur. J. 2010, 16, 5889–5894. (46) Kumar, R. J.; Karlsson, S.; Streich, D.; Jensen, A. R.; Jager, M.; Becker, H.-C.; Bergquist, J.; Johansson, O.; Hammarstr€om, L. Chem. Eur. J. 2010, 16, 2830–2842. (47) Lundqvist, M. J. Quantum Chemical Modeling of Dye-Sensitized Titanium Dioxide: Ruthenium Polypyridyl and Perylene Dyes, TiO2 Nanoparticles, and Their Interfaces. Ph.D. Dissertation, Uppsala University, Sweden, October 13, 2006. (48) J€ager, M.; Eriksson, L.; Bergquist, J.; Johansson, O. J. Org. Chem. 2007, 72, 10227–10230. (49) Gawelda, W.; Johnson, M.; De Groot, F. M.; Abela, R.; Bressler, C.; Chergui, M. J. Am. Chem. Soc. 2006, 128, 5001–5009. (50) Barigelletti, F.; Juris, A.; Balzani, V.; Belser, P.; von Zelewsky, A. J. Phys. Chem. 1987, 91, 1095–1098. (51) Gardner, J. M.; Abrahamsson, M.; Farnum, B. H.; Meyer, G. J. J. Am. Chem. Soc. 2009, 131, 16206–16214. (52) Abrahamsson, M. Tuning of the Excited State Properties of Ruthenium(II)-Polypyridyl Complexes. Ph.D. Dissertation, Uppsala University, Sweden, December 1, 2006. (53) Eyring, H. J. Chem. Phys. 1935, 3, 107–115. (54) Laider, K. J.; King, M. C. J. Phys. Chem. 1983, 87, 2657–2664.

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Influence of Triplet State Multidimensionality on Excited State Lifetimes

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