SpinâOrbit Treatment of UVâvis Absorption Spectra and Photophysics

Article pubs.acs.org/JPCA

Spin−Orbit Treatment of UV−vis Absorption Spectra and Photophysics of Rhenium(I) Carbonyl−Bipyridine Complexes: MS-CASPT2 and TD-DFT Analysis Radka Heydová,†,‡ Etienne Gindensperger,§ Roberta Romano,∥ Jan Sýkora,† Antonín Vlček, Jr.,*,†,∥ Stanislav Záliš,*,† and Chantal Daniel*,§ †

J. Heyrovský Institute of Physical Chemistry, Academy of Sciences of the Czech Republic, Dolejškova 3, CZ-182 23 Prague, Czech Republic ‡ Department of Physical Chemistry and Macromolecular Chemistry, Faculty of Science, Charles University, Albertov 6, 128 43 Prague 2, Czech Republic § Laboratoire de Chimie Quantique, Institut de Chimie UMR7177 CNRS-Université de Strasbourg, 67 070 Strasbourg, France ∥ Queen Mary University of London, School of Biological and Chemical Sciences, Mile End Road, London E1 4NS, U.K. S Supporting Information *

ABSTRACT: The lowest-lying spectral transitions in [ReX(CO)3(bpy)] (X = Cl, Br, I; bpy = 2,2′-bipyridine) complexes were calculated by means of spin−orbit time-dependent density functional theory (SO-TDDFT) and spin−orbit multistate complete active space second-order perturbation theory (SO-MS-CASPT2). Computational results are compared with absorption spectra measured in different solvents and used to qualitatively explain the temperature dependence of the phosphorescence decay parameters that were measured for the whole series of complexes. Spin−orbit excited-state calculations interpret their electronic absorption spectra as arising from a bunch of spin mixed states with a singlet component of only 50−90% (depending on the halide), and attribute the phosphorescence decay to thermal population of spin-mixed states with a substantial singlet character.

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INTRODUCTION

phosphorescent-state formation within less than 20 fs, comparable to the period of highest-frequency vibrations of the bipyridine ligand.1,2 The rationalization of these very sophisticated experiments needs the contribution from the theory. Only a few theoretical studies, most of the time based on molecular orbital approaches, have been dedicated to ISC processes in transition metal complexes. The first detailed investigations of the dynamics of singlet to triplet transitions have been performed to understand the photochemical reactivity of HCo(CO)49 and HM(CO)3 (α-diimine) (M = Mn, Re)10,11 molecules, that undergo concurrent primary photoreactions whose branching ratio is controlled by ISC from the absorbing state to the reactive states. The first direct simulation of an intersystem crossing process by wavepacket propagation on SO coupled 1E and 3A1 potential energy surfaces (PES) of HCo(CO)4 has shown that the homolytic breaking of the H−Co bond occurs within 20 fs and that the lowest 3A1 state is populated within 10 fs. The singlet

Electronic spectra, photophysics, and photochemistry of heavymetal complexes are traditionally interpreted in terms of spinfree singlet and triplet states, ignoring the strong spin−orbit coupling (SOC) due to the metal atom. Nevertheless, SOC is responsible for most of the typical photophysical features of metal complexes, such as the virtual absence of fluorescence, (ultra)fast population of triplet states, and their efficient radiative decay (phosphorescence). SOC thus underlies important applications of metal complexes in organic light-emitting diodes, as luminescent labels, probes, and photoimaging agents, as well as sensitizers of light-energy conversion. An illustration of the SOC importance is given by the recent discovery of ultrafast intersystem crossings (ISC) controlling the photophysical and photochemical properties of a number of transition metal complexes. Indeed, with the development of ps−fs time-resolved absorption/emission spectroscopies, these elementary processes are now detectable within a few tens of fs. Singlet to triplet as well as doublet to quartet or triplet to quintet ISC rates were found to range from 10 fs to a few picoseconds.1−8 Surprisingly, 1MLCT to 3MLCT (metal-toligand-charge-transfer) transitions are characterized by similar kinetics in [Fe(bpy)3]2+ and [Ru(bpy)3]2+ with evidence of the © 2012 American Chemical Society

Special Issue: Jörn Manz Festschrift Received: June 4, 2012 Revised: July 20, 2012 Published: July 20, 2012 11319

dx.doi.org/10.1021/jp305461z | J. Phys. Chem. A 2012, 116, 11319−11329

The Journal of Physical Chemistry A

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two or three ultrafast steps, the fastest one having been attributed to the 1CT → 3CT intersystem crossing (ISC).7,18−19 For halides, singlet excited-state lifetime counterintuitively increases on going from the chloride (85 fs) to the bromide (128 fs) and iodide (152 fs), whereas SOC between the singlet and triplet states increases in the order Cl < Br ≪ I due to an increase of both the admixture of the halide character to the excited states in question and the halide SOC constant.7 Analogous complexes [Re(L)(CO) 3 (α-diimine)] + (L = 4-ethylpyridine, imidazole) show ISC in the 130−180 fs range, essentially independent of the α-diimine (bipyridine and phenanthroline derivatives).7,19 Also, the nonradiative decay of the lowest triplet state is thermally activated,20 indicating the presence of rapidly decaying close-lying excited states; this hypothesis was not supported by any of the spin-free TD-DFT calculations reported so far. The goal of the present study is to investigate the vertical spin-free and spin−orbit theoretical absorption spectra of [ReX(CO)3(bpy)] (X = Cl, Br, I) complexes (Figure 1) by

and triplet excited-state quantum dynamics of HMn(CO)3 (α-diimine) and HRe(CO)3(α-diimine) performed on twodimensional PES has enabled us to decipher the mechanism of dissociation of these two complexes: (i) a direct ultrafast (∼400 fs) CO dissociation in the case of the first row transition metal compound; (ii) an indirect homolysis of the Re−H bond in the third row transition metal compound controlled by an ultrafast 1 MLCT to 3SBLCT (sigma-bond-to-ligand-charge-transfer) ISC occurring within 50 fs. The nuclear relaxation effects, apart from those describing the photochemical metal−ligand dissociation, were not included in these pioneering theoretical studies. According to the most recent experiments reported on Fe, Ru, and Re compounds,1,2,7,8 the role of structural dynamics could be very important and could explain the lack of correlation between the well-known SO heavy atom effect and the rate of ultrafast ISC processes.7,12 More recently, review articles have discussed possible consequences of SOC on the electronic structure, excited state characters, and their deactivation pathways,12 and demonstrated relations between SOC, the MLCT character of the lowest “triplet” state, its zero-field splitting, and photoluminescence, that are of paramount importance for OLED applications.13−15 Spin−orbit calculations of electronic spectra and excited states are still rare, but they consistently point to large densities of low-lying spin−orbit states and extensive singlet−triplet mixing.12,16,17 The development of quantum chemical relativistic methods enables accurate calculation of spin-free and spin−orbit absorption spectra. Whereas the use of four-component relativistic approaches is still a challenge for electronic excited-state calculations in large transition metal complexes, two-component/ two-step approaches offer a very promising alternative based either on wave functions (CASSCF/MS-CASPT2) or on density functional theory (TD-DFT). Calculated spin-free and spin−orbit absorption spectra have been compared for simple transition metal hydrides H2M(CO)4 (M = Fe, Os) and HM(CO)5 (M = Mn, Re).16 Whereas the SO effects have a little influence on the electronic absorption spectroscopy of first row transition metal complexes (Fe, Mn), the spectra of H2Os(CO)4 and HRe(CO)5 are significantly affected by SO corrections, leading to a larger number of weak transitions as compared to a few strong ones in spin-free spectra. The SO spectra are characterized by strong mixing between states with disappearance of pure singlet and triplet electronic states. It appears that considering SOC explicitly is essential to get a correct interpretation of photophysical phenomena. For example, relativistic SO TD-DFT calculations of fac-[Re(imidazole)(CO)3(phen)]+ have identified 10 SO states in the energy range between the lowest allowed MLCT transition and the ground state, in contrast to four spin-free states.12 It was thus suggested that SO states can provide a deactivation cascade for energy dissipation from the optically excited state and some of the ultrafast relaxation steps observed spectrally could correspond to nonradiative transitions between SO states, instead of their customary assignment to vibrational relaxation. Within the SO conceptual framework, it is also appropriate to treat internal conversion and intersystem crossing in a unified way as nonradiative transitions between SO states rather than two different processes. Rhenium(I) tricarbonyl complexes [Re(X)(CO)3(α-diimine)] present some photophysical puzzles that likely are related to SOC. For example, optical excitation of their lowest allowed Re(X)(CO)3 → diimine CT transition is followed by

Figure 1. Schematic structure of [ReX(CO)3bpy] (X = Cl, Br, I).

means of SO-TD-DFT and SO-MS-CASPT2 methods in order to rationalize the photophysical behavior of this class of compounds that is characterized by ultrafast electronic-vibrational relaxation dynamics upon excitation of the low-lying singlet MLCT state and temperature-dependent decay of the corresponding triplet. Comparison between spin−orbit density functional theory and wave function approaches will be another outcome of this theoretical study. The emerging SO models provide a qualitatively new insight into the spectroscopy and photophysics of this class of complexes.

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COMPUTATIONAL AND EXPERIMENTAL DETAILS Quantum Chemical Calculations. The vertical spin-free and spin−orbit absorption spectra of [ReX(CO)3(bpy)] (X = Cl, Br, I) have been computed for the DFT/PBE0 optimized geometries, schematically depicted in Figure 1, by means of time-dependent density functional theory (TD-DFT) and state average complete active space SCF/multistate complete active space perturbation theory second -order (SA-CASSCF/MSCASPT2) methods using the Gaussian 09,21 ADF,22,23 and MOLCAS24 7.6 program packages. Atomic natural orbital relativistic consistent correlated ANORCC basis sets25 have been used for the SA-CASSCF/MSCASPT2 calculations with the following triple-ζ contraction scheme: (24s, 21p, 15d, 11f, 4g, 2h) contracted to [7s, 6p, 4d, 2f, 1g] for Re, (14s, 9p, 4d, 3f, 2g) contracted to [4s, 3p, 2d, 1f] for the first row atoms, (8s, 4p, 3d, 1f) contracted to [3s, 2p, 1d] for H, (17s, 12p, 5d, 4f, 2g) contracted to [5s, 4p, 2d, 1f] for Cl, (20s, 17p, 11d, 4f, 2g) contracted to [6s, 5p, 3d, 2f, 1g] for Br. For I, a quadruple-ζ (22s, 19p, 13d, 5f, 3g) basis set contracted to [8s, 7p, 5d, 4f, 2g] has been used. A total of 16 electrons were correlated in 13 active orbitals. 11320



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The MS-CASPT2 calculations were performed in a vacuum, using SA-CASSCF wave functions, and a level shift of 0.15 was applied in order to avoid intruder-states problems. All the calculations were performed with constrained Cs symmetry. At this level of electronic structure calculations, nuclear relaxation effects in the excited states are not taken into account and the computed spectra correspond to vertical transitions. Spin−orbit spectra were calculated by the restricted active space state interaction RASSI procedure which has been modified to include the spin−orbit part of the Dauglas−Kroll Hamiltonian.26 For TD-DFT calculations, Slater type orbital (STO) basis sets of triple-ζ quality with two polarization functions for Re and double-ζ quality with one polarization function for the remaining atoms were employed. The PBE0 hybrid functional26,27 together with the scalar relativistic (SR) zero-order regular approximation (ZORA)28 and the COSMO model29 for the solvent effect corrections (CH3CN, CH2Cl2, toluene) were used in the present study. Spin orbit TD-DFT calculations were done with the ADF software. In the first step, scalar relativistic TD-DFT calculations are performed in order to determine the lowest 1,3A′ and 1,3A″ spin-free excited states. In the second step, spin−orbit coupling is applied as a perturbation to obtain transition energies to the spin−orbit A′ and A″ excited states.30 For comparison, several lowest excited states of [ReI(CO)3(bpy)] have also been calculated by the relativistic two-component zeroth-order regular approximation in the TDDFT method30 and the results were found comparable. In order to model emission properties, TD-DFT calculations were also performed at the optimized geometry of the lowest triplet state (unrestricted Kohn−Sham approach used for geometry optimization). Materials. The starting materials and solvents were used as obtained from Aldrich. [ReCl(CO)3(bpy)] and [ReBr(CO)3(bpy)] were prepared following standard procedures by refluxing the corresponding Re(CO)5X with bpy in degassed toluene for 3−4 h followed by a thorough washing with diethylether and petroleum ether.20 A novel procedure was used to synthesize [ReI(CO)3(bpy)]: 440 mg (0.8 mmol) of [Re(OTf)(CO)3(bpy)] (prepared according to ref 31) was refluxed for 3 h with 300 mg (0.98 mmol) of Bu4NI under Ar in ∼40 mL of degassed THF in the dark. The solvent was then removed under a vacuum, and the residuum was dissolved in about 40 mL of MeCN under gentle heating. (No protection from air is necessary at this stage.) A greenish-yellow crystalline solid has precipitated upon cooling the solution and small volume reduction. The product was purified by recrystallization from MeCN. Spectroscopic Measurements. Absorption spectra were obtained on a Perkin-Elmer Lambda 35 spectrometer in MeCN, CH2Cl2 (DCM), and toluene of spectroscopic quality. Emission lifetimes were measured using the time-correlated single-photon counting technique on a IBH 5000 U instrument equipped with a cooled Hamamatsu R3809U-50 microchannel plate photomultiplier. Samples were excited at 373 nm with an IBH NanoLED-03 diode laser (∼100 ps fwhm). The emission monochromator was set at the maximum of the stationary emission band. Data were analyzed using IBH Datastation2 or Microcal Origin 7.1 software. The samples were prepared in a controlled-atmosphere (0.3 ppm O2) glovebox (Jacomex) using anhydrous Aldrich SureSeal MeCN.

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RESULTS AND DISCUSSION

Experimental Absorption Spectra. UV−vis absorption spectra of [ReX(CO)3(bpy)] (X = Cl, Br, I) consist of three main features: at 380−400 nm, 290−295 nm, and 235−245 nm (Figure 2 and Table 1), that have been previously attributed to

Figure 2. UV−vis absorption spectra of [ReX(CO)3(bpy)] in different solvents.

Re(X)(CO)3 → bpy 1CT, 1IL (ππ*-bpy) and Re → CO 1 MLCT/1IL by empirical arguments,32 as well as spin-free TDDFT calculations.7,33 For X = I, an additional band emerges around 223 nm that was assigned to a higher-lying Re(X)(CO)3 → bpy 1CT transition.32 The lowest-energy absorption band around 380 nm shifts to lower energies on changing the halide ligand: Cl ≥ Br ≫ I (Figures 2 and 3-top) and on decreasing the solvent polarity: MeCN > DCM > toluene (Table 1). Detailed inspection of the band shape indicates the presence of two shoulders on the lowenergy side for all three complexes. The shoulders become resolved in the [ReI(CO)3bpy] spectrum in toluene, allowing for a Gaussian analysis that puts in evidence two weak bands at 20 150 and 22 300 cm−1, preceding the main band at 23 690 cm−1, the band-area ratio being 0.047:0.011:1; see Figure 3bottom. (Note that the respective bandwidths are widely different.) It is conceivable that the two low-lying bands originate from spin-mixed states. Below, experimental absorption spectra of [ReX(CO)3(bpy)] are interpreted under the light of spin-free and spin−orbit MSCASPT2 and TD-DFT computational results presented in the next two sections devoted to the theoretical absorption spectroscopy. Spin-Free Theoretical Absorption Spectra. The spinfree MS-CASPT2 and TD-DFT transition energies to the lowlying singlet and triplet excited states of [ReX(CO)3bpy] (X = Cl, Br, I) are reported in Tables S1 and S2 of the Supporting Information, respectively. Whereas the vis/near-UV part of the spectra has been simulated by both methods, namely, TD-DFT (solvent corrected) and MS-CASPT2 (in vacuum), the theoretical UV part of the spectrum below 275 nm has been computed only by TD-DFT (solvent corrected). The MS-CASPT2 energetics of the three complexes are qualitatively similar, with the calculated strong transitions close to the experimental bands, the characters of the low-lying states 11321



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Table 1. Experimental Absorption Spectra of [ReX(CO)3(bpy)] in MeCN, DCM, and Toluene wavelength (nm) MeCN

CH2Cl2

toluene MeCN

CH2Cl2

toluene MeCN

CH2Cl2

toluene

a

371 315 291 252 234 387 316 294 257 238 403

sh sh

sh sh

375 315 sh 292 244 392 295 245 br 405 385 316 295 244 220 402 299 245 233 496 449 422

sh sh sh

sh sh

energy (cm−1)

molar abs. (M−1 cm−1)

[ReCl(CO)3(bpy)] 26 954 31 746 34 364 39 683 42 735 25 840 31 646 34 014 38 911 42 017 24 814 [ReBr(CO)3(bpy)] 26 667 31 746 34 247 40 984 25 510 33 898 40 816 24 691 [ReI(CO)3(bpy)] 25 974 31 646 33 898 40 984 45 455 24 876 33 445 40 816 42 918 20 145a 22 295a 23 687a

2900 7400 12 900 12 100 14 500 3500 17 900 19 300

2900

Figure 3. Top: Intensity-normalized absorption spectra of [ReX(CO)3(bpy)] in toluene. Bottom: Deconvoluted spectrum of [ReI(CO)3(bpy)] in toluene. Green, individual Gaussians; red, fitted function; black, experimental spectrum. Fitted parameters (max wavenumber, fwhm, relative band area): 20150 cm−1, 1500 cm−1, 0.047; 22300 cm−1, 740 cm−1, 0.011; 23690 cm−1, 4010 cm−1, 1.000.

13 800 17 900 3700 20 100 21 500

assigned to the e1A′ (X = Cl) and d1A′ states (X = Br, I). The nature of this band is mainly ππ*(bpy) intraligand (IL) transition with contributing MLCT. The solvent corrections, not applied in the case of the MSCASPT2 protocol, have been taken into account at the TDDFT level for MeCN, CH2Cl2, and toluene, i.e., the solvents in which the experimental spectra have been recorded. The spin-free TD-DFT theoretical spectra, depicted in Figure 4,

2400 16 300 20 400 24 600 2600 18 500 22 400 24 300

Determined by Gaussian analysis, Figure 3-bottom.

changing from predominantly MLCT (4dRe → π*) states to predominantly XLCT (pπ → π*) states when changing the halide ligand from Cl to I. Two MLCT excited states, a1A″ and b1A′ calculated at 24 780 cm−1 (403 nm) and 25 700 cm−1 (389 nm), contribute to the first band centered at 380 nm in [ReCl(CO)3(bpy)]. This band is shifted to the red on going to the bromo and especially iodo complexes, in accordance with the experimental trend. The a1A″ and b1A′ low-lying singlet states were respectively calculated at 24 340 cm−1 (411 nm) and 25 590 cm−1 (391 nm) in [ReBr(CO)3bpy] and at 21 920 cm−1 (456 nm) and 24 590 cm−1 (407 nm) in [ReI(CO)3bpy]. According to the calculated oscillator strengths, the b1A′ state is the most intense contribution to the lowest experimental band centered at around 400 nm. The next intense transitions occur in all three complexes at ∼300 nm, corresponding to an absorption shoulder at about 330 nm (Figure 2). The maximum of this peak is slightly shifted to the red when going from the chloride (296 nm) to the bromide (307 nm) and iodide (322 nm) complexes. Several excited states (c1A′, d1A′, e1A′, b1A″, c1A″, and d1A″) calculated between 29 650 and 36 465 cm−1 in [ReCl(CO)3bpy], 29 340 and 36 520 cm−1 in [ReBr(CO)3bpy], and 29 470 and 34 230 cm−1 in [ReI(CO)3bpy] contribute to this peak, but the most intense contribution is

Figure 4. TDDFT (spin-free) (PBE0/PCM-CH2Cl2) simulated UV− vis absorption spectra of [ReX(CO)3(bpy)] (fwhm = 4000 cm−1).

reproduce the trends when going from the chloro to the bromo and iodo complex, in accordance with the experimental spectra. The shift of the lowest-lying transitions to longer wavelengths in the series of solvents MeCN, CH2Cl2, and toluene is reproduced by TD-DFT. Compositions of TD-DFT calculated transitions are in qualitative agreement with the MS-CASPT2 assignment. In comparison with MS-CASPT2, the lowest-lying TD-DFT transitions are more delocalized, having larger XLCT admixture. Figure S1 (Supporting Information) depicts the electron density redistribution due to the excitations to the lowest-lying a1A″ and b1A′ states. The contribution of X to HOMO and HOMO-1 from which an electron is excited is ∼25, ∼40, and ∼65% in the case of Cl, Br, and I complexes, 11322



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42% c3A″) for X = I. In the case of [ReBr(CO)3bpy], this band is attributed to the 13A′ state (86% d1A′ 14% c3A″) calculated at 32 905 cm−1 or 304 nm, that is, between the corresponding bands of the Cl and I complexes, as expected. Two states with mixed MLCT/IL character, calculated at 35 700 cm−1 (280 nm) and 36 550 cm−1 (274 nm), corresponding to the 15A″ and 16A″ excited states, respectively, contribute strongly to the farther UV part of the spectrum of [ReCl(CO)3bpy]. The intense band observed below 275 nm in the experimental spectra of the three complexes is not reproduced by the SOMS-CASPT2 approach due to the limitation of the method in terms of active space and number of accessible solutions of the CASSCF wave function. SO-TD-DFT transition energies to the low-lying excited states of [ReX(CO)3bpy] (X = Cl, Br, I) calculated with solvent correction (CH2Cl2) are summarized in Table 3. The simulated spectra are shown in Figure 5. The lowest-lying set of transitions is best discussed using the spectra measured in toluene (Figure 3) that afford the highest resolution. To compare, the lowest-lying transitions of [ReX(CO)3(bpy)] complexes calculated by SO-TD-DFT in toluene at the optimized ground-state geometry are listed in Table S3 (Supporting Information) and a correlation of spinfree and spin−orbit states of [ReI(CO)3(bpy)] is shown in Figure 6. Left and right columns show spin-free singlet and triplet states, respectively, while the SO states are presented in the middle, with dashed lines indicating the principal contributions. Figure 6 thus illustrates the spin−orbit interactions of spin-free singlet and triplet states in the formation of two sets of SO states. Excitations to the fourth and sixth spin orbit excited states cA′ and dA′ have an oscillator strength of 0.0061 and 0.0018, respectively (Table S3, Supporting Information), explaining the presence and relative intensities of the two low-energy bands in the experimental spectrum of [ReI(CO)3(bpy)] as well as the shoulders apparent for the other two complexes. These features cannot be accounted for by the spin-free calculations, where the lowest transitions to a1A″, a3A″, and a3A′ are forbidden. Figure 7-bottom compares the low-lying spin−orbit transitions calculated by the SO-TD-DFT and SO-MSCASPT2 techniques. SO-TD-DFT transitions are spread over a broader energy range and have more similar intensities than the SO-MS-CASPT2 ones. The SO-TD-DFT theoretical spectrum thus accounts better for the large widths and shoulders observed experimentally. Contrary to the experiment, SO-MS-CASPT2 predicts an increase of the lowest absorption band intensity on going from Cl to Br and I, as the oscillator strength of the strongest contributing transition increases in the order Cl(4A′, f = 0.038) < Br(5A′, 0.068) < I(5A′, 0.082). On the other hand, SO-TD-DFT predicts decreasing molar absorptivity of the lowest band Cl(eA′, f = 0.047) > Br(eA′, 0.036) > I(eA′, 0.013), in a qualitative agreement with the experimental trend, Figure 2. This difference between the two computational techniques is probably caused by a limited active space, smaller MLCT-XLCT delocalization, and the neglect of solvent in SO-MS-CASPT2. Comparing the bottom and top panels in Figure 7 vertically demonstrates the SO effects on the calculated transitions. Lowest-lying excitation energies calculated with SOC are shifted to lower wavenumbers in comparison with spinfree ones as illustrated by SO-TDDFT/COSMO−CH2Cl2 calculated shifts of ∼1410 cm−1 (X = Cl), ∼1560 cm−1 (X = Br), ∼2250 cm−1 (X = I). Moreover, it follows that SOC

respectively. The peak observed at 295 nm is assigned to ππ*(bpy) 1IL transition with contributing MLCT. The intense feature below 245 nm has a predominant MLCT character mixed with ππ*(bpy). Spin−Orbit Theoretical Absorption Spectroscopy. The spin-free calculations discussed above account for the main experimental features with several low-lying singlet excited states of significant oscillator strengths, and weak satellite states of low oscillator strengths. However, a more detailed analysis and understanding of the low-lying excited states requires spin−orbit corrections. Indeed, the presence of two weak bands at ∼20 150 and ∼22 300 cm−1 observed for [ReI(CO)3(bpy)] in toluene (Figure 3) cannot be explained by the spin-free theoretical spectra. Moreover, the presence of nearly degenerate singlet and triplet excited states, the character of which may vary from MLCT to XLCT with mixed intermediate situations, leads to a very complicated electronic picture. The spin−orbit MS-CASPT2 and TD-DFT transition energies of low-lying excited states of [ReX(CO)3bpy] (X = Cl, Br, I) are reported in Tables 2 and 3, respectively. Different notations are used to clearly distinguish the results of the two calculations: SO states of given symmetry calculated by SOMS-CASPT2 are numbered, those calculated by SO-TD-DFT are labeled by lower-case letters. The spin-free states are labeled according to Tables S1 and S2 (Supporting Information). The SO-MS-CASPT2 absorption spectrum of [ReCl(CO)3bpy] starts at 23 600 cm−1 (424 nm) followed by several weakly absorbing MLCT states between 422 and 375 nm. The maximum of the lowest band is calculated at 384 nm (f = 0.0378) and corresponds to the 4A′ excited state composed of 79% b1A′ and 20% a3A″. This absorption feature is shifted to the red in the iodo complex, being composed of several transitions starting at 21 085 cm−1 (474 nm) and ranging up to 27 800 cm−1 (360 nm), with a maximum calculated at 24 930 cm−1 (401 nm) that corresponds to the intense 5A′ excited state (f = 0.0817) composed of 86% b1A′ and 12% a3A″. The character of the lowest band in [ReI(CO)3bpy] is mainly XLCT with MLCT contributions. The bromo complex presents an intermediate situation with the lowest shoulder at 22 010 cm−1 (454 nm). The calculated maximum of the first band occurs at 25 710 cm−1 (389 nm), resulting from the 5A′ excited state composed of 86% b1A′ and ∼10% a3A″ with an oscillator strength of 0.0682. The lowest part of the theoretical spin−orbit spectrum of [ReI(CO)3bpy] can be compared to the experimental spectrum recorded in toluene (Figure 3). In contrast to the spin-free analysis developed in the previous section, the calculated spin− orbit transitions (Table 2) explain the presence of the two weak bands at low energies that are assigned to the low-lying 2A″, and nearly degenerate 2A′, and 3A′ SO states, the two latter being mainly composed of triplet contributions. The 2A′ and 3A′ states acquire some transition dipole moments by spin− orbit singlet admixtures. This important feature is confirmed by the SO-TD-DFT calculations analyzed in the next section. SO-MS-CASPT2 calculations performed in a vacuum overestimate the transition energies by about 1000 cm−1 with respect to the experimental data. An absorption above the lowest band starts at 32 900 cm−1 (304 nm) in the Cl substituted complex, red-shifted to 29 530 cm−1 (339 nm) in the iodide. The strongest transition is calculated at 33 595 cm−1 or 298 nm (14A′: 79% e1A′ 17% d3A″) for X = Cl and 31 350 cm−1 or 319 nm (15A′: 53% d1A′ 11323



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Table 2. Spin−Orbit MS-CASPT2 Transition Energies (in cm−1) to the Low-Lying Excited States of [ReX(CO)3(bpy)] (X = Cl, Br, I), Associated Wavelengths (in nm) and Oscillator Strengths f a SO composition of the SO states in terms state of spin-free states

transition energies (cm−1)

wavelength (nm)

SO composition of the SO states in terms state of spin-free states

f

X = Cl 2A′ 3A′ 1A″ 2A″ 4A′ 5A′ 3A″ 4A″ 6A′ 7A′ 5A″ 8A′ 9A′ 6A″ 10A′ 7A″ 8A″ 9A″ 11A′ 10A″ 12A′ 11A″ 13A′ 14A′ 12A″ 13A″ 15A′ 16A′ 17A′ 14A″ 15A″ 16A″ 1A″ 2A′ 3A′ 2A″ 4A′ 3A″ 4A″ 5A′ 6A′ 5A″ 7A′ 6A″ 7A″ 8A′ 9A′ 10A′ 8A″ 9A″

a3A″ (79%) + b1A′ (18%) a3A″ (84%) + a3A′ (11%) a3A″ (85%) + a3A′ (12%) a1A″ (79%) + a3A′ (18%) b1A′ (79%) + a3A″ (20%) a3A′ (84%) + a3A″ (14%) a3A′ (85%) + a3A″ (13%) a3A′ (80%) + a1A″ (19%) b3A″ (76%) + c1A′ (20%) b3A″ (95%) b3A″ (96%) c1A′ (75%) + b3A″ (22%) c3A″ (71%) + d1A′ (23%) + b3A′ (5%) b1A″ (74%) + c3A′ (23%) c3A″ (57%) + b3A′ (25%) + c3A′ (16%) b3A′ (93%) c3A″ (70%) + c3A′ (20%) + b3A′ (8%) b3A′ (81%) + c3A″ (11%) b3A′ (71%) + c3A″ (19%) + c3A′ (6%) c3A′ (74%) + c3A″ (19%) c3A′ (74%) + c3A″ (21%) c3A′ (73%) + b1A″ (20%) d1A′ (70%) + c3A″ (24%) e1A′ (79%) + d3A″ (17%) d3A′ (72%) + c1A″ (19%) d3A′ (52%) + d3A″ (42%) d3A′ (51%) + d3A″ (44%) d3A″ (80%) + e1A′ (19%) d3A″ (53%) + d3A′ (46%) d3A″ (53%) + d3A′ (46%) c1A″ (76%) + d3A′ (19%) d1A″ (94%) + d3A′ (4%) X = Br a3A″ (83%) + a3A′ (14%) a3A″ (83%) + a3A′ (14%) a3A″ (90%) + b1A′ (7%) a1A″ (50%) + a3A′ (46%) a3A′ (83%) + a3A″ (16%) a3A′ (83%) + a3A″ (15%) a3A′ (53%) + a1A″ (47%) b1A′ (86%) + a3A″ (9%) b3A″ (97%) b3A″ (96%) b3A″ (95%) b3A′ (94%) b3A′ (94%) b3A′ (93%) c1A′ (85%) + c3A″ (7%) c3A″ (46%) + c3A′ (40%) + c1A′ (10%) c3A′ (50%) + b1A″ (43%) + c3A″ (5%) c3A″ (49%) + c3A′ (45%) + b1A″ (5%)


wavelength (nm)

30 550 31 700 31 705 31 870 32 905 34 460

327 315 315 314 304 290

0.0018

35 510

281

0.0107

35 590 36 200 36 250 36 760 36 860

281 276 276 272 271

0.0012 0.0006

36 910 37 130

271 269

0.0014

21 085 21 100 21 110 21 400 24 460 24 500 24 570 24 930 27 800 27 800 27 825 28 780

474 474 474 467 409 408 407 401 360 360 359 347

28 980 28 980 29 040 29 120 29 420 29 430 29 530 30 440

345 345 344 343 340 340 339 328

30 780 30 790 30 920

325 325 323

0.0011 0.0001 0.0108

31 000

323

0.0034

31 080 31 090 31 350 32 081 32 096 32 411 32 415 34 521

322 322 319 312 311 308 308 290

0.0005 0.0001 0.0121 0.0006 0.0020

f

X = Br 23 600 23 700 23 710 24 200 26 060 26 510 26 520 26 640 29 480 29 545 29 560 30 030 31 060 31 080 31 150

424 422 422 413 384 377 377 375 339 338 338 333 322 322 321

0.0089 0.0006

31 160 31 170 31 200 31 220 32 720 32 720 32 740 32 900 33 595 34 070 34 120 34 120 34 720 34 880 34 885 35 700 36 550

321 321 320 320 306 306 305 304 298 293 293 293 288 287 287 280 274

22 010 22 015 22 130 23 170 24 655 24 660 25 320 25 710 27 590 27 600 27 635 29 430 29 450 29 460 29 550 30 040

454 454 452 431 405 405 395 389 362 362 362 340 339 339 338 333

0.0033 0.0001 0.0006 0.0016 0.0001 0.0001

30 140 30 180

332 331

0.0034 0.0003

11A′ 10A″ 12A′ 11A″ 13A′ 12A″

0.0041 0.0378 0.0001

13A″

0.0018 0.0001 0.0006

14A′ 14A″ 15A′ 16A′ 15A″

0.0003 0.0004 0.0009

17A′ 16A″

0.0009

2A′ 1A″ 3A′ 2A″ 3A″ 4A′ 4A″ 5A′ 6A′ 5A″ 7A′ 6A″

0.0007

0.0004 0.0036 0.0112 0.0012

0.0033 0.0001

0.0062 0.0044

7A″ 8A′ 9A′ 8A″ 10A′ 9A″ 11A′ 10A″

0.0048 0.0682

12A′ 11A″ 13A′

0.0323 0.3039

12A″ 13A″ 14A′ 15A′ 16A′ 14A″ 15A″ 17A′ 16A″

c3A″ (86%) + d1A′ (13%) c3A′ (54%) + c3A″ (45%) c3A′ (54%) + c3A″ (45%) b1A″ (51%) + c3A′ (48%) d1A′ (86%) + c3A″ (14%) c1A″ (53%) + d3A′ (24%) + d3A″ (15%) + d1A″ (8%) c1A″ (43%) + d1A″ (25%) + d3A″ (18%) + d3A′ (13%) 3 d A′ (52%) + d3A″ (48%) d3A′ (97%) d3A″ (100%) e1A′ (97%) + c3A″ (2%) d3A″ (65%) + d3A′ (26%) + d1A″ (9%) d3A″ (52%) + d3A′ (48%) d1A″ (56%) + d3A′ (40%) X=I a3A″ (87%) + b1A′ (9%) a3A″ (86%) + a3A′ (12%) a3A″ (87%) + a3A′ (9%) a1A″ (84%) + a3A′ (14%) a3A′ (86%) + a3A″ (9%) a3A′ (86%) + a3A″ (12%) a3A′ (85%) + a1A″ (11%) b1A′ (86%) + a3A″ (12%) b3A″ (90%) + c3A′ (7%) b3A″ (90%) + c3A′ (8%) b3A″ (93%) b1A″ (65%) + c3A′ (25%) + b3A′ (10%) c3A″ (77%) + c3A′ (14%) + b3A″ (6%) c3A″ (80%) + c3A′ (14%) + b3A″ (6%) c3A″ (85%) b3A′ (56%) + c1A″ (32%) + c3A′ (7%) b3A′ (89%) + d3A″ (6%) b3A′ (91%) + d3A″ (6%) c1A′ (90%) + d3A″ (7%) c1A″ (55%) + b3A′ (30%) + b1A″ (10%) c3A′ (72%) + c3A″ (17%) c3A′ (76%) + c3A″ (18%) d3A″ (48%) + d1A′ (36%) + e1A′ (5%) + c3A′ (5%) 3 c A′ (64%) + b1A″ (22%) + c1A″ (10%) d3A″ (86%) + b3A′ (6%) d3A″ (89%) + c1A′ (6%) d1A′ (53%) + d3A″ (42%) e1A′ (86%) d3A′ (87%) + d1A″ (11%) d3A′ (97%) d3A′ (96%) d1A″ (88%) + d3A′ (12%)

0.0060 0.0153 0.0027

0.0002

0.0078 0.0031 0.0048 0.0002 0.0009 0.0008 0.0817 0.0001 0.0011 0.0030

0.0001 0.0004 0.0025 0.0004 0.0011 0.0019

0.0165

Ground state is denoted 1A′, higher-lying states are numbered separately in each symmetry. Only the contributions of the spin-free states ≥5% are given.

a

11324



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Table 3. Solvent Corrected (CH2Cl2) SO-TD-DFT Transition Energies (in cm−1) to the Lowest-Lying Excited States of [ReX(CO)3bpy] (X = Cl, Br, I), Associated Wavelengths (in nm) and Oscillator Strengths f a SO state aA″ bA′ cA′ bA″ cA″ dA′ dA″ eA′ eA″ fA′ gA′ fA″ hA′ iA′ aA″ bA′ bA″ cA′ cA″ dA′ dA″ eA′ eA″ fA′ gA′ fA″ gA″ hA′ aA″ bA′ bA″ cA′ cA″ dA′ dA″ eA′ eA″ fA′ gA′ fA″ gA″ hA′ iA′

composition of the SO states in terms of spin-free states


X = Cl 21 160 a3A″ (70%) + a3A′ (27%) a3A″ (70%) + a3A′ (27%) 21 170 a3A″ (90%) + b1A′ (7%) 21 430 a1A″ (48%) + a3A′ (48%) 21 620 a3A′ (71%) + a3A″ (28%) 22 920 a3A′ (71%) + a3A″ (28%) 22 920 a1A″ (49%) + a3A′ (50%) 23 250 b1A′ (88%) + a3A″ (8%) 24 230 b3A′ (96%) 25 630 b3A″ (99%) 25 640 b3A″ (96%) 25 650 b3A″ (95%) 27 070 b3A″ (95%) 27 080 c1A′ (96%) 27 080 X = Br a3A″ (61%) + a3A′ (36%) 20 240 a3A″ (61%) + a3A′ (37%) 20 240 a1A″ (42%) + a3A′ (56%) 20 610 a3A″ (84%) + b1A′ (14%) 20 615 a3A′ (61%) + a3A″ (38%) 22 210 a3A′ (61%) + a3A″ (27%) 22 220 a1A″ (56%) + a3A′ (42%) 22 640 b1A′ (81%) + a3A″ (14%) 23 325 b3A′ (98%) 24 770 b3A″ (99%) 24 780 b3A″ (95%) 24 810 b3A″ (95%) 26 680 b3A″ (93%) 26 690 c1A′ (96%) 26 700 X=I a3A″ (51%) + a3A′ (47%) 19 160 a3A″ (52%) + a3A′ (47%) 19 170 a3A′ (55%) + a1A″(44%) 19 410 a3A″ (65%) + a1A′ (31%) 19 560 a3A′ (48%) + a3A″ (44%) 21 920 a3A′ (47%) + a3A″ (45%) 22 010 a1A″ (51%) + a3A′ (44%) 22 200 b1A′ (58%) + a3A″ (30%) 22 535 b3A′ (84%) 24 960 b3A″ (84%) 24 970 b3A″ (94%) 25 120 b3A″ (49%) 26 040 b3A″ (95%) 26 205 b3A′ (30%) + c1A′ (26%) + 26 320 c3A′ (14%) 26 630 c3A′ (40%) + b3A′ (36%) + d1A′ (6%)

wavelength (nm) 473 472 467 462 436 436 430 413 390 390 390 369 369 369 494 494 485 485 450 450 442 429 404 403 403 375 375 374 522 521 515 511 456 454 450 444 400 400 398 384 382 380 375

f

0.0039 0.0009

0.0009 0.0472

0.0009 0.0002 0.0013

0.0005 0.0059

0.0007 0.0356

0.0017 0.0002 0.0006

Figure 5. The SO-TD-DFT/COSMO/CH2Cl2 calculated UV−vis spectra of [ReX(CO)3(bpy)] (X = Cl, Br, and I) (fwhm = 4000 cm−1).

0.0001 0.0003 0.0073

previous computational studies of [Re(imidazole)(CO)3(phenanthroline)] and other organometallic complexes.12,16 Nature of Low-Lying SO-States and Implications for Photophysical Behavior. Understanding the nature and energetics of the optically populated and lower-lying excited states is the starting point to discuss the radiative and nonradiative deactivation pathways. On the basis of compositions of the singly occupied orbitals in the a1A′ and a3A″ spin-free excited states of [ReX(CO)3(bpy)], it has been argued that their SO interaction increases in the order Cl < Br < I, due to increasing the halide SOC constant and its pπ-electron participation in the excitations.7 However, the present SO-MSCASPT2 calculations show that the spin-composition of the optically predominantly populated SO state 4A′ (Cl) and 5A′ (Br, I) hardly changes with changing the halide, being about 79% and 86% singlet for Cl and for both Br and I, respectively (Table 2). The larger singlet participation in the case of the iodide is counterintuitive and is responsible for the calculated oscillator strength being larger than that for the chloride, contrary to the experiment. A small decrease of spin-mixing on going from Cl to I was calculated also for some other lowerlying states; compare, e.g., the 2A′ and 2A″ states of the two complexes. On the other hand, spin−orbit TD-DFT calculations show a significantly larger spin-mixing in the optically

0.0019 0.0003 0.0134

0.0015 0.0001 0.0006 0.0036

a

Ground state is denoted aA′, higher-lying states are labeled by lowercase letters separately in each symmetry. Only the contributions of the spin-free states ≥5% are given.

increases dramatically the density of close-lying states and, hence, the number of contributing transitions. Moreover, the oscillator strengths of transitions to SO states decrease as compared to spin-free states. These conclusions agree with 11325



Article

correlates with the Re−X stretching frequency instead of SOC.7 It should be noted, however, that calculations at the groundstate geometry are not fully relevant to intersystem crossing. The optically excited states of transition metal complexes undergo ultrafast (≤10 fs) intramolecular vibrational energy redistribution into low-lying vibrational modes, which is manifested by the “instantaneous” fluorescence Stokes shift.1,2,5e,g,7 This process is faster than the excited-singlet decay and can be accompanied by structural and electronic changes that are not captured by the present calculations. The large density of states is another SOC consequence important for photophysics. Calculations typically predict three spin-free and seven SO nondegenerate states lying between the optically exited state and the ground state of [ReX(CO)3(bpy)]. Moreover, a number of transitions to the SO states have nonzero oscillator strengths (Tables 2 and 3). Hence, optical excitation probably populates more than one SO state whose deactivation proceeds through a cascade of closely spaced lower-lying SO states, some of them being emissive. This multitude of processes is manifested by several constants in the femto- to picosecond time range determined by femtosecond time-resolved emission and absorption spectroscopy.7,18,19 For example, time-resolved fluorescence decay kinetics are biexponential, involving the 85−150 fs ISC discussed above and an additional component (340, 470, and 1180 fs for Cl, Br, and I, respectively) that was, within the spinfree conceptual framework, attributed to an intermediate triplet state.7 In view of the SO model, we can attribute these latter kinetics to decay of bA″ (2A″) or cA′ (2A′) SO states that are partly populated either optically or nonradiatively from eA′ (4A′ or 5A′). [ReX(CO)3(bpy)] complexes also show ns-lived phosphorescence20,32,34,35 that allows for their photonic applications36 and has been attributed to the lowest MLCT triplet state. The relevant photophysical data are summarized in Table 4.

Figure 6. Correlation of TD-DFT calculated lowest singlet (left) and triplet (right) spin-free states with SO states (middle) of [Re(I)(CO)3(bpy)] in toluene solution. Red, blue, and black arrows indicate transitions with oscillator strengths larger than 0.01, 0.001−0.01, and 0.0005−0.001, respectively. SO-TD-DFT (PBE0, COSMO-toluene) calculation.

Table 4. Phosphorescence Parameters of [ReX(CO)3(bpy)] Determined at 80 K in 2-Me-THF Glass32 and at Ambient Temperature in Degassed MeCN (This Work)a X

τ (80 K) (μs)

kr (80 K) (s−1)

knr (80 K) (104 s−1)

τ (293 K) (ns)

ΔE (cm−1)

Cl Br I

2.7 3.7 7.5

10 370 13 189 8800

36.0 25.7 12.5

28.7 52 98

565 663 612

τ, kr, and knr stand for the lifetime and radiative and nondadiative rate constants, respectively. ΔE is defined by eq 1.

Figure 7. The comparison of calculated spin-free (top) and spin−orbit (bottom) excitations of [ReI(CO)3bpy] at the TD-DFT/toluene (left) and MS-CASPT2 levels (right).

a

populated eA′ state and smaller oscillator strengths for the iodo than the chloro complex, in line with the experimental spectra. Spin-mixing in cA′ is also more extensive for I than Cl, but the difference is negligible in other low-lying SO states. The difference between the SO-TD-DFT and SO-MS-CASPT2 results can be, at least in part, accounted for by the larger MLCT-XLCT mixing in the DFT-type calculations that makes the halide effect on SOC more pronounced. Given the spinmixed character of the low-lying SO states, it seems appropriate to treat the decay of the optically populated excited states as an internal conversion between SO states, instead of intersystem crossing between pure singlet and triplet states. Indeed, the experimental decay rate of the optically populated state (Cl, (85 fs)−1; Br, (128 fs)−1; I, (152 fs)−1)

The increase of emission lifetime in the order Cl < Br < I is due to the decreasing nonradiative rate constant. Notably, the 80 K radiative decay rate constant of the iodo complex is lower than that for Br and Cl, contrary to what could be expected on the basis of SOC considerations. Experimental investigations of the emission lifetime temperature dependence in the 4−70 K range37,38 determined the zero-field splitting of the lowest 3MLCT state [ReCl(CO)3(bpy)] and revealed that the second and third SO levels lie 6.3 and 90.4 cm−1 above the lowest one. The third SO level is the most emissive one, decaying with a rate constant of 2.8 μs−1, as compared to 0.017 and 0.034 μs−1 for the first and second levels, respectively. The phosphorescence lifetime of [ReCl(CO)3(bpy)] and related complexes with 4,4′-R2-bpy 11326



Article

derivatives are temperature dependent also above 160 K and can be fitted according to eq 120,39 k + k1 exp( −ΔE /kBT ) 1 = 0 τ 1 + exp( −ΔE /kBT )

Table 5. Solvent Corrected (MeCN) SO-TD-DFT Transition Energies (in cm−1) to the Low-Lying Excited States of [ReX(CO)3(bpy)] (X = Cl, Br, and I), Associated Wavelengths (in nm) and Oscillator Strengths f Obtained at the Optimized a3A′ Geometrya

(1)

that assumes overlapping emission from two thermally equilibrated excited states separated by the energy difference of ΔE. k0 and k1 are the decay rate constants of the lower- and higherlying states, respectively. Figure 8 shows the T-dependence of

SO state

Figure 8. Temperature dependence of emission lifetimes of [ReX(CO)3(bpy)] measured in MeCN fitted to eq 1.

the phosphorescence lifetime of the three [ReX(CO)3(bpy)] complexes measured over the 5−70 °C range and fitted to eq 1. Obtained ΔE values are summarized in Table 4. These results indicate the presence of an excited state that lies several hundreds of cm−1 above the three lowest SO states (a3A″ components) and nonradiatively decays about 24(Cl), 31(Br), and 43(I) times faster than the manifold of the lowest three SO states. In previous experimental studies of temperature-dependent emission decay of Ru(II) and Re(I) complexes, the deactivating “fourth” state was assigned as a metal-centered dd state, to explain its fast nonradiative decay rate. Although this might be the case for Ru(II), such explanation is highly unlikely for Re(I) tricarbonyl-diimines whose dd states lie at very high energies. This behavior and the identity of the mysterious fourth state can be addressed using spin−orbit calculations, based on two assumptions: (i) the ns-lived emission occurs from a set of thermally equilibrated SO states populated according to Boltzmann statistics, and (ii) the equilibrium geometry of all the relevant SO states can be described by that of the lowest spin-free triplet state a3A″. The latter is a crude but computationally necessary approximation. Energies and characters of the lowest eight SO-TD-DFT states calculated at the a3A″ geometry in CH3CN are collected in Table 5. The calculated [ReCl(CO)3(bpy)] zero-field-splitting is 8 and 133 cm−1, in a reasonable agreement with the experimental values37,38 of 6 and 90 cm−1. (The experimental values were obtained in a glass, where zero-fieldsplitting is expected to be lower than in solution due to higher ππ*(IL)−MLCT mixing.) In agreement with the experiment, the calculations also indicate that the third SO state is more emissive than the second one, while the lowest one does not emit at all. In addition, the calculations of [ReCl(CO)3(bpy)] reveal the presence of another emissive state lying 986 cm−1 above the lowest excited state aA″ (i.e., 853 cm−1 above the most emissive cA′ state). These calculated energy differences

composition of the SO states in terms of spin-free states

aA″ bA′ cA′ bA″ cA″ dA′ dA″ eA′

a3A″ (89%) + a3A′ (9%) a3A″ (89%) + a3A′ (9%) a3A″ (96%) + b1A′ (2%) a1A″ (75%) + a3A′ (22%) a3A′ (86%) + a3A″ (12%) a3A′ (90%) + a3A″ (9%) a1A″ (24%) + a3A′ (76%) b1A′ (92%) + b3A′ (3%)


a3A″ (84%) + a3A′ (14%) a3A″ (84%) + a3A′ (14%) a3A″ (96%) + b1A′ (4%) a1A″ (68%) + a3A′ (29%) a3A′ (84%) + a3A″ (15%) a3A′ (85%) + a3A″ (14%) a1A″ (30%) + a3A′ (69%) b1A′ (93%) + a3A″ (4%)


a3A″ (70%) + a3A′ (27%) a3A″ (70%) + a3A′ (28%) a3A″ (85%) + a1A′ (13%) a3A′ (55%) + a1A″(43%) a3A′ (69%) + a3A″ (28%) a3A′ (68%) + a3A″ (27%) a1A″ (42%) + a3A′ (56%) b1A′ (77%) + a3A″ (13%)

transition energies ΔE wavelength (cm−1) (cm−1) (nm) X = Cl 15 472 15 480 15 605 16 458 18 171 18 172 18 378 20 440 X = Br 15 453 15 460 15 642 16 271 18 119 18 120 18 405 20 078 X=I 15 585 15 590 15 914 16 130 18 466 18 478 18 961 19 765

0 8 133 986 2699 2700 2906 4968

646 646 641 607 550 550 544 489

0 7 189 818 2666 2667 2952 4625

647 647 639 614 552 552 543 498

0 5 329 545 2881 2893 3376 4180

642 641 628 620 541 541 527 506

f

0.0001 0.0014 0.0006

0.0002 0.0579

0.0001 0.0022 0.0003 0 0.0002 0.0483

0.0001 0.0045 0.0001 0.0006 0.0001 0.0278

ΔE is the energy difference from the lowest SO excited state. The ground state is denoted aA′, higher-lying states are labeled by lowercase letters separately for each symmetry. a

are qualitatively comparable to the experimentally determined ΔE of 565 cm−1. The experimental and theoretical ΔE values correspond to two- and four-state models, respectively, and a one-to-one correspondence cannot be expected. Also, the calculated energy values are affected by the rough assumption of identical equilibrium geometries of individual SO states. In fact, the fourth state at its relaxed geometry will lie lower relative to the first three ones than calculated. SO-TD-DFT calculations allow us to assign the deactivating “fourth” state as the bA″ SO state, of MLCT/XLCT character. Its ∼75% singlet component enables a rapid nonradiative decay to the ground state. The same conclusion can be drawn for the bromide and iodide complexes where the deactivating bA″ states of decreasing singlet character from Cl (75%) to Br(68%) to I (55%) were calculated at 818 and 545 cm−1 above the lowest excited state, respectively (Table 5). The decreasing singlet contribution to this state slows down the nonradiative decay and contributes to the observed increase of room-temperature emission lifetime in the order Cl < Br < I, reported in Table 4 and Figure 8. Out of the four lowest SO states calculated at the a3A′ geometry, cA′ has the largest oscillator strength. The energies of these states, 15 605 cm−1 (Cl), 15 642 cm−1 (Br), and 15 914 cm−1 (I) match well experimental emission band maxima in MeCN at room temperature: 15 450, 15 700, and 15 800 cm−1, respectively. 11327



■

■

CONCLUSIONS Whereas both spin-free and spin−orbit quantum chemical calculations (MS-CASPT2, TD-DFT) simulate UV−vis electronic spectra of [Re(halide)(CO)3(bpy)] complexes in a reasonable agreement with experiment, they afford a profoundly different interpretation of the absorption bands and only the SO treatment can account for all the observed spectral features, namely, the low-energy shoulders. Within the spin-free model, the lowest absorption band originates from a single strong transition and two satellites occurring at higher and lower energy, respectively. The SO analysis interprets the lowest band as resulting from a whole series of weaker transitions and assigns the two lowest-lying shoulders as transitions to spin-mixed states. Notably, even the strongest transition contributing to the lowest band possesses only partial singlet character that decreases in the order Cl (88%) >Br (81%) ≫ I (58%) at the SO-TD-DFT level. The SO model reveals a high-density of spin-mixed states lying between the lowest optically populated state and the lowest excited state that has a predominantly triplet character. These states provide a deactivation pathway for the optically populated states, whose nonradiative decay can be described as a series of ultrafast internal conversions between SO states, that are vibronically coupled. Multiexponential kinetics of the ultrafast fluorescence decay can thus be, at least in part, attributed to electronic rather than vibrational relaxation. The ns-lived “phosphorescence” occurs predominantly from a cA′ spin-mixed state but may contain weaker contributions from other emissive states. The temperature dependence of the “phosphorescence” decay is explained by thermal population of a low-lying bA″ state with a substantial singlet character that presumably allows for its fast nonradiative decay to the ground state. The differences between SO-MS-CASPT2 and SO-TD-DFT underlie the importance of solvent effects accounted for by DFT-type techniques and limitations of SO-MS-CASPT2 caused by a restricted active-space size. Including SOC explicitly not only improves the quantitative correspondence with the experimental spectra but provides a physically more correct insight into the nature of the excited states involved and their deactivation pathways.

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REFERENCES

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ASSOCIATED CONTENT

S Supporting Information *

Tables showing additional data and figure showing maps of difference electron density. This material is available free of charge via the Internet at http://pubs.acs.org.

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Article

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (C.D.); [email protected]. uk (A.V.); [email protected] (S.Z.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Financial support provided by the European collaboration program COST Action CM1002 (CoDECS) and the Czech Ministry of Education grant LD11086 is gratefully acknowledged. The calculations were carried out in part at the IDRIS and CINES computer centers through a grant of computer time from GENCI. 11328



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