J. Phys. Chem. 1996, 100, 2915-2925
2915
Influence of Solvent on the Spectroscopic Properties of Cyano Complexes of Ruthenium(II) Cliff J. Timpson,1a Carlo A. Bignozzi,*,1b B. Patrick Sullivan,1c Edward M. Kober,1d and Thomas J. Meyer*,1a Department of Chemistry, UniVersity of North Carolina, Chapel Hill, North Carolina 27599-3290, Dipartimento di Chimica, UniVersita di Ferrara, Via L. Borsari No. 46, 44100 Ferrara, Italy, and Theoretical DiVision, Los Alamos National Labs, Los Alamos, New Mexico 87545 ReceiVed: October 30, 1995X
UV-visible spectra, emission spectra, and RuIII/II reduction potentials have been measured for cis[Ru(bpy)2(py)(CN)]+ (bpy is 2,2′-bipyridine; py is pyridine), cis-Ru(bpy)2(CN)2, [Ru(tpy)(CN)3]- (tpy is 2,2′: 6′,2′′-terpyridine), [Ru(bpy)(CN)4]2-, and [Ru(MQ+)(CN)5]2- (MQ+ is N-methyl-4,4′-bipyridinium cation) in twelve solvents. The shifts in the metal-to-ligand charge transfer (MLCT) absorption (Eabs) or emission (Eem) band energies with solvent increase linearly with the number of cyano ligands and correlate well with the Gutmann “acceptor number” of the solvent. Intraligand π f π* band energies also correlate with acceptor number, but with only ∼30% of the shifts for the MLCT bands. The solvent dependence arises through mixing of the π f π* transitions with lower energy MLCT transitions. MLCT absorption and emission spectra are convolutions of overlapping vibronic components, and a Franck-Condon analysis of emission spectral profiles for cis-Ru(bpy)2(CN)2* has been used to evaluate the energy gap, E0, and χ′0,gs, where χ′0,gs is the sum of the solvent reorganizational energy for the ground state below the excited state and the innersphere reorganizational energy of the low-frequency modes, χi,L, is treated classically. Both E0 and χ′0,gs correlate well with acceptor number with ∆E0/∆AN ) 44 ( 2 cm-1/AN unit and ∆χ0,gs/∆AN ) 21 ( 3 cm-1/AN unit if it is assumed that χi,L is solvent independent. From electrochemical measurements and the difference in E1/2 values for metal oxidation and bpy reduction, ∆∆G°es/∆AN = 70 ( 7 cm-1/AN unit with ∆G°es the free energy of the excited state above the ground state. These correlations show that the energy gap is far more sensitive to solvent than χ0,gs. ∆χ0,gs/∆AN can also be estimated from the relation ∆∆G°es/∆AN ) ∆E0/∆AN + ∆χ′0,gs/∆AN, which gives ∆χ0,gs/∆AN ) 26 ( 7 cm-1/AN unit. The solvent reorganizational energy of the excited state above the ground state is χ0,es. Its variation with acceptor number can be estimated from the relation ∆Eabs/∆AN - ∆G°es/∆AN ) ∆χ0,es ()13 ( 8 cm-1/AN) or from ∆Eabs/∆AN - ∆Eem/∆AN - ∆χ0,gs/∆AN ()14 ( 8 cm-1/AN), if χi,L is solvent independent. These results suggest that χ0,gs is more sensitive to solvent than χ0,es by as much as a factor of 2. ∆Eem/∆AN ) 45 ( 3 cm-1/AN unit = ∆E0/∆AN ) 44 ( 2 cm-1/AN unit, showing that the emission maximum gives accurate information about the solvent dependence of the energy gap. A model is invoked to explain the acceptor number dependence. It is based on electron pair donation from the lone pair on cyanide to individual solvent molecules through donoracceptor interactions. The model is consistent with variations in ν(CN) with acceptor number in cis-[Ru(bpy)2(py)(CN)]+ and in E1/2(RuIII/II) for the series of complexes. In this model it is assumed that donor-acceptor interactions are more important in the ground state than in the excited state, consistent with pKa measurements, and that they are additive in the number of cyanide ligands. These and H-bonding interactions in related ammine complexes perturb the internal electronic structure of the solute with important consequences. One is that χ0,gs * χ0,es although they are commonly assumed to be equal.
Introduction Specific solute-solvent interactions are known to play an important role in optical and thermal electron transfer involving transition-metal complexes.2-6 These interactions can influence both spectroscopic energies and redox potentials in a significant way. Their existence has been documented in the literature, and qualitative models have been proposed, but they have yet to be examined quantitatively. Literature examples include mixed cyano-pyridyl complexes of Fe(II)3 and Ru(II)4b-e,5 where specific interactions occur with the cyanide ligands. We extend that work here and report the effect of solvent on absorption, emission, and RuIII/II reduction potentials in the series cis-[Ru(bpy)2(py)(CN)]+, cis-Ru(bpy)2(CN)2, [Ru(tpy)(CN)3]-, [Ru(bpy)(CN)4]2-, and [Ru(MQ+)(CN)5]2-, where there is a X
Abstract published in AdVance ACS Abstracts, January 15, 1996.
0022-3654/96/20100-2915$12.00/0
sequential increase in the number of cyanide ligands. The goals were to obtain systematic data on specific solvent effects in these complexes, to analyze the effects, and to develop models to explain them. Experimental Section Materials. The solvents used in this investigation were obtained from commercial sources (Fisher, Aldrich, or Burdick & Jackson) and were of spectroscopic grade where available. Deionized water was obtained by using a commercially available ion-exchange purification system (Nanopure) and was generated © 1996 American Chemical Society
2916 J. Phys. Chem., Vol. 100, No. 8, 1996
Timpson et al.
as required. Supporting electrolytes for electrochemical measurements were reagent grade or better. The materials used in the chromatographic separations were Al2O3 (Merck) and Sephadex C-25, G-15, or LH-20 (Pharmacia). The chromatographic resins were allowed to swell in the appropriate solvent for a minimum of 3 h before use. Commercially available single-parameter (Cricket Graph) and multiparameter (Statworks) regression routines were used to plot the data and to determine linear correlations. Emission Spectral Fitting. Emission spectra for Ru(bpy)2(CN)2 were subjected to a single mode Franck-Condon analysis based on a procedure described in detail elsewhere.7 The fits were made by using a program developed at UNC by J. P. Claude. The program generates a calculated emission spectrum by using eq 1a.
I(νj) I0
5
)∑ V
[( ) [ ( E0 - Vpω 3 SMV V!
E0
exp -4 ln 2
) ]]
νj - E0 + Vpω ∆νj0,1/2
2
(1a)
In this expression, I(νj) is the emitted intensity in quanta at energy νj in cm-1 and I0 the intensity of the 0-0 transition. The quantity V is the vibrational quantum number for the acceptor mode in the ground state, and pωM is the vibrational spacing. For the bipyridyl-based MLCT excited states, pωM is the weighted sum of the quantum spacings for a series of ν(bpy) vibrations that occur from 1000 to 1600 cm-1 and a higher frequency, ν(CN), mode at ∼2080 cm-1 (eq 1c). The quantity SM is the electron-vibrational coupling constant for the combined mode. It is the sum of the S values for the contributing modes (eq 1d). It is related to the change in equilibrium displacement (∆Qe) between excited and ground states by eq 1b,
1 MωM (∆Qe)2 2 p
( )
(1b)
pωM ) ∑Sjpωj /∑Sj
(1c)
SM ) ∑Sj
(1d)
SM )
j
j
where M is the effective reduced mass of the vibration. In eqs 1c and 1d, the sums are over the coupled vibrations j. The quantity ∆νj0,1/2 in eq 1a is the full width at half-maximum of the individual vibronic components in cm-1. It includes contributions from low-frequency, intramolecular vibrations treated classically and the reorganizational energy of the solvent (χo). The quantity E0 is the V* ) 0 f V ) 0 energy difference between the excited and ground states in the single-mode approximation. In the fitting procedure, pωM was stepped manually between 1000 and 1600 cm-1 at 5-cm-1 increments, and a simplex algorithm was utilized to vary the remaining three parameters, SM, ∆νj0,1/2, and E0, until the best match between the calculated and experimental spectral profiles was obtained (as determined from the minimized least-squares difference between the two). Instrumentation. Absorption spectra were recorded at 23 ( 2 °C on a Cary 14 spectrophotometer upgraded with an OnLine Instrument System (OLIS) digital conversion package and driven with supporting OLIS spectrophotometer software version 2.1. Scan rates were 1 nm/s and were made vs a solvent blank by using matched 10-mm quartz cells. The spectral resolution was (0.5 nm over the spectral region of interest. Emission spectra were recorded at 23 ( 2 °C on a Spex Fluorolog-F212
emission spectrophotometer equipped with a 450-W xenon lamp and a cooled Hamamatsu R928 photomultiplier and were corrected for instrument response. Infrared measurements were made on a Nicolet Analytical Instruments 20-DX Fouriertransform infrared spectrophotometer; spectral resolution was (2 cm-1. Solid-state infrared measurements were obtained by using pressed KBr pellets and solution measurements by using an Aldrich variable-pathlength cell equipped with CaF2 windows. Cyclic voltamograms were recorded at 25 ( 2 °C by using a PAR Model 173 potentiostat, a PAR Model 175 sweep generator, and a Model 6414S Soltec XY recorder. Measurements were made in each solvent vs SCE and/or vs the ferrocene/ferricinium couple. A 2-mm-diameter platinum disk was the working electrode. Half-wave potentials for the Ru(III/II) couples were calculated by averaging the oxidative and reductive peak potentials. The estimated error in the reported values is (10 mV. The wave shapes were essentially invariant to scan rate variations between 20 and 100 mV/s. All waves reported were judged to be reversible although, in some cases, peak-to-peak splittings were larger than the theoretically expected 59 mV. No attempt was made to compensate for solution resistance or to correct the data for differences in diffusion coefficients for the oxidized and reduced components of the couples. Preparation of Complexes. The salts cis-[Ru(bpy)2(py)(CN)]ClO4,4a K2[Ru(bpy)(CN)4],4c and cis-Ru(bpy)2(CN)24b were prepared as described previously. K[Ru(tpy)(CN)3] was prepared by dissolving 197 mg (0.45 mmol) of Ru(tpy)Cl3,4d 2.5 mL of NEt3, and a stoichiometric amount of TIPF6 in 90 mL of an argon-degassed mixture of 2:1 methanol:acetone. The solution was heated at reflux under an argon atmosphere for 4 h. The precipitate of TlCl that appeared on cooling was removed from the dark-green solution by vacuum filtration. The solution was again placed under argon, 600 mg (10×) excess of [NEt4]CN was added, and the solution was heated at reflux for another 16 h. Following the period of reflux, the solution was concentrated to 3-4 mL and left at room temperature for 6 h. Excess [NEt4]CN was removed by filtration. The filtrate was chromatographed on a 2- × 40cm column of Sephadex LH-20. Elution with methanol resulted in the resolution of two distinct bands. The second (brown) band was collected, evaporated to dryness, and further resolved chromatographically with ethanol into a violet-brown band followed by a yellow tail on a 3- × 30-cm column of Al2O3 (80-200 mesh). The violet-brown band was dried and chromatographed once again with n-propyl alcohol on a 3- × 30-cm column of Al2O3. The second (brown) band as collected, rotary evaporated, and dried in a vacuum dessicator over CaCl2. The isolated fraction was shown to be the desired salt by infrared and elemental analyses. It was obtained in 45% yield. Anal. Calcd for K[Ru(tpy)(CN)3]‚3H2O: C, 42.85; H, 3.39; N, 16.62. Found: C, 43.0; H, 3.40; N, 16.58. The potassium salt was converted into the tetraethylammonium salt by cation-exchange chromatography on Sephadex C-25. K2[Ru(MQ)(CN)5]. A 0.1-g (0.24 mmol) amount of K4[Ru(CN)6] (Aldrich) and 0.1 g of N-methyl-4,4′-bipyridinium hexafluorophosphate4e (0.47 mmol) were dissolved in 30 mL of an argon-degassed, 1:1 water:methanol solution. Sulfuric acid (0.24 mmol) was added to the reaction mixture and the solution heated at reflux for 24 h. The pH was maintained at 4 by addition of H2SO4 as necessary. The solution was evaporated to dryness by rotary evaporation and the remaining solid was washed with 4 30-mL portions of acetone and dissolved in methanol. Unreacted K4[Ru(CN)6] was removed by filtration. The solid was dried, redissolved in a minimum volume of water, and chromatographed on a 2- × 50-cm
Spectroscopic Properties of Cyano Complexes of Ru(II)
Figure 1. UV-visible absorption spectra for [Ru(bpy)2(py)(CN)][ClO4], [Ru(bpy)2(CN)2], [NEt4][Ru(tpy)(CN)3], and [NEt4]2[Ru(bpy)(CN)4] in CH3CN at 298 ( 2 K.
Sephadex G-15 column. The first (brown) fraction was discarded. The second (yellow) fraction contained the desired complex (as indicated by cyclic voltammetry). The eluted fraction was evaporated to dryness and the salt recrystallized from methanol. The overall yield was 40%. Anal. Calcd for K2[Ru(MQ)(CN)5]. 5H2O: C, 33.67; N, 17.18; H, 3.70. Found: C, 32.88; N, 16.65; H, 3.80. The potassium salt was converted into the tetra-n-butylammonium salt by cationexchange chromatography by using Sephadex C-25. The salts and compounds used in this study were stored for a minimum of 48 h over CaCl2 in a vacuum dessicator. Stock solutions of known concentration were prepared for each by dissolving an accurately determined mass ((0.01 mg) in dried DMF in 10-mL volumetric flasks. High complex solubility, low solvent volatility, and a relatively low capacity for specific solute-solvent interaction (acceptor number ) 16) led to the decision to use DMF as the solvent for stock solutions. Molar extinction coefficients were determined from solutions prepared by micropipetting known volumes (200 µL ( 10 µL) of the DMF solutions into 10-mL volumetric flasks and carefully diluting with the desired solvent. Absorption and emission band energies (Eabs, Eem) were determined by dissolving a few milligrams of solid directly into the desired solvents. There were no discernible shifts in absorption band energies for the complexes in pure solvents vs the complexes in pure solvents with a small volume percent of DMF added. Results UV-Visible Absorption Spectra. UV-visible absorption spectra in acetonitrile are shown in Figure 1. Spectra and spectral assignments for the mono-,4a bis-,4b and tetracyano4c complexes have been reported elsewhere. Visible spectra for complexes containing polypyridyl ligands are dominated by bands arising from dπ f π* metal-to-ligand charge-transfer (MLCT) transitions to give excited states largely singlet in character separated by ∼5000 cm-1 from lower lying triplets. Given the spin-orbit coupling constant for RuIII (ξ ∼ 1200 cm-1), the spin character of these states is highly mixed.8 Intense bands appear in the UV from intraligand, π f π* transitions. Band energies and extinction coefficients in 12 solvents are listed in Table 1. The energies, and to a lesser degree, band shapes for all the MLCT bands are strongly solvent dependent. The shifts with solvent are comparable for the MLCT features throughout the visible. Shifts in the π f π* bands were only ∼30% as great as those of the MLCT bands.
J. Phys. Chem., Vol. 100, No. 8, 1996 2917 The shifts increase with the acceptor number (AN) of the solvent and with the number of cyano ligands. The acceptor number is defined as the magnitude of the chemical shift of the 31P resonance of Et PO in the solvent relative to hexane. The 3 chemical shift of Et3PO in hexane is arbitrarily assigned AN ) 0 and the chemical shift of the Et3PO:SbCl5 adduct in 1,2dichloroethane is taken as AN ) 100. The acceptor number is a dimensionless quantity which appears to provide a relative measure of the Lewis acidity of the solvent.9 Emission Spectra. With the exception of [Ru(MQ+)(CN)5]2-, the cyano complexes emit at room temperature in fluid solution. Shifts in emission energies with solvent have been reported elsewhere for Ru(bpy)2(CN)2 and [Ru(bpy)(CN)4]2-.4,5 Emission energies in 12 solvents are given in Table 1. In addition, emission spectral fitting parameters for Ru(bpy)2(CN)2 in eight solvents obtained by fitting spectra to eq 1a are listed in Table 4. Electrochemistry. The reduction potentials (E1/2) for RuIII/II couples (vs [Fe(C5H5)2]+/0 as an internal reference; +0.307 V vs SCE, 0.2 M LiClO4 in CH3CN)10 are listed in Table 1. Bipyridyl-based E1/2 values (vs [Fe(C5H5)2]+/0) for the [Ru(bpy)2(CN)2]0/- couple were acetone, -2.04; dimethylformamide, -2.03; acetonitrile, -1.98; ethanol, -2.01; and methanol, -2.03. The E1/2 values were calculated from the difference between the anodic (Ep,a) and cathodic (Ep,c) peak potentials. The difference, ∆Ep ) Ep,a - Ep,c, was generally in the range 59-70 mV. In solvents where ∆Ep was greater than 70 mV, it was nearly the same as for [Fe(C5H5)2]+/0 and taken to be electrochemically reversible. Due to solubility limitations, E1/2 for the [Ru(MQ+)(CN)5]2-/3- couple was measured in only three solvents. Infrared Spectra. The values for ν(CN) (in cm-1) from infrared spectra in KBr pellets were cis-[Ru(bpy)2(py)(CN)]ClO4, 2073 (vs); cis-Ru(bpy)2(CN)2, 2053 (vs), 2067 (vs); [NEt4][Ru(tpy)(CN)3], 2091 (m), 2067 (vs), 2058 (vs); [NEt4]2[Ru(bpy)(CN)4], 2092 (m), 2060 (vs), 2048 (vs), 2035 (vs); [N(nBu)4]2[Ru(MQ+)(CN)5], 2052 (vs), 2100 (m), where the abbreviations vs ) very strong and m ) medium indicate the relative intensities of the bands. The number of bands that appear in the spectra are consistent with the symmetries of the molecules. The exception is [N(n-Bu)4]2[Ru(MQ+)(CN)5], which exhibits only two infrared bands while three are expected. The trans symmetrical mode may be too weak to be observed11 or is obscured by the intense ν(CN) band at 2052 cm-1. The solvent dependence of ν(CN) was investigated for cis[Ru(bpy)2(py)(CN)]+ in eight solvents. The band energies in cm-1 were acetone, 2083; dimethylformamide, 2078; dimethyl sulfoxide, 2075; acetonitrile, 2079; dichloromethane, 2080; nitromethane, 2078; n-propyl alcohol, 2072; and methanol, 2067. ν(CN) is shown plotted against acceptor number in Figure 2. These studies were limited to the monocyano complex due to a lack of adequate solubility for cis-Ru(bpy)2(CN)2 in a sufficient number of solvents and the complexity of the ν(CN) region for [Ru(tpy)(CN)3]- and [Ru(bpy)(CN)4]2-. Discussion Our experimental observations add to those made earlier which show that absorption and emission energies and RuIII/II potentials in cyano-containing polypyridyl complexes of Fe(II)3 and Ru(II)4,5 have significant solvent dependences. Dielectric continuum theory provides a starting point for analyzing these data. It has been successfully applied to solvent shifts of MLCT absorption bands in polypyridyl complexes12,13 and to intervalence transfer (IT) bands in mixed-valence complexes.14 This theory predicts that correlations should exist between band energies and solvent dielectric functions whose form depends
2918 J. Phys. Chem., Vol. 100, No. 8, 1996
Timpson et al.
TABLE 1: Variations with Solvent of Eabs, Eem, and E1/2(RuIII/II) for [Ru(bpy)2(py)(CN)]+, Ru(bpy)2(CN)2, [Ru(tpy)(CN)3][Ru(bpy)(CN)4]2-, and [Ru(MQ+)(CN)5]2- at 298 ( 2 K ANa
solvent THF
8.0
acetone
12.5
pyridine
14.2
DMF
16.0
DMSO
19.3
CH3CN
19.3
CH2Cl2
20.4
CH3NO2
20.5
n-propyl alcohol
33.5
EtOH
37.1
MeOH
41.3
H 2O
54.8
absorption λmax × 10-3 cm-1 ( × 10-3 M-1 cm-1)
no. of CNligands 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5
34.13 (62.90) 33.78 30.86 (24.31) 32.67
emission λmax × 10-3 cm-1
E1/2(RuIII/II), V vs Fc+/0
28.41 (12.40) 27.93 26.65 (6.76) 25.90 (6.89)
20.53 (10.74) 18.94 20.28 (5.50) 18.76 (5.50) 17.89 (4.37)
14.58 14.04
28.65 (28.48) 28.65 (8.90) 26.25 (5.14) 26.59 (6.74)
20.92 (24.18) 19.57 (10.23) 19.53 (4.87) 18.25 (4.11) 18.55 (4.47)
14.04 14.03 12.79
28.33 (29.32) 28.57 (10.66) 26.31 (6.37) 26.59 (6.94)
20.83 (23.73) 19.72 (12.44) 19.76 (5.40) 18.35 (5.06) 19.05 (4.80)
15.01 14.44 13.09 12.53
34.01 (70.66) 33.78 (61.10) 31.35 (29.60) 33.56 (32.40)
28.57 (12.92) 28.57 (8.16) 26.04 (5.91) 25.71 (7.75)
20.70 (11.61) 19.68 (10.37) 19.60 (5.40) 17.92 (4.88) 17.89 (4.64)
13.93 14.27 13.05 12.22
0.64 0.39 0.10 -0.28
33.89 (62.19) 33.67 (60.34) 31.55 (29.49) 33.44 (34.63)
28.41 (12.24) 28.82 (9.07) 26.31 (4.78) 26.32 (7.67)
20.88 (10.37) 19.92 (10.95) 19.96 (4.73) 18.38 (4.24) 18.18 (5.37)
13.97 14.35 13.23 12.41
0.63 0.47 0.16 -0.18
34.36 (66.40) 34.13 (59.95) 31.64 (30.08) 33.90 (34.94)
29.07 (12.50) 29.15 (8.33) 26.59 (5.45) 26.74 (7.27)
21.41 (11.03) 20.16 (9.88) 20.12 (5.14) 18.55 (5.01) 18.69 (5.06)
14.84 14.16 13.26 12.41
0.68 0.45 0.17 -0.14
34.13 (64.03) 33.90 (-) 31.54 (29.31) 33.67 (33.60) 37.31 (15.54)
28.73 (11.81) 29.07 (-) 26.81 (5.40) 27.03 (6.88) 16.39 (4.63) 26.74 (14.02)
20.75 (10.45) 19.96 (-) 20.20 (5.27) 18.76 (5.06) 18.93 (4.78)
14.20 14.62 13.44 12.89
21.09 (23.27) 20.32 (9.40) 20.33 (5.04) 19.08 (4.78) 20.79 (3.23)
14.20 14.52 13.40
21.50 (10.20) 20.92 (9.76) 20.88 (4.88) 19.96 (4.65) 20.28 (4.00)
14.53 14.88 13.93 13.81
21.28 (9.89) 21.32 (9.47) 21.19 (4.83) 20.24 (4.65) 21.23 (4.56)
14.41 15.32 14.04 14.04
21.79 (9.50) 21.78 (8.72) 21.74 (4.91) 20.96 (4.81) 22.22 (4.35)
14.53 15.48 14.88 14.62
22.47 (9.88) 23.15 (8.05) 23.25 (4.50) 24.75 (4.10)
14.79 16.05 15.34 15.63
31.25 (28.03)
26.27 (4.30) 26.67 (4.06) 34.36 (62.00) 34.25 (61.29) 31.95 (30.80) 34.01 (31.90) 37.88 (16.23) 34.48 (64.07) 34.36 (59.55) 32.15 (30.47) 34.13 (34.63) 37.88 (17.97) 34.60 (60.30) 34.60 (57.90) 32.36 (31.29) 34.36 (28.30) 37.74 (17.92) 34.84 (64.13) 35.09 (53.30) 32.68 (28.30) 35.09 (27.30) 39.06 (18.14)
29.15 (11.93) 30.12 (8.40) 28.01 (4.11) 28.33 (5.47) 17.54 (4.44) 29.67 (9.45) 30.48 (8.25) 28.09 (4.25) 29.24 (5.80) 18.52 (4.10) 29.58 (10.90) 31.15 (7.25) 28.20 (4.45) 30.39 (5.25) 19.23 (4.73) 29.85 (10.67) 29.15 (2.10) 23.53 (4.50)
0.63 0.36 0.07 -0.26
0.25 0.70 0.43 0.22
0.28 0.01 0.33 0.78 0.60 0.34 0.11 0.61 0.44 0.27 0.55 0.78 0.77 0.72
a
Acceptor numbers were taken from ref 9. The absence of data is because of solvent cutoff or an absence of sufficient solubility. [Ru(MQ)(CN)5]2does not emit.
upon the assumptions made in modeling the charge-transfer process.15 In the classical limit, the energies of absorption (Eabs) and emission (Eem) are related to the internal energy charge, ∆Eo, and reorganizational energies (χ) as shown in eqs 2a and 2b.
Eabs ) ∆Eo + χ ) ∆Eo + χi + χo
(2a)
Eem ) ∆Eo - χ ) ∆Eo - χi - χo
(2b)
χi and χo are the intramolecular and solvent reorganizational energies, respectively.16 These simple relationships are exact only for Gaussian band shapes. They also assume equal force constants (quantum spacings) in the initial and final states for the vibrations and solvent librations coupled to the transitions. With unequal quantum spacings (pω * pω′ ), the reorganizational energy of the excited state above the ground state (χes) and of the ground state below the excited state (χgs) are unequal. This is illustrated in Figure 3 for absorption and emission with
Spectroscopic Properties of Cyano Complexes of Ru(II)
J. Phys. Chem., Vol. 100, No. 8, 1996 2919
TABLE 2: Fitting Parameters from Correlations with Acceptor Numbera [Ru(bpy)2(py)(CN)]+
Ru(bpy)2(CN)2
[Ru(tpy)(CN)3]-
[Ru(bpy)(CN)4]2-
18 ( 4 33.8 ( 0.11 0.88
29 ( 4 33.4 ( 0.12 0.95
37 ( 2 30.8 ( 0.07 0.98
44 ( 5 33.7 ( 0.16 0.90
48 ( 12 36.2 ( 0.48 0.91
36 ( 5 20.3 ( 0.14 0.92
83 ( 4 18.4 ( 0.10 0.99
94 ( 5 16.9 ( 0.15 0.99
140 ( 17 16.4 ( 0.47 0.94
208 ( 37 11.2 ( 1.5 0.96
20 ( 2 13.7 ( 0.08 0.95
45 ( 3 13.6 ( 0.09 0.97
58 ( 4 12.1 ( 0.11 0.98
85 ( 5 10.9 ( 0.16 0.99
b
29 ( 7 6.05 ( 0.21 0.79
40 ( 4 4.73 ( 0.11 0.95
34 ( 8 4.83 ( 0.25 0.81
73 ( 13 4.63 ( 0.42 0.92
b
51 ( 10 4.4 ( 0.2 0.87
70 ( 7 2.1 ( 0.2 0.96
91 ( 9 -0.5 ( .2 0.95
138 ( 14 -4.9 ( 0.4 0.95
158 ( 44c -0.63 ( 0.25 0.94
Eabs (πfπ*) slope intercept R2 Eabs(MLCT) slope intercept R2 Eem slope intercept R2 Eabs(MLCT) - Eem slope intercept R2 E1/2(RuIII/II) slope intercept R2
Ru(MQ)(CN)5]2-
a Slopes, intercepts, and correlation coefficients (R2) were calculated from linear regressions between the quantities indicated and the acceptor number. The solvents and their acceptor numbers are listed in Table 1. The slopes (∆E/∆AN) are in cm-1/acceptor number unit; intercepts in cm-1 × 10-3. b This complex does not emit. c Not included in Figure 6b.
TABLE 3: Fitting Parameters from Correlations between (∆E/∆AN) and the Number of Cyanide Ligands in Figure 6a slope (cm-1/AN unit per CN- ligand)
intercept (cm-1)
R2
8.5 ( 2 39 ( 3 21 ( 2 30 ( 5
10.9 ( 5 -3.5 ( 7 -0.3 ( 3 8 ( 10
0.98 0.97 0.99 0.98
Eabs(πfπ*) Eabs(MLCT) Eem E1/2(RuIII/II)
a Slopes, intercepts, and correlation coefficients (R2) are from linear regressions between (∆E (cm-1)/∆AN) and the number of coordinated cyanide ligands.
TABLE 4: Emission Spectral Fitting Parameters for Ru(bpy)2(CN)2 at 298 ( 2 Ka solvent acetone dimethylformamide acetonitrile dichloromethane ethanol methanol water (H2O) deuterium oxide (D2O)
∆G°esd E0b pωM ∆νj0,1/2b χ′o,gsc (cm-1) (cm-1) (cm-1) (cm-1) SM (cm-1) 14 240 14 360 14 500 14 820 15 270 15 390 16 190 16 140
1496 1533 1495 1413 1376 1390 1340 1390
1700 1730 1840 1670 1940 2040 2160 2200
1303 1349 1526 1257 1697 1876 2104 2182
0.72 0.71 0.66 0.71 0.71 0.69 1.22 1.15
15 540 15 710 16 030 16 080 16 970 17 270 18 290 18 320
a
Details of the fitting procedure are given in the Experimental Section. b The estimated errors for E0 and ∆νj0,1/2 are (5%. c Calculated from eq 7. d Calculated from ∆G°es ) E0 + χ′o,gs. E0 is the emission maximum for the V* ) 0 f V ) 0 vibronic component.
a coupled harmonic oscillator mode with χes ) (0.2)χgs (fes ) 0.2fgs, where the f’s are the force constants in the two states). In the classical limit with pω * pω′ and ∆ω ) |ω - ω′| , ω, ω′, the energy quantity in eqs 2a and 2b is the free energy of the excited state above the ground state, ∆Goes, giving eqs 3a and 3b.16 ∆Goes is equal to the 0-0 energy, E(0-0) in this limit.
Eabs ) ∆Goes + χes ) ∆Goes + χi,es + χo,es
(3a)
Eem ) ∆Goes - χgs ) ∆Goes - χi,gs - χo,gs
(3b)
If the excited and ground states are approximated as point dipoles in a sphere and the solvent as a dielectric continuum, the solvent-dependent parts of Eabs (Eabs,s) and Eem (Eem,s) are
Figure 2. Variations in ν(CN) with acceptor number for [Ru(bpy)2(py)(CN)]ClO4. The linear correlation shown is to the equation νjCN (cm-1) ) (2090 ( 3) - (0.48 ( 0.06)AN with R2 ) 0.89. The error bars reflect the instrumental resolution of (2 cm-1.
given by eqs 4a and 4b.13,17 Eabs,s is the sum of the solvent-
Eabs,s )
[
(
)
Ds - 1 1 2µ bg(µ bg - b µ e) 3 2Ds + 1 a
(
)]
(4a)
(
)]
(4b)
(µ bg - b µ e)2 Eem,s )
[
(
)
Ds - 1 1 + 2µ be(µ bg - b µ e) 3 2Ds + 1 a
(µ be - b µ g)2
Dop - 1 2Dop + 1
Dop - 1 2Dop + 1
dependent part of ∆Goes (∆Goes,s) and χo,es. Eem,s is the µe difference between ∆Goes,s and χo,gs. In these expressions, b and b µg are the vector dipole moments of the excited and ground states, a is the radius of the effective spherical cavity enclosing the dipoles, and Dop ()n2, where n is the refractive index of the medium) and Ds are the optical and static dielectric constants of the solvent. The internal dielectric constants of the solute and reference medium are taken to be 1. A more elaborate treatment has been developed by McRae18 which includes electronic repolarization of the solvent, solute
2920 J. Phys. Chem., Vol. 100, No. 8, 1996
Timpson et al.
Figure 3. Energy-coordinate diagram depicting the relationships in eq 3. The χ’s are the reorganizational energies for the excited state above the ground state (χes) and the ground state below the excited state (χgs), Q is the displacement coordinate, and ∆Qe is the change in equilibrium displacement. Harmonic oscillator energy curves are assumed with fes ) 0.2fgs, where the f’s are the force constants.
dipole-solvent-induced dipole, and solute dipole-solvent dipole interactions as well as mixing with other electronic transitions within the solute. Because of the difficulty in calculating individual terms, McRae presented the empirical function in eq 5 in which A, B, and C are constants characteristic of the solute and L0 is a constant characteristic of the solvent
(
Eabs,s ) (AL0 + B)
) (
)
Dop - 1 Ds - 1 Dop - 1 +C + 2Dop + 1 Ds + 2 Dop + 2
(5)
Attempts to find reasonable correlations between Eabs and any of these dielectric functions or with the simpler functions 1/Dop - 1/Ds, Dop, or Ds were unsuccessful. Correlation coefficients were
