J . Phys. Chem. 1984,88, 3425-3431 how results from cooled seeded and thermal effusive beams can be used to study the excited potential energy surface for predissociative (C2N2) and directly dissociative (BrCN and ClCN) photolysis. Reexamination of the structured B'A, X'Z+ spectrum of C2N2with ab initio calculation of the vibrational frequencies of the upper state identified the transitions at 193 nm as 194; 5: and 1; 2t4; 5: where n represents the quantum number of thermal population of the v 5 mode. The well-defined structure of the spectrum shows the upper state to be predissociatively coupled to the vibrational continuum of the ground state. The nascent quantum state distribution of C N fragments is indicative of a zero impact parameter dissociation. The rotational excitation of the C N fragments in this case must come from repulsive interaction between the two C N radicals in v5 mode during dissociation, and these two fragments will be rotating in an opposite sense. The orbital angular momentum will come mainly from parent's rotation. This implies that during the dissociation process, energy must flow out of the v4 mode and into the v5 mode. A quantitative decrease is measured in the amount of vibrationally excited C N productas the C2N2is cooled. In unexcited C2N2, no measurable population will be found with excited stretching modes. The beam cooling will primarily affect the bending v 5 mode of C2N2. Thus, a small amount of the extra energy in the v5 mode must couple to channels leading to vibrational excitation of the C N fragment. The most interesting discovery about the 193-nm photolysis of ClCN and BrCN is that there is no measurable difference between the measurements in the cooled and thermal beams. This means that the rotational distribution is dominated by the repulsion and can be treated in the nonrotating frame of the parent molecule.
-
3425
Simple use of the conservation of energy and angular momentum then allows a one-to-one mapping of the rotational state distribution onto the distribution of impact parameters. The large average amount of fragment rotational energy shows that the electronic transition is linear to bent. The sharply peaked distribution of fragment rotational quantum states and the large impact parameter imply that the dissociation is direct. Thus there is no smearing of the distribution as would be expected if the bending motion, which gives rise to the fragment rotation, were able to execute one or more cycles. Application of the FranckCondon principle shows that the photoexcitation can only reach a bending mode level in immediate contact with the inversion barrier to bending. The carbon-nitrogen bond length in the XCN molecule is very close to that of the free C N radical. Thus, the motion on the dissociative potential energy surface consists of a rapid lengthening of the X-CN bond while the molecule is undergoing a rapid, but not completed bending motion. The relative paucity of energy transferred into vibration must be a result of the maximum repulsion between the halogen atom and the C N radical occurring when the bond angle is close to ~ / 2 .The bond angle when dissociation occurs is more linear for ClCN than BrCN as there is more fragment vibrational excitation in the former case than the latter.
Acknowledgment. The work, of which this paper forms a part, was supported by the Department of Energy under Contract No. DE-AS05-76ER05056. We also acknowledge the provision of the excimer laser through NASA Grant NSG 5071. J.B.H. received support from NASA under Grant NSG 5-17. Registry No. C2N2,460-19-5; CICN, 506-77-4;BrCN, 506-68-3;CN, 2074-87-5.
Rotational Motions of the Tris( 1,lO-phenanthroline) and Tris(2,2'-bipyrldine) Complexes of Ruthenium(II)and Cobalt( III ) Ions in Solution Yuichi Masuda and Hideo Yamatera*+ Department of Chemistry, Faculty of Science, Nagoya University, Chikusa-ku, Nagoya 464 Japan (Received: September 6, 1983; In Final Form: November 28, 1983)
Rotational motions of hydrophobic complex ions, [RUL,]~'in D20 and CD3OD and [CoL3I3+in D20 (L = 1,lO-phenanthroline and 2,2'-bipyridine), were investigated by the nuclear magnetic relaxation technique. The measured spin-lattice relaxation rates of the I3C nuclei of the complex ions showed that the rotational motions of the ions were nearly isotropic. Rotational correlation times, 7, at infinite dilution, measured at different temperatures showed a linear dependence on q / T (q and T being the viscosity of the solvent and the absolute temperature, respectively) in all the present cases. In the D 2 0 solutions of [ C O L ~ ] ~ ( Sand O ~ in ) ~the CD30D solutions of [RuL3]S04,the T values of the complex ions increased with increasing concentration to a greater extent than expected from the increase in the viscosity of the solutions. These increases in the T values were attributed to the formation of the 1:l ion pairs of the complex and sulfate ions. On the other hand, a similar but more remarkable increase in the 7 value of [Ru(phen),12+in DzO was attributed to the formation of aggregates containing two [Ru(phen),lZ+ions. The observed rotational correlation times (in 10-'os, at 33 "C) of the complex ions at infinite dilution ( 7 M ) , those in the ion pair with S042- (7MX), and those in the aggregate containing two complex ions (7MM) were as follows: 7 M = 1.2, TMM = 3.4 (in D@), 7 M = 0.77, 7 M X = 0.94 (in CD3OD) for [Ru(phen),]SO,; 7 M = 1.0 (in DzO), 7~ = 0.67, 7 M x = 0.96 (in CD3OD) for [R~(bpy)j],SO4; 7 M = 1.0, 7 M X = 1.2 (in DzO) for [C~(phen),l~(SO,)~; 7 M = 0.92, 7 M X = 1.1 (in D20) for [Co(bpy),I2(SO4),. Dynamic features of the ion pairs and the aggregates are discussed by comparing the observed rotational correlation times with those obtained from a hydrodynamic treatment of prolate models of the ion pairs and the aggregate.
1. Introduction The rotational motion of nlolecules or ions in solution is one of the important features ,f the dynamic structure of solutions and is often specified by the rotational correlation time, 7. The T value for the nonpolar molecule is usually treated with a hyAdjunct Professor of the Institute of Molecular Science, Okazaki, Japan (April 1981-March 1983).
drodynamic model' or a quasi-hydrodynamic model: which has been proved to predict the 7 values satisfactorily unless specific interactions exist between solute molecules or between solute and (1) Bauer, D. R.; Brauman, J. I.; Pecora, R. J . Am. Chem. SOC.1974.96, 6840. (2) Dote, J. L.; Kivelson, D.; Schwartz, R. N. J . Phys. Chem. 1981, 85, 2169.
0022-3654/84/2088-3425$01.50/00 1984 American Chemical Society
3426 The Journal of Physical Chemistry, Vol. 88, No. 16, 1984 The rotational motion of ions in solution was studied on the N03-3-4and SCN-4 ions by the methods of the depolarized Rayleigh light scattering4 and the Raman ~ c a t t e r i n g . ~The treatment of the T values of these ions with the hydrodynamic model was not always successful due to the presence of ion-ion and ion-solvent interactions. In a previous nuclear magnetic relaxation study of solutions, we successfully usedS the hydrodynamic model to treat quantitatively the effect of the ion-ion interaction on the 7 value of [Co(en),13+ (en = ethylenediamine) in aqueous solution. This success is closely connected with the treatment in which the ion-ion interactions were represented by the ion-pair formation. The large size and weak hydration of [ C ~ ( e n )3+~ ]also favored the hydrodynamic model. Tris( 1,lO-phenanthroline) and tris(2,2’-bipyridine) complexes of cobalt(II1) and ruthenium(I1) ions are also large, and consequently, the hydrodynamic model is expected to be applicable to the rotational motions of these complex ions. Since the cobalt(II1) and ruthenium(I1) complex ions are very similar to each other in shape but have different charges, a comparison between them in the dynamical behavior will disclose a feature of the electrostatic ion-ion and ionsolvent interactions. These complex ions are also characterized by its hydrophobic nature due to the bulky hydrophobic ligands, with respect to solvation6*’and interaction with ions;* the hydrophobic nature of the ions may influence the dynamical behavior of the ions. This paper gives the rotational correlation times of the above-mentioned complex ions in solution as obtained from measured spin-lattice relaxation times of the 13C nuclei and discusses the effect of the electrostatic and hydrophobic interactions between ions on the rotational motions of these complex ions.
Masuda and Yamatera
(I, IO-pnenanthrol i n e )
Figure 1. Relationship between the spin-lattice relaxation rate, R , , of the 13Cnuclei of [Ru(phen),12+ in DzO at 33.0 O C and the concentration of [Ru(phen),]X, (cMxn):X- = C1- ( 0 ) ;Xz- = SO:- (A).
the use of an exponential fit based on the method by Kowalewski et al.I4 For several samples, the measurements of TI were repeated five times or more; consistent results (within 5%) were obtained for TI of each sample. The nuclear Overhauser enhancement factor (qNOE)was measured more than four times for each sample by the method of the gated decoupling. The error in the qNoE value was within 5%. The measurements were performed using 9.5-mm (diameter) spherical tubes in order to minimize the error in the setting up of the 90 and 180’ pulses. The temperature was 33.0 f 0.5 ‘C unless otherwise stated. The aerial oxygen dissolved in the solution had no significant effect on the T1 measurements. 2.3. Viscosity Measurement. The viscosities of the H 2 0 and MeOH solutions of each complex salt were measured at 33.10 2. Experimental Section f 0.005 ‘C with a Canon-Fenske capillary viscometer. The 2.1. Materials. The chlorides of [ R ~ ( p h e n ) ~ ][~C+~, ( p h e n ) ~ ] ~ + , viscosity of the D 2 0 solution was obtained by multiplying the [ R ~ ( b p y ) ~ ]and ~ + ,[ C ~ ( b p y ) ~were ] ~ + synthesized by the literature measured viscosity of the corresponding H 2 0 solution by 1.20, method^.^-'^ The sulfate was obtained by the double decompothe ratio of the D 2 0 to the H 2 0 viscosity at 33.00 OC. The sition of Ag2S04and the chloride of each complex. The chlorides viscosity of the C D 3 0 D solution was assumed to be the same as and sulfates of the complexes were recrystallized twice for use that of the MeOH solution. in the N M R measurement. For the preparation of the sample solution, each complex salt was dissolved in a small amount of 3. Results and Discussion D 2 0 and was dried under reduced pressure at room temperature; 3.1. Relaxation Time of the I3C Nucleus. The relaxation of after these procedures were repeated, the salt was dissolved in D 2 0 I3C nuclei is caused by various mechanisms. For the 13C nucleus (99.8%). The C D 3 0 D solutions were similarly prepared with with a directly bonded proton in the 1,lO-phenanthroline and C D 3 0 D (99.5%) in place of D20. The concentrations of the 2,2’-bipyridine ligands, the most important mechanism of the complex salts were 0.005-0.13 mol dm-3. relaxation is the magnetic dipole-dipole interaction with this 2.2. N M R Measurement. 13CN M R spectra were obtained proton. The relaxation caused by this mechanism proceeds at a on a JEOL FX-100 Fourier-transform spectrometer operating at rate (RID= l/TlD) given by eq 1,15under the condition of extreme 25 MHz. This spin-lattice relaxation time (Tl) of the 13Cnucleus was obtained by the fast inversion recovery method,’, with the pulse sequence of (1 80’ pulse-t-90’ pulse-T-),. The TI value narrowing; the condition is satisfied in the present experiments, for each sample solution was determined by a series of meawhere the ions are not so large and the solutions are not so viscous. surements with more than six different time intervals ( t ) and with Here yc and yH are the gyromagnetic ratios of 13C and ‘H, the delay time ( T ) nearly equal to TI;” the area of the signal for respectively, rCHis the distance between the 13Cnucleus and a each t was measured, and its variation with t was analyzed by proton directly bonded to it, and T~~ is the rotational correlation time of the C-H vector (rCH). The RID value can be obtained (3) James, D.;Frost, R. L. Faraday Discuss. Chem. SOC.1977, No. 64, from the observed relaxation rate (R1) and the nuclear Overhauser 48. Kato, T.; Umemura, J.; Takenaka, T. Mol. Phys. 1978, 36, 621. (qNOE) by the following equation at the exenhancement factor (4) Whittle, M.; Clarke, J. H.R. Mol. Phys. 1981, 44, 1435. treme narrowing limit:15J6 (5) Masuda, Y.; Yamatera, H. J. Phys. Chem. 1983, 87, 5339.
(6) Wada, G.; Nagao, E.; Kawamura, N.; Kinumoto, K. Bull. Chem. SOC. Jpn. 1978, 51, 1937. (7) Yamamoto, Y.; Tominaga, T.; Tagashira, S.Inorg. Nucl. Chem. Lett. 1975, 1 1 , 825. Iwamoto, E.; Tanaka, Y.; Kimura, H.; Yamamoto, Y . J. Solution Chew. 1980, 9, 841. (8) Masuda, Y.; Tachiyashiki, S.;Yamatera, H.Chem. Lett. 1982, 1065. Tchiyashiki, S.; Yamatera, H. Ibid. 1981, 1681. (9) Feiffer, P.; Werdelmann, Br. Z . Anorg. Allg. Chem. 1950, 263, 31. (10) Burstall, F. H. J . Chem. SOC.1936, 137. (11) Maki, N. Bull. Chem. SOC.Jpn. 1969, 42, 2295. (12) Fujita, I.; Kobayashi, H. Ber. Bumenges. Phys. Chem. 1972,76, 115. (13) In the fast inversion recovery method deviced by Canet et al. ( J . Magn. Reson. 1975, 18, 199), the delay time ( r ) can be much shorter than that required in the usual inversion recovery method. For several samples, the T I values were measured both by the fast inversion recovery method with T = T I and by the usual inversion recovery method with T > 7 T I . No significant differences were found between the results from the two methods.
R I D= ( V N O E.988)R1 /~
(2)
*
The measured values of q N o E were within the range of 2.0 0.1 for all the present cases. Consequently, the value of R I Dwas assumed to be equal to the observed R, value in each case (cf. eq 2). With the RID value thus obtained and the C-H bond length (14) Kowalewski, J.; Levy, G. C.; Johnson, L. F.; Palmer, L. J. J. Magn. Reson. 1977, 26, 533. (15) Lyerla, J. R. Jr.; Levy, G. C. In “Topics in Carbon-13 NMR Spectroscopy”; Levy, G. C., Ed.; Wiley: New York, 1974; Vol. 1, Chapter I.
(16) Kuhlmann, K. F.; Grant, D. M.; Harris, R. K. J . Chem. Phys. 1970, 52, 3439.
The Journal of Physical Chemistry, Vol. 88, No. 16, 1984 3427
Rotational Motions of Metal Complex Ions
T(0)/10-'0 s
R, (av.,c-rO)/s'l
-50
0
50
2
t / e c
Figure 2. Relationship between R,(av) at infinite dilution, R,(av,cO), and temperature of [Ru(phen),12+(0)and [ R ~ ( b p y ) ~(A) ] ~ in + D20 and ] ~ +in DzO. in CD30D and of [Co(phen),13+(0) and [ C ~ ( b p y ) ~(V)
of 1.09 %, (1.09 X m),I7 eq 1 gives the T~~ value for each C-H vector in the complex. Figure 1 shows the relaxation rates of the 2 (9), 3 (8), 4 (7), and 5 (6) carbon nuclei of tris( 1,lo-phenanthroline)ruthenium(II) chloride and sulfate in D20. No significant differences were observed in the R1 (or RID)values between the carbon nuclei in different positions. This allows us to assume that the C-H vectors have the same T value; Le., the rotational motion of the complex ion is isotropic. The same is true of tris(bipyridine)ruthenium(II) salts as well as of tris(phenanthro1ine)- and tris(bipyridine)cobalt(II1) salts. On the basis of these assumptions, we use the average, R,(av), of the R, values to obtain the T value from eq 1. 3.2. Rotational Motion of the Complex Ion at Infinite Dilution. The R,(av) value at infinite dilution, R,(av, P O ) or Rl(0), was determined by extrapolating the Rl(av) values at several different concentrations to infinite dilution. The R,(av, -0) values obtained for each complex ion at several temperatures are shown in Figure 2 as a function of the temperature. The rotational correlation time at infinite dilution, T(O), was calculated by substituting the Rl(0) value in eq 1. Usually the rotational correlation time is well represented by the following semiempirical equation based on the hydrodynamic theory:I8 T = CVq/kT f T O (3) where Vis the molecular volume, q the viscosity of the solution, k the Boltzmann constant, T the absolute temperature, C an experimentally determined dimensionless parameter which is concerned with the shape of the rotating molecule and the hydrodynamic boundary condition, and T O the zero-viscosityintercept which was found to be nearly equal to the classical free-rotor ) q/T at several temreorientation time. The plot of ~ ( 0 against peratures (Figure 3) showed a linear relationship with zero intercept ( T O = 0) for each complex ion in D 2 0 and in CD30D; Le., the T values at infinite dilution are represented by T
= CVq/kT
(3')
The value of V was assumed to be equal to the limiting partial (17)(a) Boyd, R.H.J . Chem. Phys. 1968,49,2574.(b) The value of the rotational correlation time is sensitive to the change in C-H bond length; it is proportional to (rC#. At the extreme narrowing limit, an uncertainty of 0.1 A in rC+ causes a possible error of about 6% in the value of the rotational correlation time. However, the discussions in which the relative values of the rotational correlation time (or the relaxation rate) are concerned, such as the discussions about the formation of ion pairs and aggregates, are not affected by such an error. (18) Madden, P. A. Annu. Reu. Phys. Chem. 1980,31, 523.
4 6 T T - ~x 103 CP ~ - 1
8
Figure 3. Plots of the values at infinite dilution ( r ( 0 ) )vs. the qT'value (1 CP = kg rn-l S - I ) . For notations, refer to the caption of Figure 2. TABLE I: The Value of C in Ea 3' at Infinite Dilution 1024v io8rM iolos(o) (25 'C)/ (25 "C), (33 "C), complex ion solvent cm3 cm S C IRu(DhenL12+ D,O 656 5.4 1.2 0.85 .. 656 5.4 0.77 1.0 CD30D 0.85 604 5.2 1.0 [RU(bPY)312+ D2O 604 5.2 0.67 1.1 CD3OD 0.83 620 5.3 1.0 [Co(phen)J3+ D20 0.86 569b 5.1 0.92 [C0(bPY)3l3+ DzO
___
~
a The V value was assumed to be equal to the limiting partial molar volume in H 2 0 (ref 7) divided by Avogadro's number. The difference between the V values in different solvents was disregarded. For the V value of the ruthenium(I1) complex ion, the value of the corresponding iron(I1) complex ion in H 2 0 was used (ref 7). "he V value of [Co( b p ~ ) ~was ] ~ +assumed to be equal to the V value of [C~(phen)~]'+ minus the difference between the Vvalues of [ R ~ ( p h e n ) ~and ] ~ +[Ru-
(bPY)312+.
molar volume of each complex ion divided by Avogadro's number. Although the limiting partial molar volume of the ion is the volume under the influence of electric striction, this effect is not remarkable in the present cases, where the ionic radius is large.I9 The C value in eq 3' was calculated for each system by assuming that the complex ion is spherical. The results are listed in Table I. The obtained C values are close to unity in all the cases; Le., this indicates that the hydrodynamic boundary conditions for the complex ions (considered as spherical rotors) is nearly sticking (C = 1 in eq 3').18 This result may be related to the large size of the complex ion, which permits one to regard the solvent as a continuum and to disregard the effect of hydration on ~ ( 0 ) .The slight differences in the C value between the systems of different complex ions and of different solvents may be partly due to the fact that the tris(phenanthro1ine) and tris(bipyridine) complex ions are not a real sphere but have three openings between the ligands. 3.3. Rotational Motion of the Complex Ion in the Presence of Ion-Ion Interaction. Figures 4, 5, and 6 give the obtained T values of the complex ions in D 2 0 and CD30D solutions against the concentrations of the sulfate and chloride of the complex. Since the linear relationship (eq 3') was observed between the 7 and q / T values (at infinite dilution) measured at different temperatures, it is reasonable to assume that the T values in solutions of different concentrations also depend on the q / T value of the solution. Then, at a constant temperature (33 " C ) , the T value (19) Millero, F. J. J . Phys. Chem. 1969,73, 2417.
,
3428 The Journal of Physical Chemistry, Vol. 88, No. 16, 1984
5,01
c o n c e n t r a t i o n o f KC1 or K2S04 / m o l ?,I 0;2 0;3
IT-^
Masuda and Yamatera c o n c e n t r a t l a n o f KCI o r K2S04 / m o l dm-3 0,l
0
.
0.2
0,3
-
~ 3 +1co(~hen)~13+
A
4.0
0
i
0,02
0,04
a
0 06
0,OB
0.10
(N2+-
Figure 6. Plots of the R,(av) and 7 values of [ C ~ ( p h e n ) ~and ] ~ +[Co(bpy)J3+in D20at 33.0 OC vs. the concentration of the chloride ( 0 )and the sulfate (A)of the respective complex ions and vs. the concentration of KCI (0) and K,SO, (A)added to the 0.005 mol dm-) D20 solution
0.12
0.08 rMX,l/
mol d K 3 [ Ru(phen) 31 2t )
Figure 4. Plots of the Rl(av) and T values of [ R ~ ( p h e n ) ~in] ~D20 + and CD30D at 33.0 "C vs. the concentration of the chloride ( 0 ) and the ] ~ +vs. the concentration of KC1 (0)and sulfate (A)of [ R ~ ( p h e n ) ~and K2S04(A)added to the 0.005 mol dm" D 2 0 solution of the chloride and
the sulfate of [R~(phen)~]~+. The broken and dotted lines indicate the expected dependence of the T values on the concentrationsof the complex salts and of the added potassium salts, respectively, when eq 4 is followed. The solid curves ([R~(phen)~]SO~) were obtained by considering the formation of the M2X and MzX2ion pairs (upper curve) and the MX ion pair (lower curve); no appreciable difference was seen between results with a = 10 and 12 8,. 0
0.04
IMX,] / m o l drF3
&
OT
i n D20
c o n c e n t r a t i o n o f K C I o r K2S04 / m o l dm-3 0,l 0.2 0,3
'
L I
0,OZ
0.04
0.06
0.08
70
0.10
[ M X n l / ~ o ldm-3 (M2+= [ R t ~ ( b p Y ) ~ l ~ * )
Figure 5. Plots of the R,(av) and T values of [ R ~ ( b p y ) ~in] ~D2O + and CD30D at 33.0 OC vs. the concentration of the chloride ( 0 ) and the sulfate (A)of [ R ~ ( b p y ) ~and ] ~ +vs. the concentration of KC1 (0) and K,SO, (A) added to the 0.005 mol dm-3D20solution of the chloride and the sulfate of [ R ~ ( b p y ) ~ ]The ~ + .broken and dotted lines indicate the expected dependence of the 7 values on the concentration of the complex salts and of the added potassium salts, respectively, when eq 4 is followed. The solid curve indicates the T values obtained with the due consideration for the formation of the [R~a(bpy)~]~+,SO?ion pair; practically the same curve was obtained for a = 10 and 12 8,.
in a solution of concentration c with a viscosity of q are related to the T value in the solution of infinite dilution, T(O), by the following equation: .(C)
= T(0)(1/90) =
do)%
(4)
where qo and qr represent the viscosity of pure solvent and the relative viscosity of the solution, respectively. The broken lines in Figures 4, 5 , and 6 indicate the concentration dependences of
of the chloride and the sulfate of the complex ions. The broken and dotted lines indicate the expected dependence of the 7 values on the concentration of the complex salts and of the added potassium salts, respectively, when eq 4 is followed. The solid curves indicate the T values obtained with due consideration for the formation of the [CoL,]'+,SO~ion pairs; assumptions of a = 10 and 12 8,gave practically the same curve in each case. the T values expected from the measured viscosities of the solutions (cf. eq 4). The observed concentration dependence of the T value agreed well with the calculated one in the solutions of the chlorides except for the D 2 0 solution of [Ru(phen),]Cl2, which showed much larger T values than the calculated ones. Among the solutions of the sulfates, only the D 2 0 solution of [Ru(bpy),]S04 showed a good agreement between the observed 7 values and those expected from the measured viscosities. The deviation of the observed from the calculated T values is especially large in the D 2 0solution of [Ru(phen)JSO4 The large increase in the 7 value with increasing [Ru(phen),]S04 concentration is attributed to hydrophobic interaction of the complex ions, as will be discussed below. The change in T values was also measured as a function of the concentration (0.1-0.3 mol dm-3) of KCl or K2S04added to the dilute D 2 0 solution of the chloride or the sulfate of each complex (0.005 mol d n ~ - ~respectively. ), These results are also shown in Figures 4, 5 , and 6 (open circular and triangular marks). When KCI was added to the D 2 0 solutions of the complex salt, the change in the T value followed eq 4 (dotted lines in the figures). This indicates that the interaction of each complex ion with a chloride ion gives no specific effect on the rotational motion of the complex ion; the r value depends only on the viscosity of the solution. A similar result was previously obtained with the aqueous solution of [C~(en),]Cl,.~ Larger T values than those from eq 4 were shown when K2SO4 was added to the solutions of the cobalt(II1) complexes. This indicates that specific interactions between the complex and sulfate ions give some friction to the rotational motion of the complex ions. The large values in CD30D solutions of the sulfates of the ruthenium(I1) complexes are also interpreted as resulting from the interaction of the complex ions with sulfate ions (see following section). On the other hand, the increases in the T values of the ruthenium(I1) complex ions in DzO caused by added KzSO4 were well explained by the increase in the viscosities of the solutions. This is demonstrated by the good fit of the dotted lines (calculated from eq 4 with measured q values) to the open triangular marks (obtained from relaxation measurements in D 2 0 solutions) in Figures 4 and 5. If the interaction between the complex and sulfate ions is electrostatic, the magnitude of the interaction is larger for a
The Journal of Physical Chemistry, Vol, 88, No. 16, 1984 3429
Rotational Motions of Metal Complex Ions
I
TABLE 11: The ~ ~ ~Value ( 0at )33 O C for the MX Ion Pair (M = Complex Ion, X = Sulfate Ion)
complex ion
solvent
a,"
[Ru(phen),I2+
CD30D
[Ru(bpy),12+
CD,OD
[Co(phen),13+
D20
10 (12) 10 (12) 10 (12) 10 (12)
[C0(bPY)3l3+
D2O
dm-3)b T M X ( O ) , s 3.5 0.94 (3.4) (0.98) 0.96 3.5 (3.4) (1.0) 2.4 1.2 (2.3) (1.3) 2.4 1.1 (2.3) (1.2)
TM(O): s 0.77
1.o 0.92
(I
complex ion of higher charge and for a solvent of lower dielectric constant. The present results are consistent with this consideration. The same reasoning also explains why the chloride ion did not directly affect the rotational motion of the complex ions. 3.4. Quantitative Treatment of the Effect of the Sulfate Ion on the Rotational Correlation Time of the Complex Ion. We assume that the increase in the T value of the Co(II1) complex ions in D 2 0 and of the Ru(1I) complex ions in C D 3 0 D can be attributed to the formation of 1:l ion pairs with sulfate ions. For the ion-association equilibrium M+X+MX
(5)
where y denotes the activity coefficient. The association constant for the metal complex ion and the sulfate ion is not available for the sulfates of the ruthenium complexes in methanol nor for the sulfates of the cobalt(II1) complexes in water. Therefore, we estimated these association constants using the Ebeling-Yokoyama-Yamatera equation;20s2'this equation had been shown to give an appropriate association constant consistent with experiments for the [Ru(phen),lz+,S0,2- ion pair in the aqueous solutionZ2and for the [Fe(phen)3]2+,S0,2- ion pair in the aqueous, methanol, and mixed solutions.23 These association constants are listed in Table 11. We also assume that the lifetimes of the ion-paired and the unpaired complex ions are sufficiently long for the correlation times, T M X and T ~ to, be defined for each species and that the T M X and T~ values at different concentrations follow eq 4. Then, we have the relation
+ ( l - xMX)(rM/vr) = xMXTMX(o)
+ (l
- XMX)TM(o)
(6)
Here, vr represents the relative viscosity of the solution, ~ M x ( 0 ) and T M ( O ) (= ~ ( 0 ) )are respectively the T M X and T~ values at infinite dilution (where qr = l), and x M Xdenotes the mole fraction of the complex ion existing in the form of the MX ion pair, i.e. XMX
Figure 7. Illustrations of the prolate models of the ion pairs and aggregates: (A) MX ion pair (M = complex ion, X = SO,2-) and (B) MM aggregate (M = [Ru(phen),12+). rM or rx are the radii of the complex ions (shown in Table I) and of the sulfate ion (2.3 A), respectively. TABLE 111: Rotational Correlation Times at 33 "C Expected from the Prolate Model (Figure 7A) of the MX Ion Pair (X = SO,'-) complex ion solvent 2rlF A 2rs,' A 1O1'TMX,l, s ~O"TMX,II, s structure of the ion pairb
[ R u ( ~ h e n ) , l2+ CD,OD 15 11 2.6 0.8 (i) (ii)
(i)
(ii)
~O"'~MX,CH(~), s (i = 3 and 8)
2.2
2.1
~O"TMX C H ( ~ ) s, (i= 2, 4 , 5 , 6,
1.5
1.5 2.0 1.8' 2.0 2.9 1.7, 2.4 2.4c 1.7, 2.4
I, and
where M and X denote the metal complex ion and the sulfate ion, respectively, the equilibrium constant at infinite dilution, KMX, is defined by
XMX(TMX/vr)
(B)
(A)
Ion size parameter. (The sum of crystal radii of the complex and sulfate ions is about 10 A. The data for a = 12 A were listed to show the extent to which the results depend on the ion size parameter.) Calculated by the Yokoyama-Yamatera-Ebeling equation (ref 20 and 21). ' T M ( O ) = ~ ( 0 ) .
r/qr =
1
0.67
= [MXl/cM
where cMis total concentration of the metal complex. The xMX values at various concentrations of the complex salt or the added sulfate were calculated with the KMX values given in Table I1 and the yM,y x , and y M x values calculated by the Debye-Huckel (20) Ebeling, W. Z. Phys. Chem. (Leipzig) 1961, 238, 400. (21) Yokoyama, Y.; Yamatera, H. Bull. Chem. SOC.Jpn. 1975,48, 1770, 3002 (corrections). (22) Yokoyama, Y.; Yamatera, H. Bull. Chem. SOC.Jpn. 1975.48, 2708. (23) Kubota, E.; Yokoi, M. Bull. Chem. SOC.Jpn. 1976, 49, 2674.
9)
1 0 " ~ ~ ~ ( s0 ) , ~0.94 a
q (= r M
1.2 1.6 1.5' 1.6 2.3 1.3, 2.0 1.9c 1.3, 2.0
[Co(phen),l 3 +
D2
0
15 11 3.3 1.o
1.8
1.2
+ YX)and rS (= YM)represent the radii of the longer
and shorter axes of the prolate. Y M and rx denote the radii of the complex ion (shown in Table I) and the sulfate ion (2.3 A). See Figure 7 and ref 25. See text. The rotational correlation time to be measured for each C-H vector is the average value over Observed. three phenanthroline ligands of the complex ion.
equation. Then, the observed 7 / v r values were plotted against xMXto determine the (hypothetical) value of ~ ~ ~ (The 0 )values . ) obtained are also shown in Table I1 together with of ~ M x ( 0thus the values of ~ ~ (and 0 KMp ) Using these values and the measured vr values, we calculated the values of T at different concentrations of the complex salts and K2S04to give the solid curves shown in Figures 5 and 6 as well as in the lower part of Figure 4. The satisfactory fit of the curves to the experimental results indicates the validity of the present treatment. The obtained T M X ( O ) values were 20-30% greater than the ~ ~ ( values. 0 ) The rotational motions of the ion-paired complex ions were approximately isoIn order to realize these increases in T due to ion pairing, we considered an extreme case for the dynamic property of the ion pair: the ion pair was assumed to maintain its configuration at least for the same order of time interval as T~~ (s). This permits one to regard the ion pair as a prolate as shown in Figure 7A; the diameter along the main axis (the longer axis) is twice the sum of the radii of the complex25and the sulfate ions, and the diameter perpendicular to the main axis (the diameter along the shorter axis) is twice the radius of the complex ion. The rotational motion of a prolate is characterized by two rotational correlation times: that of the main axis of the prolate, T M X , ~and , that around the main axis, T M X , / / . On the basis of the hydrodynamic model, these two rotational correlation times were (24) The observed rotational motions of the complex ions were approximately isotropic in the full range of the concentrations studied here, even in the concentrations where a considerable part of the complex ions form ion pairs. (25) The radius of the sulfate ion was taken as 2.3 A. Those of the complex ions are shown in Table I. The complex ions are not really spherical, and the surface of some hydrogen atoms project out of the sphere whose volume is equal to that of the complex ion.
3430 The Journal of Physical Chemistry, Vol. 88, No. 16, 1984 calculated according to Perrir1~~3~’ and are listed in Table 111. In the prolate model of the ion pair, the rotational correlation time of each C-H vector of the complex ion should show a characteristic value, depending on its direction with respect to the main axis of the prolate.28 Two representative configurations were assumed for the M X ion pair; the sulfate ion is placed (i) on the C3 axis and (ii) on the Cz axis of the complex ion. In these configurations, the main axis of the prolate coincides with (i) the C3 axis and (ii) the C2 axis of the complex ion. Then, by considering the direction of each C-H vector with respect to the main axis, the rotational correlation time of each vector, TMX,CH(~ in these two configurations was calculated from the equation3’ TMX,/I
- ‘MX,I
TMX,ll
+ TMX,I
sin2 6
Masuda and Yamatera TABLE IV: The ~ ~ ~Value ( 0a t )33 ‘C for the M,X and M2X, ~ +=, SO4,-) Aggregates in D,O (M = [ R ~ ( p h e n ) ~ ]X
a,” A
KMX, mol-‘ dm3
Kt (= K ) mol-1‘ ’ dm3
10 (12)
2s (40)
S (3)
~O”’TMM(O),~ s 10’OrM(0),s
3.4 (3.5)
1.2
“Ion size parameters. bAssociation constant for the equilibria M X
+ M + M2X (Kt) and 2MX +=
Kt =
K, was assumed (ref 30).
(MX), ( K J . An approximate equality = rq was assumed.
vtc
where 6 is the angle between the CH(i) vector and the main axis and the ‘TMX,L and 7MX,il values are listed in Table 111. The results are also listed in Table 111. Similar results were obtained for the bipyridine complexes. The rotational correlation time calculated for the C-H vector in the 3- and 8-positionswas different from that for the other C-H vectors (Table 111). This is not consistent with the observation that no significant differences were detected in the measured Figure 8. Simplified drawing for the configuration of the pair of A- and relaxation rates between different 13C nuclei.24 These results A-[Ru(phen),I2+ ions in the M2X and M,X2 aggregates (ref 30). indicate that the ion pairs take no specific configuration but have of the solution was allowed for. We further assume that the various configurations. In addition, the fact that the experimental rotational correlation time of the triple and quadrupole aggregates, value of the rotational correlation time of the ion pair ( ~ M x ( 0 ) TMM, depends linearly on the viscosity of the solution as is indicated in Table 11) is much smaller than the calculated values (TMX,CH(~) by eq 4. Then, with the approximation TMX = rMfor the system in Table 111) suggests that the configurations are not fully in question here, the observed rotational correlation time can be maintained for the time interval of T~~ (s). expressed by The dynamic feature of the structure of the ion pair elicited here can be attributed to the characteristic of the complex ions T/% = (xt -k xq)TMM(o) -b ( l - Xt - xq)TM(0) (7) lacking specific sites of interaction such-as the sites of hydrogen where bonding with anions. In other words, the major interaction between the complex and sulfate ions is electrostatic attraction xt = 2[M2X]/cM and xq = 2[MZX2]/cM between charged spheres. This is in contrast with the case of the [ C 0 ( e n ) ~ ] ~ + , Sion 0 ~ ~pair.5,29 This ion pair possesses a rigid The values of xt and xq were calculated with the association structure due to the hydrogen bond between the amine protons constant, Kt for the M2X and Kq for the M2X2aggregates, preof the complex ion and the oxygen atoms of the sulfate ion, and viously obtained.30 The rMM(0)value was determined in a way therefore the rotational motion of the ion-paired [Co(en),13+ ion similar to that for the M X ion pair in C D 3 0 D and is shown in is well represented by that of a rotating prolate. Table IV. The T values calculated with this ~ ~ ~value ( 0and) 3.5. The Effect of the Mutual Interaction between the [Ruthe association constants are shown by solid lines in the upper part ( ~ ~ h e n )Ions ~ ] ~on ’ the Rotational Motion. The T value of the of Figure 4. The agreement between the calculated and the observed values is satisfactory, showing that the increase in T is [Ru(phen)J2+ ion greatly depended on the concentration of the caused by the formation of the M2X, aggregates. The formation [Ru(phen),lZ+salts in DzO solutions. This exraordinarily large of such aggregates in D 2 0 solutions of [Ru(phen),]S04 increases dependence cannot be attributed to the interaction of the complex ion with its counteranion, since addition of K2S04to the D 2 0 the T value much more remarkably than by the formation of the solution of [Ru(phen)JS04 showed no specific effect on the T MX ion pair in CD30D solutions of [Ru(phen),]S04 and in D 2 0 value of the [ R ~ ( p h e n ) ~ion. ] ~ + Our previous on the proton solutions of [ C ~ ( p h e n )2(S04)3. ~] chemical shifts of [Ru(phen),]S04 in DzO showed that aggregates As deduced from a proton chemical shift two complex containing two [ R ~ ( p h e n ) ~ions ] ~ +are formed in the solution. On ions in the aggregate are in contact with each other, one of the the basis of experimental evidence, we proposed a model for the phenanthroline ligands of each complex ion partly occupying an aggregate in which the two complex ions are in contact with each opening between the ligands of the other complex ion (see Figure other. It is reasonable to consider that in such an aggregate the 8). In a manner similar to that for the MX ion pair, we regard the rotational motion of the complex ions in the aggregate as that rotational diffusion of the complex ion is slower than that of an unassociated complex ion. The MzX (= 2 [ R ~ ( p h e n ) ~ ] ~ + , S O ~ ~of- a prolate with a diameter of 22 A (4 times the radius of the or triple ion, abbreviated t) and M2X2(= 2 [ R ~ ( p h e n ) ~ ] ~ + , 2 8 0 ~ ~[ R ] ~ + shown in Table I) along the main axis and - ~ ( p h e n ) ~ion25 a diameter of 11 A (twice the radius of the [Ru(phen),lz+ ion) or quadrupole, abbreviated q) aggregates are assumed to exist along an axis perpendicular to the main axis (see Figure 7B). The in the solution30 and to undergo rotational motion with a charsulfate ions in the aggregate were disregarded in the present acteristic correlation time TMM; the difference in the correlation treatment, since it has been shown that the rotational motion of times between MzX and MzX2 was disregarded. The use of a the [Ru(phen),12+ ion in DzO is hardly affected by the association single correlation time common to M2X and M2X2is justifiable with the sulfate ion. Then, the rotational correlation time for the by analogy with the fact that the T value of MX in DzOwas rotation of the main axis ( T M M , I ) and that for the rotation around in the viscosity practically the same as that of M whenih-nge ) calculated according to P e r r i r ~ . ~ ~ , ~ ~ the main axis ( T M M , ~ ~ were With the approximation that the main axis coincides with the C2 (26) Perrin, F. J . Phys. Radium 1934, 5, 33; 1936, 7, 1. (27) The hydrodynamic boundary condition for the rotational motion of axis of the [Ru(phen),J2+ ion,31 the TMM,cH(~) values for each the complex ions at infinite dilution was shown to be nearly sticking (see section 3.2); the same boundary condition was assumed for the rotational motion of the prolate. (28) Huntress, W. T. Jr. Adv. Magn. Reson. 1970, 4, 1. (29) Mason, S . F.; Norman, B. J. J . Chem. SOC.A 1966, 307. (30) Masuda, Y.; Yamatera, H. Bull. Chem. SOC.Jpn. 1984, 57, 58.
(31) In the structure shown in Figure 8, the vector binding two metal complex ions, or the main axis of the prolate, does not exactly coincide with the C, axis of the complex; however, this deviation will not seriously affect the argument here.
3431
J . Phys. Chem. 1984,88, 3431-3435 TABLE V: Rotational Correlation Times at 33 "C in D,O Expected from the Prolate Model (Figure 7B) of M,X and M,X, Aggregates (M = [Ru(phen),] ,+,X = SO,,-)
2rl,a A 2r,,' A
22 11
6.0 1.2
:::} 2.7
~ O " ~ M M , C H ( ~ ) , s (i= 2, 4, 5, 6, 7, and 9)
3.0 5.0
1 0 1 0 7 ~ ~ ( 0s ) , C
3.8, 2.2 3.4
a r1 (= 2rM) and rs (= YM) represent the radii of the longer and shorter axes of the prolate, and TM denotes the radius of the [Ru(phen),] '+ ion listed in Table I. See Figure 7 and ref 25. b The rotational correlation time to be measured for each C-H vector is the average value vector over three phenanthroline ligands of the complex ion. Observed.
the value of 7MM,CH(j) obtained from the observed R 1values showed no appreciable differences between different positions. The fact that anisotropy was hardly detected in the rotational motion of the complex ion in the aggregate suggests that the configuration of the aggregate as shown in Figure 8 is not the unique one. For example, the A,A and A,A aggregates take configurations different from those of the A,A aggregate. The C-H(i) vector at the 3and 8-positions probably has a large 7MM,CH(i) value in the A,A and h,A aggregates in contrast to the case of the A,A aggregate listed in Table V. The ~ ~ ~value ( 0determined ) from the observed relaxation rate is an average of the ~ ~ ~values ( 0for) the aggregates of different configurations, since the observed relaxation rate of 13C in each position of the ligand showed a single value. If such a situation is taken into account, the agreement between the calculated TMM,CH(~)values and the experimental rMM(0)value is reasonably good. This indicates that an aggregate with a definite configuration is maintained for the time interval of at least 3 X s, the same order of magnitude as TMM, although the aggregate does not survive so long that a 7 value characteristic of the particular aggregate can be obtained.
Acknowledgment. This work was carried out as a cooperative research (1982) of the Institute for Molecular Science. We thank the Ministry of Education, Science and Culture of Japan for the results are summarized in Table V.32 support of this work (Grant-in-Aid for Scientific Research No. While the calculated 7MM,CH(i) value for the 56470039). Registry No. R~(bpy),~',15158-62-0; R~(phen),~+, 22873-66-1; (32) In the D20 solution of ruc-[Ru(phen),]SO4, two kinds of the aggreCo(bPY)33+,19052-39-2; Co(phen),'+, 18581-79-8; 2[Ru(phen),12',gate with different combinations of the optical isomers of [Ru(phen),]*', h,AL O > - , 90641-15-9; [ R ~ ( p h e n ) ~ ] S O 41745-79-3; ~, [Ru(bpy),]SO,, and A,A (and its antipode A,A), exist (ref 30). The calculation here was made 50989-45-2; [C0(bpy)J~',S04~-,74436-63-8; [C~(phen)~]~',SO>-, on the A,A aggregate. 76229-12-4.
C-H(i) vector of the phenanthroline ligands were calculated in
Intermediate-Sized Deuterium Effect on T,
+.So Intersystem Crossing in Acetaldehyde
Warren F. Beck,' Merlyn D. Schuh,* Mark P. Thomas,2 and T. John Trout3 Department of Chemistry, Davidson College, Davidson. North Carolina 28036 (Received: September 12, 1983)
Reciprocal lifetimes, extrapolated to zero pressure ( 7 f 1 ) , and rate constants for self-quenching (k,) have been measured for flash-excited T,-state acetaldehyde and its deuterated analogues. Both 70-l and k decrease with increasing deuteration and the ranges of values are 70-1 = 3400-29 000 s-l and k, = 0.52 X 107-1.8 X lo7 s-l. Reductions in 70-1and k, are very specific with respect to which hydrogens are deuterated, and the largest deuterium effect is found for the aldehyde hydrogen. The deuterium effect for acetaldehyde is intermediate in value between those for formaldehydeand larger ketones and aldehydes. Experimental evidence is presented in support of the activity of the out-of-plane deformation mode, ~ 1 4 as , the dominant accepting mode for T I So intersystem crossing.
k-l
-
Introduction Studies of the factors and structural features that control the partitioning of energy between the various decay channels of excited electronic-state molecules are of fundamental importance to chemical dynamics. In particular, the loss of electronic (vibronic) energy through radiationless decay has been of considerable experimental and theoretical interest for several decades and a general theory has evolved4 which explains the most important phenomenological aspects of radiationless transitions. For example, the lengthening of lifetimes for triplet-state (T,) aromatic hydrocarbons caused by deuterium substitution is well understood (1) Present address: Department of Chemistry, Yale University, New Haven, CT 06520. (2) Present address: Department of Chemistry, Emory University, Atlanta, GA 30322. (3) Present address: Department of Chemistry, Pennsylvania University, Philadelphia, PA 19104. (4) P. Avouris, W. M. Gelbart, and M. A. El-Sayed, Chem. Reu., 77, 793 (1977). and references therein.
0022-3654/84/2088-3431$01.50/0
and is attributed primarily to a reduction in the Franck-Condon factors for C-H stretching modes that are efficient acceptors of electronic energy.4 In general, deuterium substitution also increases the lifetimes of TI-state carbonyl containing compounds, but the causes for this important phenomenon are not as well understood. Vapor-phase alkyl ketones and aldehydes seem to belong to two classes with respect to the effect of deuterium substitution on their T1-statelifetimes. Formaldehyde alone forms one class for which deuterium substitution causes a dramatic increase in lifetime of greater than 40-f0ld.~ The second class consists of acetone, propynal, glyoxal, and biacetyl for which the deuterium effect is much smaller and lengthens the vapor-phase phosphorescence lifetimes by less than a factor of 2.6-9 (5) A. C. Luntz and V. T. Maxson, Chem. Phys. Lett., 26, 553 (1974). (6) (a) J. C. Miller and R. F. Borkman, J . Chem. Phys., 56,3727 (1972); (b) W. A. Kaskan and A. B. F. Duncan, ibid.,18, 427 (1950). (7) U. Bruhlmann, P. Russegger, and J. R. Huber, Chem. Phys. Lett., 75, 179 (1980).
0 1984 American Chemical Society
