J . Phys. Chem. 1990, 94, 2843-2847
2843
I f it is correct that the key vibrations are not so critically vibration. The large frequency variation of C,=C, stretching is dependent on the molecular conformation described by the dihedral a real physical phenomenon in So tSB. It is likely that the same angles cp, and cp2, the observed changes in the excited-state vs is true for Si tSB, although the mixing conditions could be quite ground-state spectra are the consequences of changed bond lengths different. It has been noted from the values of the force constants and angles and hence of the bond characters in the excited state. that the vibrational dynamics of the -C,H%,Hgroup is specific The broadening of the vibrational bands in the excited state of to this system as compared to, e.g., trans-but-2-ene and this is tSB-do and -a,cy'-13C2due to the coexistence of different conclearly due to the *-electron delocalization. On the other hand, formations* is then possible only if the key frequencies are slightly for the same reason there are pronounced similarities with the affected by the conformational change, Le., changed by up to A10 -C, ,H=CI2H- group of a l l - t r a n ~ - r e t i n a l .The ~ ~ ~results ~ ~ now cm-I. This means that the assumption of slowly varying dihedral available on So tSB vibrations might be helpful in understanding angles would stand equally well for the excited state. Si and radical ions TR3 spectra of tSB. The effects of I3C substitution are limited to only six out of Acknowledgment. We are grateful to Dr. W. Hub for providing 25 in-plane aBmodes, and they are very similar in the 1 6 0 0 - ~ m - ~ the sample tSB-I3Cand Dr. M. ZiniE for the sample of tSB-4-dl. region to the effects induced by deuteration at a-positions. One Z.M. is indebted to Deutscher Akademischer Austauschdienst may accept this similarity as a valid principle in understanding (Bonn) for a fellowship and to Professors F. Dorr and S . Schneider the spectra of the excited state. Hamaguchi" discusses the obtained Si Raman spectra of tSB-do, -a,a'-d2, -dlo,and - ( Y , ~ ' - ' ~ C ~ .for their kind hospitality during the stay at Garching. This work was supported by the Republic Council for Science of S. R. The observed changes parallel those described here for So Raman Croatia, a Yugoslav-German scientific cooperation program, and spectra of the same pair of isotopomers. Thus, for example, we a Yugoslav-Hungarian scientific exchange program. have found no significant changes in relative intensities in the 1200-1 100 cm-I region upon I3C substitution and the correRegistry No. tSB, 103-30-0; D, 7782-39-0; I3C, 14762-74-4. sponding HMS coefficients are in accordance with observations. Supplementary Material Available: Tables 3-6 with all obYet, as the Qii partakes somewhat of the Q ! 5character in the So state and their observed intensities are reversed in the Si state served frequencies for trans-stilbene and Table I O with frequencies spectra of the I3C isotopomer," the characters of these two viof substituted benzenes (14 pages). Ordering information is given brations are presumably reversed in the Si state. on any current masthead page.
Outer Coordination Sphere: Characterization by Nuclear Magnetic Relaxation Dispersion Cathy Coolbaugh Lester and Robert G. Bryant*-+ Departments of Chemistry and Biophysics, University of Rochester, Rochester, New York 14642 (Received: August 18. 1989)
Nuclear magnetic relaxation dispersion data obtained on aqueous solutions of potassium tris(oxalato)chromate(III), potassium tris(malonato)chromate(III), and potassium hexacyanochromate(II1) provide a characterization of magnetic relaxation effects in the outer coordination domains of the metal complexes. The data demonstrate that the water proton nuclear spin relaxation is not controlled by rotational motions of the metal complex but by the relative translational motions of the water molecules and the metal complex and, in some cases, by the electron relaxation in the metal center. Unlike previous analyses using similar approaches that employed less complete interpretive models, the present data demonstrate that the translational mobility of the water in the regions immediately adjacent to the metal ion are perturbed very little compared with properties of bulk water.
Introduction The structure and dynamics of solvent molecules outside the first coordination sphere of transition-metal complexes may impact chemical reactivity as well as the physical behavior of the complex in solution. Direct observation of molecules in an outer coordination sphere is difficult, though several characterizations using different types of structural and dynamical approaches have been reported I n addition to the fundamental interest in solute-solvent interactions, the dynamical characterization of water molecules close to metal complexes is important for an understanding of paramagnetically induced nuclear spin relaxation in solvent molecules that is of current interest in potential applications to magnetic imaging. A difficulty in isolating effects outside the first coordination sphere of a paramagnetic metal complex is that solvent nuclei may be relaxed indirectly by magnetic exchange with first-coordination-sphere n ~ c l e i . The ~ present study utilizes aqueous solutions 'Mailing address: Robert G.Bryant, Biophysics Department, University of Rochester Medical Center, Rochester, N Y 14642.
0022-3654/90/2094-2843$02.50/0
of tris(oxalato)chromate(III) ion which eliminates this possibility because this complex anion presents no first coordination sphere protons or other nuclei with magnetic moments that may couple magnetically to the observed water protons. Thus, water proton relaxation induced by the metal center must arise from interactions outside the first coordination sphere. There is the interesting possibility, however, that water molecules may hydrogen bond to the paramagnetic complex ion, for example, the oxygen atoms of the trioxalato complex.5 However, the lifetime of the hydrogen bonds may be long or short which raises the important question of defining a lifetime for a chemically significant water molecule interaction in the second coordination sphere. In the present context there are two simple reference points: the translational ( I ) Amis, E. S.; Hinton, J. F. Solvenf Effecfs on Chemical Phenomena; Academic Press: New York, 1973; Chapter 3. (2) Marcus, Y. Ion Solvation; Wiley: New York, 1985. (3) Dogonadze, R. R.; Kalman, E.; Kornyshev, A. A,; Ulstrup, J. The Spectroscopy of Solvation. The Chemical Physics of Soluafion. Part B Eisevier: New York; 1986. (4) Douglas, D. C.; Jones, G . P. J . Chem. Phys. 1966, 45, 956. (5) Taykr, (5) Taylor, D. Ausf. J . Chem. 1978, 31. 1455 1455.
0 1990 American Chemical Society
2844
The Journal of Physical Chemistry, Vol. 94, No. 7, 1990
correlation time of the water molecules in water, and the rotational correlation time of the metal complex. Excepting general dielectric effects, if the lifetime of the water next to the solute species is so short that the translational correlation time for the solvent or water is essentially unchanged compared with water or solvent translational correlation times in the absence of the solute, the outer coordination sphere interaction can have little kinetic effect. However, if the lifetime of the water molecule adjacent to the metal complex is sufficiently long and the interaction sufficiently strong that the water-metal complex may rotate as a unit, then the outer-sphere complex will have readily identifiable features, and may have an effect on the dynamics of a chemical reaction. This rotational criterion, which places the time scale of the significant interactions in the range of tens of picoseconds, is a particularly useful one in the present context because the contributions to magnetic relaxation from rotational motion of a metal ion complex and those from relative translation of the solvent and the paramagnetic particle may be distinguished based on the field dependence of the nuclear spin-lattice relaxation rates of the solvent protons. The present study provides no evidence for second coordination sphere water-metal ion complexes that are sufficiently long lived for the water to experience the rotational properties of the complex ion.
Experimental Section Potassium tris(oxalato)chromate(IIl) was prepared from potassium dichromate, oxalic acid, potassium hydroxide, and recrystallized prior to use.6 Solutions were made immediately before each set of measurements to minimize the effects of time-dependent loss of ligand on the relaxation measurements.' The water-glycerol solutions were made by weight and the metal concentration was determined in each case by the absorbance at 420 nm. Potassium tris(malonato)chromate(III) trihydrate was prepared by the method described by Chang and recrystallized from water prior to use.8 Potassium hexacyanochromate( 111) was prepared by the method described by Bauer and recrystallized from aqueous solution with e t h a n ~ l . ~Potassium hexacyanochromate(II1) solutions were prepared with a 0.025 M carbonate buffer containing a 2-fold molar excess of potassium cyanide to maintain the pH at a value of I O and to inhibit the decomposition of the complex anion. Nuclear magnetic relaxation dispersion measurements were made on an instrument that switches magnetic fields without moving the sample constructed with the assistance of Dr. Seymour Koenig and Dr. Rodney Brown 111 of the IBM Watson Laboratories as is described elsewhere.IO*" Sample temperature was controlled by using perchloroethylene as the cryogenic fluid that was thermostated in a Neslab Model RTE 8 temperature controller. Each relaxation rate involved the measurement of a minimum of 16 points in the decay curve at each magnetic field strength. Results and Discussion The relaxation data are shown in Figure 1 as a function of magnetic field strength reported as proton Larmor frequency for a 5.0 mM potassium tris(oxalato)chromate(III) solution at 282 K. The dotted curve was calculated assuming the Solomon, B l o e m b e r g e n , a n d Morgan relaxation equation that is most commonly used to analyze relaxation data in paramagnetic syst e m ~ . ' * - ' ~This analytical approach would be approximately
Lester and Bryant h
kk
-
._
O.0001
0 10
1.00 10.00 10000 Lormor Frequency (MHz)
Figure 1. The spin-lattice relaxation rate of water protons per millimole of potassium tris(oxalato)chromate(lll) at 282 K and a pH of 5.38 versus applied magnetic field strength. The solid curve was calculated by using the force-free model including electron relaxation with the best fit parameters: b = 4.5 X m, D = 1.3 X m2/s, B = 2.4 X I O I 9 rad2/s2, and = 4. I X IO-" s. The dashed curve was calculated by using the force-free model excluding electron relaxation with b = 2.9 X m and D = 3.8 X IO4 m2/s as best fit parameters. The dotted curve was calculated by using the Solomon, Bloembergen, and Morgan equations assuming three water molecules a r e bound to the complex. The parameters used are b = 3.7 X lo-'" m, T~ = 8.1 X IO-" s, T , = 3.1 X IO-" s, and B = 6.1 X I O i 9 rad2/s2.
appropriate if there were water molecules in the second coordination sphere of the complex that remained hydrogen bonded to the complex long enough to experience the rotational correlation time of the metal complex, generally in the tens of picoseconds range.15 The sharp Lorentzian character of the curve that results from a rotational modulation of the electron-nuclear coupling approach is clearly not consistent with these data. Thus, the water molecule proton relaxation cannot be dominated by water molecules in the second coordination sphere with a lifetime sufficiently long that the water proton-electron magnetic coupling is modulated by rotation of the complex. The model that more nearly describes the field dependence of the relaxation is based on the relative translational motion of the water molecules as well as the relaxation of the electron spin.16-18 There are several models that describe nuclear spin relaxation caused by modulation of the magnetic dipole-dipole couplings by relative translational diffusion of the spin-bearing molecules. Earlier models employ a uniform probability distribution function to describe the time dependence of the relative positions of the spin-bearing molecules.'6 Freed and Hwang demonstrate that these models ignore the fact that there is a minimum distance of closest approach and, therefore, a certain volume that is excluded to the molecules being considered." These authors include this boundary for the case of Brownian diffusion utilizing a hard-sphere pair correlation function to describe the interaction between the spin-containing molecules with a reflecting boundary at the distance of closest approach, b. Since this model ignores any long-range interactions between the molecules, it is called the force-free model. The analytical expression for the longitudinal relaxation rate of the nuclear spin, I , through modulation of the dipolar interaction with the electron spin, S, by the relative translational diffusion of the molecules containing these spins is l / T l = (32*/405)y?ys2h2S(S ~ z ( W S- W i )
(6) Pass. G.; Sutcliffe, H. Pracrical Inorganic Chemistry; Chapman and Hall: London, 1974; p 57. (7) Yager, T. D.; Eaton, G. R.; Eaton, S. S . Inorg. Chem. 1979, 18, 725. (8) Chang, J. C. J . Inorg. Nucl. Chem. 1968, 30, 945. (9) Brauer, G . Handbook of Preparative Inorganic Chemistry; Academic Press: New York, 1965; Vol. 11, p 1373. (IO) Hallenga, K.; Koenig, S . H. Biochemistry 1976, 15, 4255. ( 1 I ) Hernandez, G.; Brittain, H. G . ;Tweedle, M.; Bryant, R. G . Inorg. Chem., submitted for publication. (12) Solomon, 1.; Bloembergen, N . Phys. Reo. 1955, 99, 559. (13) Bloembergen, N . ; Morgan, L. 0. J . Chem. Phys. 1961, 34, 842. (14) Solomon. 1.: Bloembergen, N. J . Chem. Phys. 1956, 25, 261.
100000
+ l)(Na/IOOO)([S]/bD)X + 3j1(@/)+ 6 j 2 ( W ~+ W/)I
(1)
with the spectral density function j k ( w ) j(w) = [1
+ 5 z / 8 + z 2 / 8 ] 1( + z + z 2 / 2 + z 3 / 6 + 4z4/81 + z5/81 + z6/648j-'
(2)
( I 5) Hertz, H. G . In Water: A Comprehensive Treatise; Franks, F., Ed.; Plenum Press: New York, 1973; Chapter 7. (16) Hubbard, P. S. Pror. R. SOC.London, Ser. A 1966, 291, 537. (17) Hwang, L. P.: Freed, J . H. J . Chem. Phys. 1975, 63, 4017. (18) Freed, J . H. J . Chem. Phys. 1978, 68. 4034.
The Journal of Physical Chemistry, Vol. 94, No. 7, 1990 2845
Outer Coordination Sphere
. .
with z = ( 2wb2/ D ) ' / *
(3)
.I
I
and the translational correlation tiinc 7,
7,
E
given by
= b2/D
v
1.5-
(4)
Here, yf and ys are the nuclear and electron magnetogyric ratios, w f and us are the nuclear and electron Larmor frequencies, fz is Planck's constant divided by 2n, [SI is the molar concentration of S spins, b is the distance of closest approach between the centers of the molecules on which the I and S spins are located, and D is the relative translational diffusion coefficient given by D = Df + Ds where D, and Ds are the individual diffusion constants of the molecules containing the I and S spins. This spectral density function is valid when the electron spin relaxation time is long relative to the translational diffusion correlation time; TI,=>> 71,a condition often satisfied for organic radical^.'^*^^ When this condition fails and the electron spin relaxation contributes to the correlation function, the modified spectral density function also developed by Freed may be used.I8
+ s / 4 ] / [ 1 + s + 4s2/9 + s3/9]) s = b((iw + ( T k s ) - l ) / D ) ' / 2
j k ( w ) = Re { [ I
1 / T s = ( B / 2 ) ( 3 J ( O )+ SJ(ws)
Jciw,) =
7v/(1
+ 2J(2~s)J
+ 0'ws7v)2)
0.0
b
(8)
(IO)
and 7Vis the correlation time characterizing the fluctuations in the zero field splitting interaction. The magnetic field dependence of the water proton longitudinal relaxation rate in aqueous solutions of three chromium(lI1) complexes is shown in Figure 2. The hexacyanochromate( 111) complex is most efficient in relaxing water protons, presumably because it is small, permitting a close approach of the water molecules, and has long electron spin relaxation times because ~~
(19) Polnaszek, C. F.; Bryant, R. G. J . Chem. Phys. 1984, 81, 4038. (20) Bennett, H . F.; Brown, R. D. 111; Koenig, S. H.; Swartz, H. M. Mugn. Reson. Med. 1987. 4 , 93. (21) Rubinstein, M.; Baram, A.; Luz, Z. Mol. Phys. 1971, 20, 67. (22) Carrington. A,; Luckhurst, G.R. Mol. Phys. 1964, 8, 125.
100.00
Figure 2. The spin-lattice relaxation rates per millimole of complex for water protons versus magnetic field strength for aqueous solutions of potassium hexacyanochromate(Ill), potassium tris(ma1onato)chromate( I l l ) , and potassium tris(oxalato)chromate(lII) at 282 K. Parameters are summarized in Table 1.
complex ion
(7)
1 .oo 10.00 Larmor Frequency (MHz)
0.10
0.01
(6)
(9)
+ 2E2
I-----
TABLE I
where B is a constant related to the trace of the square of the zero field splitting tensor (A2) as
B = ( 1 2 / 2 5 ) A 2 and A2 = ( 2 / 3 ) D 2
0.5-
.-E
(5)
where Tks is the S spin relaxation time with k = 1, 2, and Re means the real part of the expression. In the limit where Tksis very long relative to T , , the spectral densities become equivalent. Application of this equation requires a model for the field dependence of the electron relaxation times. Rubinstein and coworkers have discussed this problem for the S = 3 / 2 and S = 5 / 2 aquo ions.2' Relaxation of the electron spin is thought to be due to the time modulation of the zero field splitting interaction resulting from collisions between the solvated ion and the solvent molecules. For the highly symmetrical aquo ions, permanent zero field splittings should be vanishingly small; however, a transient zero field splitting interaction is assumed to result from distortions that result from collisions with solvent molecules. A permanent zero field splitting exists for complexes which deviate from cubic symmetry such as the tris(oxalat0) and tris(malonato) complexes with D3 symmetry. Rotational motion modulates this interaction which has been treated by Carrington and Luckhurst who show that for S = 3 / 2 longitudinal and transverse magnetizations each decay biexponentially.22 However, in the extreme narrowing regime where wsr,
