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The Journal of Physical Chemistry, Vol. 82, No. 2, 1978
of five heme proteins, the electronic state lifetimes determined from optical spectra recorded at 77 K were consistent with quantum yields for heme fluorescence and resonance Raman intensities21 implying that inhomogeneous broadening of the electronic bands of these proteins must be considerably less than lifetime broadening (100-1000 cm-l). In addition, the molecular orbital picture based on extended Huckel calculations was able to rationalize the observed lifetimes which bolsters the credibility of the theoretical model. The lifetime broadening of these electronic states is up to two orders of magnitude larger than that observed for the vibrational states, 5ut taken together both sets of measurements demonstrate that the protein provides a relatively homogeneous environment for the heme. The measurements of vibrational line widths presented here were shown to confirm excited state energies determined by an application of the ligand field description of electronic states to electron spin resonance data. Aside from the spectroscopic interest in such a study, there are significant applications to biochemical studies. There are a t least two systems (cobalt substituted myoglobin39and half-reduced cytochrome oxidase40) in which the optical spectra of deoxy and photolyzed samples are indistinguishable while the electron spin resonance signals differ significantly. A comparison of resonance Raman vibrational line widths should aid in the characterization of these materials. Acknowledgment. This work has been supported by grants from NSF (BMS 75-07355) and NIH (GM 12202). I wish to thank Martin Gouterman for many stimulating discussions on the spectroscopy of metalloporphyrins. In retrospect I realize that he was aware of the possibility of these electronic-vibrational interactions before they occurred to me. I also thank J. S. Leigh, John Salerno, and Haywood Blum for useful discussions on the electron spin resonance characteristics of hemes.
References and Notes (1) T. C. Strekas and T. G. Spiro, Biochim. Biophys. Acta, 263, 830 (1972). (2) T. C. Strekas and T. G. Spiro, Biochim. Biophys. Acta, 278, 188 (1972). (3) H. Brunner, A. Mayer, and H. Sussner, J. Mol. Biol., 70, 153 (1972). (4) I. Salmeen, L. Rimai, D. Gill, T. Yamamoto, G. Palmer, C. R. Hartzell, and H. Beinert, Biochem. Biophys. Res. Commun.,52, 1100 (1973). (5) F. Adar and M. Erecinska, Arch. Biochem. Biophys., 165, 570 (1974). (6) (a) R. H. Felton, A. Y. Romans, N. T. Yu, and G. R. Schonbaum, Biochem. Biophys. Acta, 434, 62 (1976); (b) G. Rakshit, T. G. Spiro,
William B. Smith and M. Uyeda, Biochem. Biophys. Res. Commun., 71, 803 (1976). (7) E. Mayer, D. J. Gardiner, and R. E. Hester, Biochim. Biophys. Acta, 297, 568 (1973). (8) Y. Ozaki, T. Kitagawa, Y. Kyogoku, H. Shimada, T. Iizuka, and Y. Ishimura, J . Biochem., 80, 1447 (1976). (9) A. L. Verma, R. Mendelsohn, and H. J. Bernstein, J . Chem. Phys., 61, 383 (1974). (10) R. Mendelsohn, S. Sunder, A. L. Verma, and H. J. Bernstein, J. Chem. Phys., 62, 37 (1975). (11) L. D. Spaulding, C. C. Chang, N. T. Yu, and R. H. Felton, J . Am. Chem. Soc., 97, 2517 (1975). (12) W. H. Woodruff, D. H. Adams, T. G. Spiro, and T. Yonetani, J. Am. Chem. SOC.,97, 1695 (1975). (13) T. Kitagawa, M. Abe, Y. Kyogoku, H. Ogoshi, E. Watanabe, and Z. Yoshida, J . fhys. Chem., 80, 1161 (1976). (14) J. A. Shelnutt, D. C. O’Shea, N. T. Yu, L. D. Cheung, and R. H. Fekon, J. Chem. Phys., 64, 1156 (19761. S. Asher andK. Sauer, J. Chem: fhys., 64, 4115 (1976). T. G. Spiro and T. C. Strekas, Proc. Nat. Acad. Sci. USA, 69, 2622 (1972). J. M. Friedman and R. M. Hochstrasser, Chem. Phys., 1,457 (1973). L. A. Nafie, M. Pezoiet, and W. L. Peticolas, Chem. fhys. Lett., 20, 563 (1973). D. W. Collins, D. B. Fitchen, and A. Lewis, J. Chem. Phys., 59, 5714 (1973). J. M. Friedman and R. M. Hochstrasser, J . Am. Chem. Soc., 98, 4043 (1976). F. Adar, M. Gouterman, and S. Aronowitz, J. Phys. Chem., 80,2184 11976). J. M. Friedman, D. Rousseau, and F. Adar, Proc. Nafl. Acad. Sci. USA, 74, 2607 (1977). J. A. Shelnutt, L. D. Cheuna, R. C. C. Chana, N. T. Yu, and R. H. Felton. J . Chem. Phvs.. in-Dress. T. Yamamoto, G. Palmer,.D. Gill, I.T. Salmeen, and L. Rimai, J. Biol. Chem., 248, 5211 (1973). T. M. Loehr and J. S. Loehr, Biochem. Biophys. Res. Commun., . . 55, 218 (1973). T. G. Spiro and T. C. Strekas, J . Am. Chem. Soc., 98, 338 (1974). T. Kitagawa, Y. Kyogoku, T. Iizuka, and M. I.Saito, J. Am. Chem. Soc., 98, 5169 (1976). M. Gouterman in “The Porphyrins”, Vol. 111, D. Dolphin, Ed., Academic Press, New York, N.Y., 1977. F. Adar and M. E. Erecinska, FEBS. Lett., in press. M. Perrin, M.Gouterman, and C. L. Perrin, J. Chem. Phys., 50, 4137 (1969). (a) J. S. Griffith, Nature(London),180, 30 (1957); (b) “The Theory of Transition Metal Ions”, Cambridge University Press, London, 1964. G. Harris, Theor. Chim. Acta (Berl.), 5, 379 (1966). 1. Salmeen and G. Palmer. J. Chem. Phvs.. 48. 2049 11966). M. Zerner, M. Gouterman,’and H. Kobayashi, Theor. Chm. Acta (Berl.), 6, 363 (1966). C. P. S. Taylor, Biochim. Biophys. Acta, 491, 137 (1977). A. Laubereau, D. vonder Linde, and W. Kaiser, Phvs. Rev. Lett., 28, 1162 (1972). (a) P. Stein, J. M. Burke, and T. G. Spiro, J. Am. Chem. Soc., 97, 2303 (1975); (b) S. Sunder and H. J. Bernstein, J. Raman Spectrosc., 5, 351 (1976); (c) T. Kitagawa, M. Abe, Y. Kyogoku, H. Ogoshi, H. Sugimoto, and 2. Yoshida, Chem. Phys. Lett., 48, 55 (1977). T. Takano, B. L. Trus, N. Mandel, G. Mandel, 0. B. Kalhi, P. Swenson, and R. E. Dickerson, J. Biol. Chem., 252, 776 (1977). T. Yonetani, H. Yamamoto, and T. Iizuka, J. Biol. Chem., 249, 2168 (1974). J. S. Leigh and T. Yonetani, private communication.
Steroid Molecular Structure, Solution Behavior, and Carbon Spin Relaxation Times’ William B. Smith Department of Chemistry, Texas Christian University, Fort Worth, Texas 76129 (Received May 31, 1977) Publication costs assisted by The Robert A. Welch Foundation
The carbon spin relaxation times (TI)for a series of steroids have been determined at various concentrations in chloroform. Nonpolar steroids such as cholesteryl acetate and cholesteryl chloride exhibit a linear relation of l/Tl vs. viscosity. The relation fails, however, as a function of varying temperature. The T I values of the bile acid esters show evidence of hydrogen bonding associations as there is a systematic alteration with the number of available hydroxyl groups. Recently, in an examination of steroid molecular structure carbon TI relations an attempt was made to 0022-3654/78/2062-0234$01.00/0
speed acquisition times by using concentrated solutions (i.e., 1M or above). It was noted that a bad loss of spectral
0 1978 American Chemical Society
The Journal of Physical Chemistry, Vol. 82, No. 2, 1978 235
Steroid Carbon Spin Relaxation Times
?
TABLE 11: Carbon T,Values for 1.4 M Cholesteryl Acetate at Various Temperatures
rl
Carbon
27°C
~~~~
18
3
19 (CH,),va (CH)fwa
2
a
35°C
49°C
57°C
1.09 1.04 0.26 0.41
1.27 1.22 0.30 0.48
~~
0.41 0.37 0.07 0.10
0.66 0.63 0.14 0.21
Average values in brackets apply to ring carbons only.
0
2
U
5
1 5
2 0
Y
0
5
Lo
2
resolution occurred, and that this effect was related to molecular structure. Previously Wehrli2 made a similar observation on concentrated solutions of 3-cholestanone. Carbons with short relaxation times (methylene and methine carbons) were found to broaden as the concentration was increased. He attributed this to a decrease of TI values as the viscosity of the solution increased. Since molecules of this size fall in the region of motional narrowing (T, = T2) reduction in T1values ultimately will be reflected in line width effects beyond those due to magnetic field inhomogeneity. Reported here is a more detailed examination of the phenomenon with particular reference to the role of steroid structure and molecular interactions.
Experimental Section All of the steroids utilized in this study are readily available commercial items. The methyl cholate (methyl 5fl-cholanate-3a,7a,l2a-triol) was crystallized from ethanol and contained one molecule of ethanol of crystallization per ester molecule. This could be removed by prolonged heating at 90 " C under vacuum. All measurements were made on a JEOL FX-60 operating a t 15.03 MHz utilizing the fast inversion-recovery t e ~ h n i q u e .Either ~ 50 or 100 pulses, depending on the concentration, were acquired for each 7 value, and 10-20 data points were collected for each carbon. Calculations were performed by the standard auto-T1 program. Measurements of carbon spin relaxation times (TI)were made at various concentrations for methyl cholate (I),
2 E:
2 k I X , Y , 2 = OH I ? X : l Z = OH; Y = R 111 X , Y I OH. 2 = H IV x i ox; Y:1Z = E V X , Y = OAci I = OH
U
Y
0
9
rl
0 U
Y
0
V I X= OH V I 1 XI OAc V I 1 1 x= c1
methyl deoxycholate (11,methyl 5/3-cholanate-3a,l2a-diol), methyl chenodeoxycholate (111 methyl 5P-cholanate3a,7a-diol), methyl lithocholate (IV, methyl 5O-cholanat-3a-ol), methyl cholate 3,7-diacetate (V), cholesterol (VI), cholesteryl acetate (VIII). All runs were made at least in duplicate and the averages are given. Reproducibility was, in general, better than &lo%. Average values for methylene and methine carbons are given as again the average deviations €or all values of each type were &lo%. The results for these compounds in deuteriochloroform (dried over molecular sieves) a t 35 O C are given in Table I. Measurements on 1.4 M cholesteryl acetate at several temperatures are given in Table 11. Viscosity data on cholesteryl acetate and chloride a t 35 O C were taken by the standard method and are summarized in Figure 1. Viscosity values €or 1.4 M cholesteryl acetate solutions were
236
The Journal of Physical Chemistry, Vol. 82, No. 2, 1978 20 0
1
Willlam B. Smith
I
0'
c
P
/
10
20 ViSCDSltY c . p
Flgure 2. Plot of reciprocal T, for several carbons in cholesteryl acetate vs. viscosity in chloroform at 35 "C.
0.5
1.0
1.5
2.3
MOLAR CONC FAATRAT 10h
Figure 1. Plot of log viscosity vs. molar concentration for cholesteryl acetate (circles) and cholesteryl chloride (squares) in chloroform at 35
"C.
as follows: 21 "C, 11.6; 26 "C, 9.1; 35 "C, 7.8; and 50 "C 5.3 cP, respectively. 2.0
Results and Discussion It is now well established that steroid carbon T , values are dominated by the dipole-dipole relaxation mechanism for the ring carbon^.^ If so, then for these carbons T1 is given by
where yc and YH are the appropriate gyromagnetic ratios, rCH is the distance to directly attached or nearby protons and TC is the effective correlation time for rotational reorientation. Steroid molecular tumbling in solution appears to be mainly isotropic4 though preferential rotation about the long axis seems to occur in selected Bloembergen, Purcell, and Pound5 adapted Debye's theory of dielectric dispersion to the problem of NMR relaxational processes. The rotating molecule is treated as a sphere of radius a in a uniform cavity characterized by viscosity 8. The NMR rotational correlation time is given by
v,,,
where is the apparent molar volume for a solute molecule. The viscosity given in eq 2 ought really to be a microscopic rotational viscosity, but often correlations with experimentally available translational viscosities are found.6 This should be true particularly of large, platelike molecules such as steroids. From eq 1and 2 plots of l/T1 vs. q/T should be linear. The data for cholesteryl acetate (VII) at 35 "C are plotted in Figure 2 and linear behavior is observed. Similar behavior was demonstrated by the data for cholesteryl chloride. It was further observed (Figure 3) that plots of T1 vs. molar concentration for both VI1 and VI11 were linear for all carbons. There is no extant theory relating molecular structure to solution viscosity nor any known theoretical correlation between 7'1 values and molar concentrations. As will be noted in Figure 1, both VI1 and
2 I \ I
'9
+- I
0.5
1.0
1.5
W L A R CONCPXTRATTON
Flgure 3. The relation of the T I for several carbons in cholesteryl acetate vs. molar concentration In chloroform at 35 "C.
VI11 closely approximate a linear log viscosity relation vs. concentration over the range 0.5-1.7 M. This fact coupled with the equations for the lines in Figure 2 account for the behavior displayed in Figure 3. It is reasonable to expect that for solutions of VI1 and VI11 below 0.5 M where the relation to viscosity becomes more complex the linear behavior of T1 with molar concentration will fail. The proportionality of l/T1 to q/T fails for a 1.4 M solution of VI1 when determined over a range of temperatures. The data are given in Table 11. A semilog plot of the reciprocal of the viscosity vs. absolute temperature exhibits normal linear behavior from which interpolated values of the viscosity at the required temperatures can be obtained. Plots of l/Tl vs. 7 / T for various carbons were curvilinear upward. While not shown, it can be stated that the effect is small for the ring carbons but very marked for the methyl carbons, Allerhand, Doddrell, and Komorski4* have established that the methyl groups in cholesteryl chloride exhibit internal rotations which contribute to the overall dipolar relaxation. The simple q / T relation reasonably would not hold for these carbons. It remains to be established whether the small effect observed for the ring carbon is a measure of solute-solvent interaction, solute-solute interaction, or a failure of the simple form of the theory.
Steroid Carbon Spin Relaxation Times
1.5
1.0
0.5
Flgure 4. Plot of various carbon TI (s) vs. molar concentration of methyl cholate in chloroform at 35 OC.
In one experiment a 1M solution of cholesteryl acetate in deuteriochloroform was examined for line widths and resolution. Methylene and methine carbons are effected a t this concentration but not as severely as at higher concentrations. A small amount of high molecular weight polystyrene was then added to the solution, and the spectrum redetermined. Even though the solution was so viscous it could hardly be poured from the tube the line widths and resolution of the steroid spectrum were not degraded. This observation reemphasizes that microscopic rotational viscosity is the controlling factor, not the macroscopic translational viscosity, though clearly these two can be proportional for the proper solute-solute combination. In contrast to the behavior of VI1 and VIII, when T1 measurements on methyl cholate I are carried out, plots of T1 vs. [MI show marked concave upward curvature, Figure 4. This type of behavior is that expected of an
1 50
The Journal of Physical Chemistry, Vol. 82, No. 2, 1978 237
associating system. It is known that dihydroxy and trihydroxy 50-steroids self-associate by hydrogen bonding to very low concentrations in carbon tetra~hloride,~ and an extensively layered structure for the solute molecules has been proposed. Similar conclusions can be arrived at by considering the T1 values for a given type of carbon at some standard concentration (e.g., 0.5 M) for this series. The higher the value of TI the lower the degree of molecular association. Thus, the 3,7-dihydro steroid I11 is more highly associated than the 3,12 analogue 11. This is consistent with the greater steric hindrance expected a t the 12-hydroxyl compared to the 7-hydroxyl. Methyl lithocholate IV is more associated than cholesterol VI; a result in keeping with additional acceptor site offered by the carbomethoxy group in IV. Interestingly, the 12-hydroxy compound V appears to be more highly associated than IV. This may be due to the availability of the 3,7-diacetate acceptor sites in V as opposed to IV, but may also reflect the greater mass of the former. The crystal structure of the 1:l ethanol-cholic acid complex is known.s Each ethanol is surrounded by three cholic acids and a total of five hydrogen bonds are formed. The addition of ethanol to deuteriochloroform solutions of alcohol free methyl cholate I (up to 4 M equivalents) does not alter the chemical shifts of any carbon. Furthermore, the T1values for a l M solution of the 1:l ethanol-methyl cholate complex agree with the values reported in Table I for the alcohol free compound. This insensitivity to added ethanol suggests that methyl cholate may prefer to hydrogen bond to itself. If so, it is likely that dimers or high aggregates form with the polar a faces oriented inward, as has been suggested by Kovac and Eglinton8 Such a dimer would allow the methyl groups to rotate freely and would still allow isotropic tumbling. Examination of the carbon T1 values for I fails to reveal any introduction of anisotropic tumbling as a function of concentration. The counterpart of this configuration has been proposed to account for the behavior of sodium cholate in aqueous ~ o l u t i o n . Here ~ the polar a face is
I 10
Figure 5. The carbon-I3 NMR spectrum of 1 M methyl cholate (bottom), 0.5 M cholesteryl acetate (middle), and a similar mixture of the two (top).
238
The Journal of Physical Chemisfry, Vol. 82, No. 2, 1978
S. I.
directed toward the solvent, and the methyl proton lines in the NMR are extensively broadened. Finally, in Figure 5 is shown the effect of added methyl cholate upon the line widths of 0.5 M cholesteryl acetate solution. In contrast to the polystyrene results (vide supra), a perceptible broadening of the methylene and methine lines of VI1 is evidenced. A specific interaction of the two steroids must be occurring. This may be a hydrogen bonded complex between I and the acetate function on VII. However, the lack of sensitivity of I to the presence of ethanol (a certainty to react more strongly with I than an acetate ester) argues strongly against this. The nature of the interaction must at this time be considered undefined.
Smedley and I. Torrie
Robert A. Welch Foundation for support of this work.
References and Notes Presented, in part, before the 18th Experimental Conference on NMR Spectroscopy, Asilomar, Calif., April, 1977. F. Wehrli, Adv. Mol. Relaxafion Processes, 6, 139 (1974). D. Canet, G. C. Levy, and I. R. Peat, J. Magn. Reson., 18, 199 (1975). (a) A. Allerhand, D. Doddrell, and R. A. Komorski, J . Chem. Phys., 55, 189 (1971); (b) J. W. ApSimon, H. Beierbeck, and J. K. Saunders, Can. J . Chem., 53, 338 (1975); (c) G. C. Levy and U. Edlund, J. Am. Chem. Soc., 97, 5031 (1975). N. Bloembergen, E. M. Purcell, and R. V. Pound, Phys. Rev., 73, 679 (1948). (a) E. R. Andrews, "Nuclear Magnetic Resonance", Cambridge University Press, London, 1955, Chapter 5; (b) A. Abragam, "Principles of Nuclear Magnetism", Oxford University Press, London, 1961, Chapter 8. S.Kovac and G. Eglinton, Tefrahedron, 25, 3609 (1969). P. L. Johnson and J. P. Schaefer, Acta Crysfallogr., Sect. B , 28, 3083 (1972). D. M. Small, S.A. Penkett, and D. Chapman, Biochim. Biopbys. Acta, 176, 178 (1969).
Acknowledgment. The measurements of viscosity were conducted by Dr. John Albright to whom appreciation is expressed. Grateful appreciation is also expressed to The
Transport in Molten CaC12*5.99,5.33H20Under Pressure S. I. Smedley" and I. Torrie Chemistry Department, Victoria University of Wellington, Wellington, New Zealand (Received March 23, 7977)
From conductivity and volume measurements of CaC12.5.99H20over the temperature range 40-120 "C we have calculated the molar conductivities, compressibilities, and expansivities. Molar conductivities have been fitted to the emperical VTF equation to obtain parameters A, B , and To. These, along with activation volumes AV,, are compared with the available data for other hydrate melts.
Introduction Recent studies of the effect of pressure on the electrical conductivity of molten Ca(N03)*hydrate melts have shown that the empirical VTF equation
A=
exp
(T - (To' + bP)
= ApS,*/hAC,,
P
To/K
1 2000 4000 6000
adequately accounts for the observed behavior over a wide range of temperature, pressure, and composition.',' Angell has shown that for nitrate containing melts, T t , the glass transition temperature at atmospheric pressure, is linearly dependent on the average cation potential C,(NiZI/r,).334 However, the role of the anion in determining To1is not yet established, although Angell and Sares have shown that Tg, the temperature at which the rapidly supercooled glass first becomes a liquid, is dependent on anion basicity. However, Tgvalues are usually 10-20 " C above Tovalues determined from transport data and it is not at all certain that Towill follow the same pattern as Tg. Equation 1 can be interpreted in terms of the configurational entropy theory of Adam and Gibbs? for this case
B
TABLE I: Values of A , B , a n d To for CaC12.5.99H,0 O b t a i n e d bv F i t t i n g t h e D a t a t o Ea 1
(21
S,* is the minimum entropy required by the smallest possible rearranging subsystem, Ap the potential energy hindering rearrangement per molecule, and ACp is the difference between the liquid and glass heat capacities. For Ca(NO3I2-KNO3,Ca(N03)2-KN03-H20, Mg(NOJZ-HzO, and Ca(N03)2-4Hz0,B has an approximately constant value of 675 f 15 K.3v437 However, for Na2Sz03B = 583 0022-3654/78/2082-0238$0 1.OO/O
a
198 + 205 + 211 i 217 t
2 2 2 2
AIS
mol-' dm2
10-ZB/K
rz a
60.4 i 3 57.4 5 3 59.1 t 3 63.4 + 3
4.16 + 0.1 4.09 ?: 0.12 4.24 + 0.14 4.4 i 0.2
0.99938 0.99957 0.99973 0.99985
r z is t h e c o e f f i c i e n t o f determ,ination, r2 = 1for a p e r -
f e c t fit.
K8 and for other Ca(N03)2/Hz0mixtures B varies linearly with To.9 The interpretation of this parameter will be significantly improved if a series of hydrate melts with common cations and different anions are studied. This will be especially useful if the salts fall within the general range of those for which NMR, Raman spectra, and neutron scattering results are available. We chose the CaCly6Hz0 system so that we could compare the results with those for Ca(N03)2.6H20,Mg(N03)2.6H20,and MgC12.6H20. Furthermore, one or all of the abovementioned techniques have been applied to these systems.10-12 Results and Experimental Technique Experiments were conducted in accordance with the technique described p r e v i ~ u s l y The . ~ ~ ~conductance ~ and volume of CaClZ.5.99H20at 40,60,80,100, and 120 "C was measured from 1bar to 6 kbar and for CaC12.5.33Hz0at 80 and 90 OC only. The experimental conductivity results are displayed in Figure 1. In h vs. 1 / T at constant 8 1978 American Chemical Society
