2400
The Journal of Physical Chemistry, Vol. 83, No. 16, 1979
H. Fujiwara, F. Sakai, and Y. Sasakl
by Lowe and Bray in xanthine oxidase and xanthine dehydrogenase systems, which have paramagnetic Mo(V) and iron-sulfur groups which they believe to be separated by distances between 10 and 25 A. With the aid of qualitative line-shape calculations (see Figures 5 to 7) and our study on long-range superexchange, we are able to further restrict the possible estimates of the distance apart of these paramagnetic groups, without making resort to simulation of the complete spectrum. More detailed studies on specific model systems and well-characterized macromolecules are necessary in order to determine the usefulness of superexchange properties in relation to, for example, electron transport reactions. It seems possible that experimental and theoretical analysis of spin-spin coupling effects may provide some useful structural and electronic information in inorganic and inorganic biochemistry. It would be particularly helpful, in this regard, to have a better model for the anisotropy of the exchange tensor (rijEX), better than the simple Moriya estimate,’l which includes the effects of electronic delocalization.
allocation of generous amounts of computer time.
Supplementary Material Available: Derivation of the general expression for the dipole-dipole coefficient Jij”D(R12,S;q,a,P,~) (2 pages). Ordering information is available on any current masthead page. References and Notes (1) G. R. Buettner and R. E. Coffman, Biochim. Biophys. Acta, 480, 495-505 (1977). (2) G. E. Pake, J . Chem. Phys., 16, 327 (1948). (3) J. S.Leigh, Jr., J . Chem. Phys., 52, 2608 (1970). (4) C . 4 . Chao, J . Mag. Reson., 10, 1-6 (1973). (5) S.G. Carr, T. D. Smith, and J. R. Piibrow, J . Chem. SOC.,Faraday Trans. 1 , 70, 497-511 (1974). (6) P. D. W. Boyd, A. D. Toy, T. D. Smith, and J. R. Pllbrow, J. Chem. SOC.,Dalton Trans., 1549-1563 (1973). ( 7 ) J. F. Boas, P. R. Hicks, J. R. Pilbrow, andT. D. Smith, J. Chem. Soc., Faraday Trans. 2 , 74, 417-431 (1978). (8) K. L. Schepler, W. R. Dunham, R. H. Sands, J. A. Fee, and R. H. Abeles, Blochim. Biophys. Acta, 397, 510-518 (1975). (9) D. J. Lowe and R. C. Bray, Biochem. J., 189, 471-479 (1978). (10) ?. Owen and E. A. Harris, “Pair Spectra and Exchange Interactions” in “Electron Paramagnetic Resonance”, Geschwird, Ed., Plenum Press, New York, 1972. (11) T. Moriya, Phys. Rev., 120, 91 (1960). (12) B. Bieaney and K. D. Bowers, Proc. R. SOC.London, Ser. A , 214, 451 (1952). (13) S. R. P. Smith and J. Owen, J . Phys. C : Solid Stare Phys., 4, 1399 (1971). (14) D. J. Lowe, R. M. Lynden-Bell, and R. C. Bray, Biochem. J . , 130, 239-249 (1972). (15) R. E. Coffman, J. Phys. Chem., 79, 1129-1136 (1975). (16) R. C. Bray, J. Less-Common Met., 36, 413-417 (1974). (17) J. F. Gibson and R. C. Bray, Biochlm. Biophys. Acta, 153, 721-723 (1968). (18) R. E. Coffman and 0. R. Buettner, J. Phys. Chem., preceding article in this issue.
Acknowledgment. We thank Dr. Robert C. Bray and Dr. David J. Lowe for several manuscripts and preprints, and for their helpful and encouraging correspondence concerning the nature of the long-range spin-spin interactions in xanthine oxidase and xanthine dehydrogenase. We have also benefitted from helpful discussions with Dr. Leodis Davis, Dr. John Schweitzer, and Dr. William Stwalley. The University of Iowa Gerald P. Weeg Computing Center is also due our thanks for its continuing
Analysis of the Concentration Dependence of Nuclear Magnetic Resonance Parameters by Means of Chemical Equilibria. Elucidation of the Complex Formation between Dimethyltin Dichloride and Pyridine Base in Solution Hideaki Fujiwara,” Fumihiko Sakal, and Yoshio Sasaki Faculty of Pharmaceutical Sciences, Osaka University, 133- 1 Yamadakami, Suita, Osaka, Japan (Received February 5, 1979)
A procedure for the analysis of the concentration dependence of NMR parameters on chemical equilibria, utilizing the Davidon-Fletcher-Powell method of optimization, is described in detail for (1)A + B = AB, (2) A 2B = ABz, and (3) A + B = AB ( K J ,AB + B = AB2 (Kz).The procedure is applied to the Me2SnClZ+ 2,2’-bipyridine and MezSnClz + pyridine systems in CHCl2CHCl2,and the coexistence of 1:l Me2SnC12-pyridineand 1:2 MezSnClZ-pyridinecomplexes is proven in the latter system. Little has been reported about the former complex. Determination of K1 and K z in the MezSnC12 pyridine system is successful by using 2J(SnH)data (K1 = 16.6 f 1.9 dm3 mol-’ and K z = 4.44 ct 0.24 dm3 mol-‘), when the J of the 1:2 complex is taken as that of the tin compound in a large excess of pyridine, whereas only rough estimates of K1 and K 2 are available when this J is also regarded as a variable parameter in the calculation. The formation constant of the 1:l complex in the MezSnClz+ 2,2’-bipyridine system is 4500 k 320 dm2 mol-’ in CHCl,CHCl,, about twice as large as that reported in CH,CN, and reflects much weaker solvation by CHC12CHC12than by CHsCN.
+
+
Introduction Because NMR spectra of systems containing chemical equilibria reflect an equilibrium average, unless exchange rates are slow enough to allow assignment of peaks to each species involved in the equilibrium, it is necessary to fit the concentration dependence of the data to the NMR parameters of each species. Such an analysis is also valuable in other respects, because it offers quantitative 0022-3654/79/2083-2400$0 1.OO/O
information about the chemical equilibria or intermolecular interactions in solution. In the ordinary NMR measurement, however, it is sometimes difficult to satisfy the familiar condition that the concentration of one component is always much lower than that of the others, which is necessary for several simple graphic methods, such as the Benesi-Hildebrand method. Therefore, in the analysis of concentration dependence of NMR parameters, much 0 1979 American Chemical Society
The Journal of Physical Chemistry, Vol. 83, No. 18, 1979 2401
Concentration Dependence of NMR Parameters
component A can be rearranged as in attention has been devoted to the interpretation of intricate associations in the concentrated solution by means C A ~+AC A B ~ A B of a simple m0de1.l~~Recently, computer simulation of d'calcd = o n NMR concentration dependence in terms of an exact LAsolution of the equilibrium formulae has become 1 K(CAo CBo) - (root) AB - +A) = d'A + This fact, together with the sensitivity enhancement of ~KCA' NMR spectroscopy, greatly facilitates availability of this (2) method for the elucidation of chemical equilibria or intermolecular interactions in solution. where We have been employing a computer simulation method (root) = [(I f K(CA' + CB')]' - 4K2C~oC~o]112 applicable to systems with a few types of e q u i l i b r i ~ m > ~ , ~ ~ and wish to report analyses of the NMR concentration and where 4Aand $AB are the NMR parameters intrinsic dependence, which elucidate the complex formation of to species A and AB, respectively. In this case the paMe2SnClzwith 2,2'-bipyridine and pyridine in solution. rameters to be determined by simulation are K and $AB, since may be determined experimentally. Relevant Experimental Section derivatives are obtained from eq 1 as Commercial CHC12CHC12was shaken with concentrated sulfuric acid and washed successively with water, 10% Na2C03solution, and three times with water. It was then dried over P205 and distilled in a drybox under a N2 stream. Commercial pyridine (J.I.S.G.R. grade) was dried over barium oxide and distilled in a drybox. These purified where from eq 2 materials were stored over molecular sieves 4A. Commercial 2,2'-bipyridine was sublimed and stored in a desiccator. 'H NMR spectra were observed with a Hitachi R-22 spectrometer operating at 90 MHz and 34.1 "C. Chemical shifts and coupling constants were measured by a fre-a$calcd - - 1 + K(CAo + CBo) - (root) quency counter within an error of f0.1 Hz. As an internal 3 4 ~ ~ ~KCA' reference, -0.02 vol % Me4Si was added to the solvent. IZ. System A + 2B = A B p The equilibrium constant Method of Analysis K and initial concentrations CAoand CBo are given as In the least-squares method for the simulation of the NMR concentration dependence according to a chemical equilibrium, the root-mean-square deviation (A) is min-
+
+
-
rmsd =
[
C (d'obsdj
- d'calcd,i)'
]
+
(A)
+
for (1)A + B = AB, (2) A 2B = AB2, and (3) A B = AB, AB B = AB2. Our procedure is called the SCD method (simulation of a concentration dependence by the DFP method). I. System A B = AB. The equilibrium constant K and initial concentrations CAo and CBo of components A and B , respectively, are expressed by equilibrium concentrations of species A, B , and AB as follows:
K = CAB/(CACB)
KCB+ ~ X(2c,4' - CBO)CB' + CB - CBO = 0 is derived. The NMR parameter is expressed as CAd'A d'calcd
&alcd,
for
=
&&d
(5)
for component A
+ CAB24AB2 CAO
and the parameters to be determined in the simulation are K and $AB2. CAand CAB2are derived from eq 3 and 4 after CB is determined from eq 5. Relevant derivatives are
and from eq 6
CBo = CB + CAB
(4)
where CAB2is the equilibrium concentration of the species AB2. From these equations
+
From these equations, the NMR parameter,
(3)
CAo = CA
imized by seeking optimum values of parameters in f$&d,i, where 4 is a NMR parameter such as chemical shift or coupling constant and the subscript i, omitted hereafter for the brevity of formula description, denotes an individual data point. We selected F as the minimized function and employed the DFP method of optimization,'l Le., Davidon's method as described and extended by Fletcher and P o ~ e l l . ~It~utilizes J ~ first derivatives of the minimized function in adjusting initial values of the parameters (eq l). The necessary calculations are described
+
+ CAB2 CBo = CB + 2CAB2
112
2402
The Journal of Physical Chemistry, Vol. 83, No. 18, 1979
H. Fujiwara, F. Sakai, and Y. Sasaki
where from eq 4 aCAB2 = --1 a C B aK
2 aK
Finally we obtain a CB/a K by differentiating eq 5 as CB - CBo aCB _ _-aK K(~KCB'- ~ K ( ~ C -ACB')CB '
1)
111. System A + B = AB, AB + B = AB2. Equilibrium constants K, for A + B = AB and K2 for AB + B = AB2 and initial concentrations CAo and CBoare expressed as follows: K1 = CAB/(CACB)
(7)
Kz = CAB~/(CABCB)
+ CAB + CAB2 CBo = CB + CAB + 2CABz CAo = CA
(8) (9)
(10)
\ %PY
+
+
Here, derivatives of CAB and CABzwith regard to K1 and K2 are solved for from the differentiated forms of eq 7-10 as
-aCAB - - CACB + Kl(CA + l/CB)(aCB/aKl)
+
K ~ ( ~ C -A CB'))~B' ' (1 K1(CAo - CBo))CB- CBo = 0 (11)
+
+
Figure 1. Job plots of 2J("0SnH) for the Me,SnCi, 2,2'-bipyridine system in CHC12CHC12. C s , and C,, are the molarities of Me SnCi, and 2,2'-bipyridine, respectively; Cs, C, = 0.201 mol dm- 3, R,, = CB,/(CSn CB,), and AJ = Jabs,,- Jfrw.
From these equations K~K~CB K1(1 ~
1
0.5
0
1 + YZKICB
aK1
and
are derived. The NMR parameter is given as 4calcd
=
(bc&d
for component A and
C A ~ +A C A B ~ A+BC A B ~ ~ A B ?
C.4' Finally aCB/aK1and aCB/aK2are given by differentiating eq 11 (13)
and the parameters to be determined by simulation are K1, K2,4 ~and , 4B2;CA,CAB,and CBz are derivable from eq 12, 7, and 9 after CB is determined by solving eq 11. Relevant derivatives are
aCB C B - C B ' _ -aK,
KIR
and
_ dCB - -K1CB2(CB+ 2cA0 - CBo) aK2
R
where
R =~K~K~C + B2Kl(l ' + K2(2CA0- CBO))CB+ 1 + K~(CAO - Go) and
where, from eq 13
Results and Discussion Application to Complex Formation of MezSnC12with 2,2'-Bipyridine. MezSnC12is known to form a stable 1:l complex with 2,2'-bipyridine.14 Job plots15 of GH(SnCH3) and 'J(SnH), i.e., 2J(119SnH)and 2J(1"SnH), and those of I&.-3, bH-31, 8H4, and 6H-6, in 2,2'-bipyridine were obtained from first-order analysis of spectra, and all supported formation of a 1:l complex (Figure 1). The concentration dependence of GH(SnCH3) and 2J(SnH)for the Me2SnClZ + 2,2'-bipyridine system in CHC12CHClz (Figure 2), therefore, would be analyzed according to case I in the preceding section. In the calculation with K and AB as parameters, K did not converge rapidly, so that the initial value of K remained almost unimproved after the simulation. Such inconvenience has not been met in the case of relatively small K,6p9310and was overcome in the present case by employing 1/K and $AB as parameters.16 The
The Journal of Physical Chemistry, Vol. 83, No. 78, 7979 2403
Concentration Dependence of NMR Parameters
1.0
0
0.1
0 05 CEPY
0.05
0
M
0.1
M
CBPY
Figure 2. Concentration dependence of the 'H shift, G,(SnCH,), and coupling constant, 2J(''9SnH), for the Me,SnCi, 2,2'-bipyridine system in CHCI,CHCI,. Cs,is held constant at 0.05 mol dm-3.
+
1.20
u 0.1
0
0
0.2
0.1
M
CPY
0.2 M
CPY
Figure 4. Concentration dependence of the 'H shift, G,(SnCH,), and coupling constant, 'J('lgSnH), for the Me,SnCI, pyridine system in CHCI,CHCI,. Cs,is held constant at 0.04 mol dm-3.
+
'*O
t
r N 100
-5 r
h
N
80
1
0.5
0
1
0.5
0
RPY
0
Flgure 3. Job plots of the 'H shift, G,(SnCH,), and coupling constant, 'J(SnH), for the Me,SnCI, pyridine system in CHCI&HCI,. C, is the molarity of pyridine: Cs, C , = 0.199 mol dm-3, R, = Cw/(Csn AJ = Jobsd - J,,,,; ( 0 )2J(119SnH)and (A) c ), A6 = 8 o b a J( "SnH).
+ +
+
TABLE I : Parameters Determined b y t h e Analysis of NMR Concentration Dependence for t h e Me,SnCl, t 2,2'-Bipyridine System in CHCl,CHCl,
data
K, a dm3 mol-'
6H(SnCH3) 4777 'J('19SnH) 4152 'J('"SnH) 4574
S A or
JAb
1.224 ppm 68.4 Hz 65.4 Hz
6AB
or J A B
1.047 ppm 113.4 Hz 1 0 8 . 3 Hz +_
simulation processed satisfactorily and the K value thus obtained is 4500 f 320 dm3 mol-I (Table I), which is about twice as large as that obtained in CH,CN.17 This is probably due to lesser solvation by CHC12CHC12than by CH3CN. Application to Complex Formation of Me2SnC12with Pyridine. Although the 1:2 MezSnC12-pyridine complex was isolated from solution by several investigators,14there is no study of the 1:l complex. Therefore, it is of interest to determine whether or not such 1:l and 1:2 complexes coexist in solution. As a result of Job plots, 1:l and 1:2 complexes are supported separately by the GH(SnCH3)and *J(SnH)data, respectively (Figure 3). This fact may be accepted in such a way that 1:l and 1:2 complexes coexist in solution and that formation of the 1:l complex affects GH(S~CH,)more effectively than 2J(SnH)and vice versa for the formation of the 1:2 complex. The concentration dependence of 2J(SnH)is about three times larger than that of GH(SnCH3)in the Me2SnClZ+ pyridine system (Figure 4). Simulation of these 2J(119SnH)
M
+
Figure 5. Concentration dependence of 'J(SnH) for the Me,SnCI, pyridine system in CHCI,CHCI . C, is held constant at 0.025 mol dm3. (0)2J(1'9SnH)and (A) 'J('*SnH).
TABLE 11: Parameters Determined b y Analysis of the NMR Concentration Dependence for t h e Me,SnCl, t Pyridine System in CHCl,CHCl,
data
Hz
0.24 0.14 0.08
10
5 CPY
a,c
Average value of t h e three = 4500 320 d m 3 mol". 6 H(SnCH,) or 'J(SnH) of Me,SnCl, in the solvent free from base. Root-mean-square deviation. a
60
RPY
mol''
2J(119SnH) 18.5 'J("'SnH) 14.7
mol-'
Hz
Hz
Hi
Hz
4.68 4.20
68.4 65.4
88.2 87.4
112.0 107.0
0.067 0.092
Averages are K , = 1 6 . 6 (* 10%)and K, = 4.44 (?5%). 'J(SnH) of Me,SnCl, in the solvent free from base. Errors are estimated as within 2 Hz. 'J(SnH) of Me'SnCl, in the solvent containing pyridine above 7 mol d m - 3 (see Figure 5). e Root-mean-square deviation. a
+_
data, adopting four parameters l/Kl, l/K2, J Aand ~ , JAB*, resulted in scattering of the final values, Le., K1 = 8-18 dm3 mol-l, K z = 4.4-4.7 dm3 mol-l, J A B = 88-110 Hz, and JABz = 102-112 Hz, depending on their initial values. This means that a small variation in one parameter is compensated by that in others with rmsd almost unaffected. Therefore, elimination of a variable parameter is necessary for the precise determination of these parameters. If base is added in large excess to a solution of Me2SnClz,the latter would be present as the 1:2 complex exclusively. This is confirmed by the concentration dependence curve of 'J(SnH) at the -100% pyridine region (Figure 5). Thus, we can adopt the value at > 7 mol dm-3 of pyridine as the V(SnH) of the 1:2 complex. It is noticeable that the 2J(SnH)of the 1:2 complex thus determined (Table 11) is very close to those of the six-coordinated 1:l Me2SnC122,2'-bipyridine complex (Table I). Simulation of above data with three parameters was successful, and the result was reproducible within &lo% error for K1,A570 error for
2404
The Journal of Physical Chemistry, Vol. 83, No. 18, 1979
R. Bruce Martin
TABLE 111: Results of Analysis of 2 J ( 1 1 9 S n H ) C o n c e n t r a t i o n Dependence for t h e Me,SnCl, + P y r i d i n e System A c c o r d i n g to Three Equilibrium M o d e l s
model I A t B = AB AB t B = AB, 1 I A t B=AB I11 A t 2B = AB,
K , dm' mol' K, = 18.5 K , = 4.68
JAB,
JAB^,
Hz
Hz
Hz
88.2
112.0a
0.067
5.28 87sc
118.9 93.7
0.125 0.823
Assuming the presence of only the 1:2 complex, the rmsd between the simulated and the observed concentration dependence is about one order larger than experimental errors, and then the Jmz determined is too small compared to the 2J(119SnH)of the tin compound dissolved in neat pyridine. In conclusion, only the assumption of both 1:l and 1:2 complexes results in a successful simulation, proving coexistence of the two complexes.
aZJLl9 ( S H) of Me,SnCl, in the solvent containing pyridine above 7 mol dm-'. b Root-mean-square deviation. In units of (dm' mol"')2.
References and Notes (1) J. C. Davis, Jr., and K. K. Deb, Adv. Magn. Reson., 4, 201 (1970). (2) C. Lussan, J. Chim. Phys., 60, 1100 (1963). (3) H. Fujiwara, BunsekiKiki, 14, 87 (1976); Chem. Abstr. 84, 156266m (1976). (4) B. L. Shapiro and M. D. Johnston, Jr., J. Am. Chem. Soc., 94, 8185 (1972). (5) F. Inagaki, S.Takahashi, M.Tasumi, and T. Miyazawa, Bull. Chem. SOC.Jpn., 48, 853 (1975). (6) H. Fujiwara and T. Ikenoue, J . Chem. Soc., Faraday Trans. 7, 72, 2375 (1976). (7) J. W. M. Boer, C. W. Hilbers. and E. De Boer. J. Maon. Reson.. 25. 437 (1977). (8) B. T. Pennington and J. R. Cavanaugh, J . Magn. Reson., 29, 483 (1978). (9) H. Fujiwara, T. Takaba, Y. Yamazaki, and Y. Sasaki, J. Chem. Soc., Faraday Trans. 7, 75, 79 (1979). (10) H. Kawaki, H. Fujiwara, and Y. Sasaki, Chem. h r m . Bull., 26, 2694 (1978). (11) A source program DAVID written by S.Hoshino and compiled in the
K2, and f 2 Hz for J A B in duplicate experiments. It is reasonable that the estimated Jm lies between JA and Jw Treatment of the shift data was, unlike those of coupling constants, fruitless, because the concentration dependence of the shift is small (about 1/3) compared to that of the coupling constants, and experimental determination of Be,Le., GH(SnCH,) for the 1:2 complex, is difficult because of the steady increase of BH(SnCH,) on addition of an excess amount of pyridine. Further Proofs of t h e Coexistence of 1:l and 1:2 Complexes between Me2SnClzand Pyridine i n Solution. In a simulation of the concentration dependence of 2J(SnH) for the Me2SnC12+ pyridine system, we have assumed formation of both 1:l and 1:2 complexes on the bases of Job plots. This assumption was supported by the agreement between the simulated and observed concentration dependences. Further support for this conclusion is obtained by a similar examination under different conditions. In Table 111, the concentration dependence of 2J(119SnH)is simulated, assuming the presence of either a 1:l or 1:2 complex, and the result is compared with that assuming both of them. Simulation leads to an unreasonably large value of J A B if a 1:l complex is assumed; it is larger than the 2J(119SnH)of the six-coordinated 1:l complex with 2,2'-bipyridine and also larger than that of the tin compound dissolved in neat pyridine.
-
(12) (13) (14) (15) (16)
(17)
library program at the Computation Center Osaka University was cited for the minimization of functions. D. A. Pierre, "Optimization Theory with Applications", Wiley, New York, 1969, p 320. R. Fletcher and M. J. D. Powell, Computer J., 6, 163 (1963). V. S. Petrosyan, N. S.Yashina, and 0. A. Reutov, Adv. Organomef. Chem., 14, 63 (1976). R. Sahai, G. L. Loper, S.H. Lin, and H. Eyring, Proc. Natl. Acad. Sci. U.S.A., 71, 1499 (1974). As a reason for this improvement, we suggest the general relationship aG/a(l/K)= -@(aG/a K), G being an arbtrary function; the absolute value of the relevant derivative becomes fairly large when the parameter Kis replaced by 1/K. In the simulation with 1/K, relatively accurate experimental data for the concentration dependence are necessary, because, otherwise, the simulation is often interrupted to give a negative value of K . W. D. Hommick, M. C. Hughes, C. D. Schaeffer, Jr., and J. J. Zuckerman, Inorg. Chem., 15, 1391 (1976).
Choice of Nuclear Magnetic Resonance Vicinal 'H-lH and Vicinal Carboxylate 13C-lH Coupling Constant Parameters for Estimating Conformations in Amino Acids R. Bruce Martin Chemistry Department, University of Virginia, CharlottesviNe, Virginia 2290 1 (Received April 19, 1979) Publication costs assisted by the National Science Foundation
By comparison of the observed vicinal proton coupling constant between CY and /3 protons in amino acids with the observed vicinal carboxylate carbon-13 to P-proton coupling constant of 27 compounds, one can show that the six-parameter formulation for relating observed vicinal proton coupling constants to mole fractions of three staggered ethanic rotamers is only marginally better than the two-parameter formulation. Recommended values for the two vicinal proton parameters are for gauche positions JG = 2.4 Hz and for anti positions JT = 13.3 Hz. These values are in accord with vicinal a-carboxylate carbon-13to P-proton parameters of 1.2 Hz for gauche positions and 10.0 Hz for the anti position.
Substituted ethanes such as occur in a-amino acids with one a and two /3 hydrogens give rise to proton magnetic resonance spectra of 5-12 lines due to a three-spin ABXor ABC-type system.l These spectra are time averaged 0022-3654/79/2083-2404$01 .OO/O
over three predominant staggered rotamers, designated for the purpose of labeling and expressing mole fractions as t , g, and h, as illustrated in Figures 1. The bulky carboxylate and R groups are anti (trans) in the t rotamer, 0 1979 American
Chemical Society
