J. P h p . Chem. 1983, 87, 1589-1590
from our treatment of the results of Friauf, Noolandi, and Hong,17J8we find there to be already a 10% deviation of pt (for @rc= 15) from ita c~/: limiting behavior at s N 0.06, corresponding (with R rr, 20 A) to a c of - 2 X M. This is illustrated in Figure 11, which &owLpt (=[h,(c ) - h,(0)1/[1- h,(0)1, from eq 4 plotted v8. s1/2 ( = ( T R ~ ? C ~ ) Q ~ for various values of pr,. Clearly, for liquids with Pr, 2 10 (i.e., pest 5 0.054), Gn cannot properly be obtained by cq1/2 extrapolations that utilize concentrations with cq 2 2 x 10-5 M. In the case of cyclohexane, application of the clearingfield method has yielded values for Ga of 0.15 and 0.19.% Although both of these values are indeed larger than 0.12 (as expected from the upward concavity exhibited in Figure ll),they are too disparate for reliable estimation of n in eq 12 and 13. For the other liquids, either clearing-field values of Gn are not reliably known (e.g., bicyclohexyl and decalin) or when they are (as in the case of n-hexane and i s o o ~ t a n e their ) ~ ~ comparison with reported values of Gn from cq1l2extrapolations is obscured by the large variations in these extrapolations from one scavenger to the next.24 Thus, the question of whether there is indeed any difference in the forms of pt for fluorescence quenching and for chemical scavenging still (30) Tachiya, M. J. Chem. Phys. 1978,70,238 (note misprint in eq 38 which should read a2 = -(5/36 - 7/6)].
1589
cannot be answered unequivocally. The good agreement that we find between the theoretically expected form of pt and that observed in fluorescence quenching (at least with perfluordecalin) makes it difficult to understand how the chemical scavenging results could be so different especially since the conditions for validity of the approximations in the theory are not expected to be more seriously violated for the chemical process (at least not in the direction required). Clearly the resolution of this problem would be assisted by a more definitive analysis of the concentration dependence of G(P) in some solvent for which there exists a reliable value of Gn. Acknowledgment. This research was supported in part by the US.Department of Energy, Division of Chemical Sciences, Office of Basic Energy Sciences. We are also very grateful to Mr. Kaidee Lee for his helpful comments and Mr. David B. Johnston and Ms. Diane Szaflarski for their technical assistance. Finally, we wish to acknowledge our gratitude to Dr. J. Noolandi for sending us tables of numerical values of g,, (r,c),to Professor R. H. Schuler for sending us the numerical values of G(CH4)for CH3Br and CH3Cl scavenging of electrons in cyclohexane, and to Professor A. Hummel for a stimulating correspondence. Registry No. Bicyclohexyl,92-51-3;decalin, 91-17-8;cis-decalin, 493-01-6;trans-decalin, 493-02-7;cyclohexane, 110-82-7; perfluorodecalin, 306-94-5.
Molecular Complexes. 6.' The Nuclear Magnetic Resonance Shift Difference Method and General Aspects in the Nuclear Magnetic Resonance Evaluation of Formation Constants of Weak Complexes As Exemplified by Some Benzene Complexest WlHrled Lamberty, Helmut Stamm, and Jiirgen Stafe Pharmazeutisch-Chemisches Institut der Universkiit HekMberg, I m Neuenheimer FeM 364, P 6 9 0 0 Heidelberg, federal Republic of Germany (Received: March 26, 1982; I n final form: December 2, 1982)
The application of additional unspecific shielding (AUS) corrections during the evaluation of formation constants, K , of complexes is discussed for different methods used in referencing chemical shifts. The AUS effect may be nonlinear. Formation constants for the benzene complexes of p-nitrobenzaldehyde (NBA) and p-dinitrobenzene (DNB) are determined. The three proton signals of NBA provide the same K. The known AUS coefficients u2 are compared and analyzed. A partial AUS effect is described which lowers the AUS coefficient u2. By this particular AUS effect the aromatic a2 of DNB is distinctly smaller than u2of the structurally very similar aromatic NBA protons. The newly described shift difference method allows AUS corrections independent of the kind of shift referencing. Some applications of this method show that it can provide good results, if the measurements are accurate and employ a good range of saturation fraction and if the complex shift or its equivalent is distinctly different from zero. The strongly disturbing influence of large errors and low saturation fractions is demonstrated.
Introduction and General Aspects Determination of the equilibrium quotient K for the reaction A+DeAD by the NMR chemical shift is a standard method in this field, particularly if the donor is aromatic. The chemical shift Aobsd.iof an acceptor signal is measured in a series of 'Dedicated to Professor Milton Tamres on the occasion of his 60th birthday. 0022-3654/8312087-1589$0 1.5010
solutions i which contain a varying total (free and complexed) donor concentration [Doliand an (advantageously constant) total acceptor concentration [A,,]. These shifts are determined relative to the acceptor signal of a solution in which [Doliis zero (Le., relative to the signal of the free acceptor). Data reduction according to the linear equation 1, which is the Scatchard-Foster-Fyfe (ScFF) method,2
(1) H. Stamm and J. Stafe, 2.Naturforsch. B , 36, 1619 (1981),in English.
0 1983 American Chemical Society
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Lamberty et ai.
The Journal of Physical Chemistty, Vol. 87,No. 9, 1983
yields values of K from the negative of the slope and values of the complex shift Am from the ratio of the intercept (Icpt) divided by the negative of the slope. The results obtained by this method are nearly as reliable as those from the Creswell-Allred (CA) treatment,2 which has proven least sensitive to experimental errors.3 In our investigations we calculate the desired parameters by CA and then corroborate them by ScFF. However, since the ScFF plot has the advantage that it is visually informative, we prefer its use for the analysis of inconsistent or unexpected results and for the development of methodical improvements. Stimulated by inconsistent results, the AUS concept was developed with the help of ScFF plots. This led to the AUS correction which takes into account the additional unspecific (i.e., noncomplexing)shielding by the aromatic donor of the free acceptor (upfield shift by f1([Doli))and of the complexed acceptor (upfield shift by f2([Dolij).This correction gives4 &/[Doli = -K(Aoi - fd[Dolil) + K(AAD,OO + fi([Dolil/(KED~li))(2) The development of the AUS concept required differentiating symbols for the experimental shifts as well as for ~ to Am, and A,,i derived shifts. Thus, A A D ,corresponds to Aobsd,i* This refinement of the ScFF equation is important for weak complexes with aromatic donors, in which case f2([Doli\cannot be neglected. The functions fi and f 2 have a general dependence on [Doli. They are not known and cannot be determined experimentally. However, K can be calculated from very precise shift measurements if fl and f 2are linear functions of [Doli,i.e., if the signal of the free acceptor is shifted upfield by al[D0liHz and the signal of the complexed acceptor is shifted upfield by a2[DoIiHz, the latter being in addition to the familiar complex shift (i.e., Am,oo in our notation). The coefficients al and a2 indicate the probabilities of unsuccessful (Le., not complex forming) but magnetically shielding collisions of a donor molecule with a molecule of free and complexed acceptor, respectively. In this case of a linear dependence of AUS, the calculation of K is possible by subtracting a2[D0lifrom A,,i. The unknown a2 is found by a trial-and-error procedure with selected values for a2 until the best linear regression is found. The slope of this linearized function is -K, and the intercept is an approximation of KA,. This process is the AUS correction, which can be performed analogously in the CA treatment. Application of the AUS correction to experimental data leads to self-consistent and reasonable values of K and a2 in the hitherto investigated systems,lJ but there may exist (2) ScFE R. Foster and C. A. Fyfe, Trans. Faraday Soc., 61, 1626 (1965). CA: C. J. Creswell and A. L. Allred, J. Phys. Chem., 66,1469 (1962). For a description of these methods and for further references see ref 4. In ScFF the linear regression between Aow,,/[Do], and &w,, gives -K (slope) and KAm (intercept) according to A 0 ~ , / [ D O = ] , -KAobd,, + KAm, where Am is the complex shift. The small error, which is introduced by using [Do],in place of the correct concentration [D], of the free donor, can be eliminated by iteration. CA is a trial-and-error procedure, which works as follows. Select a fictitious value for K and calculate the corresponding fictitious complex concentration [AD], for each experimental [Do],according to IC([&] - [AD],) = [AD],/[D,],. Then determine the linear regression between the experimental &wJand these fictitious [AD], according to Aow,, = a[AD],/[&]. Repeat this procedure with another selected value for K until the best regression is found, Le., until the minimum value for the least-squares sum is found. The corresponding K is the best K and the corresponding slope a is the best Am. (3) H Stamm, W Lamberty, and J. Stafe, Tetrahedron, 32, 2045 (1976). (4) H. Stamm, W. Lamberty, and J. Stafe, J.Am. Chem. SOC.,102, 1529 (1980)
limitations and complications. Therefore, the basic concept and model should be remembered during an application of the AUS correction. The linear analogue4of eq 2 in its generalized form5 is eq 3, obtained by subtracting m2 from both sides of the equation. (A,,i
- m2[DolJ/[Doli =
-K(Aoi - m2[D0lJ + Icpt
(3)
where Icpt = K(AAD,OO + (ml - mJ/K) Here, the “general” coefficients ml and m2are used in place of al and a2 for reasons discussed below. The AUS concept and the AUS correction are deduced by supposing an ideal NMR reference, the signal of which does not change its position when the composition of the investigated solution is varied. In practice, this must be an external reference including corrections for susceptibility variations of the investigated solutions. In this case ml = al and m2 = a?. A second case, which allows application of an AUS correction, emerges from the first case by inclusion of the susceptibility correction in the AUS correction,l provided that the susceptibility correction is a linear function of the donor concentration, e.g., b[Do],. Then ml = al + b and m2 = a2 b. But even when an internal NMR reference is used, which inevitably shows a shift dependence f3([DOli)on donor concentration, an AUS correction according to eq 3 should be possible if the floating of the reference signal with the variation of the solution composition again is a linear function of the donor concentration, i.e., if f3([D0li\ = c[Doli. Then ml = al + c and m2 = a2 + c , This would be advantageous, because internal referencing makes measurements easier. Evidence has been presented’ that the usual reference substances do not possess the required linear dependence on [Doliwhen benzene is the donor. If the reference signal originates from two or more indistinguishable nuclei of the same molecule and if these nuclei are separated by distances large enough to allow shielding of one nucleus by one donor molecule and simultaneous shielding of a second nucleus of the same reference molecule by a second donor molecule (which is true for all common proton references), then the dependence on [Doll of the signal position not only will consist of the linear term c[D0libut will include at least a quadratic term too, as simple collision theory shows:
+
It follows that a proper proton reference substance must contain only one reference proton per molecule, which is rather impractical and difficult to realize. Alternatively the indistinguishable reference protons must be so close to one another that they all can be shielded by one donor molecule only. For benzene as the smallest aromatic donor a reference molecule with one single reference methyl group should be suitable, provided the general requirements for a reference substance are met. There is a fourth possible solution of the reference problem arising in connection with the AUS correction. This will be dealt with later. A t the moment consider a nonlinear shift dependence caused by “unsuccessfulntriple collisions with two or more indistinguishable reference protons. A nonlinear dependence is not restricted to nonpolar and noncomplexing reference substances. One has to consider the possibility of a similar behavior of (5) H. Stamm and W. Lamberty, Tetrahedron, 37, 565 (1981).
Molecular Complexes
acceptor protons (nonlinear case of AUS), if the acceptor structure points to this, i.e., if indistinguishable acceptor protons are located within the acceptor molecule at distances which allow shielding of one nucleus by one donor molecule and shielding of a second nucleus of the same acceptor molecule by a second donor molecule at the same time. The importance of a quadratic term in AUS is difficult to estimate a priori. The common acceptor molecules have a shape different from those of the common reference molecules. But above all, the AUS correction according to eq 3 should depend more strongly on m2 than on ml, so that this problem can perhaps be reduced to an analysis of shielding triple collisions of the complexed acceptor molecule which probably occur very rarely if at all as long as the size of the donor molecule is not distinctly smaller than the size of the acceptor molecule. In any case, the AUS correction leads to reasonable results for an aromatic acceptor with locally separated indistinguishable protons: 1,3,5-triacetylbenzene (TAB)Swith two groups of indistinguishable protons (three aromatic, nine protons of three methyl groups) and 4-nitrobemaldehyde ( M A , vide infra) with one single proton (aldehyde) and two groups of indistinguishable aromatic protons (2,6 or ortho positions and 3,5 or meta positions). Of course, following the discussion of benzene-induced shifts of common internal references in ref 1, one must consider not only the influence of a quadratic term in AUS but also the possibility of additional unspecific shielding of only a part of a group of indistinguishable acceptor nuclei, in the extreme case of only one nucleus out of two, three, or more. This "partial shielding" would lower a2. We shall present an example of this effect below. The Results part of this paper deals in its first section with the determination of K s of the benzene complexes of NBA and of p-dinitrobenzene (DNB). The second section discusses the a2values. The third section describes the shift difference method applicable to the evaluation of K from NMR shift data measured against an internal reference of the common type. Finally, the fourth section deals with the influence of experimental errors. The ScFF procedure is based on the approximation that [Doliis used instead of the correct concentration [DIi of only the uncomplexed donor. In all computations in this paper this inherent approximation was eliminated by iteration cycles included in the computer program. Experimental Section Materials. DNB, NBA, CC14 (Uvasol quality), C6D6 (Uvasol quality, 99.5% deuterated), Me,Si, and TSPNa (Me,SiCD2CD2C02Na)were purchased from E. Merck, Darmstadt, West Germany. DNB and NBA were recrystallized from water and dried in a desiccator; finally they were dissolved in benzene and the solutions were evaporated to dryness (azeotropic removal of residual water). Procedure. Preparation of solutions, external and internal (Me4Si)references, precision sample tubes, precision capillaries, lock of spectrometer, and recording of 'H NMR spectra on a Bruker HX 90-E spectrometer at 90 MHz are described in ref 1. Experimental Details. The temperature was 26.3 f 0.3 "C. For DNB, the NMR shifts of each solution were measured first against the internal reference and secondly against the external reference contained in a capillary. The number of scans was 200-500 for NBA solutions and about 100 for DNB solutions. [A,,] was kept constant at 0.009 956 mol/L for T4BA and at 0.010 15 mol/L for DNB. In NBA the protons at positions 2 and 6 (ortho positions relative
The Journal of Physical Chemistry, Vol. 87, No. 9, 1983
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TABLE I: Experimental Data of the NBA-Benzene System in Carbon Tetrachloride" A o i , Hz
CHO
at 90 MHz
o -H
m-H
[Doli, mol/L
ext
int
ext
int
ext
int
1.019 1.076 1.650 2.153 2.207 3.187 4.237 5.341 6.425 7.480 8.568 9.642 10.695
20.67 21.61 31.76 39.59 40.60 54.88 68.33 81.64 93.03 103.82 113.87 123.18 131.85
15.63 16.24 23.46 28.97 29.44 39.02 47.16 54.55 60.10 64.77 68.67 71.76 74.08
18.62 19.86 28.70 36.47 37.31 50.78 63.86 76.86 88.36 99.05 109.70 119.15 128.56
13.61 14.30 20.72 25.53 26.62 34.72 42.48 49.76 55.24 59.98 64.15 67.57 70.43
22.15 23.26 34.15 42.78 43.93 59.49 74.34 89.23 101.80 113.90 125.43 135.78 146.03
17.14 17.92 25.88 31.98 32.84 43.44 53.04 62.04 68.90 74.87 80.16 84.48 88.03
" Total C,D,
concentrations [Doli and experimental NBA
H NMR shifts A oi obtained both vs. external TSPNa and vs. internal Me$.
TABLE 11: Experimental Data of the DNB-Benzene System in Carbon Tetrachloride" Aoi,
[Doli, mol/L
ext
1.071 1.096 1.607 2.115 2.673 3.201 4.284
26.61 26.61 37.93 47.70 58.14 66.53 83.34
Hz int 21.24 21.52 29.86 37.36 44.62 50.84 61.89
Aoi,
Hz
[Doli, mol/L
ext
int
5.327 5.354 6.397 7.474 8.579 9.607 10.653
97.63 97.78 111.08 123.96 135.53 145.87 155.43
70.39 70.77 78.22 84.99 90.39 94.82 98.36
a Total C,D, concentrations [Doli and experimental DNB 'H NMR shifts A o i obtained both vs. external TSPNa and vs. internal Me,Si.
to aldehyde group) form a doublet-like multiplet, the shift
biof which was determined as follows. First, bifor the left-hand line of this "doublet", was read, and then AOifor the right-hand line of the same doublet, and finally the arithmetic mean was taken as the &i for the two protons. The same values (within experimental precision) for Aoi were obtained by evaluation of one doublet line only instead of forming the arithmetic mean. Thus, it was possible to determine bieven when one of the doublet lines was hidden under the signal of C6HD5. The same procedure was applied to the multiplet of the protons at positions 3 and 5 (meta positions). Calculations. K, a2 b, a2,a-8,Icpt/K, Icpt,+/K, and SDDQ (for explanation of symbols see below) were com- 2 the ~ results corrobputed with the program c ~ ~ u sand orated with the program SCAUS-MOD2.6 Both programs are available on request.
+
Results Experimental concentrations and relative shifts are listed in Tables I and 11. For NBA the corresponding ScFF plots derived from externally referenced shifts are shown in Figure 1, both without and with application of the AUS correction (independent AUS correction for each of the three signals!). The parallel corrected plots are good evidence for the correctness of the procedure and model. The computed parameters are given in Table 111. The very good agreement for K obtained from the different signals, and for all parameters obtained by different cal(6) The principles of the computer programs are given in ref 3 and 5.
Lamberty
The Journal of Physical Chemlstry, Vol. 87, No. 9, 1983
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et ai.
TABLE IV:
a, (HzLlmol) of Benzene Complexes Corrected for the Susceptibility Term ba
caffeine’
2c
TAB’ NBA
15
DNB a
10
5
,
50
100
-
150
Flgure 1. ScFF plots of NBA-benzene complex before (three upper plots) and after (threebottom plots) performance of AUS corrections. Signal marking follows the correct name of NBA (4nboobenzaldehyde): 2,6 protons are o (ortho); 3 3 protons are m (meta); aldehyde proton is CHO. Abscissa: three upper plots A,,, three bottom plots A,, a p [ D , ] , ,both in hertz. Ordinate: three upper plots Ao,/[Do],, three bottom plots (Ao, - a 2 [ D o ] , ) / [ D o both ] , , in Hz L/mol.
TABLE 111: Parameters of the Benzene Complex of NBA Computed with C A A U S ~from the Externally Referenced Data of Table I signal K, Limo1
0.1244 (0.1279 i 0.009) IcptlK, Hz 137.2 * 0.2 (133.1) m 2 ,Hz Limo1 5.02 (5.15) SDDQ,’.’ Hz2 0.227 (0.251) a SCAUS
o -H
m -H
0.1244 (0.1290 t 0.018) 110.0 t 0.3 (106.0) 6.15 (6.28) 0.324 (0.368)
0.1251 (0.1275 i 0.008) 139.4 i 0.3 (136.6) 6.21 (6.30) 0.259 (0.270)
CHO
results in parentheses.
culation procedures (CA and ScFF), is remarkable. One may regard 0.125 L/mol as the most probable value of K, since CA produces the more accurate results as shown by the SDDQ’s which indicate the goodness of fit: SDDQ = - Acalcdj)2,where &d,i are calculated from K, [A,,], [Doli,u2, and Icpt. Throughout this paper the calculated parameters are given with probably one or two more digits than justified in order to demonstrate the good agreement between results from different signals, from different calculations, or from different methods of evaluations (direct or shift difference). The CA processing of the externally referenced DNB data (Table 11) provides (ScFF results in parentheses) K = 0.1302 (0.1316) L/mol, Icpt/K = 167.4 (165.5) Hz, u2 + b = 5.49 (5.55) Hz L/mol, and SDDQ = 0.75 (0.76) Hz2. The saturation fraction [ADIi/[&] ranges from 0.11 to 0.57 for NBA and from 0.12 to 0.58 for DNB. The DNB parameters K and Icpt/K correspond very well with K and AAD (0.13 L/mol; 165 Hz making allowance for the spectrometer frequency; temperature 40 “C) determined by Johnston, Gasparro, and Kuntz7 from shifts referred to
1-Me 3-Me 7-Me 8 -H Ar-H ME! CHO o-Ar-H m-Ar-H Ar-H
2.88 3.91 3.80 3.15 2.09 4.87 3.81 4.94 5.00 4.28
Evaluated at 90 MHz
internal Me4Si. In the same manner, i.e., without AUS correction, from our own internally referred shifts Aoi (Table 11) the following values were computed with the program CA2s4(and ScIT2s4):0.1372 (0.1344) L/mol and 166.9 (168.8) Hz. The ScFF plot is linear while the one constructed from the externally referenced data without AUS correction reveals an upward curvature. Evidently the unspecific shieldingsof the DNI3-benzene complex and of MelSi are the same or nearly the same, leading to cancellation. This is confirmed by a comparison of their unspecific shielding effects. Including the susceptibility contribution, it is 5.5[Do];for the DNB-benzene complex, because u2 + b = 5.5 Hz L/mol as specified above; and it is’ 0.041[D0li2+ 4.9[D0lifor Me4% Both functions yield rather similar values, 55 and 54 Hz with [C6D6]= 10 mol/L or 27.5 and 25.5 Hz with [C6D6]= 5 mol/L. The DNB-benzene complex may be considered typical for those ‘HNMR investigations which, by simple ScFF treatment of the internally referenced data, yield a more or less linear ScFF plot. Clearly, a linear plot for a benzene complex can be expected if u2 + b has a value near 5.2 Hz L/mol (at 90 MHz). The “degree of linearity” further depends on Icpt/K and on the donor concentration range. Obviously, in an investigation of a new complex one cannot rely on mutual cancellation of the unspecific shielding effects on complex and internal reference. Discussion of u2 Values. The published u2values include the susceptibility correction 6. Since b changes its value when the donor or the solvent is changed, we have subtracted b = 1.213 Hz L/moll from all u2 values obtained by computation with CAAUS. These corrected u2 values are listed in Table IV. The highest values were found with the aromatic protons of NBA and with the methyl protons of TAB. A certain amount of the above-mentioned “partial shielding” should be operative within each methyl group of an acceptor, but because of the small interproton distances and because of the fast internal rotation the three protons of one methyl group may virtually behave as if they were one. Partial shielding should be more pronounced for two or more indistinguishable methyl groups. So, in spite of its high value the computed methyl u2 of TAB should include this lowering influence of partial shielding. The low a2’s of caffeine indicate that its methyls are embedded deeper into the molecular contour than a first glance a t the structure perhaps might reveal. While the embedding of 1-methyl was already noticed,’ the a2-lowering peri position (as in 1&dimethylnaphthalene) of 7-methyl and 3-methyl had not been recognized. As for the aromatic protons, the difference between the structurally very similar NBA and DNB evidently reflects the fact that the DNB signal originates from four indistinguishable but rather space-separated protons. In NBA (7) M. D. Johnston, Jr., F. P. Gasparro, and I. D. Kuntz, J . Am. Chem. Soc., 91, 5715 (1969).
The Journal of Physical Chemistry, Vol. 87, No. 9, 1983
Molecular Complexes
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TABLE V: Parameters of the Benzene Complex of NBA Computed with C A A U S ~from Shift Differences A,-p at 9 0 MHz and Comparison with the Results of the Direct Method (Table 111) 10
CHO/o int A , , , Hz Amax,b
ext
2.02 4.86 3.65 0.1172 (0.1222) 28.2 (27.0)
Hz Hz K , L/mol Aon,b
Icpt,-plK, H Z
2.05 4.78 3.29 0.1275 26.3
(Icpt, - Icptp)/K,' HZ a2,@-p,Hz L/mol
-
m/CHO
27.2 (27.1) - 1.10
-1.12 (- 1.09)
Hz L/mol
-0.91 (-0.85)
mlo
int
ext
int
ext
1.51 13.95 13.95 0.0393 (0.0701) 16.9 (7.4)
1.48 14.18 14.18 0.0784 (0.0110) 6.4 (151.9) 2.2 (3.5)
3.53 17.60 17.60 0.1116 (0.1206) 34.0 (31.3)
0.84 (1.01)
1.04 (-0.18) 1.19 (1.15)
- 0.08 (-0.00)
3.53 17.47 17.47 0.1246 (0.1202) 30.7 (31.9) 29.4 (30.6) 0.006 (-0.044) 0.06 (0.02)
A o n refers to the solution of highest benzene concentration [Doli. a SCAUS results in parentheses. shift difference which is not always identical with A,,,. Calculated from Table 111.
this holds for only two protons each time (two ortho and two meta protons). The lowest a2was found for the aromatic protons of TAB in agreement with the model. Shift Difference Method. This method is important because of the frequent practice of internal referencing. It requires the simultaneous shift measurements of at least two acceptor signals. When an internal reference is used, the experimental shifts 6: are found to be too large by f3{[DOli)*Thus, f3{[Doli) must be subtracted from A,,i, and correspondingly eq 3 changes to eq 4 by substituting al + f3([DO]i)and a2 + f3([DOlij for m, and m2,respectively. If there are two anisochronous acceptor protons a and p, we may transform
- f3([DOIi)- a2P0li -
&i
[Doli
-K(&i
- f3{[D0li)- a2[D0li) + K
(
AAD,OO +
a1
- a2
)
K
(4)
eq 4 to eq 5 for the proton a. Substitution of the index &i,a
= Vd[DOIi) + fd[Doli)K[D~Ii+ a2,c&[D0Ii2 + KAAD,oo,~[DoI~ + al,a[Doli)/(1 + K[DoIi) (5)
p for a yields the corresponding equation for proton p. Now, subtracting Aoi,@from Aoi,, and using &,a+
=
- &i,p
&i,a
AAD,oo~-~ = AAD,OO,@ - AAD,OO,B
alp-/?= a1.a - a1,o a2,a-8 = a2,a
- a2,8
we obtain after transformation to the usual form (&i,a-o
- a2,r8[D0li)/[D0li = -K(Aoi,a-p
- a~,a-~[Doli) + ICPta-6 (6)
where IcPt,-B = K(AAD,OO,a-B + (al,,-o - a2,@-8)/ K ) All terms containing f 3 are eliminated by subtracting A,,i,a from &i,a. Thus, forming the shift differences8 A,,i,a-6 = 6owi,,) - (aA8 - aoWjd) of two anisochronousprotons a and p for each donor concentration and subjecting the pairs (8) A small 6 is always the chemical shift relative to the reference signal.
Amax
is the largest
A,,i,,+ and [Doli to the usual AUS correction allows determination of K even from shifts determined against an internal reference with the common nonlinear behavior toward aromatics. IcptW6/Kmay be considered an approximation to the difference Am,OO,Wobetween the complex shifts for a and p. a2,a-ois the difference between the AUS coefficients a2 of a and 6. The specific case a2,a-8= 0 should be mentioned because the difference method will then yield the correct K even without an AUS correction, using, e.g., the classical ScFF equation of Foster and Fyfe (perhaps with iterative elimination of its inherent approximation error). Application of this method of shift differences and comparison with the results computed directly from externally referenced shifts A,,i are demonstrated for the benzene complexes of NBA, TAB,5 and caffeine.' The results for NBA are shown in Table V. The congruence of these results with those of Table I11 depends on the two acceptor signals used in forming the shift difference Aa+, The combinations meta/ortho and CHO/ortho provide excellent congruence for the external series and fair congruence for the internal series, indicating a higher degree of experimental scattering in the internal series. The good congruence for the combination CHO/ ortho is remarkable because of the smallness of all &,wis (compare &,, Am=, and A,,,,), which transforms any small experimental error into a severe relative error. The disagreement for the couple meta/CHO is to be explained in a different way. Neither the direct shift method (e.g., ScFF) nor the shift difference method yields an equilibrium quotient when the complex shift or its analogue is zero. Further, one cannot expect a reliable K if the complex shift or the complex shift difference AAD,OO,wo, respectively, has values near zero, because experimental scattering may then predominate and produce meaningless results. This evidently happens with the combination meta/CHO of NBA. Although the precise value of AAD,OO,a-jj is not known, the corresponding small value of Icpt,,/K virtually precludes any value distinctly different from zero. The uncertainty in AAD,OO,a-o makes it advisable in the application of this difference method not merely to rely on computational vs. [Doli. If a distinct results but to inspect the plot of h,-s curvature is not recognizable, one cannot hope for reliable computation results. Thus, there are two requirements to be observed in the application of the difference method: the curvature and a Am= much larger than experimental errors.
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The Journal of Physical Chemistry, Vol. 87, No. 9, 7983
Lamberty et ai.
TABLE VI: Parameters of t h e Benzene Complex of TAB Computed with CAAUS' from Shift Differences A ~ - Pat 90 MHzb and Comparison with Results of t h e Direct MethodS difference method, Me/Ar AO,, Hz Amax,' Hz on Hz K , Limo1 Icpt,_p/K, Hz (Icpt, - Icptp)/K,d HZ u 2 , @ - p Hz , L/mol a7,@- az,p,d Hz Limo1 a SCAUS results in parentheses. culated from results of ref 5. 3'
direct method5
int
ext
Ar, ext
Me, ext
6.14 45.72 45.72 0.1153 (0.1189) 27.3 (26.4)
6.08 45.75 45.75 0.1054 (0.1075) 30.4 (29.3)
9.87 67.82 67.82 0.1034 (0.1078)
15.94 113.57 113.57 0.1041 (0.1078)
30.3 (29.6)
30.3 (29.6)
2.88 (2.90)
2.78 (2.80)
2.78 (2.80) 2.78 (2.80) Based on experimental data from ref 5. ' For meaning of symbols see Table V.
TABLE VII: Parameters of the Benzene Complex of Caffeine Computed with CAAUS' from Shift Differences MHzb and Comparison with Results of t h e Direct Method' 01
3-Meil-Me
7-Me/l-Me
S-H/l-Me
7-Me/3-Me
8-H/3-Me
Icpt,_p/K, HZ (Icpt,
8.3 ( 7 . 4 )
7.15 86.63 86.63 0.1082 (0.1112) 142.7 (138.4) 142.0 (138.3) 0.90 (1.03) 0.92 (1.03)
7.23 82.95 82.95 0.1134 (0.1149) 145.7 (143.6) 145.3 (143.6) 0.26 (0.32) 0.27 (0.32)
6.27 70.99 70.99 0.1081 (0.1103) 134.1 (131.1) 133.7 (130.9) -0.12 (-0.03) -0.11 (-0.03)
6.35 67.30 67.30 0.1137 (0.1143) 137.2 (136.3) 137.6 (136.2) -0.77 (- 0.74) -0.76 (- 0.74)
>'
K, Limo1
-
Icptp)/K,d HZ
~ , , ~ - pHz , Limo1 u Z q Q- ~ , , p Hz , ~ Limo1
SCAUS results in parentheses.
culated from results
bf
1.02 (1.06) 1.03 (1.06)
Based on exuerimental data from ref 1.
a t 90
/P
0.88 15.65 15.65 0.1088 (0.1242) 8.6 (7.4)
A , , , Hz Amax,' HZ Aon Hz
Aa-p
Cal-
8-H/7-Me 0.08 0.36 - 3.68 0.2145 5.6 3.3 (5.3) - 0.70 - 0.65
(-0.71)
For meaning of symbols see Table V.
Cal-
ref l .
For the TAB-benzene complex the shift difference method produces parameters which agree remarkably well with the results of the direct m e t h ~ das , ~an inspection of Table VI reveals. Likewise, in the caffeine example (Table VII) the difference method works very well apart from the signal combination 8-H/7-Me. A glance at bl,A,,, and &,, of this combination indicates that a good computational result a priori would have been very improbable. The calculations were based on the data of series 1 of ref 1. Here, the hi's were measured simultaneously vs. internal and vs. external references in the same spectra. The quality of the parameters computed from the combination 3-Me/l-Me is better than expected, considering the small shift differences (see A,, and Amax in Table VII) and the small values of Icpt,,/K. Influence of Experimental Errors. Application of AUS corrections in connection with the shift difference method demands high precision of shift measurements. There are particular reasons to lay emphasis on the experimental accuracy as is now shown by a literature example. Investigations of the caffeine-benzene complex have been performed previously (see references cited in ref 1). In a recent paperg the experimental data were interpreted in terms of 1:l and 1:2 complexes. The shift measurements used internal MelSi as a reference signal. This inevitably leads to incorrect shift values &,that cannot be corrected afterward. Therefore, these data could not be subjected to a simple 1:l complex processing with inclusion of the AUS corrections. Nevertheless, this particular type of methodical error can be eliminated by the shift difference method. Accordingly, the experimental datag (after transformation of the concentrations into the molarity (9)S. Andini, L. Ferrara, P. A. Temussi, F. Lelj, and T. Tancredi, J. Phys. Chem., 83, 1767 (1979).
O
"1
-
2
Flgui 2.
4
6
8
1 0 1 2
analysis of the caffeine-benzene comC 'x with the shift difference method applied to the data of ref 9. Dependence of K on stepwise omission of lowconcentrationsamples and on omission of outlying samples. Shift differences &H/3-Me. Ordinate: Kin Umol. Abscissa: lowest sample number (sample number of lowest donor concentration)used in the computation; sample numbering according to ref 9. Plots from top to bottom: plots of K computed without omission of outlying high-concentratlon samples, plot of K computed when sample 17 always was omitted, plot of K computed when sampies 15 and 17 always were omitted. CAAUS
scale) were treated exactly like the data of ref 1 (see above and Table VII). The result was disappointing. K was always found to be too great, mostly much too great, and Icpt/K was always found to be too small, mostly much too small. The best approximation to the most probable value of K' was obtained with the difference 7-Me/3-Me: K = 0.169 L/mol. The bad results from the difference method in this case are caused by experimental errors. Simple plots of hLvs.
The Journal of Physlcal Chemistry, Voi. 87, No. 9, 1983 1595
Molecular Complexes
0.41
2
6
4
8
1 0 1 2
Figure 3. CAWS analysis of the caffeine-benzene complex with the shift difference method applied to the data of ref 9. Dependence of K on stepwise omission of lowconcentratkm samples and on omission of outlying samples. Shift differences 7-MeI3-Me. Ordinate and abscissa as in Figure 2. Plots from top to bottom: plot of K computed without omission of outlying hlghconcentratlon samples, plot of K computed when sample 17 always was omitted, plot of K computed when samples 15 and 17 always were omitted.
0.21
- 0
1 .o
”‘1
0.8
O
1
3
5
i
Figure 5. CAWS analysis of the caffeine-benzene complex with the shift difference method applied to data of ref 1. Dependence of K on stepwise omission of lowancentration samples. From top to bottom: shift differences 8-H/3-Me; shift differences 7-Me/3-Me; shift differences 3-Me/l-Me. Ordinate: K in L/mol. Abscissa: lowest sample number (sample number of lowest donor concentration) used in the computation; sample numberlng according to ref 1.
0.6
0.4
\
\
0.2 ~
~
L ... ~ .
..
J
_
_
_
-
.1 15
2 4 6 8 1 0 1 2 Figure 4. CAAUS analysis of the caffeine-benzene complex with the shift difference method applied to the data of ref 9. Dependence of K on stepwise omission of lowancentration samples and on omission of outlying samples. Shift differences 3-Me/l-Me. Ordinate and abscissa as In Figure 2. Plots from top to bottom: plot of K computed without omission of outlying high-concentration samples, plot of K computed when sample 17 always was omitted, plot of K computed when samples 9, 15, and 17 always were omitted.
[Doli reveal that sample 17 of Table I of ref 9 produces 7-methyl, and 1-methyl. outlying points at least for 8-H, Further, for 1-methyl the scattering along the whole curve is clearly recognizable because of the small absolute values of the shifts A,,c This scattering points to an uncertainty in shift measurements of about 0.5 Hz or more at 100 MHz. Inspection of the shift values of samples 12 and 13, which have virtually the same benzene concentration, shows that shift errors of at least 0.3 Hz occur. Such errors make an evaluation of reliable K values virtually impossible. This can be demonstrated by a simple error simulation as in ref 3. Introducing one shift error of 0.2 Hz into the 1-methyl data of ref 1 can produce a deviation in K of up to 20%.
Introducing two shift errors of 0.2 Hz each causes a deviation in K of up to 30%. The AUS correction is evidently very sensitive to experimental errors. However, more serious difficulties are caused by the errors for samples 2-4. Extrapolation to [Doli = 0 does not lead to 4, = 0 for any of the four caffeine signals when these three samples of lowest benzene concentration are included. I t appears that evidence against a pure 1:l complex and for a 1:2 complex was based mainly on these samples. Personlo and Deranleau” have shown that samples of low relative complex concentration [AD],/ [A,] (saturation fraction) make complex evaluations unreliable. For K = 0.115 L/mol,l the saturation fraction for samples 2-6 (sample 1has donor concentration zero) would be less than 0.1. The contribution to the K evaluation of more than one-quarter of the samples must be considered fairly unreliable. We conducted many CAAUS computations12on the shift differences of the datag in order to analyze the error influence in more detail. The shift differences 8-H/7-Me were excluded in this analysis because this combination cannot be expected to yield reliable results, as stated above. In the other combinations the computation was repeated after omission of the first sample (sample 2), after omission of the first two samples (samples 2 and 3), and so forth. This kind of analysis clearly reveals a trend of the K values toward the “best value” with increasing omission of low(10)W.B. Person, J . Am. Chem. SOC.,87, 167 (1965). (11)D. A. Deranleau, J . Am. Chem. SOC.,91,4044 (1969). (12)We thank Miss Hannelore Jackel and Dr. Barbro Beijer for providing us with the results of these computations.
J. Phys. Chem. 1983, 8 7 , 1596-1600
1598
concentration samples. The same holds for the values of Icpt,/K and while the quotient of SDDQ over the number n of samples shows a decreasing tendency. The trend of the K values is presented in Figures 2-4 for the combinations 8-H/3-Me, 7-Me/3-Me, and 3-Me/l-Me. Here and in the following discussion the variation in K of the combination 8-H/l-Me resembles that of 8-H/3-Me (Figure 2), and that of 7-Mell-Me resembles that of 7Me/3-Me (Figure 3). The uppermost plot in Figure 2 confirms the errors in the low-concentration shifts. Stepwise omission of the low-concentration samples makes K approach the most probable value of 0.115 L/mol without reaching it. The same holds for the uppermost plot of Figure 3, although in this case the decrease in K soon reaches a plateau near the most probable value (about 20% higher). In Figure 4 the general decreasing trend of K can be recognized in the uppermost plot as well, but for this combination (3Me/ 1-Me) the shift differences are much smaller than for the other combinations (compare the values of Icpt,+/K in Table VII). The influence of outlying shift values is therefore much stronger than in the other combinations. Consequently, the trend interruption caused by particularly large shift difference errors (samples 5 and 9) is striking. The influence of the outlying sample 17 was analyzed by repeating the preceding computations with omission of sample 17. The second (intermediate) plots in Figures 2-4 show the corresponding dependence of K. The approach to K = 0.115 L/mol is improved. This approach to K = 0.115 L/mol is improved further when the computation is repeated with omission of samples 15 and 17. This is shown by the bottom plots in Figures 2-4. For the combinations 7-Me/3-Me, 7-Me/ 1Me, and 3-Me/l-Me the most probable value of K is virtually matched. For the last combination sample 9 was
eliminated in addition to samples 15 and 17. The computed parameters corresponding to the last point of each bottom plot are as follows (K, Icpt,+/K, a2,01-p, SDDQIn, dimensions as usual in this paper, n is the number of data): &H/3-Me, 0.201,93.8, 1.04, 0.015; 8-H/l-Me, 0.195, 103.3, 2.06,0.013; 7-Me/3-Me, 0.122, 122.2, 0.60,0.024; 7-Me/lMe, 0.122, 132.2, 1.62, 0.057; 3-Me/l-Me, 0.131, 9.7, 1.03, 0.011. An analysis of this kind may be helpful when one evaluates K from rather scattering and uncertain shift values. The high sensitivity of the AUS correction to experimentalerrors is recognizable even with the very good caffeine-benzene shift data of ref 1. Application of the same omission procedure to shift difference data formed from series 1 of ref 1 (compare Table VII) yields Figure 5, again with a good congruence between the combinations 8-H/3-Me and 8-H/l-Me (not shown) as well as between the combinations 7-Me/3-Me and 7-Me/l-Me (not shown). The comparatively stronger error sensitivity of the combination 3-Me/l-Me is caused probably by the smallness of Icpt,+/K and of the shift differences. As for the demonstrated influence of experimentalerrors in the shift difference method one should consider a possible influence of variation in the concentration of the internal reference. We were made to realize this aspect by one of the reviewers. Perhaps, a part of some experimental errors in ref 9 might be caused by holding neither this concentration nor [A,,] sufficiently constant. Acknowledgment. This work was supported by the Deutsche Forschungsgemeinschaft. This support is gratefully acknowledged. We thank one of the reviewers and Professor Milton Tamres, Ann Arbor, for many suggestions which helped to improve the manuscript. Registry No. NBASbenzene, 65646-04-0; DNBSbenzene, 3101-95-9.
Rate Constant for the Gaseous Reaction between Hydroxyl and Propene Roland H. Smith School of Chemistry, Macquarie University, North Ryde, New South Wales 2113, Australia (Received: June 15, 1982)
Discharge flow with resonance fluorescence monitoring of hydroxyl has been used to measure the rate constant for OH + C3H6at five temperatures in the range 255-458 K. A t 298 K the rate constant k l is (1.9 f 0.3) X cm3s-l where the quoted error includes both systematic and statistical components. While it has been established that at 298 K pressures of 0.9 and 3 torr are in the limiting high-pressure region for this addition reaction, the strongly negative temperature dependence observed at these pressures, described by either k , = 1.59 X exp(1470/T) cm3 s-l (with 18% accuracy) or k l = (2.3 X (T/300)-*.*cm3 s-l (with 25% accuracy),has been used t o infer that at the higher temperatures these pressures are within the falloff region. Results are compared with previous measurements.
Introduction Three recent flash photolysis measurements of the rate constant for the reaction C3H6+ OH product (1)
-
have produced values of 1011kl/(~m3 s-l) at 298 K which agree with one another: 2.51 f 0.25 by Atkinson and Pitts,' (1) R. Atkinson and J. N. Pitts, J . Chem. Phys., 63, 3591 (1975).
0022-3654/83/20871596$01.50/0
2.56 f 0.12 by Ravishankara et a1.2 (both groups using resonance fluorescence), and 2.46 f 0.28 by Nip and Paraskevopo~los~ (using resonance absorption). However, three earlier discharge flow measurements of 10llkl disagree with one another and two are significantly different (2) A. R. Ravishankara, S. Wagner, S. Fischer, G. Smith, R. Schiff, R. T. Watson, G. Tesi, and D. D. Davis, Int. J. Chem. Kinet., 10,783 (1978). (3) W. S. Nip and G. Paraskevopoulos, J . Chem. Phys., 71, 2170
(1979).
0 1983 American Chemical Society
