792
D. L. De Fontaine, D. K. Ross, and B. Ternal
(19) W. C. Baily and H. S. Story, J. Chem. Phys., 60, 1952 (1974). (20) S. Engstrom, H. Wennerstrom, B. Jonsson, and G. Karlstrom, to be submitted for publication. (21) H. Gustavsson, G. Lindblom, B. Lindman, N.-0. Persson, and H. Wennerstrom in “Liquid Crystals and Ordered Fluids”, Vol. 2, J. F. Johnson and R. S. Porter, Ed., Plenum Press, New York, N.Y., 1974,
p 161. (22) N. 0. Persson and B. Lindman, Mol. Cryst. Liquid Cryst., In press. (23) D. Bailey, A. D. Budtingham, F. Fujlwara, and L. W. Reeves, J. &gn. Reson., 18, 344 (1975). (24) F. Fujiwara, L. W. Reeves, and A. S. Tracey, J. Am. Chem. Soc., 96, 5250 (1974).
Two Improved Methods for the Determlnation of Association Constants and Thermodynamic Parameters. The Interaction of Adenosine 5’-Monophosphate and Tryptophan D. L. De F o n t a h , + D. K. Ross, and
B. Ternai’
La Trobe University, School of Physical Science, Bundmra, Vlctoria 3083, Australla (Recelved November 8, 1976)
A refinement of the Scatchard method for the determination of association constants in 1:lcomplexes is presented which is not restricted by assumptionson the relative concentrationsof the components. A temperature variation method is developed which is shown to yield accurate values of the association constant and thermodynamic parameters from one set of measurements using a smaller sample than is required by other methods. For a 1:l complex formed by two species A and B we have the equation A+B+AB
and, in the equilibrium situation, we can define the association constant ( K ) which represents the proportion of complex formed. Thus where [XI, is the concentration of compound X at equilibrium. Now, let Ai and Bi be the initial concentration of A and B, respectively, and let p denote the fraction of A which is complexed. Then Ai - pAi is uncomplexed and eq 1 can be written in the form PAi P (2) (Ai - pAi)tBi - PAi) - (1 p)(Bi - PAi) where B has an equal or larger concentration than A. Now the fraction of Ai which is complexed at equilibrium can be identified with the ratio 6J6, where Si is the difference between a measured parameter such as a NMR chemical shift or an extinction coefficient of the completely uncomplexed A and the partially complexed A. Here 6, is the difference between the values of the parameters in the completely complexed and the completely free A. The former value cannot be measured directly but is usually obtained by a graphical method. Thus, we write
K=
which is known as the Scatchard equation. K could be obtained from the slope and hence 6, from the intercept of a straight line fit of the experimental data vs. Si). Prior to Scatchard‘s treatment, values of K and 6, were usually found by using the reciprocal form proposed by Benesi and Hildebrand3
1
1
1
I
(3) Scatchard has reported’ a method for calculating the association constant when the initial concentration of one species is very much in excess of the other. Therefore, if Bi >> Ai, then (2) and (3) can be combined to give
P = fiilfic
6, =
A slight rearrangement of this equation leads to SJBi = K(6, Si)
KAi
+ other terms in Ai/&
leading to Person’s absorption isotherm’
1
Present address: Faculty of Medicine, Riyadh University, Riyadh, Saudi Arabia. The Journal of Physlcal Chemlstry, Vol. 81, No. 8 , 1977
and fitting a straight line to the experimental data (6&) and so obtaining (1/K6,) which is the slope and 1/6, which is the intercept. In an alternative procedure, Scott4plotted a straight line through the data given by (Bi/6i,Bi)in which case the slope is (1/6,) and the intercept is (l/K6,). Thus his equation is B. Bi 1 A=Si 6, KS,
+-
These two methods are clearly mathematically equivalent, and both de end upon the initial condition Bi >> Ai. Deranleau points out that the Scatchard equation is the best method of the three for two reasons: (1)it is the only plot in which the errors are not open ended, and there is a constant error function between S = 0.2 and S = 0.75 where S is the saturation fador or the fraction of the total curve followed; and (2) it is the only method where the experimenter is not free to choose the scale for the plot, and it is obvious at a glance what portion of the complete curve has been covered (Figure 1).
B
Results and Discussion Since the advent of computer technology, it has become possible to refine the methods of Scatchard, Benesi-
793
Determination of Association Parameters
THE SCOTT PLOT
THE B E N E S I - H I L D E B R A N D PLOT
T H C SCA‘CHAFD _______
PLOT
Flgure 1. A comparison of the Scatchard, Benesi-Hildebrand, and Scott data treatments taken from ref 5.
Hildebrand, and Scott which are based on the fitting of straight lines to experimental data. The requirement that Bi >> Ai can be dropped and the full association equation (eq 2) can be used. Some non-linear least-squares methods in the determination of association constants have been mentioned in the literature.6 On combining eq 2 and 3, it can be shown that
+
Si= (6,/2Ai)[Ai + Bi t ( l / K ) - {[Ai Bi t (l/K)]’ - 4AiBi}”2] (4) where the negative root is appropriate because Ji/6, < 1. At this stage it is convenient to write 1, = Ai
+ Bi + (1/K) - {[Ai t Bi t (l/R)]’
- 4AiBi}”2
(5) The object of the exercise is to determine the constants K and 6, for which the above eq 4 “best” fits the experimental data. The convention is adopted here that the “best” fit is the least-squares fit and this is defined so that
E
= j= 1
[Si - 6,1i/2Ai]*
is a minimum and where the summation is taken over all the experimental points. Thus, both aE/a& and aE/aK should vanish. The first of these leads ,to the condition
S,Cli2/4Ai2= CSili/2Ai and the second to the condition li’ *“2Ai{Ai + Bi + (1/K) - Zj)
(6)
(7) Hence, on eliminating a,, a transcendental equation for K
is obtained. The value of K can be calculated by using a numerical technique7which is a combination of the method of “false position” and the method of “trisection”. A printout of the program is available from the authors. It should be recalled that these equations all apply only if 1:l complexes are formed. To test this it has been common practice to first obtain a Job plotaigunless there is reason to assume a 1:l complex initially. The relative concentrations of A and B are varied uniformly from 100% A through to 100% B, and one particular resonance is followed. For a 1:l interaction, the Job plot has a maximum at 0.5 when [Alai is plotted against mole fraction. The greatest source of error when using concentration dependence to calculate K must lie in the preparation of samples, simply because each point on the concentration shift curve represents a different sample. If greater accuracy is required, the number of points must be increased and hence if expensive or inaccessible materials are to be used this requirement may (a) preclude the repetition of the experiment and/or (b) necessitate the use of dilute samples. A Variable Temperature Method. In an attempt to overcome these difficulties, a different method to obtain the association constant was sought. As part of an extended NMR investigation, the interaction of A and B where a t least one component contained an aromatic moiety, Le., hydrophobic bonding, or 7r-r interactions were present, was of interest to us. Laszlo and Williams” reported an instance in which the association constant, K , was calculated by following the chan e in chemical shift as a function of temperature. Others1’- have also followed similar variable temperature procedures to determine K and thermodynamic parameters. The concept, at first glance, appears simple: protons within the complex which are located above the aromatic portion of an adjacent molecule experience an upfield shift in the NMR spectrum compared with the situation in the absence of the interaction. As the temperature is lowered, there is an increase in the chemical shift difference between the uncomplexed and partially complexed situations. This is consistent with the fact that at lower temperatures, molecular mobility, on the average, is less, and hence there is a greater degree of association present. As low solute concentrations are used, the solution viscosity can be ascribed entirely to the solvent, which in the present situation is water. Although the viscosity of water changes from approximately 9 mP at 20° to approximately 3.4 mPI5 at SOo, this change is not significant when using the temperature variation method, as the chemical shift due to complex formation a t each temperature is determined from two solutions (one containing A and B and the other only one of these) of virtually the same viscosity. Therefore, raising the temperature can be thought of as the converse of adding an excess of one component (as is done with the concentration dependence method). Laszlo and Williamslo considered solvent-solute interactions. Here, eq 2 is applicable, where & is substituted for a,, and as the concentration of A and in particular B are maintained constant, these symbols are not subscripted. Thus, in the variable temperature method, eq 2 is the governing equation, as it is for the concentration method, but with the difference that now p = &/ac. Here at represents the difference in chemical shift of a particular resonance (or another suitable parameter, e.g., UV absorbance, etc.) in A at a given temperature when in the presence of B (i.e., 8A+B) and in the absence of B (i.e., 6A), Le., at = 6A+B - 8A.
Q
The Journal of Physcal Chemkitw, Vol. 81, No. 8, 1977
D. L. De Fontaine, D. K. Ross, and B. Ternai
704
\"2
I\.
30
0 1 " " ' " ' " " " ' l 16 20 24 28 32 36 40 44 48 52 56 60 6 L 68 -2
78 80
TEMP('C)
Figure 2. The variable temperature plot of the differences in chemical shifts of a mixture of AMP and tryptophan methyl ester HCI, compared with AMP only. 0.01 M AMP and 0.25 M tryptophan at pH 7 were used.
Mole Fraction of T r y p l o p h a n
Figure 4. The Job plot for the interaction of AMP and tryptophan at 21 O C , pH 7.
TABLE I: A Comparison of the Association Constants ( M - l , 21 C) as Determined by Concentration and Temperature Variation Methods for the AMP-Tryptophan Interaction Position
Figure 3. The concentration dependence of the chemical shifts of the AMP base protons from the interaction of AMP and tryptophan methyl ester HCI at 21 OC, pH 7. 0.01 M AMP was used.
A suitable example which may be considered here is the interaction of tryptophan and adenosine 5'-monophosphate (AMP); this and similar interactions have been studied by HBlbne and D i m i c ~ l i ~and ~ ~others,18-20 ~' and hence the complex formation between these solutes is fairly well understood. The 'H resonances of AMP, i.e., H-8, H-2, and anomeric, were followed principally because these resoThe Journal of Physical Chemistry, Vol. 8 I , No. 8 , 1977
Method
H-2
H-8
H, ' (anomeric)
Concentration Temperature
6.36 1.15
4.07 2.45
5.96 1.13
nances (cf. tryptophan) were sharp, well separated, and the protons were, fortunately, well distributed around the heterocyclic rings. The 6t vs. T (the chemical shift difference between the complexed and free forms of AMP vs. temperature for the AMP-tryptophan interaction) plots are shown in Figure 2. The 6i vs. ratio of tryptophan/AMP plots (concentration method) are shown in Figure 3. As the previously mentioned equations for calculating the association constant only apply to 1:l complexes, it is necessary to check the molecularity of the association. Therefore, a Job plot at 21 "C was obtained (Figure 4). As the curves were symmetrical about the concentration ratio of 0.5, the association was considered to be 1:l. Foster21 suggested that the Job plot was not always capable of distinguishing between interactions of different stoichiometry but HBl6ne and Dimicoli2' used the Job method to show that in acidic media, due to the changes borne by the solutes, the interaction between tryptophan and adenosine (compared with tryptophan and cytidine) contained some 2:l as well as 1:l complexes. It can be seen that the concentration-shift curves have an asymptote to a 6,, but it is not clear from the temperature curves what temperature should be considered to give the correct 6,. The technique Laszlo and Williams used to solve this problem was to extrapolate their 6, vs.
795
Determination of Association Parameters
2624.
22. 20. 18. 16.
4
z 04-
14. 12. 10.
08 ' i
'
"
"
"
'
'
Figure 5. 200-
TABLE 11: The Chemical Shift Changes (Hz) which Would Occur in the Fully Bound Complexes (Concentration Compared with Temperature Methods) for the AMP-Tryptophan Interaction Position
Method
H- 2
H-8
HI' (anomeric)
Concentration Temperature
64.5 152.5
57.8 89.0
45.7 107.2
180 -
160
140.
s 120.
B
gC (temperature)
\ \ \ \ \
100 -
\
.-. \
\
80-
\
\
/Sc
40
'\
\
observed range \\-
~
20.
(concentr at ion )
\
60.
T curves back to 0 K, assume that the shift so obtained was in fact that of the fully associated complex, and to calculate K from this value. If their treatment is followed, the K values shown in Table I are obtained. It is also of interest to note the corresponding ais, i.e., the shifts in the fully bound complexes (Table 11). I t is clear that the association constant as determined from the temperature variation method is significantly smaller than that from the concentration method, and conversely, that the extrapolated 6, shifts from the temperature method are much larger than those from the concentration method. The magnitude of K depends on 6i (or 6,) and 6,. As 6210c(temperature method) is actually one point on the concentration curve, and these agree, therefore the point of disagreement between the two methods is most likely to be 6, (temperature). In case the molecularity of the association should change with temperature, a Job plot at 11 "C was also obtained (Figure 5). Once again the maxima are at concentration ratio 0.5, indicating a 1:l association. In addition, a check on the pH as a function of temperature was made, and it was found that the variation in pH was within the accuracy specifications of the pH meter. Hence, undue errors in the chemical shifts as a result of pH changes should not be present. If the extrapolation back to 0 K is considered, the presence of a very slight curvature in the chemical shift-temperature plot within the observed relatively narrow temperature range, as compared with a straight line variation, could lead to a very large error in the estimation of 6, (Figure 6). Thus, as the extrapolation back to 0 K appears to overestimate 6,, this step should not be used in the calculation of K. Hence, there is a very real problem in calculatin the correct value of 6,. Abraham' did not explicitly calculate the association constant, but eliminated K from a series of equations, and simultaneously matched the chemical shift-temperature data with the three parameters, 6,, AH, and AS. Procedures such as these, where a number of parameters are
i/
\
extrapolated range
01 -273
L
-173
-73
+27
+77
TEMP ('C)
Flgure 8. The chemical shift-temperature plot for H-2 in the AMPtryptophan Interaction, showing the relation between the observed range and that when an extrapolation to 0 K is carried out.
simultaneously solved, are prone to significant error. A more common procedure whenever temperature has been used in the context of association constants in the l i t e r a t ~ r e ~ ~has - ~ ~been - ~ ' to perform a series of concentration dependence experiments at different temperatures, and hence calculate K a t these temperatures. From this, AH (the enthalpy of the interaction) and AS (the entropy of interaction) can be obtained. The relationships between the various thermodynamic parameters arez8
A G = -RT In K
(8)
and
AG
=
AH - TAS
(9)
Thus l n K = - -A- -S
R
AH RT
where AG is the free energy of interaction, and R is the gas constant. Therefore, for a constant value of AS, plots of In K vs. T'(van't Hoff plot) should be approximately linear, with a slope of -AH/R. (The plot will be linear provided AH is independent of temperature.) In order to ascertain the effect of 6, on the linearity of the In K vs. T' plot, and using the temperature-shift data of H-2 from the AMP-tryptophan interaction, the corThe Journal of Physlcal Chemlstty, Vol. 87, No. 8, 1977
706
-5
D. L. De Fontalne, D. K. Ross, and B. Ternal
TABLE 111: The Calculated 6 ,and Association Constants (21 " C) for the AMP-Tryptophan Interaction, as Derived from the Variable Temperature Method (Using the Linearization of the van't Hoff Plot)
,994-
L
Y
u
,993 -
Position
L
al
992-
H-2
C
Fz
c
Q
,991 -
fi,
I I
io
60 100 150 sc ( Hz.) Flgure 7. The 6, vs. correlation coefficient curve for H-2 of the AMP-tryptophan Interaction, showing a maximum at approximately 65 Hz.
relation coefficient (r) for eight cases were calculated with the following results: Hz, r = 0.9585 (2) 6, = 40.0 Hz, r = 0.9875
(1) 6,
= 35.0
(3) 6, = 50.0 Hz, r = 0.9935 (4) 6, = 64.5 Hz, r = 0.9940 (5) 6 , = 80.0 Hz, r = 0.9934
(6) 6, = 100.0 Hz, r = 0.9927 (7) 6 , = 152.5 Hz, r = 0.9916 (8) 6, = 1600.0 Hz, r = 0.9911 Cases 4 and 7 represent the 6, values as determined by concentration and temperature dependence (0 K extrapolation), respectively. A plot of 6, vs. r forms a curve of the type shown in Figure 7, and it appears that the value of 6, at which maximum correlation between In K and T' is achieved is 6, 65 Hz. The relationship between 6, and r suggests that a possible method to calculate 6, from variable temperature
-
'
57.9 6.60
Hz
K , M-I
.990L I O 20 30 40 50 60
A.MP
994162-
t
60.
- ..
AMP
t
Tryptophan
anorneric
H2 a.
58 56r,
54. 52 50 48 -
,994146'
:'
56
I t35t
,99838
io
59
&c(Hz) d A M P +Tryptophan
.... .... .. * .. *
..
37
(r)
58
57
*..
H2
,998471
,996697r
39
40
41
Sc(Hz )
42
43
G,A +Tryptophan , ,.* H2 '
.. ...
36
.998341
I
51
52
53 54 Sc(Hz)
55
54 55 Sc(Hz)
56
57
Flgure 8. Correlation Coefficient (4 vs. 6, (from temperature data) for a number of amino acid-nucleotide combinations. The Journal of Physical Chemistry, Vol. 81, No. 8 , 1977
Hi' anomeric 41.5 5.60
data would be to assume an initial value for 6, and obtain the correlation coefficient for the relationship In K vs. T1. Then, the value of 6, could be varied until the maximum value of the correlation coefficient is found. To ascertain if this procedure does yield a unique value for 6, a detailed computer listing of the 6, vs. r values in the region of r (maximum) was generated and plotted (Figure 8) for a number of cases. I t is obvious that there is, usually, noise about the maximum point (because increments in r are very small compared with increments in 6,) and, in addition, that in the region r,, f2 Hz the curve can be approximated by a parabola. In general it was found that parabolic curve fitting resulted in a shift in 6, of not more than 0.5 Hz from the value obtained without it. The 6, and association constant values for the three base positions in AMP in the AMP-tryptophan interaction as determined by the linearization of the van't Hoff plot are listed in Table 111, and Figure 9 shows the plot of In K vs. T 1for AMP + tryptophan (H-2 resonance). Varying 6, to improve the linearity of In K vs. T 1is in effect the same as optimizing the value of AH which satisfies the data, and comparisons of Tables I, 11, and I11 indicate that this is indeed a valid method for the determination of K. Prior to this method of 6, (temperature) determination, the K values were far too low and 6, values too large when compared with the corresponding values obtained by the concentration method. While it is not necessary that the 6, (temperature) values should agree with 6, (concentration)
Tryptophon ..e.*
H- 8 54.2 3.17
787
Determination of Association Parameters
1.8
16 1.4 1.2
In K
1.o
.8 .6 .4
.2
-2Y 28
'
29
20
31
+
32 %lo-'
33
34
35
I
36
Flgure 9. The van7 Hoff plot for the H-2 resonance of the AMPtryptophan interaction.
TABLE IV: A Comparison of t h e T h e r m o d y n a m i c Parameters for t h e I n t e r a c t i o n between A M P and T r y p t o p h a n a t 25 " C as Determined by Moritaa and from t h e Present W o r k
(a) M o r i t a a (b)Presentwork
-AH, kcal/ mol
cal/mol deg
-AS,
1.28
6.8
18.5
H-2
1.02
HI'
0.96 0.70
6.7 6.7
19.0 19.3
2.6
6.6
H-8 a
-AG, kcal/ mol
Reference 18.
exactly as, after all, the physical processes involved are different, the agreement should be better than that obtained when extrapolation to 0 K is used, if K values are to agree at all. Considering the H-2 resonance in AMP, the K value (concentration) is 6.36 M-l, compared with 6.60 M-l via linearization of the van't Hoff plot and 1.15 M-' via extrapolation to 0 K. Figure 10 shows the correlation of K as determined by concentration variation compared with the two methods of temperature variation (linearization of In K vs. T-' and extrapolation to 0 K) for a number of different amino acid-nucleotide combinations. It is clear that the agreement between the association constant as determined by (a) concentration variation and (b) that determined by optimization of In K vs. T1is much better than between (a) and (c) when the chemical shift is extrapolated to 0 K to give 6, by temperature variation. Morita18 used UV spectroscopy to determine the association constant, and hence AG, for AMP + tryptophan. In addition, AH and A S were determined from the traditional van't Hoff plot. For comparison purposes, Table IV lists the values of AG, AH, and A S at 25 "C for the interaction (a) as determined by Morita, and (b) as determined by us. The values of AH and A S for H-2 and H{ are in surprisingly good agreement with Morita's work. The correlation coefficient for the van't Hoff plot for H-8 is significantly poorer than for H-2 or H1' (0.988 compared with 0.998) and this may explain the lack of agreement between AH and A S for H-8 and the other positions within AMP. The association constant at 25 "C as calculated by Morita is 8.67 M-l, and from the present work (H-2) is 5.62 M-l. Morita used UV spectroscopy and, with that technique, the association constant and thermodynamic parameters are determined for the molecule tw a whole. This is compared with the NMR method, where these values are determined for different positions within the molecule.
OV' ' 0
2
'
'
4
'
'
6 Kcon,,
'
' 8
'
'
10
'
'
12
( Ih o l e )
Flgure 10. The correlation of Kdetermined by concentration variation compared with the two methods of temperature variation for a number of tryptophan-amino acid interactions: (0)represents the linearization of the van't Hoff equation; (0)represents the extrapolation to 0 K, and the straight llne indicates the position of exact correlation between association constants determined by concentration compared with temperature methods. The number refers to the following sites in tryptophan-amino acid interactions: GpA (1) A-8 (2) A-2 (3) A-anomeric, dAMP (4) A-8 (5) A-2 (6) A-anomeric; AMP (7) A-2 (8) A-8 (9) Aanomeric.
As the values of AH and A S (H-2 and H{) from the two techniques agree so well (compared with the association constants or AG), this might indicate that AH and A S as determined via NMR may be applicable to the interaction as a whole, as compared with K values which refer to particular positions within the molecule. Therefore, depending on the information required, it is possible to determine the association constant with equal validity by varying the concentration or the temperature and, in general, if AH (and AS, AG) is required, the determination of K by the variable temperature method would require less expenditure of effort and, from the point of view of sample preparation, would possibly involve less error. A computer program is available from the authors upon request.
Experimental Section All chemical shift work was performed on a JEOL PFT-100 NMR spectrometer with D20solvent supplying the deuterium lock. A Metrohm precision compensator E388 was used to measure the pH. Adenosine 5'-monophosphate sodium salt and L-tryptophan methyl ester HC1 were obtained from Sigma Chemical Co. Both were of high purity and used without further purification. Deuterium oxide (99.75%) was obtained from the Australian Atomic Energy Commission, and solutions were adjusted to pH 7 with citric acid-phosphate buffer. The association constant determinations (concentration variation) were carried out at the NMR probe temperature (21 "C) and the temperature was controlled by the built-in variable temperature accessory, and calibrated with standard samples. It is estimated that the stated temperatures are accurate to i l "C. AMP (2 mg/0.5 mL) was used in both the concentration and temperature variation methods. When determining the association constant by the concentration method, the ratio of tryptophan/AMP was varied (the concentration of AMP was constant), and the chemical shift of the AMP resonances were noted. Acetonitrile was used as an internal reference (6 = 2.02). The Journal of Physical Chemistry, Voi. 81, No. 8 , 1977
798
K. Ohbayashi, H. Aklmoto, and I.,Tanaka
A 1:l sample of AMP:tryptophan gave chemical shifts which were considered too small to be used accurately, i.e., the proportion of complexed AMP/ tryptophan was relatively small. Therefore, for variable temperature work, samples were prepared in which the ratio of AMP:tryptophan was 1:25. References and Notes (1) G. Scatchard, Ann. N.Y. Acad. Sci., 51, 660 (1949). (2) W. B. Person, J. Am. Chem. Soc., 87, 167 (1965). (3) H. A. Benesi and J. H. Hildebrand, J. Am. Chem. Sac., 71, 2703 (1949). (4) R. L. Scott, Red. Trav. Chim. Pays-Bas., 75, 787 (1956). (5) D. A. Deranleau, J. Am. Chem. Soc., 91, 4044 (1969). (6) J. A. Ibers, D. V. Stynes, H. C. Stynes, and 8. R. James, J Am Chem SOC.,96, 1358 (1974). (7) F. S. Aston, “Numerical Methods That Work’’, Harper and Row, New York, N.Y., 1970. (8) P. Job, Compt. Rend., 180, 928 (1925). (9) R. Sahai, 0. L. Loper, S. H. Lin, and H. Eyrlng, Proc NatL Acad Sci. U.S.A., 71, 1499 (1974). (10) P. Laszlo and D. H. Williams, J. Am. Chem. Soc., 86, 2799 (1966).
(11) (12) (13) (14) (15) (16) (17) (18) (19) (20) (21) (22) (23) (24) (25) (26) (27) (28)
R. J. Abraham, Mol. Phys., 4, 369 (1961). J. V. Hatton and W. G. Schneider, Can. J. Chem., 40, 1285 (1962). J. N. Murre11and V. M. S. Gill, Trans. Faraday Soc., 61, 402 (1965). S. Wold, Acta Chem. Scand., 25, 336 (1971). E. W. Washbum, Ed., “International Crkical Tables of Numrlcal Data, Physics, Chemistry, and Technobgy”, Vol. V, McGrawWll, New Yolk, N.Y., 1929, p 10. J. L. Dimlcoll and C. HBiBne, Blochimie, 53, 331 (1971). C. HWne, T. MontenayOarestier,and J. L. Mmicoli, 8bchim. Bkphys. Acta, 254, 349 (1971). F. Morita, Blochim. Biophys. Acta, 343, 674 (1974). K. 0. Wagner and R. Lawaczeck, J. Magn. Reson., 8, 164 (1972). M. GuBron, C. Chanchaty, and T. D. Son, Ann. N . Y . Acad. Sci., 222, 307 (1973). R. Foster, Ed., “Molecular Complexes”, Vd. 11, Elek. Sclence, London, 1974. J. L. Dimlcoli and C. HBIBne, J. Am. Chem. Soc., 95, 1036 (1973). I. D. Kuntz, Jr., and M. D. Johnson, Jr., J. Am. Chem. Soc., 80, 6008 (1967). D. R. Eaton, Can. J. Chem., 47, 2645 (1969). V. Balevichlus and L. Kimtys, Org. Magn. Reson., 6, 180 (1976). H. L. Llao and D. E. Martire, J. Am. Chem. Soc., 96, 2058 (1974). J. B. Homer and M. C. Cooke, J. Chem. SOC. A , 2862 (1969). F. C. Andrews, “Thermodynamics: Principles and Applicatlons’ , Wley-Interscience, New York, N.Y., 1971, p 225.
Emission Spectra of CH30, C2H50, and i-C3H70Radicals Keljl Ohbayashi, Hajlme Aklmoto,’ and Ikuzo Tanaka’ Department of Chemistry, Tokyo Institute of Technology, Ohokayama, Meguro-ku, Tokyo, 152, Japan (Received March 19. 1976; Revised Manuscript Received February 7, 1977)
Emission spectra of CHSO, C’HbO, i-C3H70, and NO are obtained in the photolysis of corresponding alkyl nitrites by iodine, mercury, xenon, and krypton lamps. The excitation thresholds to produce RO fluorescence are also determined as 6.02 eV (CH30),5.90 eV (C&O), and 5.82 eV (i-C3H70).The (0,O)band of the electronic transition of CH30 between the ground state and the first excited state is estimated to lie near 305 nm. The ratios of electronic quenching rates to fluorescence rates of RO with 13 foreign gases are determined and from the self-quenching rates the fluorescencelifetimes are estimated as follows: -3 1.18 (CH30),-1 ps (CzHbO),and
Introduction Alkoxy1 radicals are supposed to be important intermediates in the combustion and hydrocarbon oxidation processes.’ However, the spectroscopic information has been scarcely obtained thus far even for the prototype alkoxyl radical, CH30. The near ultraviolet photolysis (300 < X < 400 nm) of alkyl nitrites in the gas phase has been considered to produce alkoxyl radicals in the major primary process3 R O N 0 t hu -+ R O t NO (1) However, although first ascribed to CH30,4the transient species whose absorption spectrum was observed in the flash photolysis of methyl nitrite was later reassigned to HNO which would be formed in the secondary p r o c e ~ s . ~ Thus the absorption spectra of CH30 and higher homologues have not been found. Emission spectra were first observed by Style and Ward6 in the photolysis of CH30N0 and C2H50N0 using a hydrogen continuum lamp. The species giving the emission bands in the near-ultravioletto visible region were proposed to be CH30 and CzHbO, respectively. In order to establish the fluorescence of alkoxyl radicals, the emission spectra in the photolysis of CH30N0, C2H60N0, i-C3H70N0, and t-C4HgON0 using iodine (206.2, 187.6 nm), mercury (184.9 nm), xenon (147.0,129.5 The Journal of Physlcal Chemistry, Vol. 81, No. 8 , 1977
nm), and krypton (123.6, 116.5 nm) lamps as well as a deuterium continuum lamp were investigated. Photolysis by the iodine or the mercury lamp gave the emission spectra between 290 and 450,330 and 500, and 360 and 520 nm for CH30N0, CzH50N0 and i-C3H70N0, respectively. From the threshold energies of the exciting photons required to give the emissions, the emitters are most likely the first electronically excited states of CH30,CzHbO, and i-C3H70,respectively. No emission was observed when t-C4HgON0was photolyzed by the iodine or the mercury lamp. When these nitrites were photolyzed by the xenon or the krypton resonance lamp, 6 and y bands of NO were observed but no emission of alkoxyl radicals was observed. The ratios of electronic quenching to fluorescence rates for the excited CH30, CzH50, and i-C3H70radicals by 13 foreign gases were obtained. Experimental Section Methyl, ethyl, and isopropyl nitrites were prepared by the dropwise addition of 50% H2S04to saturated solutions of NaNOz in methanol, ethanol, and 2-propanol, respectively. They were purified by gas chromatography (column, dimethylsulfolane),degassed, and stored in darkened traps at -80 “C. Commercially available tert-butyl nitrite (Tokyo Kasei Co.) and ethyl nitrate (Tokyo Kasei Co.)
