- Email: [email protected]
Association constants and nmr association shifts for several chloroform-base hydrogen-bonded complexes
.IOIRK:,l.
OP RIO,.E~‘III.AR
SPECTROSC’OI’T
Association Constants Several Chloroform-Base BENTZ
B.
HOWARD,CHARLES
10,
115-130
(1’363)
and nmr Association Shifts for Hydrogen-Bonded Complexes* F. JI‘MPER,t
AND
~UERLE
T. EMERSON~
The chemical shifts of chloroform in solutions with several hydrogen bonding bares in either cyclohexane or carbon tetrachloride as solvent were measured at 25” with a precision of fO.002 ppm. Chloroform-base association const,ant.s and association shifts were calculated by fitting the data using an 1RM 709 nonlinear least squares program. Corrections were applied for the effects of dispersion interaction and self- and solvent association. Listing the Ijase, association con&ant, and association shift in ppm to low field in t.hat order, the resulting values are: triethylamine, 1.70, 1.472; diethgl ether, 3.76, 0.905; diethyl ether, 1.46, 1.266;isopropyl ether, 2.06, 1.126; acetonitrile, 1.14, 0.973; acetone, 2.07, 1.419; and pyridine, 1.90, 2.271. The first t,wo are in cyclohesane, t.he rest in CC14 The difference between the association constant,s of dietjhyl ct.her in the two solvents is nokd as being anomalously large. The effect, of the anisotropy of the base can readily be seen in the association shifts of the Ijyridine and acet,onitrile complexes.
Hydrogen bonding association constants have heen studied systematically in relat,ively few instances; where comparison is possible, values in the literature are not in \-cry good agreement with each other (I). The measurement of nmr chemical shifts, however, has been shown to be a powerful tool in this field (2). It has been used to study the association of some alcohols (:I), certain carbosylic acids (If), pyrrole and pyrrole-pyridine (j), and chloroform lvith several bases (6). The combination of the sensit.ivity of t,he chemical shift. to hydrogen bon& ing and the high precision attainable in its measurement gives nmr an advantage * This work was support.ed in part by a grunt from the Research Corporation, ill p:trt 1,~ a cant ract, Sth the U. S. Air Force Office of Scient.ific Resrarch, and in part, by :I cont.r:tct with the 1)ivision of Biology and Medicine, U. S. Atomic Energy Commission. t Sllbmittrd in partial fulfillments of requirements for the degree of I)octor of Philosoph) in chemistry :It, Florida Statp ITniversity. Present address: lkll Telephone I,aborat,ories, Murray Hill, New Jersey. 1 l’rrsent atldress: Ikpartment of ( hemistry, W;~.VIX~State IYniverFity, l)et,roit, ILlich~ igan. 117
118
HOWARD,
JUMPER,
AND
EMERSON
over older techniques used for quantitative studies, although the inability to detect very low concentrations is a disadvantage. The difference in the chemical shift between the bonding proton in its associated and unassociated form is of considerable interest in itself, since it is possible to derive theoretical estimates of this quantity from models of hydrogen bonding systems (7), and also since it has been proposed as a possible measure of hydrogen bond strength (8). Chloroform has several advantages as a choice as a proton donor: (1) It presumably forms only one-to-one complexes. (2) The association constants are in a convenient range for study by this technique. (3) The complications due to self-association are not serious. The original impetus for this work was the need for reliable association constants of some chloroform-base complexes for use in the determination of their dipole moments; this part of the research will be presented in a future article (9). In this work we evaluate association constants and association shifts for chloroform with triethylamine, diethyl ether, isopropyl ether, acetonitrile, acetone, and pyridine in the solvents carbon tetrachloride or cyclohexane. II. EXPERIMENTAL
Alcohol was removed from spectrograde chloroform with concentrated sulfuric acid (10) and subsequent washing and drying shortly before use. After preliminary drying, spectrograde acetone, acetonitrile, pyridine, and analytical grade triethylamine were treated with Linde 4 A molecular sieve to remove the final
FIG. 1. Examples of the change of the proton chemical shift of CHC13 as a function of solvent-base composition, measured at 25” on a 40 Mc/sec spectrometer, relative to cyclohexane as an internal standard. Circles represent 0.50 M CHC13 in triethylamine and cyclohexane. Triangles represent 0.37 M CHClz in diethyl ether and CC14 .
CHCl,-BASE
ASSOCIATION TABLE
I
C)R~ERVED AND CORRECTED PROTON CHEMICAL SHIFTS FOR C~ci, CYPLOHEXANE SOLUTIONS AT 25" RELATIVE TO INTERNAL
- &,h (ppm) 5. G585
5.8875 6.0143 6.1028 6.2225 6.2960 6.3200 5.6655 5.8838 6.0125 6.0983 6.2158 (i.2910 6.3178 5.6780 5.8650 5.9980 Ci.0865 (i.2Ofi5 (i .2823 (i .3125 5.7045 5 .8500 5.9fi4.3 Ii. 0545 li. 1808 fi.2’55 d I (i .2(i33
- 6 (ppm) ~__ 5.6578 5.8883 6.0165 6.1065 6.2293 6.3058 6.3313 5.6643 5.8840 G.0143 6.1018 6.2220 6.3003 6.3288 5.6760 5.8645 5.9990 6.0890 6.2123 6.2910 0.3225 5.7005 5.8478 5.9633 Ii.0550 6.1843 6.2330 6.2700
I l!)
BY NMR
IN L)IETH~L CYCLOHESANE
ETHICR-
mcu (moles)
nf;) (moles)
n,” (moles)
0.024783 0.024783 0.024783 0.024783 0.024783 0.024783 0.024783 0.037305 0.037305 0.037305 0.037305 0.037305 0.037305 0.037305 0.061808 0.061808 0.061808 0.061808 0.061808 0.061808 0.061808 0.12386 0.12386 0.1238G 0.12386 0.12386 0.12386 0.12386
0.0 0.047428 0.095236 0.14073 0.23904 0.33337 0.37940 0.0 0.047839 0.095291 0.14221 0.23821 0.33327 0.38181 0 0
0.044131 0.39458 0.34915 0.30502 0.21055 0.12026 0.076400 0.43148 0.38551 0.3398ri 0.29460 0.20210 0.11198 0.065610 0.41315 0.36943 0. -32207 0.2761-I 0.18502 0.094156 0.049383 0.36(i!Xi 0.32338 0.277GO 0.23191 0.110!)6 0.09631 0.05113
0.045772
-
0.094667 0.14277 0.23832 0.33390 0.38009 0.0 0.04611 0.09443 0.14237 0.23797 0.28571 0.33300
of water. Analytical grade diethyl ether was fractionally distilled from sodium wire and isopropyl ether from P&L. Spectrograde solvents C(& and csyclohexane were used without further purification. For each lease, a total of from 21 to 40 solutions were prepared by weight, the concentration of chloroform always being kept below about 0.1 mole fraction. This minimizes the possibility of two chloroform molecules complexing to a single base molecule; furthermore, the corrections for self-- and solvent assoriation art a less significant fraction of the total shift when the stoichiometric concentration of chloroform is kept small. The base concentration was varied from zero to almost pure base. When CC14 was the solvent, approximately 0.005 mole fra&on cyclohcxane was present in each solution to serve as internal reference. ?Y’mr samples consisted of approximately 0.5 ml of solution in a 5 mm o.d. pyres tuhc. The samples were frozen wit’h liquid air and the tubes sealed imtraces
120
HOWARD,
JUMPER, TABLE
OBSERVED
AKjn
EMERSOX
II
AND CORRECTED PROTON CHEMICAL SHIFTS FOR CHCI, 1~ PYRIL)INE.CC~~ S~LDTIONS AT 25” RELATIVE TO INTERNAL CYCLOHESANE*
- &br @pm)
-
6 (ppm)
tica (moles)
5.8098 6.1730 6.4040 6.5595 6.7988
5.8098 6.1745 6.4070 6.5638 6.8060
0.012357 0.012357 0.012357 0.012357 0.012357
0.0 0.062000 0.12570 0.18588 0.30902
6.9723 7.0460
6.9823 7.0575
0.012357 0.012357
0.43555 0.49670
5.8100 6.1293
5.8098 6.1303
0.037305 0.037305
0.0 0.061689
6.3658 6.5370 6.7730 6.9500 7.0305 5.8095 6.1198 6.3423 6.5138 6.7608 6.9400 7.0235
6.3683 6.5410 6.7798 6.9598 7.0418 5.8088 6.1205 6.3445 6.5173 6.7673 6.9493 7.0343
0.037305 0.037305 0.037305 0.037305 0.037305 0.061808 0.061808 0.061808 0.061808 0.061808 0.061808 O.OG1808
0.12199 0.18726 0.30962 0.43308 0.49450 0.0 0.062517 0.12341 0.18681 0.31247 0.43225 0.49760
* Amount
of cyclohexaue,
II,o,
0.49805 0.44796 0.39587 0.34599 0.24407 0.13760 0.086718 0.47778 0.42731 0.37771 0.32401 0.22210 0.11951 0.067415 0.45725 0.40589 0.35627 0.30368 0.19926 0.099168 0.044015
is 0.005601 mole in each solution.
mediately with a hot flame. Because of the decomposition of unstabilized chloroform, the solutions were refrigerated until used, and the chemical shifts measured within about a day after their preparation. The nmr chemical shift of chloroform was measured as a function of the base and solvent concentrations, relative to cyclohexane as an internal reference, the temperature being kept at 25 f 1°C. A Varian 40.0 Mc/sec high-resolution spectrometer was used. The chemical shifts were determined by linear interpolation between two bracketing sidebands generated by modulating the magnetic field with a Hewlett-Packard model 200CD audio oscillator. These sideband frequencies were measured to one part in lo5 with a Hewlett-Packard model 523B electronic counter, using the period count mode of operation. Eight to ten measurements of the chemical shift were averaged for each solution. The resulting average deviations were always approximately 0.002 ppm. Fig. 1 illustrates typical variations of the proton chemical shift of chloroform at a fixed concentration as a function of the base concentration. The shift is always to lower field with increasing base and exhibits a marked curvature. Tables I and II contain the experimental chemical shift data for chloroform-di-
CHCla-BASE ASSOCIATION
BY XMR
121
ethyl ether in cyclohexane and chloroform-pyridine in carbon tetrachloride. These are typical examples of data obtained for the systems studied. Experimental data for all systems studied are not included because of their bulk. Complet,e tables will be supplied by the authors on request. III. TREATMEKT
OF I)ATA
T’;vrn t,hough the reference molecule, cyclohexane, presumably does not intsract, chemically with any of the other components of the solutions, a small difference in chemical shift between chloroform and cyclohexane which is not due to hydrogen bonding would be expected to arise from the difference between the t,wo molecules in their nonspecific van der Waal’s interactions with the surrounding molecules. Bn attempt has been made to correct at least in part for this using a semiempirical method suggested by Nick et al. (II), in which the shift due to nonspecific interactions is found to be a function of the diamagnetic susceptibilit8y of the medium and the molar volume of the observed mole:cule. This correlation has recently been shown to have a t,heoretical basis arising from the effect of dispersion interactions on nmr shifts (12). For shifts measured to an internal reference, the corrected shift, rrlativcl to infinite dilution in solvent, takes the form
fs = SC& +
(a - ar) ( X.?- x)
(1)
in which 8’s are chemical shift’s, o( and CX?are the so-called ‘%hape factors” for the molecule under observation and the reference molecule, respectively, and xs and x arr volume magnetic susceptibilities for solvent and solution, respectively. The quantity (Yhas been shown to be approximately inversely proportional to t,hc molar volume; interpolating from the data of Glick et al. (11)) it is estimatcad that 01 - q. = 0.18 for chloroform with cyclohexane as reference. The solution magnetic susceptibilities were estimated assuming volume additivity. Values of the corrected chemical shift 6 are also listed in Tables I and II for two of t,hr systems studied. The correction term is always small-less than 0.01 ppm -so t,hat’ errors in estimating susceptibilities or (Y’Sare not likely to be import,ant,. For solutions of chloroform and a base in CC14 , there are assumed to be t,hrect vompc%ing ctluilihria: chloroform-base association, the self association of cthloroform, and t.he (probable) associat,ion of chloroform to carbon tetrachloride ( I;{). The observed chemicsal shift (after correction) is then a weight#ed average over all chloroform containing species (1,5). Thus 6 = 6,. + inr/‘,~r’))A& + (nd/,~,O)A?i,+ (n,,,‘n,.O)A&, .
(2,
Throughout this work, 6, represents the chemical shift of unassociated chloroform; the n’s are numhers of moles of the components; the Ah’s are association shift#s (i.e., t,he differences in chemical shift between the unassociated and associated forms of chloroform); and the subscripts c, 0, .c, d, s, s.r, and r, refer to
122
HOWARD, JUMPl$R, AND
EMERSON
chloroform, base, base complex, dimer, solvent, solvent complex, and reference molecule, respectively. The numbers of moles of chloroform, base, and reference have zero superscripts and are the stoichiometric amounts. The other components without superscripts are given as equilibrium numbers of moles. Making the common assumption that activities are proportional to concentration (15), the mole ratios of Eq. (2) can be obtained from the three mole fraction equilibrium constant expressions, JiZ = %ft,?‘&/(n$-
% -
2nd -
?&)(nbo -
Kd = nm/(n:
n, -
2nd -
n,,)‘,
-
nZ),
(3)
and K,, = n,,nd(n~
-
n, -
2nd -
G)(Q”
-
naz),
where the total equilibrium number of moles is nt = neo + nbo + 72,’ + n,’ -
nz -
nd
-
nsz
.
The estimation of Kd , KS, , A&, and A&, from nmr shift measurements on chloroform in cyclohexane and CCL has previously been described (13). The values used in all calculations are listed in Table III. Equations (2) and (3) give 6 implicitIy as a function of the known concentrations, the known constants, and the unknown parameters K, , A&, and A&. The problem then reduces to finding the values of the unknowns which best reproduce the observed variations of 6 with concentration. This is done by using a general nonlinear least squares refinement procedure in which initial estimates of the unknown parameters are iteratively improved to a best least squares fit. To use this method, calculated values of the independent variable 6* and its derivatives with respect to each of the three unknown parameters are needed for TABLE
III
ASSOCIATION CONSTANTS AND ASSOCIATION SHIFTS FOR THE HYDROGEN BONDING OF CHLOROFORM TO SEVERAL BASES AT 25",CORRECTED FOR SELF- AND SOLVENT ASSOCIATION Base
Solvent
EtsN Et20 Et?0 (isopropyl)& CHzCN (CH,)&O CsHsN
CsH,, CsH,, CCL CCI, CCL CCL CCL
CHCI, ccl,
CsH,z ccl,
-Aa (ppm) 4.70 3.76 1.46 2.06 1.14 2.07 1.90 0.13” 0.10”
f f f f f f f f f
0.12 0.10 0.04 0.08 0.04 0.05 0.04 0.03 0.03
1.472 0.905 1.266 1.126 0.973 1.419 2.271 l.gn (1.g8
f zk f +z f f f zk f
0.011 0.008 0.018 0.019 0.019 0.014 0.023 0.3 0.3)
* These values and error limits differ slightly from those reported in Reference cause of t,he improved computational method described in the present work.
1.3 be-
CHCl,-BASE
.4SHOCIATlON
12::
BY KMR
every experimental point in each successive iteration cycle.’ The values of substitution into Eq. (2) are oht#ained rag*, nd*, and nsx* needed for subsequent by simultaneous solution of Eqs. (3). A considerable simplification is made possible by the fact that I& and S,, are quite a bit smaller than Kz*. Algebraic manipulation of Eq. (3) yields the expressions n,
*
=
1 2
11,”
+
n2
( ns0 + K,”
,n,n _ +
’
Ii:! >I
1
(4)
,
* n,,
= -B
+
n,*j+ R’l”“,
[II2 + 4A(n,~“)‘(a,”-
and n,z* = Kc&&’
-
al* -
~n%)/[K,,ns” + (2&
-
K&:l,
with
R’ =
-&I[1
+
(&
-
K,,‘)~K:,J(&?.
(10,
These equations are written in the most’ convenient form for solution by a numerical iteration procedure. Since n,,* and I$, are small, R and R’ are small compared to the other terms in Eqs. (4) and (3, respectively. Initially, R is assumed zero and an approximation to n,* obtained from Eq. (-I). This is suhstituted in Eq. (5), with R’ taken as zero, and an approximation to nrz found. .\n approximation to ,n,l* is obtained from Eq. (6) and new values of R and I?’ calculat.ed from Eels. (9) and (101 for use in the next cycle. This is continued nnt.il t,here a,re no furt,her changes in the calculated values, which are t,hen substit,uted int’o Eq. (2) t’o get 6*. The parGal derivat’ives are then given immediately by X,/C?& = 1,
&S,i’aA?i, =
n,*/n,.’ 9
(11)
and iWak’,
= A6,*(n,.“k’,*[(~~,*)-’
-
+
(n,,’ -
except, for nb” = 0 when a6/6k’, 1 ‘The rstimaks of the unknown I)y askrisk superscripts.
(n,” + ,nb”+ ,nsof 2nd* -
n,* -
nro n~J’
nz* +
a,~* -
(nd -
n:x)m’ n,*)p’]\m ‘,
= 0.
pnrsmeters
and values calculated
from them are denotetl
124
HOWARD, JUMPER, AlhiD EMERSOK
For the two cases in which cyclohexane was used as solvent, there is no evidence for association with solvent. The calculations, however, can be carried out as a special case of the preceding formulas, in which K,, is assumed t,o be negligibly small and ,n,.’ is zero. All of the computations were carried out in a single operation on an IBM 700 computer, the function and its derivatives being calculated in a subprogram added to the general least squares program.2 The values of the association constants and association shifts obtained are listed in Table III. The value of 6, is constant and is found to be --:i.6506 ppm f 0.0017 ppm. The standard deviations of the unknowns are determined automatically within the program and are also given in Table III. These measures of the precision do not include the effect of the uncertainties in the constants K,, , A&, , Kd , and A& . In CC&, when these constants are changed by amounts equal to their standard deviations (given in Table III ,I, the calculated values of K, change by 4-S%, and A& by 3%) both somewhat greater than the calculated standard deviations. The corresponding effect on the cyclohexane constants is negligible. IV. l~ISCUSYION There are few values of association constants in the literature which can be directly compared with our result,s. Those available from IR or nmr measurements are given in Table IV. A comparison of results indicates that nmr is presently capable of providing more precision then infrared absorption, and therefore at least potentially more accurate values of hydrogen bonding association constants, particularly for interactions as weak as those under consideration. With one exeeption (16) the agreement of the literature values with our results is adequate, considering that the indicated accuracy of the earlier work is relatively poor and that no corrections were made for possible self- or solvent association. In order to examine the effect of omitting these corrections, our data in carbon tetrachloride solutions were treated as described above but assuming no self- or solvent association. The values thus obtained are listed in Table V. All of the K, values in carbon tetrachloride are lower by about 1.50/n, this effect being produced primarily by leaving out solvent association, rather than self association. The constants in cyclohexane are only very slightly lowered [e.g., K, = 4.6 (m.f.)-’ for (C2Hs),K-HCCl.?] if no self association correction is introduced, since the chloroform concentration is kept low. The variation of K, values among bases in the same solvent is surprisingly small-the largest change being produced by changing solvents for the diethyl ether complex rather than by changing the proton acceptor. Moreover, the presumably similar diethy and di-isopropyl ether complexes in CC14 exhibit a rather large difference between their equilibrium constants when compared to the small variation among other pairs of chloroform-base complexes, which surely cover a * L)etails
of this program
can be obtained
by writ)ing to the authors.
CHCl,-BASE
88SOCIATION TABLE
LITERATURE
TAI,VES OF ASSOCTATION Association constant [im.f.)-‘1
Base
BY
123
NMR
IV
CONSTAKTS
FOR CHLOROFORM-BASE
COMPLEXES
Temperature
___ 1 3.7 3.0 18
(f:*Hs) ,N fC.‘sHs) .iN (CzHa).& tC?Hr,)d)
zt * * +
I” 1.02, b 1.0 2)a, c
25” 25”d 28” “Room temp.” None
given
nmr, binary mixt. IR, CIXl, in Ccl, nmr, binary mixt. IR, CDCI, in binary mist. IR, CI)Cl, in binary
c f g h
i
mist. 3 f 1.8 *
tCtHe):O (CH,)&O
2s 0.6
None
given 28”
IR, CUC13 in Ccl, nmr, binary mist.
i
P
:’ Constants have been approximately converted from units of liters/mole. ‘) Precision limits have been estimated from t,he original data. 0 A questionable approsimat,ion has been made in determining these values. Recalculxt,ion indicates that the data can he fitted at least as well with equilibrium constants con ?;ist,ent, with the results of our work. ClG. M. Barrow (private communication). * See Reference 17. f <:. 34. Barrow and E. A. Yerger, J. .-IuL. Chettl. Sot. 76, 5247 (1954). E See Reference 6. ‘I See Reference 16’. I M. Josien. J. Leickman, and N. Fuson, Rlrll. SW. chits Frunce p. 188 (1958). TABLE
V
ASSWI..ITWN CONSTANTB AND SHIFTS CALCUL.~TEU FOR CHLOROFORM-BASE COMPLEXES IN Ccl4 , ASSUMING NO SELF- OR SOLVENT ASSOCIATION Base __.
I!&0 (isopropyl)& CHZC’N tCHs)zCO C&N
Kl(m.f.)-‘] ~.~______ 1.22 l.i7 0.91 1.75 l.lil
f & f + f
0.04 0.08 0.05 0.04 0.0-l
- A6 @pm) 1.072 0.940 0.752 1.251 2.152
f 0.021 + 0.020 f 0.024 ZIZ 0.014 f 0.029
wider range of base strengths. Encouragingly, however, these two K, values used in conjunction with dielectric measurements on the same solutions give equal dipole moments for the two complexes (9). This seems to he good indirect evidence for the internal consistency of constants determined in the same solvent. The marked difference in the association constants for the diethyl ether complex in the two solvents does not’ seem to he readily explainable, although it has been noted previously (Reference 1, p. 222 and Reference 17) that hydrogenbonding association constants are smaller in carbon tetrarhloride than in hgdro-
126
HOWARD, JUMPER, AND EMERSON
carbon solvents. The existence of this anomaly is interesting but disturbing; it reveals deficiencies in the present models-including our own relatively detailed one-used for interpreting this type of measurement, even though it proves possible to fit the observed data quite precisely. There is some evidence from the dipole moments (9) of the complexes which suggests that this difference might involve an actual change in the geometrical form of the diethyl ether complex with change of solvent. In any case, it does not seem reasonable to attribute all of this discrepancy to activity terms in the equilibrium constants, since nonelectrolyte solutions, in general, do not deviate as greatly from ideal behavior (18) as would be necessary (as long as hydrogenbonded complexes are treated as separate chemical entities, which keeps the effect of the association from being included in the activities). Table V shows that the difference between the equilibrium constants of diethyl ether in the two solvents is only increased by omitting solvent association, and even the result that the corresponding hydrogen-bonding shifts are apparently brought closer together is an artifact, since the reference points are no longer the same: For the calculations of Table V, 6, is - 5.8084 f 0.0016 ppm (the infinite dilution shift of CHC13 in CC14 without a correction for solvent association). More likely sources of error are further contributions to the chemical shift which have not been included in Eqs. (1) and @). Equation (1) probably adjusts the data reasonably well for the shift due to the difference between chloroform and cyclohexane in their dispersion interaction with the surroundings (12) but does not correct for the polar reaction field of the chloroform molecule (19, 20). The latter would be expected to have its greatest effect for the higher dielectric constant bases, such as acetone and acetonitrile. (In view of this, the association constant for the chloroform-triethylamine complex is probably the most reliable of all, since the difference in dielectric constants between triethylamine and cyclohexane is small.) However, this effect would not be expected to be negligible even for the small difference between the nonpolar solvents, carbon tetrachloride and cyclohexane, since the reaction field varies most rapidly with dielectric constant in the low dielectric constant region. In addition, even though an internal reference is used, there may be a small contribution to the shift from the magnetic anisotropy of some molecules in the surrounding medium-one which does not vanish with rotational averaging (21). Pyridine and acetonitrile would be especially suspect, since they have quite large anisotropies. Whatever the cause of the apparent change in equilibrium constant (and association shift) on changing solvents, the existence of this effect indicates that treating the data in the way we have done cannot be completely adequate. This can be made clear by considering the diethyl ether results. Even if the hypothesis of two different complexes in the two solvents is correct, the fact that measurements are made over the entire range of solvent-base compositions means that the apparent equilibrium constant must be made to vary in at least one of
CHCLBAHE
ASSOCIhTION
13Y SMIt
12'7
the two sets of measurements. This, of course, has not been taken into account in the calculations. More generally, it can be said that if the results vary with solvent then almost surely they will also depend on solvent-base composition. hnother difficulty of a similar nature is the strong dependence of the derived values of association constant and shift upon one another. It is readily seen from Eqs. (2j and (3) that 8b -
6,. = A&&/(&
+
t),
(1”)
where & is the shift of (Lhloroform at infinite dilution in the pure base. I:or :L given base, 6bis a constant and 6, is independent of solvent because of the solvent association correction. This means, therefore, that the difference in the diethyl ether complex equilibrium constants also shows up as a complementary diff’erenw in the hydrogen-bonding shifts. In general, if K, is larger than the true valtw, A& lvill be too small, and conversely. Fortunately, AL should not be affected as much as K, by these inadequacies in the treat,ment of the data; the following qualitative conclusions based on relative values of the association shifts arc’ unlikely to be changed. It should be noted that many of the difficulties of the type mentioned here seem to have been fairly generally ignored in the literat’ure. Where nmr measurements have been used to obtain the association constants quoted from t#heliterature, values of association shifts have also been given, OI can be obtained from the original data. Martin (17) gives As, = - 1..5 f 0.1 for triethylamine-chloroform. This is identical with the value which can be d+ rived via l&l. i 12) from the work of Huggins et ab. (6), whose results can also f 0.15 for the chloroform complex with acrt’onr. be used to get AS, = -1.1 Thrse association shifts are considerably less sensitive to experimental errorsand almost surely to temperature differences-and agree bett,er with our rtsult s t,han the corresponding equilibrium constant,s. Schneider, Bernst,ein, and I’ople (22) have interpreted the association shift, as arising (to simplify somewhat) from two main sources: (1) the electrostatic field produced by the base at the proton, and (2) the magnetic anisotropy of the baw. The first effect should always cause a negative shift,; the second is either posit,ive or negative depending upon the orientation of the magnetic anisotropy tensor of the base. Primarily because negative shifts are always observed, they proposed that the electrostatic effect dominates the anisotropy effect. However, our results and the following analysis suggest that the large magnetic anisotropies of pyridine and acetonitrile strongly influence the association shifts of their chloroform complexes. h proton bonded to the nitrogen atom is presumably in the plane of the pyridine molecule. In this case, the r-electron currents around the aromatic ring give rise to a magnetic field which enhances the applied field at the hydrogenbonded proton. Thus, the electrostatic and anisotropy effects act in the same
128
HOWARD,
JUMPER,
AND
EMERSON
direction in pyridine, both causing a negative shift of the resonance frequency. In the acetonitrile complex the chloroform proton lies along the C-N bond axis; the ?r electrons of this triple bond would be expected to produce a shift in the positive direction. This analysis provides the simplest explanation for pyridine and acetonitrile having, respectively, the largest (most negative) and smallest (least negative) association shifts found in CC& . A simple but crude estimate of the anisotropy effect in the pyridine complex can be made using the aromatic ring current model. The latter has yielded an anisotropy shift of approximately -2 ppm for the benzene (or equally well in this approximation, pyridine) ring protons (23, 24). The greater distance of the hydrogen-bonded proton from the ring center-about 3.2 A as compared to 2.5 W-should reduce the effect. Making use of l’ople’s (23) approximation of an induced point dipole at the center to represent the magnetic field of the ring, we note that the effect should decrease with the inverse cube of the distance, to a value of approximately - 1 ppm for the part of the shift of the chloroform proton which comes from the ring-current produced anistropy of pyridine. If this value is subtracted from the observed Ah, for the pyridine complex, the remaining shift is in the range of the association shifts of the complexes of ethyl ether, isopropyl ether, and acetone. The latter molecules do not have large magnetic anisotropies and thus might be expected to have considerably smaller contributions to their shifts from this source. The magnetic anisotropy of acetonitrile is not small, but it probably should have somewhat less than half the effect of benzene on a neighboring molecule, from a comparison of the nmr shifts of methane in these two solvents (!Z). The anisotropy contribution to the association shift of the acetonitrile complex is on this basis estimated to be about fO.4 ppm. Thus the remaining part of the shift, which is primarily the electrostatic part, is about - 1.3 ppm in Ccl4 , more or less independent of the base in our limited sample. There is no other discernible reasonable correlation of the association shifts-either before or after subtracting the estimated anisotropy contributions-with any other obvious property of the bases; in particular, acetonitrile and triethylamine have the largest and smallest dipole moments (26) of the bases studied and on this account might have been expected to have, respectively, relatively large and small electrostatic contributions to their association shifts. Hameka (7) has carried out a more detailed quantum mechanical calculation of the contribution to the association shift of the electrostatic and anisotropy effects-which he calls more generally the polarization and intermolecular magnetic effects-for the particular case of the ammonia hydrogen bond. He finds -0.45 ppm for the electrostatic term and - 1.02 ppm for the anisotropy contribution. The hydrogen bond in ammonia is probably not unlike that in chloroformtriethylamine, but the exact agreement of the calculated value of - 1.47 ppm for the association shift of the former with our measurements on the latter is un-
CHCla-BASE
ASSOCIATION
HE- NMR
I”!1
douhtedly fortuitous. Hameka’s computation shows, however, that the association shift does provide another experimental test of theoretical models of hydrogen bonding, since it can probably generally he ralculatcd in a relativeI> simple way. In disagreement with the conclusion of Schneider d al. (B), Hameka suggests t,hat the intermolecular magnet’ir shift may always be the predominating t,crm; our analysis indicates that although this term can be large, it, is prohahly usually smaller than the electrostatic shift. The measurements in pyridinc nerd some special attention since the possihilit\ of forming txo distinct. types of complexes has to he (aonsidered: ( 1) the hydrogen bond t,o t,he nitrogen lone pair electrons, and (2) the proton bonding to the T electrons. It is readily shown t,hat e\wi if both forms exist simultaneously, II+;. ( 2) through ( 11 ) are still correct hut with K, = K,, + K, and A6, = A&,k’,.:;(K,, + k’,)
+ A&k’,i’(k’,,
+ k’,),
( 1:; /
where II, and P refer to the lone pair and K complexes. Since t#hc t)wo association shifts would he expected to have opposite signs (NW ahore), A& could he cvcn larger than the observed AS,, whereas the true hydrogen-bonding equilibrium constant Ii,, would bc smaller than 17, . The latter is, if anyt’hing, already smallc~ than might have been expected for a base as strong as pyridine, while the asaociaCon shift. is already the largest among our results. Thus we SW no rvidcncv to warrant thp inclusion of the added cwnplicat.ion of simultaneous T c~ornplcsing in thr inkrpretation of our results.
‘I& allthors wish to esprcss their appreciation for the use of the Florida State IJniversit>IISM 709 completing facilities, supported in part hy Notional Science Foundation Grant. Ko. (+-17X7. In pxrticular, we thank Mr. I)onald Mart,in of the Computing Center staff for providing the general nonlinear least squares subprogram used in this work. In ztddition, we want to express our gratitude to 011r colleagues. Ik. 1~. A. Kromhotlt :cnd 1 jr. B. Linder, for stimulating disclwsions.
REFERENCES I, 3. 3.
4. 5. 6’. 7. 8.
(i. (‘. PIYENTEI. .~NUA. 1~. M&LELLAN, “The Hydrogen Bond,”
pp. 223, 365-386. Freeman, Han Francisco, 1960. .J. A. POPLIS, W. G. S(*HPZEII)ER,ASI) H. J. BERNSTEIN, “High-1tesolllt ion Nuclear hlagnrtic Resonance,” pp. %X-~k21. McGraw-Hill, New E’ork, 1959. E. 1). BECKER, U. LIDI)EL, AXI) J. N. SHOOLERY, 6. dfol. Spectroscopy/ 2, 1 (195s); bl. $.I(-NI)PRS AND J. B. HYNE, J. Chrn?. Phys. 29, 25.3, 1319 (1958); J. (‘. D.ZVIS,
130
HOWARD,
JUMPER,
AND
EMERSON
3. B. B. HOWARD AND C. F. JUMPER (to be published). 10. A. WEISSBERGER, E. S. PROSKAUER, J. A. Rmums, ANU E. E. TOOPS, JR., “Organic 2nd ed., p. 111. Interscience, New York, 1955. Solvents,” 11. R. E. GLICK, D. F. KATES, AND S. J. EHRENSON, J. Chem. Phgs. 31, 567 (1959). 12. B. B. HOWARD, B. LINDER, AND M. T. EMERSON, J. Chem. Phys. 36,485 (1962). fS. C. F. JUMPER, M. T. EMERSON, AND B. B. HOWARD, J. Chem. Phys. 36, 1191 (1961). f4. H. 8. GUTOWSKY AND A. SAIKA, J. Chem. Phys. 21, 1088 (1953). 15. F. J. C. R~SSOTTI AND H. ROSSOTTI, “The I>etermination of Stability Constants,” Chap. 2. McGraw-Hill, New York, 1961. 16. R. C. LORD, B. NOLIN, ANI) H. D. STIDHAM, J. _4m. Chem. Sot. 77, 1365 (1955). 17. M. MARTIN, T>octoral thesis, Universite de Paris, (1961). 18. See, for example, J. S. ROWLINSON, “Liquids and Liquid Mixtnres,” Chap. 4. Academic Press, New York, 1959. 19. A. D. BUCKINOHAM, Can. J. Chem. 38, 300 (1960). 20. P. DIEHL AND R. FREEMAN, Mol. Phys. 4, 39 (1961). 21. M. J. STEPHEN, Mol. Phys. 1, 223 (1958). $8. W. G. SCHNEIDER, H. J. BERNSTEIN, AND J. A. POPLE, J. Chem. Phys. 23, 601 (1958). 23. J. A. POPLE, J. Chem. Phys. 24, 1111 (1957). 24. J. S. WAUGH AND R. W. FESSENDEN, J. dnt. Chern. Sac. 79, 846 (1957). 25. A. I>. BUCKINGHAM,T. SCHAEFER, AND W. G. SCHNEIDER, b. Chem. Phys. 32.1227 (1960). 26. A. A. MARYOTT AND F. BUCKLEY, “Table of Dielectric Constants and Electric Dipole Moments of Substances in the Gaseous State, ” Nat,ional Bnreau of Standards Circular 537. U. S. Government Printing Office, Washington, D. C., 1953.
OP RIO,.E~‘III.AR
SPECTROSC’OI’T
Association Constants Several Chloroform-Base BENTZ
B.
HOWARD,CHARLES
10,
115-130
(1’363)
and nmr Association Shifts for Hydrogen-Bonded Complexes* F. JI‘MPER,t
AND
~UERLE
T. EMERSON~
The chemical shifts of chloroform in solutions with several hydrogen bonding bares in either cyclohexane or carbon tetrachloride as solvent were measured at 25” with a precision of fO.002 ppm. Chloroform-base association const,ant.s and association shifts were calculated by fitting the data using an 1RM 709 nonlinear least squares program. Corrections were applied for the effects of dispersion interaction and self- and solvent association. Listing the Ijase, association con&ant, and association shift in ppm to low field in t.hat order, the resulting values are: triethylamine, 1.70, 1.472; diethgl ether, 3.76, 0.905; diethyl ether, 1.46, 1.266;isopropyl ether, 2.06, 1.126; acetonitrile, 1.14, 0.973; acetone, 2.07, 1.419; and pyridine, 1.90, 2.271. The first t,wo are in cyclohesane, t.he rest in CC14 The difference between the association constant,s of dietjhyl ct.her in the two solvents is nokd as being anomalously large. The effect, of the anisotropy of the base can readily be seen in the association shifts of the Ijyridine and acet,onitrile complexes.
Hydrogen bonding association constants have heen studied systematically in relat,ively few instances; where comparison is possible, values in the literature are not in \-cry good agreement with each other (I). The measurement of nmr chemical shifts, however, has been shown to be a powerful tool in this field (2). It has been used to study the association of some alcohols (:I), certain carbosylic acids (If), pyrrole and pyrrole-pyridine (j), and chloroform lvith several bases (6). The combination of the sensit.ivity of t,he chemical shift. to hydrogen bon& ing and the high precision attainable in its measurement gives nmr an advantage * This work was support.ed in part by a grunt from the Research Corporation, ill p:trt 1,~ a cant ract, Sth the U. S. Air Force Office of Scient.ific Resrarch, and in part, by :I cont.r:tct with the 1)ivision of Biology and Medicine, U. S. Atomic Energy Commission. t Sllbmittrd in partial fulfillments of requirements for the degree of I)octor of Philosoph) in chemistry :It, Florida Statp ITniversity. Present address: lkll Telephone I,aborat,ories, Murray Hill, New Jersey. 1 l’rrsent atldress: Ikpartment of ( hemistry, W;~.VIX~State IYniverFity, l)et,roit, ILlich~ igan. 117
118
HOWARD,
JUMPER,
AND
EMERSON
over older techniques used for quantitative studies, although the inability to detect very low concentrations is a disadvantage. The difference in the chemical shift between the bonding proton in its associated and unassociated form is of considerable interest in itself, since it is possible to derive theoretical estimates of this quantity from models of hydrogen bonding systems (7), and also since it has been proposed as a possible measure of hydrogen bond strength (8). Chloroform has several advantages as a choice as a proton donor: (1) It presumably forms only one-to-one complexes. (2) The association constants are in a convenient range for study by this technique. (3) The complications due to self-association are not serious. The original impetus for this work was the need for reliable association constants of some chloroform-base complexes for use in the determination of their dipole moments; this part of the research will be presented in a future article (9). In this work we evaluate association constants and association shifts for chloroform with triethylamine, diethyl ether, isopropyl ether, acetonitrile, acetone, and pyridine in the solvents carbon tetrachloride or cyclohexane. II. EXPERIMENTAL
Alcohol was removed from spectrograde chloroform with concentrated sulfuric acid (10) and subsequent washing and drying shortly before use. After preliminary drying, spectrograde acetone, acetonitrile, pyridine, and analytical grade triethylamine were treated with Linde 4 A molecular sieve to remove the final
FIG. 1. Examples of the change of the proton chemical shift of CHC13 as a function of solvent-base composition, measured at 25” on a 40 Mc/sec spectrometer, relative to cyclohexane as an internal standard. Circles represent 0.50 M CHC13 in triethylamine and cyclohexane. Triangles represent 0.37 M CHClz in diethyl ether and CC14 .
CHCl,-BASE
ASSOCIATION TABLE
I
C)R~ERVED AND CORRECTED PROTON CHEMICAL SHIFTS FOR C~ci, CYPLOHEXANE SOLUTIONS AT 25" RELATIVE TO INTERNAL
- &,h (ppm) 5. G585
5.8875 6.0143 6.1028 6.2225 6.2960 6.3200 5.6655 5.8838 6.0125 6.0983 6.2158 (i.2910 6.3178 5.6780 5.8650 5.9980 Ci.0865 (i.2Ofi5 (i .2823 (i .3125 5.7045 5 .8500 5.9fi4.3 Ii. 0545 li. 1808 fi.2’55 d I (i .2(i33
- 6 (ppm) ~__ 5.6578 5.8883 6.0165 6.1065 6.2293 6.3058 6.3313 5.6643 5.8840 G.0143 6.1018 6.2220 6.3003 6.3288 5.6760 5.8645 5.9990 6.0890 6.2123 6.2910 0.3225 5.7005 5.8478 5.9633 Ii.0550 6.1843 6.2330 6.2700
I l!)
BY NMR
IN L)IETH~L CYCLOHESANE
ETHICR-
mcu (moles)
nf;) (moles)
n,” (moles)
0.024783 0.024783 0.024783 0.024783 0.024783 0.024783 0.024783 0.037305 0.037305 0.037305 0.037305 0.037305 0.037305 0.037305 0.061808 0.061808 0.061808 0.061808 0.061808 0.061808 0.061808 0.12386 0.12386 0.1238G 0.12386 0.12386 0.12386 0.12386
0.0 0.047428 0.095236 0.14073 0.23904 0.33337 0.37940 0.0 0.047839 0.095291 0.14221 0.23821 0.33327 0.38181 0 0
0.044131 0.39458 0.34915 0.30502 0.21055 0.12026 0.076400 0.43148 0.38551 0.3398ri 0.29460 0.20210 0.11198 0.065610 0.41315 0.36943 0. -32207 0.2761-I 0.18502 0.094156 0.049383 0.36(i!Xi 0.32338 0.277GO 0.23191 0.110!)6 0.09631 0.05113
0.045772
-
0.094667 0.14277 0.23832 0.33390 0.38009 0.0 0.04611 0.09443 0.14237 0.23797 0.28571 0.33300
of water. Analytical grade diethyl ether was fractionally distilled from sodium wire and isopropyl ether from P&L. Spectrograde solvents C(& and csyclohexane were used without further purification. For each lease, a total of from 21 to 40 solutions were prepared by weight, the concentration of chloroform always being kept below about 0.1 mole fraction. This minimizes the possibility of two chloroform molecules complexing to a single base molecule; furthermore, the corrections for self-- and solvent assoriation art a less significant fraction of the total shift when the stoichiometric concentration of chloroform is kept small. The base concentration was varied from zero to almost pure base. When CC14 was the solvent, approximately 0.005 mole fra&on cyclohcxane was present in each solution to serve as internal reference. ?Y’mr samples consisted of approximately 0.5 ml of solution in a 5 mm o.d. pyres tuhc. The samples were frozen wit’h liquid air and the tubes sealed imtraces
120
HOWARD,
JUMPER, TABLE
OBSERVED
AKjn
EMERSOX
II
AND CORRECTED PROTON CHEMICAL SHIFTS FOR CHCI, 1~ PYRIL)INE.CC~~ S~LDTIONS AT 25” RELATIVE TO INTERNAL CYCLOHESANE*
- &br @pm)
-
6 (ppm)
tica (moles)
5.8098 6.1730 6.4040 6.5595 6.7988
5.8098 6.1745 6.4070 6.5638 6.8060
0.012357 0.012357 0.012357 0.012357 0.012357
0.0 0.062000 0.12570 0.18588 0.30902
6.9723 7.0460
6.9823 7.0575
0.012357 0.012357
0.43555 0.49670
5.8100 6.1293
5.8098 6.1303
0.037305 0.037305
0.0 0.061689
6.3658 6.5370 6.7730 6.9500 7.0305 5.8095 6.1198 6.3423 6.5138 6.7608 6.9400 7.0235
6.3683 6.5410 6.7798 6.9598 7.0418 5.8088 6.1205 6.3445 6.5173 6.7673 6.9493 7.0343
0.037305 0.037305 0.037305 0.037305 0.037305 0.061808 0.061808 0.061808 0.061808 0.061808 0.061808 O.OG1808
0.12199 0.18726 0.30962 0.43308 0.49450 0.0 0.062517 0.12341 0.18681 0.31247 0.43225 0.49760
* Amount
of cyclohexaue,
II,o,
0.49805 0.44796 0.39587 0.34599 0.24407 0.13760 0.086718 0.47778 0.42731 0.37771 0.32401 0.22210 0.11951 0.067415 0.45725 0.40589 0.35627 0.30368 0.19926 0.099168 0.044015
is 0.005601 mole in each solution.
mediately with a hot flame. Because of the decomposition of unstabilized chloroform, the solutions were refrigerated until used, and the chemical shifts measured within about a day after their preparation. The nmr chemical shift of chloroform was measured as a function of the base and solvent concentrations, relative to cyclohexane as an internal reference, the temperature being kept at 25 f 1°C. A Varian 40.0 Mc/sec high-resolution spectrometer was used. The chemical shifts were determined by linear interpolation between two bracketing sidebands generated by modulating the magnetic field with a Hewlett-Packard model 200CD audio oscillator. These sideband frequencies were measured to one part in lo5 with a Hewlett-Packard model 523B electronic counter, using the period count mode of operation. Eight to ten measurements of the chemical shift were averaged for each solution. The resulting average deviations were always approximately 0.002 ppm. Fig. 1 illustrates typical variations of the proton chemical shift of chloroform at a fixed concentration as a function of the base concentration. The shift is always to lower field with increasing base and exhibits a marked curvature. Tables I and II contain the experimental chemical shift data for chloroform-di-
CHCla-BASE ASSOCIATION
BY XMR
121
ethyl ether in cyclohexane and chloroform-pyridine in carbon tetrachloride. These are typical examples of data obtained for the systems studied. Experimental data for all systems studied are not included because of their bulk. Complet,e tables will be supplied by the authors on request. III. TREATMEKT
OF I)ATA
T’;vrn t,hough the reference molecule, cyclohexane, presumably does not intsract, chemically with any of the other components of the solutions, a small difference in chemical shift between chloroform and cyclohexane which is not due to hydrogen bonding would be expected to arise from the difference between the t,wo molecules in their nonspecific van der Waal’s interactions with the surrounding molecules. Bn attempt has been made to correct at least in part for this using a semiempirical method suggested by Nick et al. (II), in which the shift due to nonspecific interactions is found to be a function of the diamagnetic susceptibilit8y of the medium and the molar volume of the observed mole:cule. This correlation has recently been shown to have a t,heoretical basis arising from the effect of dispersion interactions on nmr shifts (12). For shifts measured to an internal reference, the corrected shift, rrlativcl to infinite dilution in solvent, takes the form
fs = SC& +
(a - ar) ( X.?- x)
(1)
in which 8’s are chemical shift’s, o( and CX?are the so-called ‘%hape factors” for the molecule under observation and the reference molecule, respectively, and xs and x arr volume magnetic susceptibilities for solvent and solution, respectively. The quantity (Yhas been shown to be approximately inversely proportional to t,hc molar volume; interpolating from the data of Glick et al. (11)) it is estimatcad that 01 - q. = 0.18 for chloroform with cyclohexane as reference. The solution magnetic susceptibilities were estimated assuming volume additivity. Values of the corrected chemical shift 6 are also listed in Tables I and II for two of t,hr systems studied. The correction term is always small-less than 0.01 ppm -so t,hat’ errors in estimating susceptibilities or (Y’Sare not likely to be import,ant,. For solutions of chloroform and a base in CC14 , there are assumed to be t,hrect vompc%ing ctluilihria: chloroform-base association, the self association of cthloroform, and t.he (probable) associat,ion of chloroform to carbon tetrachloride ( I;{). The observed chemicsal shift (after correction) is then a weight#ed average over all chloroform containing species (1,5). Thus 6 = 6,. + inr/‘,~r’))A& + (nd/,~,O)A?i,+ (n,,,‘n,.O)A&, .
(2,
Throughout this work, 6, represents the chemical shift of unassociated chloroform; the n’s are numhers of moles of the components; the Ah’s are association shift#s (i.e., t,he differences in chemical shift between the unassociated and associated forms of chloroform); and the subscripts c, 0, .c, d, s, s.r, and r, refer to
122
HOWARD, JUMPl$R, AND
EMERSON
chloroform, base, base complex, dimer, solvent, solvent complex, and reference molecule, respectively. The numbers of moles of chloroform, base, and reference have zero superscripts and are the stoichiometric amounts. The other components without superscripts are given as equilibrium numbers of moles. Making the common assumption that activities are proportional to concentration (15), the mole ratios of Eq. (2) can be obtained from the three mole fraction equilibrium constant expressions, JiZ = %ft,?‘&/(n$-
% -
2nd -
?&)(nbo -
Kd = nm/(n:
n, -
2nd -
n,,)‘,
-
nZ),
(3)
and K,, = n,,nd(n~
-
n, -
2nd -
G)(Q”
-
naz),
where the total equilibrium number of moles is nt = neo + nbo + 72,’ + n,’ -
nz -
nd
-
nsz
.
The estimation of Kd , KS, , A&, and A&, from nmr shift measurements on chloroform in cyclohexane and CCL has previously been described (13). The values used in all calculations are listed in Table III. Equations (2) and (3) give 6 implicitIy as a function of the known concentrations, the known constants, and the unknown parameters K, , A&, and A&. The problem then reduces to finding the values of the unknowns which best reproduce the observed variations of 6 with concentration. This is done by using a general nonlinear least squares refinement procedure in which initial estimates of the unknown parameters are iteratively improved to a best least squares fit. To use this method, calculated values of the independent variable 6* and its derivatives with respect to each of the three unknown parameters are needed for TABLE
III
ASSOCIATION CONSTANTS AND ASSOCIATION SHIFTS FOR THE HYDROGEN BONDING OF CHLOROFORM TO SEVERAL BASES AT 25",CORRECTED FOR SELF- AND SOLVENT ASSOCIATION Base
Solvent
EtsN Et20 Et?0 (isopropyl)& CHzCN (CH,)&O CsHsN
CsH,, CsH,, CCL CCI, CCL CCL CCL
CHCI, ccl,
CsH,z ccl,
-Aa (ppm) 4.70 3.76 1.46 2.06 1.14 2.07 1.90 0.13” 0.10”
f f f f f f f f f
0.12 0.10 0.04 0.08 0.04 0.05 0.04 0.03 0.03
1.472 0.905 1.266 1.126 0.973 1.419 2.271 l.gn (1.g8
f zk f +z f f f zk f
0.011 0.008 0.018 0.019 0.019 0.014 0.023 0.3 0.3)
* These values and error limits differ slightly from those reported in Reference cause of t,he improved computational method described in the present work.
1.3 be-
CHCl,-BASE
.4SHOCIATlON
12::
BY KMR
every experimental point in each successive iteration cycle.’ The values of substitution into Eq. (2) are oht#ained rag*, nd*, and nsx* needed for subsequent by simultaneous solution of Eqs. (3). A considerable simplification is made possible by the fact that I& and S,, are quite a bit smaller than Kz*. Algebraic manipulation of Eq. (3) yields the expressions n,
*
=
1 2
11,”
+
n2
( ns0 + K,”
,n,n _ +
’
Ii:! >I
1
(4)
,
* n,,
= -B
+
n,*j+ R’l”“,
[II2 + 4A(n,~“)‘(a,”-
and n,z* = Kc&&’
-
al* -
~n%)/[K,,ns” + (2&
-
K&:l,
with
R’ =
-&I[1
+
(&
-
K,,‘)~K:,J(&?.
(10,
These equations are written in the most’ convenient form for solution by a numerical iteration procedure. Since n,,* and I$, are small, R and R’ are small compared to the other terms in Eqs. (4) and (3, respectively. Initially, R is assumed zero and an approximation to n,* obtained from Eq. (-I). This is suhstituted in Eq. (5), with R’ taken as zero, and an approximation to nrz found. .\n approximation to ,n,l* is obtained from Eq. (6) and new values of R and I?’ calculat.ed from Eels. (9) and (101 for use in the next cycle. This is continued nnt.il t,here a,re no furt,her changes in the calculated values, which are t,hen substit,uted int’o Eq. (2) t’o get 6*. The parGal derivat’ives are then given immediately by X,/C?& = 1,
&S,i’aA?i, =
n,*/n,.’ 9
(11)
and iWak’,
= A6,*(n,.“k’,*[(~~,*)-’
-
+
(n,,’ -
except, for nb” = 0 when a6/6k’, 1 ‘The rstimaks of the unknown I)y askrisk superscripts.
(n,” + ,nb”+ ,nsof 2nd* -
n,* -
nro n~J’
nz* +
a,~* -
(nd -
n:x)m’ n,*)p’]\m ‘,
= 0.
pnrsmeters
and values calculated
from them are denotetl
124
HOWARD, JUMPER, AlhiD EMERSOK
For the two cases in which cyclohexane was used as solvent, there is no evidence for association with solvent. The calculations, however, can be carried out as a special case of the preceding formulas, in which K,, is assumed t,o be negligibly small and ,n,.’ is zero. All of the computations were carried out in a single operation on an IBM 700 computer, the function and its derivatives being calculated in a subprogram added to the general least squares program.2 The values of the association constants and association shifts obtained are listed in Table III. The value of 6, is constant and is found to be --:i.6506 ppm f 0.0017 ppm. The standard deviations of the unknowns are determined automatically within the program and are also given in Table III. These measures of the precision do not include the effect of the uncertainties in the constants K,, , A&, , Kd , and A& . In CC&, when these constants are changed by amounts equal to their standard deviations (given in Table III ,I, the calculated values of K, change by 4-S%, and A& by 3%) both somewhat greater than the calculated standard deviations. The corresponding effect on the cyclohexane constants is negligible. IV. l~ISCUSYION There are few values of association constants in the literature which can be directly compared with our result,s. Those available from IR or nmr measurements are given in Table IV. A comparison of results indicates that nmr is presently capable of providing more precision then infrared absorption, and therefore at least potentially more accurate values of hydrogen bonding association constants, particularly for interactions as weak as those under consideration. With one exeeption (16) the agreement of the literature values with our results is adequate, considering that the indicated accuracy of the earlier work is relatively poor and that no corrections were made for possible self- or solvent association. In order to examine the effect of omitting these corrections, our data in carbon tetrachloride solutions were treated as described above but assuming no self- or solvent association. The values thus obtained are listed in Table V. All of the K, values in carbon tetrachloride are lower by about 1.50/n, this effect being produced primarily by leaving out solvent association, rather than self association. The constants in cyclohexane are only very slightly lowered [e.g., K, = 4.6 (m.f.)-’ for (C2Hs),K-HCCl.?] if no self association correction is introduced, since the chloroform concentration is kept low. The variation of K, values among bases in the same solvent is surprisingly small-the largest change being produced by changing solvents for the diethyl ether complex rather than by changing the proton acceptor. Moreover, the presumably similar diethy and di-isopropyl ether complexes in CC14 exhibit a rather large difference between their equilibrium constants when compared to the small variation among other pairs of chloroform-base complexes, which surely cover a * L)etails
of this program
can be obtained
by writ)ing to the authors.
CHCl,-BASE
88SOCIATION TABLE
LITERATURE
TAI,VES OF ASSOCTATION Association constant [im.f.)-‘1
Base
BY
123
NMR
IV
CONSTAKTS
FOR CHLOROFORM-BASE
COMPLEXES
Temperature
___ 1 3.7 3.0 18
(f:*Hs) ,N fC.‘sHs) .iN (CzHa).& tC?Hr,)d)
zt * * +
I” 1.02, b 1.0 2)a, c
25” 25”d 28” “Room temp.” None
given
nmr, binary mixt. IR, CIXl, in Ccl, nmr, binary mixt. IR, CDCI, in binary mist. IR, CI)Cl, in binary
c f g h
i
mist. 3 f 1.8 *
tCtHe):O (CH,)&O
2s 0.6
None
given 28”
IR, CUC13 in Ccl, nmr, binary mist.
i
P
:’ Constants have been approximately converted from units of liters/mole. ‘) Precision limits have been estimated from t,he original data. 0 A questionable approsimat,ion has been made in determining these values. Recalculxt,ion indicates that the data can he fitted at least as well with equilibrium constants con ?;ist,ent, with the results of our work. ClG. M. Barrow (private communication). * See Reference 17. f <:. 34. Barrow and E. A. Yerger, J. .-IuL. Chettl. Sot. 76, 5247 (1954). E See Reference 6. ‘I See Reference 16’. I M. Josien. J. Leickman, and N. Fuson, Rlrll. SW. chits Frunce p. 188 (1958). TABLE
V
ASSWI..ITWN CONSTANTB AND SHIFTS CALCUL.~TEU FOR CHLOROFORM-BASE COMPLEXES IN Ccl4 , ASSUMING NO SELF- OR SOLVENT ASSOCIATION Base __.
I!&0 (isopropyl)& CHZC’N tCHs)zCO C&N
Kl(m.f.)-‘] ~.~______ 1.22 l.i7 0.91 1.75 l.lil
f & f + f
0.04 0.08 0.05 0.04 0.0-l
- A6 @pm) 1.072 0.940 0.752 1.251 2.152
f 0.021 + 0.020 f 0.024 ZIZ 0.014 f 0.029
wider range of base strengths. Encouragingly, however, these two K, values used in conjunction with dielectric measurements on the same solutions give equal dipole moments for the two complexes (9). This seems to he good indirect evidence for the internal consistency of constants determined in the same solvent. The marked difference in the association constants for the diethyl ether complex in the two solvents does not’ seem to he readily explainable, although it has been noted previously (Reference 1, p. 222 and Reference 17) that hydrogenbonding association constants are smaller in carbon tetrarhloride than in hgdro-
126
HOWARD, JUMPER, AND EMERSON
carbon solvents. The existence of this anomaly is interesting but disturbing; it reveals deficiencies in the present models-including our own relatively detailed one-used for interpreting this type of measurement, even though it proves possible to fit the observed data quite precisely. There is some evidence from the dipole moments (9) of the complexes which suggests that this difference might involve an actual change in the geometrical form of the diethyl ether complex with change of solvent. In any case, it does not seem reasonable to attribute all of this discrepancy to activity terms in the equilibrium constants, since nonelectrolyte solutions, in general, do not deviate as greatly from ideal behavior (18) as would be necessary (as long as hydrogenbonded complexes are treated as separate chemical entities, which keeps the effect of the association from being included in the activities). Table V shows that the difference between the equilibrium constants of diethyl ether in the two solvents is only increased by omitting solvent association, and even the result that the corresponding hydrogen-bonding shifts are apparently brought closer together is an artifact, since the reference points are no longer the same: For the calculations of Table V, 6, is - 5.8084 f 0.0016 ppm (the infinite dilution shift of CHC13 in CC14 without a correction for solvent association). More likely sources of error are further contributions to the chemical shift which have not been included in Eqs. (1) and @). Equation (1) probably adjusts the data reasonably well for the shift due to the difference between chloroform and cyclohexane in their dispersion interaction with the surroundings (12) but does not correct for the polar reaction field of the chloroform molecule (19, 20). The latter would be expected to have its greatest effect for the higher dielectric constant bases, such as acetone and acetonitrile. (In view of this, the association constant for the chloroform-triethylamine complex is probably the most reliable of all, since the difference in dielectric constants between triethylamine and cyclohexane is small.) However, this effect would not be expected to be negligible even for the small difference between the nonpolar solvents, carbon tetrachloride and cyclohexane, since the reaction field varies most rapidly with dielectric constant in the low dielectric constant region. In addition, even though an internal reference is used, there may be a small contribution to the shift from the magnetic anisotropy of some molecules in the surrounding medium-one which does not vanish with rotational averaging (21). Pyridine and acetonitrile would be especially suspect, since they have quite large anisotropies. Whatever the cause of the apparent change in equilibrium constant (and association shift) on changing solvents, the existence of this effect indicates that treating the data in the way we have done cannot be completely adequate. This can be made clear by considering the diethyl ether results. Even if the hypothesis of two different complexes in the two solvents is correct, the fact that measurements are made over the entire range of solvent-base compositions means that the apparent equilibrium constant must be made to vary in at least one of
CHCLBAHE
ASSOCIhTION
13Y SMIt
12'7
the two sets of measurements. This, of course, has not been taken into account in the calculations. More generally, it can be said that if the results vary with solvent then almost surely they will also depend on solvent-base composition. hnother difficulty of a similar nature is the strong dependence of the derived values of association constant and shift upon one another. It is readily seen from Eqs. (2j and (3) that 8b -
6,. = A&&/(&
+
t),
(1”)
where & is the shift of (Lhloroform at infinite dilution in the pure base. I:or :L given base, 6bis a constant and 6, is independent of solvent because of the solvent association correction. This means, therefore, that the difference in the diethyl ether complex equilibrium constants also shows up as a complementary diff’erenw in the hydrogen-bonding shifts. In general, if K, is larger than the true valtw, A& lvill be too small, and conversely. Fortunately, AL should not be affected as much as K, by these inadequacies in the treat,ment of the data; the following qualitative conclusions based on relative values of the association shifts arc’ unlikely to be changed. It should be noted that many of the difficulties of the type mentioned here seem to have been fairly generally ignored in the literat’ure. Where nmr measurements have been used to obtain the association constants quoted from t#heliterature, values of association shifts have also been given, OI can be obtained from the original data. Martin (17) gives As, = - 1..5 f 0.1 for triethylamine-chloroform. This is identical with the value which can be d+ rived via l&l. i 12) from the work of Huggins et ab. (6), whose results can also f 0.15 for the chloroform complex with acrt’onr. be used to get AS, = -1.1 Thrse association shifts are considerably less sensitive to experimental errorsand almost surely to temperature differences-and agree bett,er with our rtsult s t,han the corresponding equilibrium constant,s. Schneider, Bernst,ein, and I’ople (22) have interpreted the association shift, as arising (to simplify somewhat) from two main sources: (1) the electrostatic field produced by the base at the proton, and (2) the magnetic anisotropy of the baw. The first effect should always cause a negative shift,; the second is either posit,ive or negative depending upon the orientation of the magnetic anisotropy tensor of the base. Primarily because negative shifts are always observed, they proposed that the electrostatic effect dominates the anisotropy effect. However, our results and the following analysis suggest that the large magnetic anisotropies of pyridine and acetonitrile strongly influence the association shifts of their chloroform complexes. h proton bonded to the nitrogen atom is presumably in the plane of the pyridine molecule. In this case, the r-electron currents around the aromatic ring give rise to a magnetic field which enhances the applied field at the hydrogenbonded proton. Thus, the electrostatic and anisotropy effects act in the same
128
HOWARD,
JUMPER,
AND
EMERSON
direction in pyridine, both causing a negative shift of the resonance frequency. In the acetonitrile complex the chloroform proton lies along the C-N bond axis; the ?r electrons of this triple bond would be expected to produce a shift in the positive direction. This analysis provides the simplest explanation for pyridine and acetonitrile having, respectively, the largest (most negative) and smallest (least negative) association shifts found in CC& . A simple but crude estimate of the anisotropy effect in the pyridine complex can be made using the aromatic ring current model. The latter has yielded an anisotropy shift of approximately -2 ppm for the benzene (or equally well in this approximation, pyridine) ring protons (23, 24). The greater distance of the hydrogen-bonded proton from the ring center-about 3.2 A as compared to 2.5 W-should reduce the effect. Making use of l’ople’s (23) approximation of an induced point dipole at the center to represent the magnetic field of the ring, we note that the effect should decrease with the inverse cube of the distance, to a value of approximately - 1 ppm for the part of the shift of the chloroform proton which comes from the ring-current produced anistropy of pyridine. If this value is subtracted from the observed Ah, for the pyridine complex, the remaining shift is in the range of the association shifts of the complexes of ethyl ether, isopropyl ether, and acetone. The latter molecules do not have large magnetic anisotropies and thus might be expected to have considerably smaller contributions to their shifts from this source. The magnetic anisotropy of acetonitrile is not small, but it probably should have somewhat less than half the effect of benzene on a neighboring molecule, from a comparison of the nmr shifts of methane in these two solvents (!Z). The anisotropy contribution to the association shift of the acetonitrile complex is on this basis estimated to be about fO.4 ppm. Thus the remaining part of the shift, which is primarily the electrostatic part, is about - 1.3 ppm in Ccl4 , more or less independent of the base in our limited sample. There is no other discernible reasonable correlation of the association shifts-either before or after subtracting the estimated anisotropy contributions-with any other obvious property of the bases; in particular, acetonitrile and triethylamine have the largest and smallest dipole moments (26) of the bases studied and on this account might have been expected to have, respectively, relatively large and small electrostatic contributions to their association shifts. Hameka (7) has carried out a more detailed quantum mechanical calculation of the contribution to the association shift of the electrostatic and anisotropy effects-which he calls more generally the polarization and intermolecular magnetic effects-for the particular case of the ammonia hydrogen bond. He finds -0.45 ppm for the electrostatic term and - 1.02 ppm for the anisotropy contribution. The hydrogen bond in ammonia is probably not unlike that in chloroformtriethylamine, but the exact agreement of the calculated value of - 1.47 ppm for the association shift of the former with our measurements on the latter is un-
CHCla-BASE
ASSOCIATION
HE- NMR
I”!1
douhtedly fortuitous. Hameka’s computation shows, however, that the association shift does provide another experimental test of theoretical models of hydrogen bonding, since it can probably generally he ralculatcd in a relativeI> simple way. In disagreement with the conclusion of Schneider d al. (B), Hameka suggests t,hat the intermolecular magnet’ir shift may always be the predominating t,crm; our analysis indicates that although this term can be large, it, is prohahly usually smaller than the electrostatic shift. The measurements in pyridinc nerd some special attention since the possihilit\ of forming txo distinct. types of complexes has to he (aonsidered: ( 1) the hydrogen bond t,o t,he nitrogen lone pair electrons, and (2) the proton bonding to the T electrons. It is readily shown t,hat e\wi if both forms exist simultaneously, II+;. ( 2) through ( 11 ) are still correct hut with K, = K,, + K, and A6, = A&,k’,.:;(K,, + k’,)
+ A&k’,i’(k’,,
+ k’,),
( 1:; /
where II, and P refer to the lone pair and K complexes. Since t#hc t)wo association shifts would he expected to have opposite signs (NW ahore), A& could he cvcn larger than the observed AS,, whereas the true hydrogen-bonding equilibrium constant Ii,, would bc smaller than 17, . The latter is, if anyt’hing, already smallc~ than might have been expected for a base as strong as pyridine, while the asaociaCon shift. is already the largest among our results. Thus we SW no rvidcncv to warrant thp inclusion of the added cwnplicat.ion of simultaneous T c~ornplcsing in thr inkrpretation of our results.
‘I& allthors wish to esprcss their appreciation for the use of the Florida State IJniversit>IISM 709 completing facilities, supported in part hy Notional Science Foundation Grant. Ko. (+-17X7. In pxrticular, we thank Mr. I)onald Mart,in of the Computing Center staff for providing the general nonlinear least squares subprogram used in this work. In ztddition, we want to express our gratitude to 011r colleagues. Ik. 1~. A. Kromhotlt :cnd 1 jr. B. Linder, for stimulating disclwsions.
REFERENCES I, 3. 3.
4. 5. 6’. 7. 8.
(i. (‘. PIYENTEI. .~NUA. 1~. M&LELLAN, “The Hydrogen Bond,”
pp. 223, 365-386. Freeman, Han Francisco, 1960. .J. A. POPLIS, W. G. S(*HPZEII)ER,ASI) H. J. BERNSTEIN, “High-1tesolllt ion Nuclear hlagnrtic Resonance,” pp. %X-~k21. McGraw-Hill, New E’ork, 1959. E. 1). BECKER, U. LIDI)EL, AXI) J. N. SHOOLERY, 6. dfol. Spectroscopy/ 2, 1 (195s); bl. $.I(-NI)PRS AND J. B. HYNE, J. Chrn?. Phys. 29, 25.3, 1319 (1958); J. (‘. D.ZVIS,
130
HOWARD,
JUMPER,
AND
EMERSON
3. B. B. HOWARD AND C. F. JUMPER (to be published). 10. A. WEISSBERGER, E. S. PROSKAUER, J. A. Rmums, ANU E. E. TOOPS, JR., “Organic 2nd ed., p. 111. Interscience, New York, 1955. Solvents,” 11. R. E. GLICK, D. F. KATES, AND S. J. EHRENSON, J. Chem. Phgs. 31, 567 (1959). 12. B. B. HOWARD, B. LINDER, AND M. T. EMERSON, J. Chem. Phys. 36,485 (1962). fS. C. F. JUMPER, M. T. EMERSON, AND B. B. HOWARD, J. Chem. Phys. 36, 1191 (1961). f4. H. 8. GUTOWSKY AND A. SAIKA, J. Chem. Phys. 21, 1088 (1953). 15. F. J. C. R~SSOTTI AND H. ROSSOTTI, “The I>etermination of Stability Constants,” Chap. 2. McGraw-Hill, New York, 1961. 16. R. C. LORD, B. NOLIN, ANI) H. D. STIDHAM, J. _4m. Chem. Sot. 77, 1365 (1955). 17. M. MARTIN, T>octoral thesis, Universite de Paris, (1961). 18. See, for example, J. S. ROWLINSON, “Liquids and Liquid Mixtnres,” Chap. 4. Academic Press, New York, 1959. 19. A. D. BUCKINOHAM, Can. J. Chem. 38, 300 (1960). 20. P. DIEHL AND R. FREEMAN, Mol. Phys. 4, 39 (1961). 21. M. J. STEPHEN, Mol. Phys. 1, 223 (1958). $8. W. G. SCHNEIDER, H. J. BERNSTEIN, AND J. A. POPLE, J. Chem. Phys. 23, 601 (1958). 23. J. A. POPLE, J. Chem. Phys. 24, 1111 (1957). 24. J. S. WAUGH AND R. W. FESSENDEN, J. dnt. Chern. Sac. 79, 846 (1957). 25. A. I>. BUCKINGHAM,T. SCHAEFER, AND W. G. SCHNEIDER, b. Chem. Phys. 32.1227 (1960). 26. A. A. MARYOTT AND F. BUCKLEY, “Table of Dielectric Constants and Electric Dipole Moments of Substances in the Gaseous State, ” Nat,ional Bnreau of Standards Circular 537. U. S. Government Printing Office, Washington, D. C., 1953.