T H E
J O U R N A L
OF
PHYSICAL CHEMISTRY
Registered in U.5‘. Patent Ofice @ Copyright, 1969, by the American Chemical Society
VOLUME 73, NUMBER 10 OCTOBER 1969
The Effect of Hydrogen Bonding on the Barrier to Rotation about Amide Bonds’,’ by Robert C. Neuman, Jr., Warner R. Woolfenden,aand Violet Jonas Department of Chemistry, University of California, Riverside, California 98602
(Received March 1’7, 1969)
The activation parameters for C-N rotation in N,N-dimethylacetamide and N,N-dimethylacetamide-& have been determined as a function of concentration in the solvent formamide. These data and the nmr spectral properties for these systems indicate that hydrogen bonding between dimethylamides and formamide stabilizes the planar ground state leading to higher rotational barriers. Rotation about the central C-N bond in the amide functional group is restricted due to electron delocalization (1)416and this property imparts rigidity to proteins A-
2
and polypeptidesP An additional factor contributing to the secondary structure of these macromolecules is intramolecular hydrogen bonding between peptide linkages (2) .6 Independently of the many geometrical restrictions which these and other types of interactions impose on protein structure, such hydrogen bonding might be expected to increase the C-N rotational barrier of a peptide bond over that for the nonhydrogenbonded state by stabilizing the charge separation in the planar ground state.6c In an early study, we determined the rotational barriers for several N,N-dimethylamides and thioamides in the solvent formamidejo The intent of that study was not directed towards an understanding of the possible effects of hydrogen bonding on C-N rotational barriers and this possibility only became apparent when unusually high rotational barriers were obtained. These data were derived, however, from an approximate
nmr analysis method which we and others have shown can give erroneous result~.6&J~J Since the possible hydrogen-bonding interaction between an N,N-dimethylamide and the solvent formamide represents an intermolecular model for the hydrogen-bonding interaction between component peptide groups of a protein, we have completely reinvestigated the potential effect of formamide hydrogen bonding on the rotational barriers of N,N-dimethylacetamide (DMA) and N,N-dimethylacetamide-& (DMA-d3) us(1) This is part V, Studies of Chemical Exchange by Nuclear Magnetic Resonance; part I V : R. C. Neuman, Jr., W. Snider, and V. Jonas, J.Phys. Chem., 72,2469 (1968). (2) Support by the U. 5. Public Health Service (National Institute of General Medical Sciences) through Grant GM-13342 is gratefully acknowledged. (3) National Science Foundation College Teacher Research Participant, Summer 1968. (4) H. S. Gutowsky and C. H. Holm, J. Chem. Phys., 25, 1228 (1956). (5) (a) R. C. Neuman, Jr., andV. Jonas, J.Amer. Chem. Soc., 90, 1970 (1968); (b) R. C. Neuman, Jr., D. N. Roark, and V. Jonas, ibid.,89, 3412 (1967) : (c) R. C. Neuman, Jr., and L. B. Young, J. Phys. Chem., 69,2570 (1965), and references therein. (6) (a) H. R. Mahler and E. H. Cordes, “Biological Chemistry,” Harper and Row, Publishers, New York, N. Y . , 1966; (b) L. A. LaPlanche and M. T. Rogers, J. Amer. Chem. Soc., 86,337 (1964); ( 0 ) L. A. LaPlanche, H. B. Thompson, and M. T. Rogers, J. Phys. Chem., 69, 1482 (1965). (7) (a) A. Allerhand and H. S. Gutowsky, J. Chem. Phys., 41, 2115 (1964); (b) A. Allerhand, H. S. Gutowsky, J. Jonas, and R. A. Meinzer, J. Amer. Chem. Soc., 88, 3185 (1966).
3177
R. C. KEUMAN, JR.,W. R. WOOLFENDEN, AND V. JONAS
3 178
ing the method of total nmr line shape a n a l y s i ~ . ~ * # ~ The results demonstrate that: (1) a specific intermolecular interaction exists between formamide and 3 DMA or DRIA-d3; ( 2 ) this interaction increases their C-N rotational barriers; and (3) this is best interpreted DMA-F. However, we would expect that the value of in terms of hydrogen bonding (2). 6v, in such a complex would be essentially identical with that for (DR/IA)2since the relative shieldings of the two Results and Discussion NCH3 groups in DMA should be mainly a function of The concentration dependence, in carbon tetrachlothe respective positions of the two amide linkages. ride solution, of the nonexchanging chemical shift Such a dipolar interaction should thus lead to little (6v,) between the two NCH3 resonances of DR4A concentration dependence of 6vm for DMA in formam(Figure 1)) as well as those for DRIF and the coride. Since a relatively large dependence is observed responding thioamides, has been interpreted in terms of (Figure l), the structures of D M A - F and (DMA)2are a monomer-dimer self-association equilibrium as shown probably quite different. A hydrogen-bonded DMA. F in eq 1 for DMA.lb88 complex (2) would satisfy this criterion.6c The activation parameters for C-N rotation in DMA 2DRIA (DNA)z (1) in dilute formamide solution will represent the properSuch an interpretation immediately raises questions ties of D M A - F and those for neat DATA represent the concerning the meaning of activation parameters for the properties of (DMA)2. Kinetic analyses of the spectral C-X rotational reaction as determined from variable data for intermediate concentrations of DMA in formtemperature nmr spectra. In neat DbIA, the measured amide will give rate constants and activation paramrotational barriers probably correspond to those for and the true rotational barrier for monomeric DMA would be observed only in very dilute solutions of DMA in noninteracting solvents such as carbon tetra~ h l o r i d e . ~Rabinovits has now studied the concentration and temperature dependence of the apparent rotational rate constant for DllIF in carbon tetrachloride.1° His data demonstrate a small, but discernible, decrease in the apparent AF* for rotation as D M F concentration is decreased, indicating that AF* for (D;11F)2is slightly greater than that for D M F monomer (vide infra). While such data are not available for DMA, the similarity in the 6vm us. concentration curves for DATA and D M F in carbon tetrachloride suggest that a similar trend would be observed.lb The concentration dependence of 6v, for DMA in formamide is contrasted with that for DMA in carbon tetrachloride in Figure 1. The marked difference in the C O N C E N T R A T I O N ( m o l e s / liters ) shape of these curves implies that a specific solventFigure 1. Concentration dependence of the nonexchanging solute interaction between DMA and formamide (F) chemical shift ( 8 ~ between ~ ) the two NCHDresonance signals (eq 2 ) competes favorably with DMA self-association. of DMA (37") in carbon tetrachloride (solid points) and
lot /
DRlA
+F
formamide (open points).
DMA-F
(2)
It should be particularly noted that 6v, is relatively constant below 0.3 M DAIA in formamide while the value of 6v, in carbon tetrachloride has not reached its limiting low concentration value a t 0.07'%1 DRIA,lb the lowest concentration studied. l1 These contrasting observations are expected for the two respective reaction types shown in eq 1 and 2 . Self-association of S,N-dimethylamides (eq 1) presumably leads to a dimer held together by dipolar interactions between the respective polar oxygen and nitrogen atoms on the t w o amide molecules (3).lb,* This type of interaction should also be possible for The Journal of Physical Chemistry
(8) Independently, Dr. M . Rabinovitz has come to the same conclusions from a study of both the concentration and temperature dependences of the spectral properties of DMF in carbon tetrachloride; M. Rabinovitz and A. Pines, J. Chem. SOC.,B, 1110 (1988). (9) It is possible that higher aggregated forms of N,N-dimethylamides are present in their neat solutions.1b This possibility will not alter our conclusions even though we shall refer only to (DMA)z or (DMF)z for convenience. (10) (a) Dr. Rabinovitz kindly supplied us with a preprint of his manuscript outlining this study. (b) M. Rabinovits and A. Pines, J. Amer. Chem. Soc., 91, 1585 (1989). (11) The concentration of DMA in mol/l. has been used in Figure 1 because it allows the clearest contrast of the relative concentration dependence of & Y , in the two solvents. All subsequent data will be expressed in terms of mol % dimethylamide in the solvent. The quantities are related in Table I.
EFFECT OF HYDROGEN BONDING ON AMIDE-BOND ROTATION
3179
Table I : Rotational Kinetic D a t a for DMA-da and DMA in Formamide" k , seo-l
7 -
Temp,
9.8%
9.9%
OC
DMA-da
DMA
54.3 58.7 69.1' 71.9 75.3 75.4 76.2 82.1 87.1 88.4 Gv,(av)*
...
29.1%
42.3%
100%
DMA
DMA
DMA-dsb
1.39 2.22 5.05 6.28 8.36
1.67 2.86 5.75 7.65 10.46
2.29 3.60 7.39 10.27 13.51
5.21 7.79 19.21 24.30 32.00
9.06 13.33 22.12 26.32 8.2
10.94 16 89 26.04 33 * 33 8.5
14.45 24.04 35.46 40.32 8.9
34.55 55.00 81.10 89.57 10.0
0.924 1.67 4.00 5.15 6.76
1.40 3.70 4.67 6.60 6.90
...
... 7.62 11.55 18.38 21.37 7.7
10.53 18.45 20.41 7.8
7
19.5% DMA
... I
a Concentrations of DMA or D M A d are expressed as mol %. The corresponding concentrations in mol/l. for the DMA mol %values 9.9, 19.5, 29.1, and 42.3 are 2.2, 3.9, 5.3 and 6.8, respectively. Derived from the Arrhenius equation using the activation parameters Temperature uncertain; data not used in activation parameter calculations. previously reported. These averages of the "best-fit" values of 6v, are in the units of Ha; over the temperature range shown in this table these quantities were temperature independent within experimental error ( h O . 1 Hz).
eters corresponding to formal species composed of the equilibrium distributions of the subspecies DMA. F and and the apparent properties of these formal species would be expected t o be intermediate to those of
Table 11: Values of 6xA.F' for the Rotation Reaction of DMA in Formamide as a Function of DMA Concentration"jb Temp, OC
54.3 58.7 69.1 71.9 75.3 76.2 82.1 87.1 88.4 Av value'
---
9.9%
1.13 1.02 1.07 1.06 1.08 1.05 1.10 1.06 1.03 1.07 h 0.03
19.5%
0.86 0.83 0.91 0.93 0.93 0.93 1.00 0.93 0.88 0 . 9 1 =t 0.05
hAF* 29.1 %
0.74 0.66 0.82 0.79 0.77 0.80 0.83 0.81 0.71 0.77 0.05
--
.-.
42.3%
100%
0.53 0.51 0.65 0.59 0.60 0.61 0.58 0.59 0.57 0.58 0.05
0 0 0 0 0 0 0 0 0 0
a ~xAF* is defined as A F * ( z mol c%: DMA) - AF* (100 mol % DMA). Values of AF* calculated using the data in Table I and the equation k = (k'T/h)e( - A F * / R T } ; units of kcal mol-1. Mol % DMA in formamide. The temperature dependence of the values of ~ M A Fhas * been ignored.13
I
I5-
,
I
,
I
,
I
I
I
,/'
These data indicate that AF*(DMA.F) is about 1.3 kcal mo1-I greater than AF*((DMA)2). The kinetic data obtained by Rabinovitzlo indicate that AF*(DhIF monomer) could be about 0.5 kcal mol-' less than AF*((DMF)2).14 If these latter data are a reasonable approximation to the relative values of AF*(DMA monomer) and AF*((DMA)2), the quantity AF*( D N A - F ) may be almost 2 kcal mol-1 greater than AF*(DMA monomer). The kinetic data in Table I have been used to obtain activation parameters and these are given in Table 111. (12) The quantity ~ M A F *in all cases is defined as AF* (z mol % dimethylamide) - AF* (100 mol % dimethylamide). The symbolism follows that of E. Grunwald and J. Leffler, "Rates and Equilibria of Organic Reactions," John Wiley & Sons, Inc., New York, N. Y., 1967. (13! Since the values of 631AF* are relatively small and compare very similar reactions, their temperature dependence should also be quite small and this has been neglected in the calculation of the average values. (14) The kinetic data of Rabinovita,lo when cast into the form 6xAF*,lz*la show qualitatively the same functional dependence toward concentration as our data in Figure 2. However, the concentration dependence is smaller and all of the values of S ~ I A F *are negative. Volume 73, Number 10 October 1969
R. C. NEUMAN, JR.,W. R. WOOLFENDEN, AND V. JONAS
3180
Table 111: Activation Parameters for C-N Rotation in DMA and DMA-dl in Formamide Amide
DMA-ds
Solvent
Neat* Formamide
DMA
a
Activation free energy a t 298.2"K.
Concn, mol %
kcsl
100.0 9.8 9.9 19.5 29.1 42.3
19.6 21.3 20.9 19.6 19.5 19.5
mol-1
Log A
=t0 . 3
13.8 zk 0 . 2 14.2 f 0 . 3 14.0 f 0 . 3 13.2 =k 0 . 3 13.3 f 0 . 4 13.4 f 0.2
=I= 0.6
f 0.4 f 0.5 f 0.0 f 0.3
a
18.2 19.4 19.3 19.0 18.8 18.7
' From ref 5a.
The standard deviations for the values of E, and log A were derived from the least-squares derivation of these parameters. Values of AF* calculated from these parameters show the same trend with concentration as previously observed from the values of ~ M A F given * in Table I1 and Figure 2.15 A comparison of the Arrhenius activation parameters for DMA-ds (9.8 mol %) with those previously obtained for neat DMA-d3 (Table 111) shows the change in E, and log A which would be expected for a hydrogen-bonding interaction in DillAqF. The values of both E, and log A are larger for the system predominantly composed of the subspecies DMAeF (-10 mol yo DMA-d3) compared to neat DMA-dz which is predominantly (DMA)Z. The larger value of AF* for DMAeF indicates that although the quantities ME, and 8~ log A compensate, the enthalpy-related term ME^) dominates. A comparison of the four sets of Arrhenius parameters for the various concentrations of undeuterated DMA shows no clear trend. We have previously commented that the unsymmetrical N(CH3)2 line shape of DMA precludes the application of the complete Gutowsky-Holm line shape equation to the total line shape.5a The asymmetry in the I\T(CH& doublet is due to unequal CCH3, NCH3 coupling and this problem is virtually eliminated by deuterium substitution in CCH3. We have now found, however, that since the low-field NCH3 resonance line of DMA is coupled to CCH3 to only a very small degree, the complete G-H equation can be applied to this one resonance line with good success. This is evident in a comparison of the data for DMA (9.9 mol %) and DMA-d3 (9.8 mol %).16 However, this approach most certainly leads to small compensating errors in E, and log A.l7 Thus, while we
The Journal of Physical Chemistry
AF*ZQW kcsl/mol-1
Ea,
have complete confidence in our values of ~ M A Ffor " the undeuterated DMA systems,17 the small trends expected in the Arrhenius parameters for undeuterated DMA as a function of concentration are probably masked.
Experimental Section Materials. The synthesis of X,N-dimethylacetamide-d3 (DMA-d3)6aand the purification p r o c e d u r e ~ l b ~ ~ ~ for DMA and formamide have been previously described. The DMA-formamide solutions were prepared by weight. Kinetic Studies. Complete details of our methods of spectrum generation and analysis techniques have been reported.6*zb The ethylene glycol chemical shift "thermometer" was calibrated by insertion of a copper-constantan thermocouple into a spinning sample tube containing ethylene glycol. The plot of chemical shift vs. temperature was linear over the range 45-155" and fit the equation T ( " C ) = 193.4 - 1.6916~. This relationship is applicable only to a 60-MHz nmr spectrometer.18 (15) These values of AF* were calculated using the equation AF* = RT In (k'T/h) - RT In A Ea which results from equating the Arrhenius and transition state theory rate equations. Since the method of determination of Ea and log A leads to compensating errors in these quantities, the random errors associated with the values of AF* will be less than the standard deviations of the values of Ea. (16) The differences in the activation parameters for DMA and DMA-da could result in part from an isotope effect. It has been p r e dicted that AF* for DMA-ds might be about 0.2 kcal/mol greater than the value of DMA.6, (17) The phenomenon of virtually perfect E , log A compensation due to systematic errors in analysis or generation of nmr kinetic data is well doc~mented.b~
