NMR Dynamics Lab - Determination of Transition Barriers and Rotation Rates for N.,N-Dimethylacetamide

N,N-Dimethylacetamide (DMA) is a planar molecular having a large rotational barrier about the amide bond. Because of its similarity to peptide bonding geometry, DMA is often used to model peptide rotational barriers to examine conformational changes which are energetically feasible.

In DMA, the N-methyl groups are magnetically nonequivalent, depending on whether the group is cis or trans to the carbonyl.  As a result of DMA's rotational restrictions, protons on the N-methyl groups give rise to two separate NMR peaks (near a d of 3.0) at room temperature.  For higher temperatures, rotation rates increase, causing the two NMR peaks to widen due to shorter lifetimes (quicker exchange) of the two conformers. As temperature is further increased (more rapid rotation), the two peaks merge (at the coalescence temperature).  Above the coalescence temperature, the merged peak width decreases as temperature increases.  This continues until exchange effects no longer contribute to spectral peak widths.
 

Line Shape Analysis

Line shape analysis of these observed NMR peak shapes allows determination of rotational rate constants at various temperatures.  From the known line shape function for two equivalent exchanging groups, four approximations are commonly used to calculate rate constants under conditions ranging from slow to rapid exchange on the NMR time scale.

1.  Slow Exchange:  Below the coalescence  temperature and for NMR temperatures at which the two peaks are well resolved (less than ~20% overlap), the rate constant can be calculated using :

k = p * (he-ho)                                                                           (1)
where ho is the Full Width at Half-Height (FWHH) for peaks showing no exchange effects and he is the FWHH for peaks widened from exchange effects.

2.  Intermediate Exchange:  Below the coalescence  temperature and for NMR temperatures at which the two peaks overlap significantly (minimum between two peaks at least ~20% of peak intensity), the rate constant can be calculated using:

k = p * 2-1/2  * (Dno2 -  Dne2)1/2                                                                  (2)
where Dno and  Dne  are peak separations (in Hz) for spectra without and with exchange effects respectively.

3.  Coalescence:  At the coalescence temperature, the peaks merge into a flat-topped peak and the rate constant can be found with:

k = Dno* p / 21/2                                                                                               (3)

4.  Rapid Exchange: At temperatures at least 10-15 degrees above the coalescence point, the width of the merged peak may be used to calculate k:

                    k = 0.5 * p *  Dno2* (he - ho)-1                                                                 (4)

Kinetic Models and Thermodynamics

The internal rotation about the amide bond is an equilibirum process. The Eyring absolute rate theory can be used to calculate activation parameters.

The rate constant for the exchange of methyl groups (i.e. for rotation about the amide bond) is:
 

k  =  k * kB T / h * exp (-DG‡/RT)                                                       (5)
 
k  =  k *  kB T / h * exp( DS‡/R) * exp(-DH‡/RT)                                                       (6)
 where kB is Boltzmann's constant, h is Planck's constant,  k is the transmission coefficient (the fraction of reactant reaching the transition state that goes on to form product--normally assumed to be one), and DG‡, DH‡, and DS‡ are the free energy of activation, the enthalpy of activation, and the entropy of activation respectively.

From the linear plot of ln(k/T) vs 1/T, the entropy and enthalpy of activation can be calculated:
 

        ln (k/T) = {ln ( k *  kB / h) +  DS‡/R} - DH‡/R * (1/T)                                           (7)
 The Arrhenius Equation relates rate constants to activation energies:
 
k = A * exp(-Ea/RT)                                                                               (8)


where Ea is the activation energy and A is the pre-exponential factor.  From a plot of ln (k) vs 1/T, Ea can be calculated.

Requirements

1.  Determine the coalesence temperature of DMA by collecting proton NMR spectra at multiple temperatures. Start at room temperature and collect an NMR spectrum every 10 degrees.  Collect sufficient spectra to determine Tc within one degree.  After Tc has been determined, collect spectra at 10, 15, and 20 degrees above Tc.

2.  Use the cursers to find the both peak locations and the peak full-width at half maximum for the downfield peak.

3.  Use the appropriate line shape analysis equations listed above to determine rate constants for the measured temperatures.

4.  Create Eyring and Arrhenius plots and regressions of your data and calculate DG‡(298), DH‡, DS‡, and Ea.

5.  Use these literature values for DMA rotation parameters: DH‡ = 83.68 kJ/mol,  DS‡ = 19.6648 J / K-mol, and  Ea =  86.1904kJ/mol.