Conformation of secondary amides. A predictive algorithm that correlates DFT-calculated structures and experimental proton chemical shifts

Article abstract of DOI:10.1021/jo026695z

The magnetic deshielding caused by the amido group on CON-CHα protons of secondary amides can easily be correlated with DFT-based structures at the B3LYP/6-31G* level of theory via a novel algorithm that refines previous models, such as the classical McConnell equation. The shift is given by δ = a + 2.16 cos²(α - 35)/d, where α denotes the virtual dihedral angle resulting from linking the carbonyl and the α-carbons and d is the distance (A) between the shifted proton and the carbonyl oxygen. Notably, in this equation a is a parameter that can be optimized for different solvents, namely, CDCl₃, DMSO-d₆, and D₂O. For the development of these correlations, the preferential conformation of amides is taken from the optimized structures in the gas phase obtained at the DFT level. The deshielding on anti and gauche protons in both rotamers of (Z)-acetamides and E/Z isomers of formamides has been evaluated. This methodology has proved to be highly reliable, allowing us to discard ab initio or DFT conformational arrangements when shifts calculated by the above-mentioned equation differ from the experimental values. Thus, the anti disposition between the CHα proton and the N-H bond appears to be the more stable conformation of simple amides. For amides bearing only one proton at Cα, a local syn minimum can equally be characterized. The rotational barriers around the CON-alkyl bond along with the pyramidalization of the amido group have also been reassessed. As the conformation is taken away from anti or local syn minima, the nonplanarity of the amido group appears to increase.

Full text of DOI:10.1021/jo026695z

Con for m a tion of Secon d a r y Am id es. A P r ed ictive Algor ith m Th a t
Cor r ela tes DF T-Ca lcu la ted Str u ctu r es a n d Exp er im en ta l P r oton
Ch em ica l Sh ifts†
Mart ´ı n Avalos, Reyes Babiano,* J os e´ L. Barneto, Pedro Cintas, Fernando R. Clemente,
J os e´ L. J im e´ nez, and J uan C. Palacios
Departamento de Qu ı´ mica Org a´ nica, Facultad de Ciencias, Universidad de Extremadura,
E-06071 Badajoz, Spain
reyes@unex.es
Received November 12, 2002
The magnetic deshielding caused by the amido group on CON-CHR protons of secondary amides
can easily be correlated with DFT-based structures at the B3LYP/6-31G* level of theory via a novel
algorithm that refines previous models, such as the classical McConnell equation. The shift is given
2
by δ ) a + 2.16 cos (R - 35)/d, where R denotes the virtual dihedral angle resulting from linking
the carbonyl and the R-carbons and d is the distance (Å) between the shifted proton and the carbonyl
oxygen. Notably, in this equation a is a parameter that can be optimized for different solvents,
3 6 2
namely, CDCl , DMSO-d , and D O. For the development of these correlations, the preferential
conformation of amides is taken from the optimized structures in the gas phase obtained at the
DFT level. The deshielding on anti and gauche protons in both rotamers of (Z)-acetamides and E/Z
isomers of formamides has been evaluated. This methodology has proved to be highly reliable,
allowing us to discard ab initio or DFT conformational arrangements when shifts calculated by
the above-mentioned equation differ from the experimental values. Thus, the anti disposition
between the CHR proton and the N-H bond appears to be the more stable conformation of simple
amides. For amides bearing only one proton at CR, a local syn minimum can equally be
characterized. The rotational barriers around the CON-alkyl bond along with the pyramidalization
of the amido group have also been reassessed. As the conformation is taken away from anti or
local syn minima, the nonplanarity of the amido group appears to increase.
In tr od u ction
C-methyl and N-methyl groups. However, theoretical
calculations often lead to contradicting results depending
on the level of theory and basis sets, suggesting both syn
and anti conformations. In general, Hartree-Fock-based
methods give little conformational preference for the
methyl group on the nitrogen atom, though favoring syn
The accurate description of the amide linkage is of
utmost importance for understanding the conformation
of peptide bonds and a series of fundamental in vivo
processes such as protein-protein interactions and fold-
ing.1 There are numerous studies aimed at elucidating
the conformational preference of amides, and N-methyl-
acetamide has largely been assessed for this purpose as
this substance provides an appropriate mimicry of the
peptide bond involving two rotational barriers, for the
,2
3
conformers. Calculations by Krimm and associates of
amide stretch vibrational frequencies in N-methylaceta-
mide and small peptides indicate that the former adopts
preferential Z and E geometries having a C-methyl
hydrogen eclipsing the oxygen and an N-methyl hydrogen
4
eclipsing the NH group. Later on, studies carried out to
*
To whom correspondence should be addressed. Phone: +34-924-
2
89380. Fax: +34-924-271149.
ascertain the effect of hydrogen bonding on amide I and
†
Dedicated to the memory of Max Perutz (1914-2002). Nobody else
5
II vibrational frequencies by Tasumi et al. and Kubelka
understood so admirably the stereochemical matching and folding of
peptide chains.
6
and Keiderling also suggest a preferential syn arrange-
(
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(
(
1
1
0.1021/jo026695z CCC: $25.00 © 2003 American Chemical Society
Published on Web 02/04/2003
1
834
J . Org. Chem. 2003, 68, 1834-1842

Conformation of Secondary Amides
proton10 and carbon or nitrogen shift tensors have equally
proved to be useful markers of local protein structure.
CHART 1. Syn a n d An ti Con for m a tion s for Z a n d
E Isom er s of Secon d a r y Am id es
1
1
A salient drawback of using N-alkylated acetamides
as reduced models lies in the fact that experimental NMR
data are only available for Z conformers owing to their
greater stability. Complex acetamides such as those
derived from amido sugars also exhibit a preferential or
exclusive Z-anti geometry as revealed by both NMR
1
2
studies in solution and X-ray crystallography. N-Meth-
ylacetamide, however, is the only simple acetamide that
allows one to study the E conformer by NMR spectros-
copy.13 In stark contrast, N-substituted formamides exist
as mixtures of Z and E isomers, thereby enabling a direct
comparison between calculated and experimentally avail-
able data. Formamide itself, the simplest model, has been
the subject of extensive spectroscopic and computational
studies.14 The rotational barriers for N,N-dialkyl-substi-
tuted formamides have also been investigated theoreti-
1
5
cally, including the effect of a hydrogen-bonding solvent.
Detailed studies on hydrogen-bonding interactions have
1
6
been provided for N-alkylformamides as well. The ro-
tational microwave spectrum, in the frequency range of
1
8-40 GHz, along with ab initio calculations of N-
ment. Calculations at B3LYP/6-31G*, MP2/6-31G*, and
MP2/6-31+G** levels for a series of acetamides, including
N-methylacetamide itself, invariably predict that the
lowest energy conformer is the Z-anti conformer.7 In
particular, the use of methods involving electronic cor-
relation and diffuse functions appears to be important
for representing lone pairs and delocalized structures,
thereby accounting for a greater charge distribution of
methylformamide suggests a conformer with the methyl
group cis to the carbonyl oxygen, though the equilibrium
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983, 3, 443-452. (b) J im e´ nez, M. A.; Nieto, J . L.; Herranz, J .; Rico,
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the amide linkage than once thought as suggested by
Wiberg and others.8 Moreover, the Z-anti orientation
could also be inferred from the chemical shifts of the
N-CHR protons as a proton situated anti to the NH
proton consistently resonates ∼0.8 ppm further downfield
than a proton located in a gauche disposition.7 As
indicated in Chart 1 the conformational sphere of a
secondary amide can be described, in an unambiguous
fashion that clarifies obsolete cis and trans terms, by the
torsion angles φ and æ defining the rotamer states about
each of the two C-N bonds involved in the amide bonds
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22, 311-333. (c) De Dios, A. C.; Pearson, J . G.; Oldfield, E. Science
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(vide infra). NMR spectroscopy and computation are thus
two methods which can be applied complementarily with
considerable power to the conformational analysis.
The most reliable feature of NMR data as an experi-
mental tool is the fact that chemical shifts do precisely
reflect the magnetic anisotropy originated by the amide
function and they are likewise sensitive to other local
effects provided by solvents and substituents. Within this
context it is fair to mention that HR chemical shifts are
repeatedly used as diagnostic probes of secondary struc-
ture in peptides and proteins. Therefore, some correla-
tions between torsional angles and observed shifts have
been proposed, although patterns cannot often be defined
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2
7, 4538-4541.
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Neuefeind, J .; Zeidler, M. D.; Poulson, H. F. Mol. Phys. 1996, 87, 189-
9
with accuracy. Likewise, correlations based on amide
2
01. (g) Adalsteinsson, H.; Maulitz, A. H.; Bruice, T. C. J . Am. Chem.
(
6) Kubelka, J .; Keiderling, T. A. J . Phys. Chem. A 2001, 105,
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1
(
(
1
Coville, M.; J i, D.; Tsai, J .-C.; Wu, G. J . Org. Chem. 1992, 57, 7093-
099. (c) Wiberg, K. B.; Rablen, P. R. J . Am. Chem. Soc. 1995, 117,
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7
2
J . Org. Chem, Vol. 68, No. 5, 2003 1835

Avalos et al.
conformation of the methyl group could not be found.17
Two recent studies mainly focused on N-methylforma-
mide and N-methylacetamide give evidence of similar
arrangements of the methyl groups with respect to the
CONH group to represent global minima. Thus, Nandini
and Sathyanarayana describe ab initio calculations at the
HF/6-31+G* level on the molecular geometry and the
CHART 2. Set of Str u ctu r es 1-21
1
8
vibrational spectra of such amides, whereas Wiberg and
Roush have evaluated the methyl rotational barriers for
various N-methylamides and thioamides at the MP2 level
1
9
using a higher basis set, 6-311+G**. For N-methylform-
amide E-anti and Z-syn conformations were found to be
the most stable geometries by 0.88 and 0.33 kcal/mol with
respect to the E-syn and Z-anti ones, respectively.
Notably, the lowest energy conformer (Z-syn) exhibits a
marked pyramidalization at the nitrogen atom (i.e.,
deviation of the alkyl group from the H-N-C-O plane).
Similarly, the lowest energy conformation for both (E)-
and (Z)-N-methylacetamide was found to be syn.19 Such
results disagree with experimental conformations based
on proton chemical shifts and related DFT and ab initio
methods which point to a preferential Z-anti arrange-
7
ment. We have judged that a step forward to clarify the
structure of secondary amides is a further reassessment
of theoretical and empirical data for E and Z isomers.
Theoretical geometries and experimental magnetic de-
shielding can be correlated through a linear plot, and
predictions appear to be quantitative within statistical
confidence limits. This new correlation will afford a fresh
approach to interpreting and predicting suitable confor-
mations for amides, with putative extrapolations to
amide linkage in larger molecules.
Resu lts a n d Discu ssion
As mentioned before, the configurational and confor-
mational spectrum of simple amides can adequately be
denoted as a function of two torsional angles, φ and æ.
These angles are conceptually different from the torsion
angles [φ] and [ψ], used to characterize the secondary
structure of peptides and proteins, and should not be
misused as equivalents at all. Chart 1 depicts the
limiting syn and anti conformers for both E and Z
isomers.
Ma ter ia ls a n d Meth od s
Acetamides 1 and 2, formamide 7, and cyclic amides 15 and
1
6 were obtained from commercial suppliers and used without
2
0a
20b
20c
20d
20a
further purification. Compounds 3, 4, 5, 6, and 9
were prepared and purified according to protocols described
previously. Compounds 8, 10, 11, 12, 13, and 14 were prepared
by reaction of formic acid with the corresponding amine, as
23
2
0a
described for 9. Formamides 10, 11, and 12 crystallized from
diethyl ether, while 8, 13, and 14 were purified by vacuum
distillation.
Model compound studies have been undertaken on E
and Z isomers of the acyclic formamides 7-14, as well
as on the cyclic derivatives 2-pyrrolidone (15) and δ-vale-
rolactam (16), which can only be present as E isomers.
Experimental data for acetamides 1-6, the subject of a
DFT and ab initio calculations were carried out using the
2
1
Gaussian98 package. The stationary points were character-
ized by frequency calculations to verify that minima and
transition structures have zero and one imaginary frequency,
respectively. Zero-point vibrational energies have been com-
puted and scaled at the corresponding levels of theory, B3LYP/
7
previous study, and some chirally modified sugar amides,
1
7-21, have also been included for parallel discussions
and to enlarge the statistical basis (Chart 2).
6
-31G* (0.9806), HF/6-31G** (0.9181), MP2/6-31G* (0.9670),
2
2
One of the most classical methods for calculating
proton shifts based on magnetic anisotropy was developed
and MP2/6-31+G** (unscaled).
All NMR data were collected at 400 MHz in perdeuterated
solvents (CDCl , DMSO-d , and D O, 99.9% D) with chemical
3
6
2
shifts referred to tetramethylsilane (TMS) as the internal
standard (δ ) 0.00 ppm).
(21) Frisch, M. J .; Trucks, G. W.; Schlegel, H. W.; Scuseria, G. E.;
Robb, M. A.; Cheeseman, J . R.; Zakrzewski, V. G.; Montgomery, J r.,
J . A.; Stratmann, R. E.; Burant, J . C.; Dapprich, S.; Millam, J . M.;
Daniels, A. D.; Kudin, K. N.; Strain, M. C.; Farkas, O.; Tomasi, J .;
Barone, V.; Cossi, M.; Cammi, R.; Mennucci, B.; Pomelli, C.; Adamo,
C.; Clifford, S.; Ochterski, J .; Petersson, G. A.; Ayala, P. Y.; Cui, Q.;
Morokuma, K.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.;
Foresman, J . B.; Cioslowski, J .; Ortiz, J . V.; Baboul, A. G.; Stefanov,
B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Gomperts, R.;
Martin, R. L.; Fox, D. J .; Keith, T.; Al-Laham, M. A.; Peng, C. Y.;
Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.; J ohnson, B.; Chen,
W.; Wong, M. W.; Andres, J . L.; Gonzalez, C.; Head-Gordon, M.;
Replogle, E. S.; Pople, J . A., Gaussian, Inc., Pittsburgh, PA, 1998.
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(23) Amino Acids, Peptides and Proteins; Young, G. T., Ed.; The
Chemical Society: London, 1972; Vol. 4, p 455.
(
17) Fantoni, A. C.; Caminati, W. J . Chem. Soc., Faraday Trans. 1
996, 92, 343-346.
18) Nandini, G.; Sathyanarayana, D. N. J . Mol. Struct.: THEO-
1
(
CHEM 2002, 579, 1-9.
(
19) Wiberg, K. B.; Rush, D. J . J . Org. Chem. 2002, 67, 826-830.
(20) (a) LaPlanche, L. A.; Rogers, M. T. J . Am. Chem. Soc. 1964,
8
6, 337-341. (b) Nerdel, F.; Goetz, H.; Fenske, M. J ustus Liebigs Ann.
Chem. 1963, 665, 21-34; Chem. Abstr. 1963, 59, 12612d. (c) Furniss,
B. S.; Hannaford, A. J .; Smith, P. W. G.; Tatchell, A. R. Vogel’s Textbook
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1
836 J . Org. Chem., Vol. 68, No. 5, 2003

Conformation of Secondary Amides
TABLE 1. B3LYP /6-31G* Tor sion a l P a r a m eter s a n d
protons in a gauche disposition for both rotamers of 8
En er gy Differ en ces (k ca l/m ol) for F or m a m id es 7-9
(φ ≈ 57°), and a conformation placing the proton of (E)-9
minimum
transition state
pyram
and (Z)-9 in a gauche orientation (φ ) 61° and 56°,
respectively).
isomer
φ
æ
pyram
φ
æ
∆E
The calculated rotational barrier for the methyl group
in the E rotamer of N-methylformamide (7) is higher than
for its Z counterpart. This situation changes for N-ethyl-
and N-isopropylformamides (8 and 9), and the barriers
for their Z isomers are ∼1.4 kcal/mol higher in energy
than those of the E isomers. Clearly, the increasing steric
hindrance of the alkyl group contributes to increasing
rotation barriers (Table 1, 0.80-0.07 kcal/mol in 7 versus
7
7
8
8
9
9
E
Z
E
Z
E
Z
179.9 180.2
179.2 0.0
185.3 178.0
191.4 356.5
180.0 180.0
179.7
179.9
183.2
187.6
180.0
170.8
0.0 180.0
0.0 0.0
57.8 180.0
57.4 0.0
55.7 184.5
61.3 0.4
180.0
180.0
180.0
180.0
173.2
179.3
0.80
0.07
3.09
4.44
2.78
4.26
157.9
3.6
by McConnell in the late 1950s.24 Assuming that the atom
whose shift is being considered and the anisotropic source
are far apart, such a shift is given by
2
.78-4.44 kcal/mol in 8 and 9).
Since this work uses N-methylformamide as a probe
molecule looking at structural effects on the proton shift,
it was also convenient to check the reliability of DFT
versus ab initio calculations. Data gathered in Table 2
reveal that both DFT (B3LYP/6-31G*) and MP2/6-31G*
methods, and even an ordinary, but of lower accuracy,
method such as the HF/6-31G** level provide similar
results in terms of the φ and æ torsions, and energy
differences between E and Z isomers (∆E ) 0.9-1.0
kcal/mol). However, the use of diffuse functions at the
MP2/6-31+G** level results in a substantially different
structure for (Z)-7 in which the amido group becomes less
planar (æ ) 3.0°) and the methyl group adopts a disposi-
tion close to a syn conformation (φ ) 18.0°). Thus, the
amide nitrogen for this rotamer increasingly pyramidal-
izes in arrangements other than the preferred anti
conformation.
3
-1
2
δanis ) (3L R )
ø (3 cos θ - 1)
(1)
o
∑
ii
i
o
where L denotes Avogadro’s constant, R is the distance
between the shifted atom and the center of the group
magnetic anisotropy, øii is a component of the magnetic
i
susceptibility tensor, and θ is the angle between the i
axis (i ) x, y, z) and the vector R. That relationship can
be simplified in the case of an axially symmetric group
such as the amide function:
3
-1
2
δanis ) (3L R ) ∆ø(3 cos θ - 1)
(2)
o
where ∆ø is the difference between magnetic susceptibili-
ties along the axis of symmetry and within the plane of
symmetry and θ is the angle between the vector R and
the normal to the plane of axial symmetry.
For comparative purposes, the E isomer of N-methyl-
acetamide (1) shows, in different theoretical models, φ
torsion angles close to either 30° or 19° (Table 2), due to
steric crowding between the methyl groups. Again, the
nonplanarity of the nitrogen atom is consistently ob-
served for conformations far from a syn or anti disposition
The direct application of McConnell’s equations meets
a series of important limitations, as the center of the
group anisotropy is often denoted arbitrarily and numer-
ous chemical functions possess small magnetic suscep-
tibilities. Delocalized structures, however, constitute a
notable exception, and thus, Sitkoff and Case have found
a good agreement between the DFT data and the sus-
(φ ) 0° or 180°). For the Z rotamer ((Z)-1), calculations
at the MP2/6-31+G** and HF/6-31G** levels give evi-
dence of a clear-cut pyramidalization (∼170°) for φ torsion
angles of 17.8° and 24.6°, respectively.
ceptibility values in eq 1 or 2 for the alanine dipeptide.9
Th eor etica l Ca lcu la tion s. In a preliminary screening
of formamides 7-14 in the search of their energy profiles
i
As discussed earlier for the rotamers of 9, formamides
10, 12, and 13 bearing only one proton at the CON-CHR
group, show syn local minima along with the minimum
energy conformations which were found to be again the
anti forms (∆Esyn-anti ) 1.64-4.05 kcal/mol). In every
case the Z-anti rotamers are also lower in energy
2
5
carried out at a semiempirical (PM3) level, the anti
disposition was invariably detected as the most stable
conformer irrespective of which configuration (E or Z)
was considered. Overall, however, the predictions were
not reliable enough because E isomers were always found
to be more stable than their Z counterparts and, in
addition, geometries for both minima and maxima at the
PM3 level were markedly different from those found in
DFT or ab initio calculations.
At the B3LYP/6-31G* level we have first concentrated
on models 7-9, which contain three, two, and one proton,
respectively, at the CO-NCHR moiety. In these forma-
mides the anti conformation was significantly more stable
for both rotamers with φ values between 157.9° and
(∆EE-anti-Z-anti ) 0.74-1.36 kcal/mol). Similarly to the
structural situation encountered for the rotamers of 8,
the formamides 11 and 14 having two hydrogen atoms
at the CON-CHR moiety exhibit minimum energy
conformations that correspond to Z-anti arrangements
at the B3LYP/6-31G* level of theory. Once again the
pyramidalization bias takes place for conformations that
deviate from anti as well as local syn conformations
(Table 3).
A direct comparison between the set of formamides
1
91.4° (Table 1). In the case of (E)-9 and (Z)-9 it was also
7
8
-14 with the series of acetamides 2-6 indicates that
possible to characterize a local minimum that corre-
sponds to a syn conformation (see the Supporting Infor-
mation, Figure S1). Finally, the saddle points were
determined to be a syn conformation (φ ) 0.0°) for both
the latter structures possess energy differences between
their E-anti and Z-anti rotamers that are significantly
higher (1.93-3.16 kcal/mol versus 0.69-1.36 kcal/mol for
formamides; see the Supporting Information and Table
(
E)-7 and (Z)-7, a conformation having both methylenic
3
). This result agrees with the coexistence of both rota-
mers in solution as the formyl proton lowers the conges-
tion of the E isomer from what it would have been with
(
(
24) McConnell, H. M. J . Chem. Phys. 1957, 27, 226-229.
25) Stewart, J . J . P. J . Comput. Chem. 1989, 10, 209-220.
J . Org. Chem, Vol. 68, No. 5, 2003 1837

Avalos et al.
TABLE 2. Tor sion a n d P yr a m id a liza tion An gles (d eg) a n d En er gy Differ en ces (k ca l/m ol) for E a n d Z Rota m er s of
1
a n d 7
E isomer
Z isomer
compd
model chemistry
φ
æ
pyram
φ
æ
pyram
∆EE-Z
1
B3LYP/6-31G*
MP2/6-31G*
MP2/6-31+G**
HF/6-31G**
B3LYP/6-31G*
MP2/6-31G*
MP2/6-31+G**
HF/6-31G**
29.0
30.0
29.7
188.8
192.2
191.8
186.7
180.2
179.6
180.0
180.0
165.6
160.2
160.4
169.2
179.7
180.7
180.1
180.0
180.0
176.3
17.8
0.0
358.5
3.6
4.0
0.0
0.4
3.0
0.1
180.0
183.1
170.3
170.1
179.9
179.0
172.2
179.8
2.47
2.64
2.72
2.70
0.85
0.98
1.23
1.02
18.6
24.6
7
179.9
180.2
180.0
180.2
179.2
178.7
18.0
179.3
TABLE 3. Tor sion a n d P yr a m id a liza tion An gles (d eg) a n d En er gy Differ en ces (k ca l/m ol) for th e F or m a m id es 8-14 in
th e Ga s P h a se a t th e B3LYP /6-31G* Level
isomer
φ
æ
pyram
isomer
φ
æ
pyram
∆Esyn-anti
∆EE-anti-Z-anti
8
8
E-anti
Z-anti
185.3
191.4
180.0
157.9
158.8
229.1
179.7
190.9
161.7
174.3
182.2
202.9
172.9
166.2
178.0
356.5
180.0
3.6
182.7
4.1
181.1
355.6
177.1
352.3
178.6
356.8
183.9
4.0
183.2
187.6
180.0
170.8
176.1
170.7
179.3
193.1
186.2
197.4
182.0
188.3
173.8
171.4
0.71
9
9
1
1
E-syn
Z-syn
0 E-syn
0 Z-syn
7.4
0.1
34.4
183.0
0.0
192.3
357.0
174.8
179.9
160.4
190.8
9 E-anti
9 Z-anti
10 E-anti
10 Z-anti
1
1
12 E-anti
12 Z-anti
13 E-anti
13 Z-anti
1
1
2.43
1.64
2.36
2.01
0.74
1.36
1.04
1.03
0.85
0.69
333.5
1 E-anti
1 Z-anti
1
1
1
1
2 E-syn
2 Z-syn
3 E-syn
3 Z-syn
311.0
12.6
21.6
1.2
170.9
354.2
187.8
0.1
194.3
182.5
166.9
179.4
1.95
4.05
2.38
1.71
4 E-anti
4 Z-anti
a methyl group. On the other hand, the energy differences
between syn and anti conformations, irrespective of
which E or Z rotamer is considered, are only slightly
results at the B3LYP/6-31G* level give evidence of the
existence of planar structures and that pyramidalization
increases away from the canonical syn and anti confor-
mations.
From the above results it appears that the B3LYP/6-
31G* model does predict an anti conformation to be the
favorable arrangement for both rotamers of formamides
in the gas phase. Overall, there seems to be a pronounced
preference to adopt that conformation in the case of the
E isomers. Moreover, there are no significant deviations
between simple formamides and acetamides with respect
to their preferential conformation.
lower for the formamides 9, 10, and 12 (∆Esyn-anti
)
1
.64-4.05 kcal/mol) than for the corresponding aceta-
mides 3, 4, and 6 (∆Esyn-anti ) 1.86-4.33 kcal/mol) in
which both conformational minima can be observed. It
must be stressed that N-CR rotational barriers are
significant (Table 1 and the Supporting Information,
Figure S1) with the sole exception of the Z rotamer of
N-methylformamide ((Z)-7) in which the barrier is cal-
culated to be similar to that of N-methylacetamide (∼0.07
kcal/mol). In contrast, the E rotamers for N-methylac-
etamide and N-methylformamide show different profiles
in both conformational minima and transition structures,
because N-methylacetamide exhibits little or no variation
until φ ) 30° whereas for torsion angles >30° the barrier
rapidly increases due to the repulsion with the methyl
group. The transition structure is reached at φ ) 60° with
NMR Rela tion sh ip s. This follows our recent work on
acetamides to test the reliability of quantum models to
yield a good agreement between structure and experi-
mental proton chemical shifts. It has been shown that
primary acetamides do preferentially exist in a Z-anti
disposition.7 The population of the E isomer of N-
methylacetamide is very low, which contrasts with the
appreciable figures observed for the E isomers of forma-
mides 7-14 in different solvents (Supporting Informa-
tion, Table S4), thus extending this methodology to both
amide conformers.
7
a barrier of 0.27 kcal/mol (see the Supporting Informa-
tion).
Even though our DFT and ab initio studies do consis-
tently predict a favorable anti arrangement for E and Z
rotamers of simple acetamides and formamides, certain
model cases are still the subject of controversy and have
a somewhat confusing history as pointed out in our
introductory remarks, especially in relation with the
structure of the amido group. Numerous studies aimed
at solving this situation simply reveal that the nitrogen
As shown by Shoolery and others,30 through a simple
empirical relationship, the chemical shifts for methylene
(28) For a recent development of the MM4 force field for amides,
see: Langley, C. H.; Allinger, N. L. J . Phys. Chem. A 2002, 106, 5638-
5
652.
(29) For experimental microwave values of rotational barriers, see:
inversion mode is very floppy with negligible barriers
Kojima, T.; Yano, E.; Nakagawa, K.; Tsunekawa, S. J . Mol. Spectrosc.
1987, 122, 408-416.
between planar and nonplanar configurations.2
6-29
Our
(
30) (a) Shoolery, J . N. Varian Associates Technical Information
Bulletin; Palo Alto, CA; Vol. 2, No. 3. (b) Friedrich, E. C.; Gates Runkle,
K. J . Chem. Educ. 1984, 61, 830-832. (c) Friedrich, E. C.; Gates
Runkle, K. J . Chem. Educ. 1986, 63, 127-129. (d) Beauchamp, P. S.;
Marquez, R. J . Chem. Educ. 1997, 74, 1483-1485.
(
26) Fogarasi, G.; Szalay, P. G. J . Phys. Chem. A 1997, 101, 1400-
408.
27) Samdal, S. J . Mol. Struct.: THEOCHEM 1998, 440, 165-174.
1
(
1
838 J . Org. Chem., Vol. 68, No. 5, 2003

Conformation of Secondary Amides
TABLE 4. Ma gn etic Desh ield in g (p p m ) Or igin a ted by
higher rotational barriers than their Z isomers. In the
case of formamides having only one proton at CR, both
the anti and syn forms can be observed, although the
former appears to be the most stable structure for the E
rotamers (by about 1.95-2.43 kcal/mol). In addition, both
the anti (δanti ) 1.98 ppm) and gauche (δgauche ) 2.08 ppm)
protons are similarly affected by the magnetic anisotropy
of the amide function as reflected by the low statistical
deviation of the set (δanti - δgauche ) -0.10 ppm).
th e Am id e F u n ction on CON-CHr P r oton s for Am id es
1
-6 a n d 17-21 in CDCl3
∑
n/n ( SD
compd
δanti
δgauche
δanti - δgauche
1
1
1
-6
2.42 ( 0.06
2.41 ( 0.07
2.42 ( 0.05
1.64 ( 0.01
1.69 ( 0.05
1.66 ( 0.04
0.78 ( 0.01
0.72 ( 0.05
0.76 ( 0.04
7-21
6 and 17-21
At this point, it may be somewhat surprising that the
local deshielding for gauche protons, which lie beyond
the plane of the amide function, is found to be slightly
higher than for the corresponding and otherwise coplanar
anti protons. A preliminary estimation based on
and methine protons in CDCl
evaluated by eq 3,
3
solution can roughly be
δCH,XYZ ) 0.23 + σ + σ + σ
(3)
X
Y
Z
2
4
McConnell’s relationship (vide supra) reflects the direct
dependence of amide magnetic anisotropy on the angle
where σ
X
, σ
Y
, and σ
Z
are constants for the different
substituents. For the case of an amide group, that
relationship can also be utilized to determine the deshield-
ing caused by the amide function (δamide) on a particular
proton (δobsd):
(θ) between the vector R (the distance between the amide
and the shifted proton) and the normal to the plane of
axial symmetry (i.e., the amide group). Accordingly, this
angular contribution makes the protons out of the amide
plane, such as gauche protons, much less deshielded.
However, as pointed out earlier, quantitative predictions
may be premature as data for the susceptibility tensor
δamide ) δobsd - (0.23 + σ + σ )
(4)
X
Y
In addition that deshielding is an average magnitude as
anti and gauche hydrogen atoms at CR rapidly intercon-
vert at room temperature:
(ø) are scarce, although figures for formamide indicate
that this tensor is approximately axially symmetric about
the normal to the amide plane.31
To shed light on the magnetic anisotropy of the E
isomers, a further computation has been accomplished
on 15 and 16, which are constrained in an E geometry.
δamide ) δanti/n + (n - 1)δgauche/n
(5)
where n is the number of protons at CR.
Table 7 (see also Figure S2 in the Supporting Informa-
tion) collects the results of the lowest energy structures
for which the torsion angle values (with respect to the
Table 4 briefly summarizes our previous results on the
magnetic anisotropy found for three different sets of
model compounds: acetamides 1-6, O-acetylglucona-
mides 17-21, and the entire range of both sets. Such
1
H proton) are located at 55° for 15 and at 47° for 16.
Clearly, the angled structures remain anchored in a
gauche conformation, and therefore, the magnetic deshield-
ing (δamide) is equivalent to δgauche, which has been
determined to be 2.26 and 2.17 ppm for 15 and 16,
respectively. These anisotropies are still greater than the
data are consistent with a preferential Z-anti conforma-
tion for these substances.7
We have equally determined for the Z rotamers of
formamides 7-14 the deshielding caused by the amide
function on R-hydrogen atoms located in anti and gauche
arrangements (Table 5). These figures lie consistently
about 2.52, 1.69, and 0.83 ppm for δanti, δgauche, and
δ
gauche values found for the acyclic series (Table 6). This
fact can be partly explained by the conformational
rigidity and steric congestion of these cyclic derivatives.
The existence of such effects on shielding makes it
impossible in practice to obtain a perfect model and hence
a close correlation between chemical shifts. In fact, the
literature cautions against applying chemical shift data
δ
anti-δgauche, respectively, having very low statistical
deviations. These chemical shifts are close to, though
slightly higher than, those found for acetamides and
chiral gluconamides. Therefore, the alkyl-CO group
appears to have a small effect on the whole anisotropy.
A direct comparison between data from Tables 4 and 5
enables deshielding on anti and gauche protons caused
by the presence of a methyl group of 0.10 and 0.05 ppm,
respectively, to be determined.
3
2
from acyclic model compounds to cyclic derivatives. In
view of the unusually high magnetic anisotropy of 2-pyr-
rolidone, this substance has been removed from the data
set that we shall discuss below. Its inclusion, however,
would slightly modify (∼1%) the overall fit of the data.
In contrast, 16 has been maintained as removal of its
magnetic anisotropy contribution causes a negligible
variation in the statistical fitting.
The dispersion of chemical shifts is nearly absent as
demonstrated in the fit statistics (SD values) in Table 5.
The latter result suggests the existence of a common and
prevalent conformation which has, in turn, been assigned
to be the Z-anti form. The magnetic deshielding found
experimentally also agrees with the calculated DFT and
ab initio structures.
Having established a representative sampling of ac-
etamide and formamide torsion angles at the B3LYP/
6
-31G* level and the corresponding magnetic deshielding
The DFT values for the E rotamers of formamides
7
-14 are equally consistent with an anti conformation,
(
31) (a) Pauling, L. Proc. Natl. Acad. Sci. U.S.A. 1979, 76, 2293-
294. (b) Schmalz, T. G.; Norris, C. L.; Flygare, W. H. J . Am. Chem.
Soc. 1973, 95, 7961-7967. (c) Flygare, W. H. Chem. Rev. 1974, 74,
53-687.
32) J ackman, L. M.; Sternhell, S. Applications of Nuclear Magnetic
and Table 6 gives the magnetic anisotropies on anti and
gauche protons of these substances. It must be recalled
that the anti form appears to be the only conformational
minimum for formamides bearing two and three hydro-
gen atoms at CR (e.g., 7, 8, 11, and 14) which exhibit
2
6
(
Resonance Spectroscopy in Organic Chemistry, 2nd ed.; Pergamon
Press: Oxford, 1972; p 160.
J . Org. Chem, Vol. 68, No. 5, 2003 1839

Avalos et al.
TABLE 5. Ma gn etic Desh ield in g (p p m Sca le) Ca u sed by th e Am id e F u n ction on CON-CHr P r oton s for th e Z Rota m er s
of F or m a m id es 7-14 in CDCl3
compd
δobsd
σ
δamide
δanti
δgauche
δanti - δgauche
7
8
9
1
1
1
1
1
2.86
3.36
4.18
5.23
4.49
6.34
4.02
3.28
(H, H)
1.95
2.11
2.59
2.49
2.09
2.45
2.53
2.13
2.52
1.67
1.70
0.85
0.82
(H, Me)
(Me, Me)
(Me, Ph)
(H, Ph)
(Ph, Ph)
(Me, Et)
(H, Et)
2.52
2.59
a
0
2.49a
2.52
1
2
3
4
1.66
0.86
a
2.45
2.53a
2.52
1.74
0.78
∑
n/n ( SD
2.52 ( 0.06
1.69 ( 0.04
0.83 ( 0.04
a
Values taken for the averaging calculation.
TABLE 6. Ma gn etic Desh ield in g (p p m Sca le) Ca u sed by th e Am id e F u n ction on CON-CHr P r oton s for th e E Rota m er s
of F or m a m id es 7-14 in CDCl3
compd
δobsd
σ
δamide
δanti
δgauche
δanti - δgauche
7
8
9
1
1
1
1
1
2.94
3.29
3.71
4.71
4.42
5.78
3.42
3.19
(H, H)
2.03
2.04
2.12
1.97
2.02
1.89
1.93
2.04
1.98
2.06
2.10
-0.08
-0.12
(H, Me)
(Me, Me)
(Me, Ph)
(H, Ph)
(Ph, Ph)
(Me, Et)
(H, Et)
1.98
2.12a
1.97a
1.98
0
1
2
3
4
2.06
-0.08
a
1.89
1.93a
1.98
2.10
-0.12
∑
n/n ( SD
1.98 ( 0.10
2.08 ( 0.02
-0.10 ( 0.02
a
Values taken for the averaging calculation.
TABLE 7. Tor sion An gles (d eg) a n d Ma gn etic
Desh ield in g (p p m ) for Am id es 15 a n d 16
CHART 3. Vir tu a l Dih ed r a l An gle (r) Defin ed for
th e Z a n d E Rota m er s of F or m a m id es a n d
Aceta m id es
compd
φ(CONH-CH1) φ(CONH-CH2) δobsd δamide ) δgauche
1
1
5
6
54.8
47.3
-65.7
-69.7
3.41 2.26
3.32 2.17
∑
n/n ( SD
2.22 ( 0.06
angle but also the distance between the shifted atom and
any point of the anisotropy source should be involved.
Looking at the graph, however, there are really only four
clusters of data points, which correspond to the four
possible E/Z and anti/gauche conformational combina-
tions. Consequently, it seems appropriate to fit the data
to an equation that has a few adjustable parameters.
2
With these premises a plot of δamide versus cos (R - 35)/
d, where d is the distance (Å) between the shifted proton
and the carbonyl oxygen atom, with conventional least-
squares optimization becomes linear with a regression
2
coefficient of r ) 0.94 (eq 6, Figure 2).
2
δ ) a + 2.16 cos (R - 35)/d
(6)
Remarkably, the angular function in eq 6 does repro-
duce the anisotropic effect as well. It might be argued
that the latter correlation gives rise to anisotropies
regardless of the distance between the given atoms. In
fact, logical solutions can only be obtained for the typical
O-CN-CHR distances encountered in amides. Moreover,
eq 6 can be regarded as a convenient surrogate of the
classical McConnell equation to calculate the magnetic
anisotropy in amides and as having a series of inherent
pluses. In particular, no magnetic susceptibilities are
required, and geometrical parameters can be precisely
determined.
F IGURE 1. Magnetic deshielding (δamide) caused by the amide
function (ppm scale) versus the virtual dihedral angle R (deg)
for amides 1-14 and 16.
for such structures, it is now possible to provide a
schematic diagram (Figure 1) of the magnetic deshielding
(δamide) as a function of the virtual torsion angle H-C-
C-O (R) resulting from the bonding between the carbonyl
carbon and the CR atom as defined in Chart 3.
Experimental data can be fitted to a fourth-order
polynomial plot that most resembles in profile the cos2
function with an approximate phase difference of 35°
(Figure 1). The lack of symmetry as evidenced by the
Equation 6 can be parametrized in solvents other than
downward curvature suggests that not only the dihedral
3 6 2
CDCl , notably DMSO-d and D O, two common solvent
1
840 J . Org. Chem., Vol. 68, No. 5, 2003

Conformation of Secondary Amides
TABLE 8. Exp er im en ta l a n d Ca lcu la ted (B3LYP /6-31G* Str u ctu r es) Ma gn etic Desh ield in gs (δa m id e) for th e E Rota m er of
N-Meth yla ceta m id e in Deu ter a ted Solven ts
CDCl3
DMSO-d6
calcd
D2O
calcd
calcd
exptl
δamide
1.99
exptl
δamide
1.75
calcd
exptl
δamide
1.94
φ
R
d
δH
δamide
δH
δamide
δH
δamide
2
9.0
32.5
150.1
259.8
4.340
3.997
4.064
2.19
1.79
1.78
1.92
1.99
1.59
1.58
1.72
2.09
1.69
1.68
1.82
1
2
47.0
68.8
TABLE 9. Exp er im en ta l a n d Ca lcu la ted Ma gn etic
An isotr op ies for Am id es 1 Z, 7 E, a n d 7 Z a t Differ en t
Th eor y Levels in Deu ter a ted Solven ts
CDCl3
DMSO-d6
D2O
model
calcd exptl calcd exptl calcd exptl
isomer
chemistry
δamide δamide δamide δamide δamide δamide
1
7
7
Z
Z
E
B3LYP/6-31G* 1.94 1.89 1.74 1.63 1.84 1.66
MP2/6-31G*
MP 2/6-31+G** 2.23
HF /6-31G** 2.18
1.97
1.77
2.03
1.98
1.87
2.13
2.08
B3LYP/6-31G* 1.94 1.95 1.74 1.67 1.84 1.83
MP2/6-31G*
MP 2/6-31+G** 2.21
HF/6-31G** 1.93
1.94
1.74
2.01
1.73
1.84
2.11
1.83
B3LYP/6-31G* 2.02 2.03 1.82 1.80 1.92 1.96
F IGUR E 2. Correlation between δamide and the function
2
cos (R - 35)/d for amides 1-14 and 16. Empirical shifts were
As pointed out earlier (Table 2), DFT, HF, and MP2
model chemistries offer different results for the Z isomers
of 1 and 7. Table 9 summarizes again the experimental
and calculated δamide values using the R (deg) and d (Å)
parameters generated by these models. Irrespective of
which model chemistry or solvent was adopted, there is
a good agreement between theory and experiment, no-
3
taken from CDCl solutions at 400 MHz.
systems employed in NMR studies of amides and pep-
tides. To fit the amide anisotropies in these solvents, the
intercept a for the corresponding linear plot has been
recalculated using the same least-squares optimization
as above to give the following values: 1.69 ( 0.08
3
tably in CDCl , with the exception of the structures
(
CDCl
larger deviations (0.14-0.16) observed in DMSO-d
O with respect to those of CDCl (<0.1) are logical
3
); 1.49 ( 0.14 (DMSO-d
6
); 1.59 ( 0.16 (D
2
O). The
obtained at the HF/6-31G** and MP2/6-31+G** levels,
which show large deviations (such figures are given in
bold). These discrepancies result from the wrong con-
former being predicted as the lowest in energy. Thus, it
is relevant to conclude that only theoretical models
predicting anti conformations are consistent with the
experimental anisotropies encountered for simple amides.
As a final illustration, no discrepancies were found either
for the E rotamer of N-methylformamide, as every ab
initio or B3LYP method predicts the anti arrangement
to be the most stable conformer (Table 9 and the
Supporting Information).
6
and
D
2
3
assuming that the Shoolery equations have been param-
etrized for the latter solvent.
Accordingly, we have calculated δanti and δgauche shifts
in DMSO-d
6 2
and D O using eq 6 and hence the theoretical
δ
amide values by means of eq 5. The experimental δamide
estimates have been obtained using the modified Shool-
ery equation (eq 4). In both deuterated solvents the
difference between theory and experiment shows an RMS
error of 0.12 and 0.14 ppm in DMSO-d
6 2
and D O,
respectively, within a (0.30 ppm interval (see the Sup-
porting Information, Table S5 and Figure S3).
Con clu sion s
Nevertheless, the agreement between experimental
and calculated anisotropies (δamide) should also be valid
in the limiting cases, in which neither syn nor anti
conformations can precisely be defined. Thus, our calcu-
lations for the E rotamer of N-methylacetamide, the less
populated isomer in solution, suggest a preferred con-
formation when the φ dihedral angle is ∼29°. A likely
reason for this torsion angle is a balance between a
favorable anti conformation while the repulsion between
methyl groups is kept at a minimum. For this rotamer,
In this paper we describe a primarily computational
study of the conformational behavior of secondary form-
amides with respect to rotation about the CON-alkyl
bond. At the B3LYP/6-31G* level the anti conformation
appears to be the most stable structure for both E and Z
rotamers. Local minima corresponding to syn arrange-
ments have only been detected for formamides containing
only one proton at the CON-CHR position. The barrier
heights for CON-alkyl rotation increase as the bulkiness
of the alkyl group increases, although an almost negli-
gible barrier is found for the Z rotamer of N-methylform-
amide (and N-methylacetamide as well). Magnetic shield-
ings are also calculated for the CHR protons in anti and
gauche arrangements for both E and Z rotamers, and it
is shown that there is a significant and systematic
dependence of the experimental chemical shift on the
3
the CON-CH protons can be observed in some deuter-
ated solvents (Table 8). The application of eq 6 gives rise
to a good agreement between the experimental and
calculated deshieldings in the three solvents studied.
Here, the calculated δamide is the average contribution of
H
the three hydrogen atoms (δ ) arising from eq 6.
J . Org. Chem, Vol. 68, No. 5, 2003 1841

Avalos et al.
torsion angle and the distance between the shifted proton
comments and suggestions that have largely improved
the first draft.
and the oxygen atom, via the optimized expression δ )
2
a + 2.16 cos (R - 35)/d. The latter empirical relationship
allows the measured chemical shift to serve as an
experimental proof of structure. As concluding remarks,
the B3LYP/6-31G* method used for the majority of the
calculations presented has been shown again and again
to yield high-quality results at low computational cost,
and so is quite appropriate for the present application
to the conformational analysis of ordinary amides.
Su p p or tin g In for m a tion Ava ila ble: Figures of computed
variation in the energy profile (kcal/mol) for E and Z rotamers
of formamides 7-9, torsional curves for formamides 15 and
1
6, and a plot of the observed values in three different solvents
2
versus cos (R - 35)/d, Tables of B3LYP/6-31G* torsional
parameters and energy differences (kcal/mol) for N-methyl-
acetamide, acetamides 3, 4, and 6, and acetamides 2 and 5,
populations (%) of the E rotamer for 1 and formamides 7-14
in different solvents, experimental and calculated (eq 6)
Ack n ow led gm en t. Financial support from the Min-
istry of Science and Technology (Grant PB98-0997) and
the J unta de Extremadura-Fondo Social Europeo (Grant
IPR00-C021) is gratefully acknowledged. J .L.B. and
F.R.C. thank the J unta de Extremadura and the Uni-
versity of Extremadura, respectively, for their scholar-
ships. Finally, we thank the reviewers for their valuable
6 2
deshieldings on CON-CHR protons in DMSO-d and D O, and
experimental and calculated (eq 6) magnetic anisotropies for
amides (E)-1 and (E)-7 at different theory levels in deuterated
solvents, and Cartesian coordinates of calculated minimum
energy and saddle point structures. This material is available
free of charge via the Internet at http://pubs.acs.org.
J O026695Z
1
842 J . Org. Chem., Vol. 68, No. 5, 2003