Modern Polymer Spect..

250 5 Vibuntiorid Si7ectvoscop.y of Polypeptides
5.3.1 N-Methylacetamide
Normal mode calculations on NMA have been done with both empirical and scaled
ab iizitio force fields. In the empirical force field calculations, the CHj group has
been treated as a point mass, using a UBFF [52] as well as a GVFF [51, and as an
all-atom structure, again with a UBFF [53] and a GVFF [54, 551. In the ah iizitio
calculations, a variety of basis sets and scaling methods have been used: 4-31G,
with adjustment of mainly diagoiial force constants to liquid-state fi-equencies of
NMA and its isotopomers [56]; 4-31G and 4-31G*, with no scaling [57]; 4-21, with
four general scale factors and some approximated force constants [58]; and 4-31G*,
with 10 scale factors [59], optimized to matrix-isolated frequencies [60].
All of the above calculations have been on the isolated molecule, even though in
many cases comparisons have been made with experimental results on hydrogenbonded
systems (such as the neat liquid). The first noimal mode calculation on
a hydrogen-bonded system was at 4-31G* on NMA-(H20)2, in which one H2O
molecule was hydrogen bonded to the CO group and the other to the NH group,
with scale factors optimized to IR and Raman data on the aqueous system [61]. In
view of the absence of infomiation on the detailed water structure associated with
the NMA molecule in aqueous solution, this was considered to be a satisfactory
minimal model for representing the normal modes of hydrogen-bonded NMA.
(A 4-31G calculation 011 NMA-(H20)3 has also been done [62].) Subsequently, a
3-21G calculation was done on NMA-(fomiamide)z, NMA-(FA)?, using six
general scale factors [63]. In view of the determination that diffhe functions are
necessary to give a planar symmetric peptide group in the isolated molecule 1251,
the NMA-(H20)2 calculations have been repeated at 6-31 + G* [64], and these are
discussed below.
Early studies [52, 65, 661 sought to describe the characteristic vibrational modes
of the peptide group. In addition to the localized NH s mode, which is subject to
Fermi resonance interactions [5], there are other relatively localized modes, labeled
amide I-VII (although it was recognized [66] that some of these, because of their
delocalization, would be more variable than others). These amide modes have been
used as a basis for discussions of peptide spectra, and in Table 5-1 we describe them
and compare the PEDs for isolated and aqueous hydrogen-bonded NMA. It should
be noted that these results are on fully optimized structures (all frequencies real),
in both cases the conformation being N,Ct. (The symbol indicates that the in-plane
N-methyl hydrogen is cis to the (N)H and the in-plane C-methyl hydrogen is trans
to the (C)O.)
The amide I mode is primarily CO s, both in NMA and NMA-(H20)2. However,
the additional contributions to the eigenvector depend very much on the
specifics of the calculations (only contributions to the PED of 2 10 are given in
Table 5-l), as well as, of course, on the absence or presence of hydrogen bonding.
For NMA, the next largest contributor in a CH3 point-mass calculation is CN s
[52, 51, whereas in an all-atom calculation it is CCN d [55, 591. The situation for
NMA-( H20)2, where the lower frequency is an obvious consequence of hydrogen
bonding, is complicated by the experimentally demonstrated coupling of CO s
and HOH b 167, 681, which makes the latter the next largest contributor. In NMA-