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Y. Ozaki et al.
Fig. 4.8 a An IR spectrum
in the 3800–3000 cm −1
region and b a NIR spectrum
of the 7600–6000 cm −1
region of diluted methanol in
CCl 4
not to vary due to isotopic substitution, and hence, isotope shifts involve only with
mass effects. Taking a diatomic molecule as an example, one can calculate the magnitude of an isotope shift. Frequency of a stretching vibration of the diatomic molecule
is given by Eq. (4.1)
ν =
1
2π
k
μ
(4.1)
if ν
is the frequency for replacing an atom having a mass m 1 with an isotope having
a mass m 1 ’, the following relation holds:
ν
ν =
μ
μ
(4.2)
where μ
= m 1
m 2 / (m 1
+m 2 ). As Eq. (4.2) reveals, the larger the difference between
m 1 and m 1
, the larger the isotope shift is. Since ν/ ν
= 1.36 if H is replaced with
D, a C–H stretching vibration of saturated hydrocarbon, which is located in the
vicinity of 2900 cm
−1 , shifts close to 2100 cm
−1 . Figure 4.9 shows calculated three
vibrational modes (Amide I’, II’, and III’) of deuterated N-methylacetamide and
the corresponding modes of the nondeuterium-substituted one (Amide I, II, and III
modes) are displayed in Fig. 2.11 [16]. Band shifts induced by the deuterium substitution are rather large for the Amide II and III modes since NH bending vibrations
contribute to these two modes, but the Amide I mode, being principally a C=O