2 Principles and Characteristics of NIR Spectroscopy
29
Amide I
Amide II
Amide III
Fig. 2.11 Three normal vibrations of N-methylacetamide which is a model of an amide group
characteristic of C = O stretching vibration. Meanwhile, the amides II and III are
coupling modes of C-N stretching vibrations and N-H in-plane bending vibrations.
Of the three, the amides I and II appear strongly in IR spectra, and in Raman spectra
the amide I and III appear intense. The amide I, II and III bands of proteins are found
generally in the regions of 1690-1620 cm
−1 , 1590-1510 cm
−1 and 1320–1210 cm
−1 ,
respectively. These modes are known to sensitively reflect secondary structures of
polyaminoacids, peptides, and proteins. In NIR spectra bands due to the overtones
and combinations of amide modes such as the combination of NH stretching mode
and Amide II appear.
2.2.2.5 Quantum Mechanical Treatment of Vibrations of Polyatomic
Molecules
Now, let us study vibrations of polyatomic molecules using quantum mechanics. A
kinetic energy T and a positional energy V are expressed as:
Therefore, a total energy H is:
T =
1
2
n
i=1
˙
Q
2
i
(2.24)
V =
1
2
n
i=1
λ i Q
2
i
(2.25)
Therefore, a total energy H is:
H = T + V =
1
2
n
i=1
˙
Q
2
i +
1
2
n
i=1
λ i Q
2
i
(2.26)
Replacing ˙
Q with −ih/2π・d/d Q again and calculating ˆ
H , we can obtain a
Schrodinger equation of vibrations of polyatomic molecules.
−
h
2
8π 2
n
i=1
∂
2
ψ
∂ Q
2
i
+
1
2
n
i=1
λ i Q
2
i ψ = Eψ
(2.27)