compared to the same group that does not have the hydrogen bond.
Because the secondary structure has well-defined hydrogen-bonding
patterns, this results in highly characteristic vibrational spectra. For
example, the amide I mode has typical frequencies at: 1650 – 1660 cm−^1
for an αhelix, 1630 –1640 cm−^1 for a βsheet, and 1680 –1700 cm−^1 for
no hydrogen bond.
The effect of hydrogen bonding can be understood by reviewing the
properties of vibrational states. For a mass, m, attached to a wall by a spring
with a characteristic constant, k, the mass will vibrate with a vibrational
frequency ω(eqn 11.7):
(11.36)
We can represent a simple bond between two atoms as a spring, with
a spring constant kattached to two masses, m 1 and m 2. In this case, we
need to include the contribution of the mass of the second atom to the
vibrational frequency ω. This is done through the reduced mass μ:
(11.37)
then
(11.38)
The effect of hydrogen reducing the vibrational frequency can be modeled
as decreasing the bond strength or increasing the effective mass. The sen-
sitivity of the vibrational frequency to such effects allows identification of
the contributions that individual atoms make to the vibrational spectra
through isotopic substitution.
Consider a CO bond in a protein. Normally it is composed of^12 C^16 O and
a typical bond strength would be 1900 N m−^1. This leads to a vibrational
frequency of:
(11.39)
(11.40)
(11.41)
A
().
=
××−
−
−
1
23 10
1900
(^101) 114 10
1
π cm s^26
Nm
kgg
= 2167 cm−^1
A== =
νω
ccππμc
1 k
2
1
2
μ=.
=
×
+
=×
mm
mm
CO m
CO
p
12 16
12 16
606 ( .1 67 10×=×−−^27 kg) 1 14. 1026 kg
ω
μ
=
k
μ
μ
=
+
=+
mm
mm m m
12
12 1 2
11 1
or
ω=
k
m