94
4 Rotation of the Polyatomic Molecule
the Second World War thanks to availability of microwave hardware developed for
radars (microwave sources–mainly klystrons and detectors).
The simplest spectrometer consists of a coherent source (historically a klystron),
a cell containing the gas at low pressure and a detector (crystal diode) measuring
the microwave power. The cell is generally a rectangular waveguide of 1–3 m length
sealed at each end with a microwave transmitting window and connected to a vacuum
line. The use of such a spectrometer is extremely limited (except in the millimeterwave range where the absorption is stronger) because: (i) the absorption of the gas is
weak (ii) there are strong spurious cell absorptions iii) the noise due to the detector
is important.
The sensitivity is improved by applying a modulation to the source. A tuned amplifier with a finite pass band permits to reduce the noise by two orders of magnitude.
The most used spectrometer up to the eighties was the Stark-modulated spectrometer
introduced by Hughes and Wilson (1947). An on–off square-wave electric field is
applied to the gas. When the field is on, the rotational energy levels are split by the
Stark effect, and the Stark components are at a different frequency of the zero-field
line. The effect is the same as the instantaneous appearance and disappearance of
the gas. The signals are thus modulated at the frequency of the square-wave and
are detected using a narrow-band amplifier followed by a phase-sensitive detection
technique, which allows the signal components, which are phase-coherent with the
reference voltage to reach the output. Thanks to the Stark spectrometer thousands of
spectra were recorded. However, this kind of spectroscopy has several weaknesses:
It lacks of resolution, its sensitivity is sometimes not good enough (in particular the
measure the spectra of isotopologues in natural abundance), and for large molecules,
the recorded spectra are extremely crowded and difficult to assign.
To improve the resolution (and marginally the sensitivity), a superheterodynedetection bridge-spectrometer with double phase-demodulation was proposed
(Rudolph and Schwoch 1971) with no success.
To improve the sensitivity, thanks to the advent of minicomputers (and later
microcomputers), computer-controlled Stark-effect spectrometers were used which
allowed adding up scans, thus improving greatly the signal/noise ratio (Gwinn et al.
1968).
Actually, the best method to increase at the same time the resolution and the
sensitivity is to use the Fourier transform (FT) technique as will be described below
in Sect. 4.12.2.
There are two main ways to simplify the spectra. The first one is to use a gas jet
into which the sample is seeded. Adiabatic cooling of the rotational and vibrational
degrees of freedom in a supersonic jet considerably simplifies the rotational spectrum
as only low-J transitions in the ground vibrational state are observed.
The second method is double resonance (Woods et al. 1966; Baker 1979; Jones
1979). Consider three energy levels |1 > , |2 > , and |3 > with respective populations
N 1 , N 2 , and N 3 . Assume that transitions are allowed between |1 > and |2 > , and |2
> and |3 > , see Fig. 4.3. The sample is irradiated simultaneously at two different
frequencies: The pump at the frequency of the transition ν 12 = |2 > ← |1 > is used
to saturate it, while the second source (signal) is at the frequency of the transition
4 Rotation of the Polyatomic Molecule
the Second World War thanks to availability of microwave hardware developed for
radars (microwave sources–mainly klystrons and detectors).
The simplest spectrometer consists of a coherent source (historically a klystron),
a cell containing the gas at low pressure and a detector (crystal diode) measuring
the microwave power. The cell is generally a rectangular waveguide of 1–3 m length
sealed at each end with a microwave transmitting window and connected to a vacuum
line. The use of such a spectrometer is extremely limited (except in the millimeterwave range where the absorption is stronger) because: (i) the absorption of the gas is
weak (ii) there are strong spurious cell absorptions iii) the noise due to the detector
is important.
The sensitivity is improved by applying a modulation to the source. A tuned amplifier with a finite pass band permits to reduce the noise by two orders of magnitude.
The most used spectrometer up to the eighties was the Stark-modulated spectrometer
introduced by Hughes and Wilson (1947). An on–off square-wave electric field is
applied to the gas. When the field is on, the rotational energy levels are split by the
Stark effect, and the Stark components are at a different frequency of the zero-field
line. The effect is the same as the instantaneous appearance and disappearance of
the gas. The signals are thus modulated at the frequency of the square-wave and
are detected using a narrow-band amplifier followed by a phase-sensitive detection
technique, which allows the signal components, which are phase-coherent with the
reference voltage to reach the output. Thanks to the Stark spectrometer thousands of
spectra were recorded. However, this kind of spectroscopy has several weaknesses:
It lacks of resolution, its sensitivity is sometimes not good enough (in particular the
measure the spectra of isotopologues in natural abundance), and for large molecules,
the recorded spectra are extremely crowded and difficult to assign.
To improve the resolution (and marginally the sensitivity), a superheterodynedetection bridge-spectrometer with double phase-demodulation was proposed
(Rudolph and Schwoch 1971) with no success.
To improve the sensitivity, thanks to the advent of minicomputers (and later
microcomputers), computer-controlled Stark-effect spectrometers were used which
allowed adding up scans, thus improving greatly the signal/noise ratio (Gwinn et al.
1968).
Actually, the best method to increase at the same time the resolution and the
sensitivity is to use the Fourier transform (FT) technique as will be described below
in Sect. 4.12.2.
There are two main ways to simplify the spectra. The first one is to use a gas jet
into which the sample is seeded. Adiabatic cooling of the rotational and vibrational
degrees of freedom in a supersonic jet considerably simplifies the rotational spectrum
as only low-J transitions in the ground vibrational state are observed.
The second method is double resonance (Woods et al. 1966; Baker 1979; Jones
1979). Consider three energy levels |1 > , |2 > , and |3 > with respective populations
N 1 , N 2 , and N 3 . Assume that transitions are allowed between |1 > and |2 > , and |2
> and |3 > , see Fig. 4.3. The sample is irradiated simultaneously at two different
frequencies: The pump at the frequency of the transition ν 12 = |2 > ← |1 > is used
to saturate it, while the second source (signal) is at the frequency of the transition