The tables accompanying the spectra contain all the lines that went into
the calculation of the spectrum and should contain all lines that might
interfer with the calibration lines. The tables all have a similar format
with the exception of the quantum numbers necessary to specify the transition.
Wavenumbers
The first column gives the wavenumber for the line in units of cm-1.
To convert to frequency units (MHz), multiply by 29 979.2458. The
wavenumbers are calculated values because they are more reliable than
individual line measurements and the uncertainties in the calculated
wavenumbers can be accurately estimated.
Asterisks
Following the wavenumber is a space for an asterisk (*). If the
asterisk is present, it indicates that the wavenumber has been determined from
heterodyne frequency measurements and is certified to be as accurate as the
uncertainty indicates. All lines without asterisks are of uncertain accuracy
regardless of how small the uncertainty may be and should never be used
for calibration.
In assigning the asterisks no consideration was given to problems related
to overlapping with other transitions. The tables list nearby lines that may
cause problems with overlapping and the user must exercise judgment in
determining if such overlapping will impair the accuracy of the measurement.
The asterisk only certifies the accuracy of the line position in the
hypothetical absence of any other nearby lines. Obviously, the resolution
of the instrumentation being used will determine if a nearby line might
invalidate the accuracy of the calibration line.
Uncertainties
The uncertainties in the wavenumbers are given after the wavenumbers in
those cases where there is reason to believe that a good estimate of the
uncertainty can be made. Even so, the uncertainty in the lines not designated
with an asterisk should be taken with some degree of skepticism.
The uncertainties given in the tables are twice the estimated standard error
as calculated from the variance-covariance matrix given by the least-squares
fit that determined the constants used to calculate the wavenumbers. The
uncertainties refer to the accuracy of each individual transition. In general,
the wavenumber separation of two nearby lines for the same vibrational
transition of the same molecular species will be given more accurately than
the uncertainty might lead one to believe. That is because the relative
differences between the rotational energy levels are usually known more
accurately than the differences in the vibrational energy levels.
On the other hand, the separation of two lines that are due to absorption
from two different isotopic species is probably known no more accurately
than the uncertainty would lead us to believe.
Lower State Energy
As an aid in calculating intensities at different temperatures, the tables
contain a column giving the separation (in cm-1) of the lower state
energy level from the ground state.
Intensity
The fourth column of numbers contains an estimate of the intensity for each
transition at a temperature of 296 K. The format for the intensity values
is the standard computer format consisting of a decimal value followed by the
exponent (the power of ten multiplying the decimal value). The intensities
given in the wavenumber tables are integrated line intensities (given in units
of cm/molecule) rather than peak intensities. The units given in the tables
can be converted to the more common units of cm-2 atm-1
at 296 K by multiplying by 2.479 × 1019.
The intensity values are only given as an aid in
estimating the appearance of the spectrum, they should not be treated as well
determined values. The intensities given for weak lines and especially for the
rarer isotopomers may be in error by 50 percent or more.
Quantum Numbers
In every case the upper and lower state J-values are given last,
next to the date. For CO, CS2, OCS, and N2O, the upper
state vibrational quantum numbers are given first followed by the lower state
vibrational quantum numbers. For NO the upper state quantum numbers F,
omega, and v are given followed by the lower state values. For the
bending vibrations and for NO the symmetry of the state is indicated by the
e/f notation.
Date of Entry
The month, day, and year are given to indicate when the last change was
made in the entry.
Molecular Species
A two or three digit number is used to indicate the isotopic species
responsible for the absorption line. The code consists of combining the last
digit of the atomic mass (rounded to the nearest whole number) for each atom
in the molecule. For example, 12C16O would be 26, while
16O12C32S would be 622.
Description of Spectra
The spectral illustrations are actually calculated spectra rather than
reproductions of real measurements. This gave us more flexibility in choosing
effective pressures and pathlengths that seemed most appropriate to illustrate
even the weak lines. Comparison with real spectra measured in our own
laboratory or illustrated in published works showed that the spectra given in
this atlas are adequate for identifying the calibration lines. Some weak
transitions may be absent from the calculated spectrum even though they might
be found in a real spectrum of comparable pressure and pathlength. Certainly,
absorption due to common impurities such as H2O or CO2
will not be found in these spectra.
Arrows
At the top of each spectrum arrows indicate the positions of the lines
that have asterisks, i.e. those lines that have been determined by
frequency measurements. These are the lines that have been most accurately
measured although the user must exercise caution in making sure that nearby
lines shown in the table do not affect the proposed measurement. (see
Description of Tables, Asterisks)
How Spectra Were Calculated
The atlas is divided into sections according to the vibrational transitions
involved. At the beginning of each section the parameters (slit width, dipole
derivative, Herman-Wallis constants) used in calculating the spectrum are
given. The lines were first given a width and shape dictated by the Doppler
width of the line and then convolved with the pressure broadened width.
The spectra were then converted from absorption coefficient to a percent
transmission scale and convolved with an instrument function.
As with any digitized spectrum, regardless of whether it is calculated or
measured, the peak intensity of sharp lines may show some irregularity
depending on whether the true peak falls on a digitized point or slightly
misses it. The spectra were plotted with a digitizing interval of about
0.0003 to 0.001 cm-1. Close doublets that should have the same
intensity may show slight intensity differences because of this digitizing
effect.
