The tables accompanying the spectra contain all the lines that went into the calculation of the spectrum and should contain all lines that might interfere with the calibration lines. The tables all have a similar format with the exception of the quantum numbers necessary to specify the transition.
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.
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.
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.
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 wave number 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.
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 (when hyperfine structure is shown in the tables), Ω, 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.
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, while16O12C32S would be 622.
The spectral illustrations are actually calculated spectra rather than reproductions of real measurements. This gave us more flexibility in choosing effective pressures and path lengths 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 path length. Certainly, absorption due to common impurities such as H2O or CO2 will not be found in these spectra.
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.