MOLECULAR PROPERTIES



Useful links to fundamental molecular data:

  • JPL Molecular Spectroscopy

  • Splatalogue - database for astronomical spectroscopy

  • NIST Recommended Rest Frequencies for Observed Interstellar Molecular Microwave Transitions




  • Simple Rotational Energy Levels and Transitions

    Molecule Isotope Isotope Isotope Isotope
    CO 13CO C17O C18O 13C18O
    CN 13CN
    CS C33S C34S 13CS
    SiO 29SiO 30SiO
    SiS 29SiS 30SiS Si34S
    C2H
    HCN H13CN HC15N DCN D13CN
    HNC HN13C H15NC DNC
    HCO+ H13CO+ HC18O+ DCO+
    N2H+ N2D+
    HCS+
    OCS O13CS OC34S 18OCS
    HC3N H13CCCN HC13CCN HCC13CN DC3N
    p-CH3CN p-13CH3CN p-CH313CN
    o-CH3CN o-13CH3CN o-CH313CN
    p-CH3CCH p-CH3C13CH
    o-CH3CCH o-CH3C13CH
    SO 34SO
    SO2 34SO2
    H2CO H213CO HDCO
    H2CS

    Notes about diagrams:

    1. The frequencies listed on these pages are generally accurate to 5 MHz or better (except for molecules with hyperfine structure; see note 3). Use the JPL Molecular Spectroscopy webpage to obtain more accurate values for line frequencies.

    2. The relative optical depths for transitions are calculated for a Boltzman population distribution at a temperature of 60 K. The optical depth is normalized so that the highest optical depth transition has log(tau) of unity. The true optical depth in a cloud depends on the molecular abundance and H2 column density, as well as the temperature and density. The sole purpose of the log(tau) column is to give an indication of the relative strengths of different transitions under interstellar conditions. More useful predictions of relative intensities can be obtained by using the LVG program in miriad.

    3. Hyperfine structure is not included in the graphs or calculations of line frequencies. Molecules which include nitrogen will usually exhibit hyperfine structure which is important in determining line frequencies and transition probabilities.

    4. Some molecules are not as simple as you might expect due to nuclear or electronic spin. For example CO is simple but SO is not because its ground electronic state is 3-sigma. Other molecules (e.g. SO2 and CH3OH have very rich energy level diagrams and many transitions due to bent bonds and 3-dimensional structure. O-H bonds in molecules are usually troublesome (e.g. CH3OH and H2O)



    THE EXCITATION OF ROTATIONAL LEVELS OF MOLECULES



    Boltzmann Distributions of Rotational Level Populations

    For a thermalized molecule, the level populations are described by a Boltzman distribution at the gas kinetic temperature, normalized by the partition function. The following graphs show the relative populations of various levels as a function of kinetic temeprature. All populations have been normalized such that the sum over all levels equals unity.

    Thermalized Level Populations
    CO CN CS SiO SiS
    C2H HCN DCN HNC DNC
    HCO+ DCO+ N2H+ N2D+ HCS+
    OCS HC3N

    Except for deutrated species, the energy level shifts associated with isotopic species are not large enough to alter the qualitative behavior of the level populations so non-D isotopic species are not presented here.


    Optically Thin Statistical Equilibrium

    If the density of the gas is insufficient to thermalize a molecule, the level populations will depend on the density and temperature of the gas, and the optical depth in the molecule's lines. If all transitions of the molecule are optically thin, the level populations will achieve a statistical equilibrium between collisions upward and radiative transitions downward. The level populations are then dependent on the density and the temperature, but not the optical depth (i.e. not the molecular column density). In the high density limit, the levels become thermalized and show a Boltzman distribution; in the low density limit, the level populations come into equilibrium with the cosmic background radiation. The following graphs show the behavior of the level populations as a function of density of temperature for conditions covering the regime typical of molecular clouds.

    Statistical Equilibrium Level Populations
    CO CS HCN SiO HCO+
    N2H+ HCS+ SiS OCS HC3N

    The relative level populations can be characterized by an excitation temperature relative to the next lower state, regardless of the fact that the level populations are not thermal. The excitation temperature is defined between two levels such that the Boltzman factor, at the excitation temperature, times the ratio of the statistical weights yields the ratio of the populations. The excitation temperature defined in this way can be larger or smaller than the true gas kinetic temperature; it can even be negative. When the excitation temperature is greater than the kinetic temperature, the molecule is super-thermal in that transition. When the excitation temperature is negative, the transition is capable of masing. The following graphs show the behavior of the excitation temperature for a number of molecules.

    Statistical Equilibrium Excitation Temperatures
    CO CS HCN SiO HCO+
    N2H+ HCS+ SiS OCS HC3N
    OCS HC3N