The files in the
Entries section contain predictions for atoms and molecules of
astrophysical and atmospheric interest as well as some documentation on
which data have been used for the predictions.
At present, the aim of of this page is to supplement data bases such as the
JPL catalog. Herb Pickett's programs
**SPFIT** and **SPCAT** have been
used for the most part to generate the predictions.

After some general remark, a brief description of the format of the catalog entries follows below along with remarks on the selection rules and assignments, comments on the reliability of the predictions, remarks on the partition function, and some useful equations.

The structure of the files is described in
detail in the Letter
**THE COLOGNE DATABASE FOR MOLECULAR SPECTROSCOPY, CDMS**
by H. S. P. Müller, S. Thorwirth, D. A. Roth, and G. Winnewisser;
*Astron. Astrophys.* **370** (2001) L49 – L52.

An update on the CDMS has appeared very recently:
H. S. P. Müller, F. Schlöder, J. Stutzki, and
G. Winnewisser, **THE COLOGNE DATABASE FOR MOLECULAR SPECTROSCOPY, CDMS:
A USEFUL TOOL FOR ASTRONOMERS AND SPECTROSCOPISTS**,
*J. Mol. Struct.* **742**, 215–227 (2005).

Please acknowledge use of the CDMS by citing these articles. You are
very welcome to state the web address also.
We recommend to cite the original sources of the data too, which are given
in the documentations, at least as far as this is feasible.
Since the format in the CDMS catalog is identical to the one in the
JPL catalog information can also be found
in the article SUBMILLIMETER, MILLIMETER, AND MICROWAVE
SPECTRAL LINE CATALOG by H. M. Pickett, R. L. Poynter,
E. A. Cohen, M. L. Delitsky, J. C. Pearson, and
H. S. P. Müller; *J. Quant. Spectrosc. Radiat. Transfer*
**60** (1998) 883 – 890.

Some catalog entries are available with frequencies in units of
cm^{–1}. This applies mainly to light hydrides and some
stable molecules that might be of interest as secondary standards
in the laboratory or in radioastronomical observations.

Vibration-rotation transitions in the
far-infrared region have been included for C_{3}.
They may be included in a greater number in the near future.
Vibration-rotation transitions in the mid-infrared region are
currently not considered to be included in the database. If there is a
genuine interest for such information to be included in our database
please use the comments and suggestions
option below in order to suggest species. Information on background
literature is desirable !!

As in the JPL catalog, the species are sorted according to their
molecular weight in atomic mass units, which also constitutes
the first three digits of the six digit
**molecule tag**
(with leading zeros frequently omitted),
the fourth digit is a 5 (to avoid any conflict with the
JPL numbering scheme), and the last two digits
are used to number entries with the same molecular weight.

**Comments and suggestions**
are very welcome. Please visit the
Contact section.

Each line in a given catalog entry corresponds to one spectral feature,
some of which might be overlapped. The information given for the
spectral features is shown below for two lines of
H_{2}C^{18}O.

Frequency of the line (usually in MHz, can be in
cm^{–1}; see below); uncertainty of the line (usually in MHz, can be in
cm^{–1}; see below); base 10
logarithm of the integrated intensity at 300 K (in
nm^{2}MHz); degree of freedom in the rotational
partition function (0 for atoms, 2 for linear molecules, and 3 for
non-linear molecules; lower state energy (in
cm^{–1}); upper state degeneracy
** g_{up}**; molecule tag (see
below) – a negative value indicates that both line frequency and
uncertainty are experimental values; coding of the quantum
numbers; and finally the quantum numbers.

1872169.0570 0.2000 -1.3865 3 887.6325165 -32503 30327 325 26 324 1872505.7621 0.2374 -2.3388 3 1107.9703 55 32503 30327 622 26 621

REMARKS

The line position and its uncertainty are **either** in units of
**MHz**, namely if the uncertainty of the
line is greater or equal to zero; **or** the units are in
**cm ^{–1}**, namely if the
uncertainty of the line is less or equal to zero !

with ** g_{I}** the spin-statistical weight
and

Common factors in

**Note:**

the degree of freedom in the rotational partition function has been
provided because of tradition. It is not needed in any of the calculations
or conversions. A linear molecule will only have the value of 2 if
exactly 1 value of *K* or corresponding quantum numbers is permitted
(per vibrational state). A molecule with several allowed values of *K*
has an additional degree of freedom and is better considered as a
non-linear molecule.

The six digit molecule tag consists of
the molecular weight in atomic mass units for the first three digits
(here: 2×1 + 12 + 18 = 32), a 5, and the last two digits are
used to differenciate between entries with the same molecular weight.

**Note:** leading zeros are frequently omitted.

The quantum numbers are given in the
following order:

*J*
(or *N*);
*K _{a}* and

for the upper state followed immediately by those for the lower state (see also below).

*N*is the total rotational angular momentum excluding electron and nuclear spins. For singlet molecules,*J*, the total rotational angular momentum including electron spin, is equal to*N*.*K*and_{a}*K*are the projections of_{c}*N*onto the*A*and*C*inertial axes, respectively. For symmetric top molecules, only*K*is needed (instead of*K*and_{a}*K*) along with + or –, which designate the parity; if redundant, the latter might be omitted. Instead of_{c}*K*, L or*l*may be used for linear molecules.*v*is a**state number**! It specifies different vibrational or electronic states. It may also be used to distinguish between different species that have been fit simultaneously. Details on the meaning of the state numbers are given in the documentation !

**Note:**More than one state number may be needed to designate one vibrational state – this is the case, for example, for a degenerate (e.g. bending) state of a symmetric top molecule !*F*_{1}. . .*F*designate spin quanta. In general, the electron spin*S*is coupled to the rotational angular momentum first, followed by nuclear spins. In this case*F*_{1}=*J*.

**Very Important:**

Exactly two characters are available for each quantum number. Therefore,
half integer quanta are rounded up ! In addition, capital letters are used
to indicate quantum numbers larger than 99. E. g. A0 is 100, Z9 is 359.
Small types are used to signal corresponding negative quantum numbers.

Since the program was written for asymmetric top molecules, some of the quantum numbers may be redundant.

Six quantum numbers are available at most to describe the upper and
lower state, respectively. In case more quantum numbers are needed,
even if some of them are redundant, the only spin designating quantum
numbers are *n, F*, were
*n* is an aggregate spin number.

Strictly speaking, only the final quantum number *F*, which includes
all effects of rotation etc. as well as electronic and nuclear spins,
is a good one; meaning that it has a well-defined an unambiguous meaning.
And this holds only in the absence of an electric or magnetic field.
Mixing effects mediated by, e. g., vibration-, fine structure-
(electronic spin), or hyperfine structure-rotation interaction
(nuclear spins) frequently will prevent
*N*, *K*, *v*, *J*, or *F _{i}*
from being good quantum numbers in general. Of course, in many instances
these quantum numbers are reasonably meaningful over a large range of
quantum number combinations. Only the selection rule

The projections of the rotational angular momentum onto the *a*- and
*c*-axes are described by the quantum numbers *K _{a}*
and

The ** a-type** transitions are described by
Δ

The assignment of quantum numbers may seem to be a straightforward issue.
While this is true in many simple systems this is
**not** the case in general !!
Mixing effects are model-dependent, and in extreme cases the assignment of
certain levels can be altered based on very small changes in the parameter
– even more so if the parameter set is different.

The assignment of, e. g., *K* quantum numbers is not always unique.
To avoid assignment of one quantum number to more than one state, quantum
numbers are assigned to levels in the order of increasing ambiguity.

The presence of more than one non-zero spin will cause assignment ambiguities.
To minimize these assignment ambiguities, certain rules apply how the various
spin-angular momenta are coupled to the rotational angular momentum. Usually,
they are coupled in order of decreasing size.
**Exception:** one set of equivalent nuclear
spin-angular momenta is coupled to the combined spin-rotational angular
momentum last. The same applies if two different spin-angular momenta are
coupled together before they are coupled to the combined spin-rotational
angular momentum. Thus, the electronic spin-angular momentum is usually
coupled to the rotation first.
**Exception:** if the effects of the
nuclear spin-electron spin coupling are larger than the effects caused by
the electronic spin alone. This may happen in particular in some radicals
with Σ electronic state, e. g. in ^{13}CN, the order of
the spins is ^{13}C, electron, ^{14}N. Quantum number
assignments **always** refer to Hund's case
(b). Alternative assignments may be available as non-default in the future.

The predicted uncertainties of the transition frequencies are model dependent. Therefore, an additional parameter employed in the fit will cause these to increase in general. Basically for the same reason, extrapolations should always be viewed with some caution since these may be affected by spectroscopic parameters that could not be determined thus far. In contrast, interpolations should be reliable in most instances.

If a large number of transition frequencies has been measured and is included in a fit the predicted uncertainties can be much smaller than the experimental uncertainties for a large range of quantum numbers. One should keep in mind that these smaller uncertainties are only meaningful if the experimental uncertainties are caused by purely statistical effects. For that matter, the predictions in the CDMS catalog have experimental transition frequencies and uncertainties nerged into the catalog file to indicate a more conservative means.

Recent catalog entries often contain some estimates as to how far the predictions should be reliable. Here "reliable" means that the transition frequencies should be found within three to ten times the predicted uncertainties.

The partition function *Q*
is very important to calculate intensities
of molecular lines at a given temperature. In general, only data for the
ground vibrational state have been considered in the calculation of *Q*
for a certain species. If excited vibrational states have been taken into
account this will be mentioned in the documentation. Usually, individual
contributions of the vibrational states are given in the documentation, too,
or a link is given to a separate file containing the information.

Spin-statistical weight-ratios have been considered in most instances.
**NOTE:** Common factors have been devided off
in order to keep *Q* and *g _{up}* small. Therefore, it is
strongly advizable to compare

In very cold regions of the ISM it may be important to consider *ortho*
and *para* states separately. The energy of the lowest rotational or
rotation-hyperfine level is 0 by default. The energy of the lowest level for the
other spin-modification(s) is usually given in the documentation. Strictly speaking,
one should consider *Q* values for the different spin-modifications separately
– at least at low temperatures. We intend to provide this information in the
near future.

Here are some equations the user of the CDMS
catalog may find helpful. They are taken from

SUBMILLIMETER,
MILLIMETER, AND MICROWAVE SPECTRAL LINE CATALOG

by H. M. Pickett,
R. L. Poynter, E. A. Cohen, M. L. Delitsky, J. C. Pearson, and
H. S. P. Müller;

*J. Quant. Spectrosc. Radiat. Transfer*
**60** (1998) 883 – 890.

- The intensity
*I*(*T*) is calculated according to

*I*(*T*) = (8π^{3}/3*hc*)*ν**S*µ_{g}_{g}^{2}(*e*)/^{–E"/kT}– e^{–E'/kT}*Q*_{rs}(*T*)

with*ν*and*S*being the line frequency and strength, respectively, µ_{g}the dipole moment along the molecular_{g}*g*-axis,*E"*and*E'*the lower and upper state energy, respectively, and*Q*_{rs}the rotation-spin partition function at the temperature*T* - With
*I*(*T*) in nm^{2}MHz,*ν*in MHz, and µin D one obtains_{g}

*I*(*T*) = 4.16231 × 10^{–5}*ν**S*µ_{g}_{g}^{2}(*e*)/^{–E"/kT}– e^{–E'/kT}*Q*_{rs}(*T*) - Or conversely

*S*µ_{g}_{g}^{2}= 2.40251 × 10^{4}*I*(*T*)*Q*_{rs}(*T*)*ν*^{–1}(*e*)^{–E"/kT}– e^{–E'/kT}^{–1}**Note:**While frequently it is straightforward to calculate*S*from_{g}*S*µ_{g}_{g}^{2}by deviding through the respective µ_{g}^{2}, this is not always correct or applicable, for example in cases of strong vibration rotation interaction. - The intensity in nm
^{2}MHz is converted to cm^{–1}/(molecule/cm^{2}) by dividing the catalog intensity by

2.99792458 × 10^{18} *A*=*I*(*T*)*ν*^{2}(*Q*_{rs}(*T*)/*g*_{up}) (*e*)^{–E"/kT}– e^{–E'/kT}^{–1}× 2.7964 × 10^{–16}s^{–1}- Combined with
**2.**one obtains

*A*= 1.16395 × 10^{–20}*ν*^{3}*S*µ_{g}_{g}^{2}/*g*_{up}

**Note:**Numerical problems may occur in eq. 1, 2, 3 and 5 if the frequency*ν*is small with respect to the lower state energy*E"*. It is advisable to take the following expressions into accout: -
*e*=^{–E"/kT}– e^{–E'/kT}*e*(1 –^{–E"/kT}*e*^{–(E' – E")/kT}) =*e*(1 –^{–E"/kT}*e*^{–ν/kT}) - With
*ν/kT*much smaller than 1 one obtains

1 –*e*^{–ν/kT}≈*ν/kT*

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