\newcommand{\species}{298}
\newcommand{\nlines}{1,448,153}
\pagenumbering{roman}
\setcounter{page}{3}
\newpage
\begin{center}{\large ABSTRACT}\end{center}
\begin{quote}
\vspace{.25in}
This report describes a computer-accessible catalog of submillimeter,
millimeter, and microwave spectral lines in the frequency range between 0 and
10,000 GHz (i.e., wavelengths longer than 30 $\mu$m). The catalog can be
used as a planning guide or as an aid in the identification and analysis of
observed spectral lines. The information listed for each spectral line
includes the frequency and its estimated error, the intensity, the lower state
energy, and the quantum number assignment. This edition of the catalog has
information on \species{} atomic and molecular species and includes a total of
\nlines{} lines.
The catalog has been constructed by using theoretical least squares fits of
published spectral lines to accepted molecular models. The associated
predictions and their estimated errors are based upon the resultant fitted
parameters and their covariances. Future versions of this catalog will add
more atoms and molecules and update the present listings as new data appear.
The catalog is available on-line via anonymous ftp at
spec.jpl.nasa.gov and on the world wide web at
\url{http://spec.jpl.nasa.gov}.
\end{quote}
\label{ABSlabel}
\pdfbookmark[1]{ABSTRACT}{ABSlabel}
\newpage \makebox[1in]{}
\newpage
\begin{center}{\large FOREWORD}\end{center}
Revision 2 of the Submillimeter Spectral Line Catalog incorporated
a number of changes: (1) a quantum number format, (2) addition of a complete
set of partition functions for each species,
(3) a computer-accessible directory of species,
(4) a table of relative abundances of the isotopes under terrestrial
conditions, (5) a new format for the individual species descriptions,
(6) eighteen new species, and (7) thirty revised species.
The present version is changed only by the addition of new and revised
species. The changes are as follows:
\begin{center}
\begin{tabular} {@{}rlrlrl@{}}
\multicolumn{6}{c}{\bf NEW SPECIES, REV.~4 (93)}\\
\tagname & \tagname & \tagname\\
7001 & Li-6-H & 8001 & LiH & 8002 & Li-6-D \\
9001 & LiD & 13003 & CH+ & 19004 & H3O+ \\
25002 & NaH & 27004 & C-13-N & 28008 & HCNH+ \\
28009 & CO+ & 29006 & CO-17 & 29007 & HOC+ \\
30010 & HOC-13+ & 30011 & NO+ & 30012 & DOC+ \\
31003 & HDCO & 31004 & HO-18-C+ & 31005 & HNO \\
32006 & D2CO & 32007 & DNO & 37002 & C3H \\
37003 & c-C3H & 38003 & C3D & 38004 & CCC13H \\
38005 & C13CCH & 38006 & c-C3D & 40003 & SiC \\
40004 & SiC-v1 & 40005 & KH & 41007 & SiC-13 \\
41008 & CaH & 41009 & CH3NC & 42004 & CaD \\
42005 & K-41-H & 44010 & HCP & 44011 & AlOH \\
45009 & DCP & 45010 & HOCO+ & 45011 & AlOD \\
45012 & O-17-CO & 46008 & CH3OCH3 & 46009 & AlF \\
46010 & NS & 46011 & DOCO+ & 46012 & HOC-13-O+ \\
46013 & O-18-CO & 48009 & NS-34 & 49003 & C4H \\
49004 & MgCCH & 50008 & C3N & 50009 & MgCN \\
50010 & MgNC & 51004 & HCCNC & 51005 & HCCNC-v7 \\
51006 & HCCNC-v6 & 51007 & HCCNC-v5 & 51008 & HNCCC \\
52012 & DNCCC & 53007 & C2H3NC & 54007 & HCCCHO \\
56007 & CCS & 56008 & C2H3CHO & 57001 & C-13CS \\
57002 & CC-13S & 58001 & CCS-34 & 58002 & NaCl \\
60003 & CH3OCHO-A & 60004 & CH3OCHO-E & 60005 & NaCl-37 \\
61003 & C5H & 62005 & AlCl & 62006 & C5D \\
64003 & AlCl-37 & 66002 & OS-34-O & 66003 & CaNC \\
69002 & C3H7CN & 73001 & HC6 & 74001 & KCl \\
74002 & C2H5OOCH & 75002 & H2NCH2COOH-I& 75003 & H2NCH2COOH-II\\
76008 & KCl-37 & 76009 & C4Si & 89001 & Sr-88-H \\
90001 & Sr-88-D & 92001 & C5S & 94001 & C5-34-S \\
96001 & HOBr-79 & 98002 & HOBr-81 & 99002 & HC7N \\
112001 & Se-80-O2 & 123001 & HC9N & 147001& HC11N \\
\end{tabular} \\[2ex]
\begin{tabular} {@{}rlrlrl@{}}
\multicolumn{6}{c}{\bf REVISED SPECIES, REV.~4 (24)}\\
\tagname & \tagname & \tagname\\
26001 & CN, v = 0, 1& 27002 & HNC & 28001 & CO \\
28007 & DNC & 29001 & C-13-O & 30001 & CO-18 \\
33001 & HO2 & 34001 & O-18-O & 34002 & H2S \\
34004 & H2O2 & 38002 & c-C3H2 & 39001 & c-HC-13-CCH \\
39002 & c-HCC-13-CH & 39005 & c-C3HD & 41001 & CH3CN \\
46004 & C2H5OH & 49001 & O3-sym-O-17 & 49002 & O3-asym-O-17\\
52007 & SiCC & 53001 & C2H3CN & 55001 & C2H5CN \\
80001 & HBr-79 & 82001 & HBr-81 & 98001 & H2SO4 \\
\end{tabular}
\end{center}
For reference, the changes in Rev.~3 are:
\begin{center}
\begin{tabular} {@{}rlrlrl@{}}
\multicolumn{6}{c}{\bf NEW SPECIES, REV.~3 (55)}\\
\tagname & \tagname & \tagname\\
4001 & H2D+ & 19003 & H2O-17 & 20002 & HF \\
20003 & H2O-18 & 21001 & HDO-18 & 21002 & DF \\
27003 & HCN-v2 & 32005 & O2 snglt dlta & 33002 & O-17-O \\
37001 & DCl & 38002 & C3H2 & 39001 & C-13-3H2a \\
39002 & C-13-3H2s & 39003 & C3HD & 39004 & DCl-37 \\
40002 & NaOH & 42003 & NH2CN & 43002 & HNCO \\
43003 & AlO & 44006 & DNCO & 44007 & HN-15-CO \\
44008 & HNC-13-O & 44009 & N2O-v2 & 45005 & HCS+ \\
45006 & HNCO-18 & 45007 & NN-15-O & 45008 & N-15-NO \\
46007 & N2O-18 & 48008 & O3-v1,3+v2 & 50007 & CH3Cl-35 \\
51002 & ClO-v1 & 52007 & SiCC & 52008 & CCCO \\
52009 & CH3Cl-37 & 52010 & CH2F2 & 52011 & CH2F2-v4 \\
53003 & C-13-CCO & 53004 & CC-13-CO & 53005 & CCC-13-O \\
53006 & Cl-37-O-v1 & 54006 & CCCO-18 & 63002 & HNO3-v7 \\
63003 & HNO3-v9 & 63004 & HNO3-v6 & 63005 & HNO3-v8 \\
63006 & HNO3-v5 & 66001 & COF2 & 67001 & OCl-35-O \\
68001 & CCCS & 69001 & OCl-37-O & 70001 & CCCS-34 \\
79001 & HOONO2 & 98001 & H2SO4 & 102001 & ClOOCl \\
104001 & Cl-37-OOCl \\
\end{tabular} \\[2ex]
\begin{tabular} {@{}rlrlrl@{}}
\multicolumn{6}{c}{\bf REVISED SPECIES, REV.~3 (28)}\\
\tagname & \tagname & \tagname\\
3001 & HD & 12001 & C-atom & 13001 & C-13-atom \\
14002 & N-atom-D-state & 17001 & OH & 18003 & H2O \\
19002 & HDO & 20001 & D2O & 28001 & CO \\
32001 & O2 & 32002 & O2-v1 & 33001 & HO2 \\
34003 & PH3 & 34004 & H2O2 & 36001 & HCl \\
38001 & HCl-37 & 46006 & NO2 & 48004 & O3 \\
48005 & O3-v2 & 48006 & O3-v1,3 & 48007 & O3-2v2\\
51002 & ClO& 52006 & HOCl & 53002 & Cl-37-O \\
54005 & HOCl-37 & 63001 & HNO3 & 64001 & S2 \\
64002 & SO2 \\
\end{tabular} \\
\end{center}
For reference, the changes in Rev.~2 are:
\begin{center}
\begin{tabular} {@{}rlrlrl@{}}
\multicolumn{6}{c}{\bf NEW SPECIES, REV.~2 (18)}\\
\tagname & \tagname & \tagname\\
13002 & CH & 17004 & NH3-v2 & 20001 & D2O \\
25001 & CCH & 26001 & CN & 26002 & CN-v1 \\
29004 & HCO & 29005 & NNH+ & 30009 & NND+ \\
33001 & HO2 & 46006 & NO2 & 48007 & O3-2v2\\
49001 & O3-sym-O-17& 49002 & O3-asym-O-17& 50005 & O3-s-O18-v2\\
50006 & O3-a-O18-v2& 97002 & Cl-35-NO3 & 99001 & Cl-37-NO3 \\
\end{tabular} \\[2ex]
\begin{tabular} {@{}rlrlrl@{}}
\multicolumn{6}{c}{\bf REVISED SPECIES, REV.~2 (30)}\\
\tagname & \tagname & \tagname\\
16001 & O-atom & 17001 & OH & 17002 & NH3 \\
18001 & OD & 18003 & H2O & 18005 & H2O-v2 \\
19001 & HO-18 & 19002 & HDO & 27001 & HCN \\
29002 & HCO+ & 30002 & HC-13-O+ & 30003 & DCO+ \\
31001 & HCO-18+ & 32001 & O2 & 32002 & O2-v1 \\
34001 & O-18-O & 41005 & CH3CCD & 44001 & CS \\
44002 & SiO & 45001 & C-13-S & 46001 & CS-34\\
48004 & O3 & 48005 & O3-v2 & 48006 & O3-v1,3\\
50003 & O3-sym-O-18& 50004 & O3-asym-O-18& 52006 & HOCl\\
54005 & HOCl-37 & 63001 & HNO3 & 64002 & SO2 \\
\end{tabular} \\
\end{center}
For reference, the new and revised species listed in the first revision of
this catalog are:
\begin{center}
\begin{tabular} {@{}rlrlrl@{}}
\multicolumn{6}{c}{\bf NEW SPECIES, REV.~1 (9)}\\
\tagname & \tagname & \tagname\\
18004 & NH2D & 18005 & H2O-v2 & 34004 & H2O2 \\
44005 & CH3CHO-E & 48005 & O3-v2 & 48006 & O3-v1,3 \\
52006 & HOCl & 54005 & HOCl-37& 63001 & HNO3 \\
\end{tabular} \\[2ex]
\begin{tabular} {@{}rlrlrl@{}}
\multicolumn{6}{c}{\bf REVISED SPECIES, REV.~1 (24)}\\
\tagname & \tagname & \tagname\\
17002 & NH3 & 18002 & N-15-H3 & 18003 & H2O \\
29003 & CH2NH & 30007 & CH2ND & 32001 & O2 \\
32002 & O2-v1 & 32003 & CH3OH & 34002 & O-18-O \\
34002 & H2S & 34003 & PH3 & 45003 & NH2CHO \\
51002 & ClO & 53002 & Cl-37-O & 55001 & C2H5CN \\
56001 & CH3CH2C-13-N& 56002 & CH3C-13-H2CN& 56003 & C-13-H3CH2CN\\
56005 & CH2DCH2CN-s & 56006 & CH2DCH2CN-a & 60001 & OCS\\
61001 & OC-13-S & 62001 & OC-34-S & 62002 & O-18-CS\\
\end{tabular} \\
\end{center}
\newpage
\tableofcontents \label{TOClabel}
\pdfbookmark[1]{TABLE OF CONTENTS}{TOClabel}
\newpage
\pagenumbering{arabic}
\section{INTRODUCTION}
This report describes a computer-accessible catalog of submillimeter,
millimeter, and microwave spectral lines in the frequency range between 0 and
10,000 GHz (i.e., wavelengths longer than 30~$\mu$m). The catalog is intended
to be used as a guide in the planning of spectral line observations and as a
reference that can facilitate identification and analysis of observed
spectral lines. The selection of lines for the catalog is based on the
project needs of astronomers and atmospheric scientists.
The catalog is constructed using theoretical least squares fits and
predictions based on spectral lines, mostly obtained from the literature. In
subsequent versions of the catalog, more molecules will be added and
existing molecular listings will be updated as new data appear.
The catalog is available on-line via anonymous ftp at spec.jpl.nasa.gov and
on the world wide web at http://spec.jpl.nasa.gov.
The format of the data is given in Section 2. Section 3 gives conversions
between different measures of spectral line intensity. General comments on
the precision of the spectral line positions and intensities are given in
Section 4, while species-specific comments are reserved for Section 6.
Section 5 gives the format of quantum numbers as they appear in the catalog.
Documentation for each molecular or atomic species is listed in Section 6 in
order of the ``species tag.'' This tag is a six-digit number in which the
three most significant digits represent the mass number of the molecule or
atom and the last three digits are an accession number for the given mass.
Usually there is a separate tag for each vibration-electronic state of a
particular molecule.
\section{DATA FORMAT}
\subsection{Line Files}
The catalog line files are composed of 80-character lines, with one line entry
per spectral line. The format of each line is:
\label{lfmt}
\begin{tabular}{@{}lccccccccr@{}}
FREQ, & ERR, & LGINT, & DR, & ELO, & GUP, & TAG, & QNFMT, & QN${'}$, & QN${''}$\\
(F13.4, & F8.4, & F8.4, & I2, & F10.4, & I3, & I7, & I4, & 6I2, & 6I2)\\
\end{tabular}
\begin{tabular}{lp{4.5in}}
FREQ: & Frequency of the line in MHz.\\
ERR: & Estimated or experimental error of FREQ in MHz.\\
LGINT: &Base 10 logarithm of the integrated intensity
in units of \linebreak nm$^2$$\cdot$MHz at 300 K. (See Section 3 for
conversions to other units.)\\
DR: & Degrees of freedom in the rotational partition
function (0 for atoms, 2 for linear molecules, and 3 for nonlinear
molecules).\\
ELO: &Lower state energy in cm$^{-1}$ relative to the lowest energy
spin--rotation level in ground vibronic state.\\
GUP: & Upper state degeneracy.\\
TAG: & Species tag or molecular identifier.
A negative value flags that the line frequency has
been measured in the laboratory. The absolute value of TAG is then the
species tag and ERR is the reported experimental error. The three most
significant digits of the species tag are coded as the mass number of the
species, as explained above.\\
QNFMT: &Identifies the format of the quantum numbers
given in the field QN. These quantum number formats are given in Section 5
and are different from those in the first two editions of the catalog.\\
QN${'}$: & Quantum numbers for the upper state coded
according to QNFMT.\\
QN${''}$: & Quantum numbers for the lower state.\\
\end{tabular}
\subsection{Directory File}
The catalog contains a special directory file called catdir.cat
Each element of this directory is an 80-character record with the following
format:\\
\begin{tabular}{@{}lcccr}
TAG, &\hspace{.45in} NAME,\hspace{.45in} & NLINE,\hspace{.45in} & QLOG, &
VERSION\\
(I6,X, & A13, & I6, & 7F7.4, & I2)\\
\end{tabular}
\begin{tabular}{lp{4.5in}}
TAG:& The species tag or molecular identifier.\\
NAME: & An ASCII name for the species.\\
NLINE: & The number of lines in the catalog.\\
QLOG: & A seven-element vector containing the base
10 logarithm of the partition function for temperatures of 300~K, 225~K, 150~K,
75~K, 37.5~K, 18.75~K, and 9.375~K, respectively.\\
VERSION: & The version of the calculation for this
species in the catalog.\\
\end{tabular}
\subsection{Documentation files}
The documentation files are stored natively as ASCII LaTex files for each species.
Postscript, LaTex, and PDF versions of this publication are also available on line.
The documentation files provide the
intensity and frequency cut-offs, partition functions at representative temperatures,
assumed dipole moments, literature citations for the experimental lines, and a brief
description of the nature of the Hamiltonian model used in the calculation. The
documentation file also includes a suggested isotopic correction based on cosmic abundances.
This correction includes the appropriate statistics for equivalent nuclei. Note
the catalog intensities do not include this isotopic correction.
In this edition of the catalog, several of the species have spectra that are
extended to 10,000 GHz, so the documentation includes a maximum frequency
cutoff. For almost all species, a strength cutoff was also employed:
\begin{displaymath}
10^{\rm LGINT}\; > \;10^{\rm LOGSTR0}\;\;+\;\;(\nu/300 GHz)^2 \cdot
10^{\rm LOGSTR1}
\end{displaymath}
A blank entry for LOGSTR1 means that the second term was not included. We have
found that LOGSTR1 is often a useful cut-off parameter to account for the decreased
sensitivity of instrumentation with increasing frequency or as a means to capture
lines with comparable transition dipoles. The partition functions listed (Q)
in the catalog include rotation and spin statistics but usually do not include
vibrational or electronic corrections. (Exceptions such as H$_2$O and
O$_3$ are noted.) Calculation of Q is based on a sum over states. At higher
temperatures, the sum-over-states calculation is replaced by a classical
calculation when the latter is larger due to a limited number of states in the
catalog. The spin statistics included in the partition function are sometimes
divided by a common factor, but the partition functions are always
consistent with the statistics used for intensities in the catalog. This common
factor is not always documented, but the choice should be clear from the GUP field
in the line file.
\section{INTENSITY UNITS AND CONVERSIONS}
The units of intensity given in the catalog, nm$^2$$\cdot$MHz, are based on the
integral of the absorption cross-section over the spectral line shape. The
value of the intensity is calculated for 300~K and is directly comparable with
the common infrared intensity unit of cm$^{-1}$/(molecule/cm$^2$). The latter
is obtainable by dividing the catalog intensity by $2.99792458 \times
10^{18}$.
The line intensity in the catalog, I$_{ba}$ (300~K), is obtained from
\begin{eqnarray}
I_{ba}(T) &=& (8\pi^3/3{\rm hc})\nu_{ba}\;^xS_{ba}\;\mu_x^2
[e^{-E^{''}/kT} -e^{-E^{'}/kT}]/Q_{rs} \label{eqi1}\\
&=&4.16231\times 10^{-5}\nu_{ba}\;^xS_{ba}\;\mu_x^2
[e^{-E^{''}/kT} -e^{-E^{'}/kT}]/Q_{rs}\label{eqi2}
\end{eqnarray}
where $\nu_{ba}$ is the line frequency, $^xS_{ba}$ is the line strength,
$\mu_x$ is the dipole moment along the molecular axis $x$, E${''}$ and E${'}$
are the lower and upper state energies, respectively, and Q$_{rs}$ is the
rotation-spin partition function (using the same zero of energy as E$^{'}$ and
E${''}$). In Eq.(\ref{eqi2}), I$_{ba}$ has units of nm$^2$$\cdot$MHz, $\nu_{ba}$
has units of MHz, and $\mu_x$ has units of Debye. In many molecules, there are
several dipole moment projections and there even may be mixing between dipoles.
In such cases, $^xS_{ba}\;\mu_x^2$ is replaced with the sum of the
squares of the transition dipoles for each $M$ component in the line.
For magnetic dipole transitions, Eq.(\ref{eqi2}) can be used with the conversion that a
Bohr magneton is equivalent to 0.009274 Debye. Note that with this definition
the intensities are defined with respect to the total concentration of the
vibration-electronic state of the species. No vibrational partition function
is included, except where explicitly stated in the documentation.
Care is taken to assure that $^x$S$_{ba}$ and Q$_{rs}$ are
determined with the same state degeneracies.
For the catalog, Eq. (\ref{eqi2}) is evaluated for T = T $_\circ$ = 300~K.
Values of I$_{ba}$ at other temperatures can also be obtained from Eq.(1)
once the temperature dependence of Q$_{rs}$ is known. For linear molecules,
Q$_{rs}$ is proportional to T in the limit where the energy spacings are small
compared with kT. For nonlinear molecules, Q$_{rs}$ is proportional to
T$^{3/2}$ in the same limit. Explicitly, $I_{ba}$(T) is
\begin{eqnarray}
I_{ba}(T) & = & I_{ba}(T_\circ) [Q_{rs}(T_\circ)/Q_{rs}(T)]\frac{e^{-E^{''}/kT}
-e^{-E^{'}/kT}}{e^{-E^{''}/kT_\circ}-e^{-E^{'}/kT_\circ}} \label{eqi3}\\
& \cong & I_{ba}(T_\circ)\cdot(T_\circ/T)^{n+1}e^{-(1/T - 1/T_\circ)E^{''}/k}\label{eqi4}
\end{eqnarray}
where n = 1 for a linear molecule and 3/2 for a nonlinear molecule.
Eq.(\ref{eqi4}) requires that $E{'}-E{''}$ is small compared with $kT$ and $kT_\circ$.
Absorption coefficients of collision-broadened lines can be obtained from $I_{ba}$
with the relation
\begin{equation}
\alpha_{\rm max} = \frac{I_{ba}(T)}{\Delta\nu}(T_\circ/T) \times 102.458
\mbox{ cm}^{-1}\label{eqi5}
\end{equation}
in which $\Delta\nu$ is the half-width at half-height in MHz at 1 torr partial
pressure of the absorber at temperature T, $I_{ba}$ is in units of nm$^2$$\cdot$MHz, and
$\alpha_{\rm max}$ is in units of cm$^{-1}$.
The power transmission through a uniform
medium of length $L$ at the peak of the line is exp($-\alpha_{\rm max}L$). The attenuation is
$\alpha_{\rm max}L\times 4.3429$ in dB.
The corresponding value of
$\alpha_{\rm max}$ in the thermal Doppler limit is
\begin{equation}
\alpha_{\rm max} = \frac{I_{ba}(T)p}{\Delta\nu_d}(T_\circ/T) \times 151.194
\mbox{ cm}^{-1}\label{eqi6}
\end{equation}
in which p is the partial pressure of the absorber in torr, and $\Delta\nu_d$ is
the Doppler half-width at half-height in units of MHz.
The Doppler width is given by
\begin{equation}
\Delta\nu_d = 1.17221 \times 10^{-6} \times \nu_{ba} \sqrt{(T/T_\circ)(28/m)}\label{eqi7}
\end{equation}
in which $m$ is the mass of the absorber (in atomic mass units).
The explicit inverse temperature dependence in
Eqs.(\ref{eqi5}) - (\ref{eqi6}) is due to the conversion of density to pressure units.
There is additional implicit temperature dependence in $I_{ba}(T)$ and in the widths.
In Eqs.(\ref{eqi7}) - (\ref{eqi10}), $\nu_{ba}$ is the line frequency in MHz.
The absorption cross-section of an interstellar absorber integrated over a 1
km/s-velocity interval is
\begin{equation}
\sigma_{ba} = \frac{I_{ba}}{\nu_{ba}} \times 2.99792\times 10^{-9} \mbox{ cm}^2. \label{eqi8}
\end{equation}
The power transmission through a uniform medium of length $L$ and number density $\rho$ is
exp($-\sigma_{ba}\rho L$).
The inverse of $\sigma_{ba}$ is the column density per unit optical depth in
the same 1 km/s-velocity interval.
The average spontaneous emission rate from the upper states into the lower
states is
\begin{eqnarray}
A_{ba} & = &
I_{ba}(T)\;\nu_{ba}^2[Q_{rs}/g^{'}][e^{-E^{''}/kT} -
e^{-E^{'}/kT}]^{-1} \times 2.7964 \times 10^{-16} \mbox{ sec}^{-1}\label{eqi9}\\
& \cong
&I_{ba}(T_\circ)\;\nu_{ba}[Q_{rs}(T_\circ)/g^{'}] e^{E{'}/kT_\circ}
\times 1.748 \times 10^{-9} \mbox{ sec}^{-1} \label{eqi10}
\end{eqnarray}
in which g$^{'}$ is the degeneracy of the upper state. The value of
g$^{'}$ is listed as part of the spectral line information in the catalog.
Values of Q$_{rs}$ are listed in the documentation and on the directory file.
Eq.(\ref{eqi10}) requires that $h\nu_{ba}$ is small compared with $kT$ and $kT_\circ$.
It should be noted that the information to make all the intensity conversions given
above is available from the directory file and from the line files, with the exception
of the collisional broadening coefficients. As a matter of policy, we have not included
collisional linewidths in the catalog because of the large variety of different
collision partners relevant for the laboratory, the Earth's atmosphere, and the
atmospheres of the other planets.
When $\nu \cong \nu_{ba}$, the absorption coefficient is
\begin{equation}\label{eqi11a}
\alpha(\nu) = n \sum_{a,b} I_{ab} f_{ab}(\nu - \nu_{ab})
\end{equation}
where n is the number denity of absorbers and $f_{ab}(\delta)$ is
an area-normalized line shape. Further away from line center
\begin{equation}\label{eqi11}
\alpha(\nu) = n \nu \tanh(\nu/2 k T) \sum_{a,b} \bar{I}_{ab}
\left[f_{ab}(\nu - \nu_{ab}) + f_{ab}(\nu + \nu_{ab})\right]
\end{equation}
where $\bar{I}_{ab}$ is defined by
\begin{equation}\label{eqi12}
I_{ab} = \nu_{ab} \tanh(\nu_{ab}/2 k T) \bar{I}_{ab}
\end{equation}
Note that in Eq.\ (\ref{eqi11a}) and (\ref{eqi11}), the sum over
$a$ and $b$ is restricted to $\nu_{ab} > 0$.
\section{GENERAL COMMENTS ON PRECISION}
The expected errors of the frequency as listed in the catalog are usually
based on a propagation of errors estimated from a least squares fit of the
observed frequencies to a model Hamiltonian, using the following equation:
\begin{equation}
\varepsilon_n^2 = \sum_{kj} \frac{\partial\nu_n}{\partial p_k}
\frac{\partial\nu_n}{\partial p_j}\;\;V_{kj}
\end{equation}
in which $\varepsilon_n$ is the estimated error of frequency $\nu_n$ and
V$_{kj}$ is an element of the least square variance-covariance matrix for the
parameters p$_k$. This variance-covariance matrix is determined from the
observed lines by
\begin{equation}
(V^{-1})_{kj} = \sum_m \frac{\partial\nu_m}{\partial p_k}
\frac{\partial\nu_m}{\partial p_j}\;\;\varepsilon_m^{-2}
\end{equation}
in which the summation over $m$ is over the experimental lines using
experimental uncertainies, $\varepsilon_m$. The diagonal elements of $V$ are
the squares of the parameter uncertainties and the off-diagonal elements of
$V$ are products of the parameter uncertainties and correlation coefficients.
The experimental uncertainties generally given in the literature vary from 1.6-$\sigma$ estimates to 3-$\sigma$ estimates and are usually
``guesstimates." Unfortunately, many authors do not even report their
experimental uncertainties. Therefore, the expected errors in predicted lines
obtained from fits based on such data will usually reflect this ambiguity in
laboratory uncertainties through Eq. (10) and (11). In some cases, the quality
of the least squares fit of the parameters to the experimental lines can be a
guide to the statistical nature of the experimental uncertainties. Whenever
possible, the expected errors in this catalog will reflect an expected 95\%
confidence interval based on the model used to fit the data. However, the
errors can be different from this design goal by factors of three just due to
the quality of the input error estimates. Lines with an expected error greater
than 1 GHz have been dropped from the catalog.
The expected errors can only be computed relative to the model used. There
are at least two ways the model can be ``wrong" for the predicted frequencies.
First, higher order centrifugal distortion terms may no longer be negligible
for the predicted frequencies. This effect will generally be important for
lines of higher J or K than the laboratory-determined data set. In a sense,
the predictions are then a form of extrapolation rather than interpolation and
are therefore more suspect. A second factor leading to discrepancies in the
predicted frequencies comes from ``resonances." These resonances come from a
near overlap of energy states that are coupled by elements of the Hamiltonian
matrix. Poor predictability comes when these elements are neglected in the
model or are treated inadequately by some form of perturbation theory. Such a
neglect of coupling elements is always necessary at some level in any
practical calculation. A major contributing problem is that often the
existing data set is not sensitive to the parameters that are needed to
characterize the resonances.
Precision in the intensity estimates is generally less critical than precision
in the frequency. Contributing to intensity uncertainty are errors in the
dipole moment, errors in the line strength $^xS_{ba}$, and errors in the
rotation-spin partition function (the vibration-electronic partition
defined on the basis of concentrations of the given vibration-electronic
state). Dipole moment errors come directly from the experimental
determination and indirectly from the J dependence of the dipole moment due to
centrifugal mixing of the vibrational states. Line strength errors can come
from deficiencies in the model Hamiltonian and are particularly severe when
resonances have been inadequately accounted for. Partition function errors
are relatively benign but can become significant if the classical formulae are
used at low temperatures for small molecules. With the exception of
unanticipated resonances and poorly determined dipole moments, worst-case
errors in the intensity will generally be at the 1\% level or lower.
Many molecular models are found in the literature. In
principle, a very general model should be able to treat every possible case.
In practice, this is hardly ever done. A specific model is most frequently
used for every case, mainly because every author starts with a different
viewpoint of the problem. In our case, we have tried to develop a program
that will treat a wide variety of problems with a minimum of adaptation. This
saves a great deal of time in the initial setup, and provides a uniform
output format for the final results. Most importantly, the basic treatment is
the same for every molecule, regardless of the model used, so that a high
degree of consistency can be maintained, facilitating comparisons between
different molecules. The particular model needed to analyze a specific
problem is treated as a subroutine. For certain problems, this subroutine can
be quite simple, but for others, it is more complex.
Simple singlet sigma diatomic, linear, and symmetric rotor molecules are
treated together. Asymmetric rotors with and without various complicating
interactions are treated exactly, without any perturbation expansions. This
is done by employing the Hamiltonian operators to generate the matrix
elements. All possible operators can be used, so any conceivable interaction
can be included initially.
Comments on specific models are given for the individual species.
\section{FORMAT OF QUANTUM NUMBERS}
For the later editions of this catalog, we have attempted to use a quantum
number format convention that allows the quantum numbers to be accessed
easily by computer (see Table 1). First, the upper and lower quantum number sets have been
separated into distinct fields. Second, the quantum format designations
have been defined to have more accessible information encoded in them.
The quantum number format
designation, QNFMT, is a 4-digit quantity in the catalog. We divide
QNFMT into a series of digits so that
\begin{displaymath}
{\rm QNFMT} = Q \cdot 100 + H \cdot 10 + NQN
\end{displaymath}
in which Q determines the type of molecule (see Table 1), H determines the
coding of half-integer quantum numbers, and NQN is the number of quantum
numbers for each state. Q is defined so that MOD(Q,5) is the number of primary
quantum numbers. If NQN is greater than the number of primary quantum numbers,
the degeneracy is derived from the last quantum number. Otherwise, the
degeneracy is derived from the first quantum number. H is a 3-bit binary code
for the existence of half-integer quantum numbers for the {\it last three}
quantum numbers. The least significant bit refers to quantum number NQN and is
1 if the last quantum number is half-integer. In the catalog, all half-integer
quantum numbers are rounded {\bf up} to the next integer.
The parity given may not always be experimentally determined, but the
parity convention is guaranteed to produce parities of the same sign for
interacting states and to produce a change in parity across dipole allowed
transitions. It should be noted that for symmetric top transitions with no
K splitting, the
parity designation is frequently dropped. Unless otherwise stated below,
the parity of prolate symmetric tops follows the parity of K$_{+1}$ for the
corresponding asymmetric top level, while for oblate tops, the parity follows
K$_{-1}$. For example, the level $5_{3,2}$ for an asymmetric rotor has K = 3
for a prolate symmetric top quantum field, and K = $-$2 for an oblate top. Hund's
case (b) quanta are similar to symmetric top quanta except that K is replaced
with $\Lambda$. Hunds's case (a) quanta also have parity encoded in the
$\Lambda$ field. The correlation between parity and e,f designations should
follow the recommendations of J. M. Brown {\em et al.}, 1975, J. Mol.~Spect.~
{\bf 55}, 500. For reference, this convention is
\begin{tabular}{lccl}
\multicolumn{4}{c}{\bf TABLE 1. QUANTUM NUMBER FORMATS}\\
&&&\\
\cline{1-4}
&&&\\
\multicolumn{1}{c}{\bf Type} & \multicolumn{1}{c}{\bf Q} & \multicolumn{1}{c}{\bf DR} &
\multicolumn{1}{c}{\bf Quantum Order}\\
&&&\\
\cline{1-4}
&&&\\
Atom & 0 & 0 & (J),(F),$\cdots$\\
&&&\\
Linear --- $\Sigma$ & 1& 2& N,(J),(F$_1$),(F$_2$)(F)\\
&&&\\
Linear --- Case b & 2& 2& N, $\Lambda$,(F$_1$),(F$_2$),(F)\\
&&&\\
Linear --- Case a (2S+1 odd)& 3& 2& J,$\Omega$, $\Lambda$,(F$_1$),(F$_2$),(F)\\
&&&\\
Linear --- Case a (2S+1 even)& 8& 2& J+$\frac{1}{2}$,$\Omega+\frac{1}{2}$,
$\Lambda$,(F$_1$), (F$_2$),(F)\\
&&&\\
Symmetric rotor & 2 & 3 & N,K,(J),(F$_1$),(F$_2$),(F)\\
&&&\\
Symmetric rotor with vibration & 13 & 3 & N,K,v,(J),(F$_1$),(F)\\
&&&\\
Asymmetric rotor & 3 & 3 & N,K$_{-1}$,K$_{+1}$,(J),(F$_1$),(F)\\
&&&\\
Asymmetric rotor with vibration & 14 & 3 & N,K$_{-1}$,K$_{+1}$,v,(J),(F)\\
&&&\\
\cline{1-4}
\end{tabular}
\begin{tabular}{rp{4.in}}
Conventions: & \\
1.& Half-integer quantum numbers are rounded up.\\
2.& The sign of $\Lambda$ and K refers to the parity under
inversion of spatial coordinates, {\it not} the sign of the operator.\\
3.& Quantum numbers in parentheses are optional.\\
\end{tabular}\\
\newpage
$$\begin{array}{llcrlc}
&\makebox[0in][l]{For odd-spin multiplicity:}\\
\mbox{if}& p (-1)^{J+1/2} &=& -1,&\mbox{then} &e\\
\mbox{if}& p (-1)^{J+1/2} &=& 1,&\mbox{then} &f\\[1ex]
&\makebox[0in][l]{For even-spin multiplicity:}\\
\mbox{if}& p (-1)^{J} &=& 1,&\mbox{then} &f\\
\mbox{if}& p (-1)^{J} &=& -1,&\mbox{then} &e\\
\end{array}$$
where $p$ is $\pm 1$ according to the parity. Care must be used because this
convention is not universally followed in the literature.
\section{DOCUMENTATION BY SPECIES}
In this edition of the catalog, several of the species have spectra that are
extended to 10,000 GHz, so the documentation below includes a maximum frequency
cutoff. For almost all species, a strength cutoff was also employed:
\begin{displaymath}
10^{\rm LGINT}\; > \;10^{\rm LOGSTR0}\;\;+\;\;(\nu/300 GHz)^2 \cdot
10^{\rm LOGSTR1}
\end{displaymath}
A blank entry for LOGSTR1 means that the second term was not included. The
partition functions listed (Q) include rotation and spin statistics but
usually do not include vibrational corrections. (Exceptions such as H$_2$O and
O$_3$ are noted.) Calculation of Q is based on a sum over states. At higher
temperatures, the sum-over-states calculation is replaced by a classical
calculation when the latter is larger due to a limited number of states in the
catalog. The spin statistics included are only a partial set but are
consistent with the intensities in the catalog.
\subsection{Isotope Corrections}
For convenience, we have included an isotope correction for the rarer isotopes
that includes effects of redundant substitution. The atomic abundances used
are listed in Table 2. It should be stressed that the intensities in the catalog
do not contain an isotope correction.
\newpage
\begin{center}
{\bf TABLE 2. ASSUMED RELATIVE ISOTOPIC ABUNDANCES \\
FOR CATALOG DESCRIPTION}
\begin{tabular}{cccc}
&&&\\
\cline{1-4}
&&&\\
{\bf Isotope}&\multicolumn{1}{c}{\bf Log (abundance)} &
{\bf Isotope}&\multicolumn{1}{c}{\bf Log (abundance)}\\
&&&\\
\cline{1-4}
&&&\\
$^1$H & 0.000& $^2$H &\makebox[0 pt][r]{-}3.824\\
$^6$Li &\makebox[0 pt][r]{-}1.131& $^7$Li &\makebox[0 pt][r]{-}0.033\\
$^{12}$C & 0.000& $^{13}$C &\makebox[0 pt][r]{-}1.955\\
$^{14}$N & 0.000& $^{15}$N &\makebox[0 pt][r]{-}2.432\\
$^{16}$O & 0.000& $^{17}$O &\makebox[0 pt][r]{-}3.432\\
$^{18}$O &\makebox[0 pt][r]{-}2.690& $^{28}$Si &\makebox[0 pt][r]{-}0.035\\
$^{29}$Si &\makebox[0 pt][r]{-}1.327& $^{30}$Si &\makebox[0 pt][r]{-}1.506\\
$^{32}$S &\makebox[0 pt][r]{-}0.022& $^{33}$S &\makebox[0 pt][r]{-}2.125\\
$^{34}$S &\makebox[0 pt][r]{-}1.376& $^{35}$Cl &\makebox[0 pt][r]{-}0.122\\
$^{37}$Cl &\makebox[0 pt][r]{-}0.611& $^{79}$Br &\makebox[0 pt][r]{-}0.296\\
$^{81}$Br &\makebox[0 pt][r]{-}0.306\\
&&&\\
\cline{1-4}
\end{tabular}
\end{center}
\newpage
\subsection{List of Species in This Catalog}
Table 3 lists all the species provided in this catalog, by tag and name.
\begin{center}
{\bf TABLE 3. LIST OF SPECIES}
\end {center}
\input{catdir}
\newpage
\addcontentsline{toc}{subsection}{Species Documentation Pages}