T.D.S. spectroscopic databank for spherical tops: DOS version

Pergamon

J. Qumf. Spectrosc. Radiar. Transfer Vol. 52, No. 314, pp. 459-479, 1994

0022-4073@4)0007~5 Copyright 0 1994 Elscvicr Science Ltd

Printed in Great Britain. All rights reserved . . 0022-4073/94 -$7.00 + 0.00

T.D.S. SPECTROSCOPIC DATABANK FOR SPHERICAL TOPS: DOS VERSION

VL. G. TYLJTEREV,~~ Yu. L. BABIKOV,~ S. A. TASHKUN,~ V. I. PEREVALOV,~ A. NIKITIN,~ J.-P. CHAMPION,~ CH. WENGER,~ C. PIERRE,~ G. PIERRE,~ J.-C. HILICO,~ and

M. bETE$

TLaboratory of Theoretical Spectroscopy, Institute of Atmospheric Optics, Russian Academic of Sciences, 634055, Tomsk, Russia, and fLaboratoire de Physique, URA CNRS 1796, Universite de Bourgogne,

6 bd Gabriel 21000, Dijon, France

Abstract-T.D.S. is a computer package concerned with high resolution spectroscopy of spherical top molecules like CH,, CF,, SiH,, SiF,, SnH,, GeH4, SF,, etc. T.D.S. contains information, fundamental spectroscopic data (energies, transition moments, spectroscopic constants) recovered from comprehensive modeling and simultaneous fitting of experimental spectra, and associated software written in C. The T.D.S. goal is to provide an access to all available information on vibration-rotation molecular states and transitions including various spectroscopic processes (Stark, Raman, etc.) under extended conditions based on extrapolations of laboratory measurements using validated theoretical models. Applications for T.D.S. may include: education/training in molecular physics, quantum chemistry, laser physics; spectroscopic applications (analysis, laser spectroscopy, atmospheric optics, optical standards, spectroscopic atlases); applications to environment studies and atmospheric physics (remote sensing); data supply for specific databases; and to photochemistry (laser excitation, multiphoton processes). The reported DOS-version is designed for IBM and compatible personal computers.

1. INTRODUCTION

T.D.S. is the abbreviation of the research project with double translation: “Traitement de Don&es Spectroscopiques” or “Tomsk-Dijon-Spectroscopy project”. It has been undertaken by two groups from Laboratoire de Spectronomie Moleculaire (SMIL), UniversitC de Bourgogne and Laboratory of Theoretical Spectroscopy (LTS), IOA, Tomsk. The T.D.S. project is concerned with high resolution spectroscopy of spherical top molecules and their isotopically substituted derivatives. These molecules are known for the complexity of their spectra as well as for their specific role in advanced fundamental and applied research in molecular physics and quantum chemistry.

As a result of this project, the T.D.S. spectroscopic databank has been created which is of quite different conception than available spectroscopic databases like HITRAN,’ GEISA,’ JPL-catalog,3 ATLAS,“ etc. Whereas existing databases are focused mainly on absorption/transmittance data, the goal of the T.D.S. databank is to provide an access to all available information on vibration- rotation states and to offer a possibility to a user to study various spectroscopic processes, including Raman, Stark, two-photon, etc., under extended conditions.

For this reason it is organized in a different way. Contrary to traditional spectroscopic databases which are essentially compilations of observed data and calculated data issued from independent theoretical or empirical models, the T.D.S. databank contains fundamental spectroscopic data (energies, transition moments, spectroscopic constants) recovered from comprehensive modeling and simultaneousfitting of experimental spectra. Particular attention is paid to interpretation, precision estimation, and extrapolation of laboratory measurements via validated theoretical model.

The T.D.S. software is written in C.

#Present address: GSMA, URA CNRS D 1434, Facultb des Sciences, BP 347, 51062 Reims, France.

459

460 VL. G. TYUTEREV et al

2. PHILOSOPHY OF THE T.D.S. DATABANK

It is well known that various kinds of spectroscopic processes provide complementary information on molecular vibration-rotational states and transitions, due to quite different precision% spectral coverage, and selection rules. For example, most information on ro-vibrational states for totally symmetrical vibrations of spherical top molecules comes from Raman spectra, microwave transitions giving much more precise rotational spacings which may help to resolve overlapping lines in the infrared, etc. It seems to be even more important for line intensities especially in the case of dense spectra. Various types of observed spectra are not always directly compatible; frequently they are not in good agreement within “experimental error bars”. Also because of specific instrumental limitations they may not provide a complete spectrum coverage.

In order to use all these pieces of information in full one should convert various observed data to a consistent set of more fundamental characteristics, i.e., to make experimental data reduction using a consistent theoretical model. Ideally, if a theoretical model is perfect, a synthetic spectrum would be more complete than any separate experimental record, since it accumulates information from all available experimental origins. Of course, it will be never absolutely perfect, but the present development in the theory of spherical top spectra allows one to achieve experimental accuracy for most transitions from low-lying vibrational states. So we believe that it is possible to simulate different types of spectroscopic processes to fill spectral gaps which had not been studied experimentally so far, to fix blended lines, to predict new transitions under extended condition, etc.

The above considerations determine the T.D.S. databank philosophy.

How it is Jilled?

Figure 1 illustrates the principle of creation of the T.D.S. databank. All available spectra of various types are processed together using the theoretical model and a least-squares fitting procedure with observed data weighting such as to reflect their individual accuracies and reliability. The results are included in the T.D.S. databank if the precision of data fitting is comparable with the experimental one.

What does it contain?

The T.D.S. data bank includes:

Fundamental data (energy levels/transition moments) Spectroscopic constants

EXPERIMENTAL SPECTRA : IR, (all origins) Mw,

RAMAN, . . .

1 SIMULTANEOUS

DATA REDUCTION

I

Fig. 1. The diagram illustrating the way to fill the T.D.S. databank.

T.D.S. spectroscopic databank for spherical tops 461

Statistics (precision) Software utilities and Graphic tools.

Spectral line parameters are not stored. They are calculated from the above fundamental data according to user’s requests for specified conditions and transition types.

What can a user get out of it?

Information available from T.D.S. is illustrated by Fig. 2. Statistics include: Obs-Calc for line parameters (when available), standard deviations (Std. dev.) for recovered spectroscopic constants, std. dev. for calculated transitions, distribution of data (including std. dev. for fitted data vs J).

All the information stored in and available from T.D.S. is self-consistent: for all molecules, spectroscopic constants are recovered using the same approach in data reduction with models built according to the same method; stored energy levels and wavefunction mixing coefficients exactly correspond to sets of stored spectroscopic constants; calculated transition frequencies exactly correspond to ro-vibrational energy levels. The error propagation is taken into account through the entire chain of analysis, from observed spectra to fitted constants and further to calculated transitions. Once it is done, the results become easy to exploit. The goal of T.D.S. is to provide powerful tools to access high resolution spectroscopic results on spherical tops: no extensive investment in sophisticated theory or software installation is required by users to exploit up-to-date modeled data for research and applications.

3. THEORETICAL MODEL AND DATA REDUCTION

Such an approach is only meaningful if a theoretical model describing high-resolution spectra of a chosen family of molecules is good enough. Basic requirements for a model in question are fairly obvious. It has to: (a) take into account the variety of intramolecular interactions and molecular symmetry properties in a complete enough way; (b) reproduce fitted observed data with an accuracy close to the experimental precision of high-resolution spectra; (c) be correctly formulated for a solution of “reversed problem” to allow good convergence of a least-square- fitting; its parameters should be stable, statistically well defined and have certain physical meaning to be considered as spectroscopic constants; and (d) provide a reasonable extrapolation (prediction) of data not included in the fits.

From the very beginning, the theory of spherical rotors has been more complex than for other molecules primarily because symmetry properties increase the degeneracies of the levels. Moreover, due to the nature of the chemical bonds, numerous quasi-degenerate states give rise to vast and

ENERGIES, splittines.

sra&effectt. Wavefunction,

ResoaancC, mixing

CALCULATED ADDITIONAL TRANSITIONS INFO, (IR. m. WN. Rcf-, TWO-PHOTON) List of

SMJTATED predictiCm8, s- HelP

4 w +STATISTICS.

Fig. 2. Schematic presentation of the types of information available from the T.D.S.


complicated resonance perturbations. Near coincidences between the bending vibrational frequencies (02 z 04) on the one hand, and between the stretching vibrational frequencies (0, r 03) on the other hand are a common feature for most tetrahedral molecules. Such coincidences characterize the so-called polyad patterns, which should be treated simultaneously due to existence of resonance coupling terms. Practically no excited vibrational state of light spherical tops can be really regarded as isolated. Basically for tetrahedral molecules there are two types of interacting- state polyads. Associated definitions are given in Table 1.

For silane type molecules one has ground vibrational state (GS), bending dyad (B-Dyad), bending

triad (B-Triad), etc., then stretching dyad (S-Dyad), and so on. For methane, the situation is complicated by Fermi-resonances due to additional near coincidences between stretching vibrations and two quanta of bending vibrations o, E o3 z 20, E 204, the states concerned being coupled by large interaction terms. As a result, the five vibrational states located around 3000 cm-’ form an interacting system called Pentad.

Table 1. Polyads definition

-Ii,, Gq, s”H,

Definition of Polyads of Interacting Vibrational States:

Cs: (0000)

BJW: (0100)/(0001) (Bending modes)

B_Triad: (02001/~01011/(00021 (Bending modes)

B_Tetrad: ~0300~/~0201~/~0102~/(0003) (Bendingmodes

s_Dyad:

S-Triad:

(Stretching modes)

(Stretching modes)

kthane

Definition of Polyads of Interacting Vibrational States:

GS: (00001

Dyad: (0100)/(0001)

Fbtad: ~1000~/~00101/~0zoo~/~0101~/~00021

sFe Definition of Vibrational States: (Stretching modes)

GS: Ground State Ulgl

0010: v (Flu)

0020: 2v3 (l=O,Alg;1=2,Eg+F2g)

0030: (1=l,Flu;1=3,Alu+Flu+F2u)

The predictions for SFe have been made using Tetrahedral (instead of

Octahedral) Tensor Notations. The following rules lead to the usual

conventional symmetry labeling (rovibrational levels):

GS / 2V3 Al,A2,E,Fl,F2 -> Al& A22, Eg. Fig, F2g

v3 / 3v3 Al,A2,E,Fl,F2 -> A2u, Alu, Eu, F2u, Flu 1


The theoretical method for an account of the dramatic effects of perturbations on line positions and strengths satisfying the above condition (a) has been developed by the Dijon group,w using the formalism of irreducible tensor operators. For vibrational states coupled by resonance interactions the above requirement (c) becomes particularly important and difficult to fulfil. Phenomenological spectroscopic parameters, being highly correlated, apparently lose a physical meaning: they were statistically poorly determined and showed dramatic discrepancies in values obtained by different authors. The study of ambiguities of phenomenological mathematical models (e&ctive Hamiltonians) for interacting states, explaining above discrepancies, has been initiated by the Tomsk group ‘IS’~ in connection with contact transformations for a quasi-degenerate case.‘0*‘5 Later on, a development of models,‘3*‘4 satisfying the requirement (c) for various polyads of spherical tops?, becomes a subject of joint efforts by both group~,‘~-~~ partly in the frame of the T.D.S. project. It allowed the introduction, in the practice of data reduction, the models containing reliable spectroscopic constants for spherical tops. Applications to actual fitting of experimental spectra showed the following consequences:‘7-22.2426 (i) convergence of least -square fit is drastically improved; (ii) the number of adjustable parameters may be considerably decreased without deterio- ration of the quality of calculations; (iii) recoveredparameters are much better determined statistically and much less correlated. A detailed description of the theoretical model for spherical tops may be found in the recent review in Ref. 9 and also in Ref 16.

Examples of recent data reductions for spherical top spectra may be found in Refs. 20,21,24-28. Typically, the above condition (b) proved to be satisfied: an experimental accuracy of high-resolution measurements was achieved in calculations (10e3 to 5 x 10-5cm-’ for line positions in IR and 100 kHz in MW, as well as 3% in best analysis for line intensities). Theoretical models were also successfully validated against predictions of new transitions which were confirmed by later measurements [the condition (d)]. The review of available analysis of spherical top spectra will be done separately.29

4. ORGANIZATION OF THE DATABANK-OPTIONS AND POSSIBILITIES OF THE GRAPHICAL SOFTWARE PACKAGE

The T.D.S. DOS version provides user friendly interface with multiple window, menus, colored plots, and real-time simulations of spectroscopic processed mentioned above. It includes commands and parameters for the following features:

Interactive numerical data handling (energy levels; transitions; statistics; spectroscopic constant sort. Select functions, export functions). Interactive graphical data display [energy diagrams; resonance mixing of wavefunctions; synthesis of spectra (stick/Gauss/Lorentz/Voigt/Transmission). Zoom functions, hard copy functions]. On-line information (references: experiment/theory/analysis). On line help.

The T.D.S. interface is built in such a way that it does not require any particular professional knowledge in the domain of spherical top spectra from the user. The user is guided through various options and possibilities by the program itself. At any step he is prompted to choose from several possibilities. These offers are visualized as far as possible to make them easy to understand. In an “educational period” he may choose between them or “zoom” and observe a sequence of pictures one after another. At any time a user may change his mind and go some steps back in order to correct his choices which are stored in memory. Alternatively, being more prepared, a user may input the required conditions, get energy levels, resonance mixing coefficients of wavefunctions, spectroscopic parameters, line positions, line strengths, together with associated statistics in a numerical form, write them in a file for personal use, print them out, make a copy screen for pictures and so on.

tThe contribution to theoretical studies by the Moscow University group is acknowledged: sf papers (13-l 6) and references therein.


The principal scheme of the T.D.S. databank and of associated software package is presented by the following diagram (Fig. 3). In order to avoid complications, it gives only basic idea of possibilities without going into the details of options and commands which are more numerous.

When the T.D.S. package is run the user faces the Starting Menu with 3 basic choices: SUMMARY, VIBRATIONAL LEVELS and BANDS (Theoretical review is optional). VIBRATION LEVELS and BANDS represent two principal graphical screens for management of the package and spectroscopic information. The idea of both screens is to start with a bird’s_eye overview and then provide the user with successively deeper and deeper insight to the detail.

VIBRATIONAL LEVELS screen

This screen is designed for spectroscopists or other users who are aware of some basic elements of molecular quantum states theory. It displays vibrational energy levels for every molecule included in the databank. Selected molecules are always highlighted [Fig. 4(b)]. For a “highlighted” molecule one can get more information (top menu). The ZOOM option magnifies a vibrational level picture [central window in Fig. 4(a), (b)] and displays symmetry labeling, splitting of degenerate sublevels due to intramolecular interactions, and energy values in wavenumbers.

The option MOLECULE provides basic information about the chosen molecule [Fig. 4(b)] and also access to the list of AVAILABLE PREDICTIONS. Further, one can choose any vibration level

Starting menu

VIB. LEVELS

$ BANDS

-). Screen

L

Molecule (choice)

I I r______-_____________ ------‘T

Basic Info.

f

List of BANDS &

PREDICTIONS . . \ \ \-

\

STATISTICS

Profile simulation

RAMAN ________________.

TWO-PHOTON

Synthetic spectrum

Fig. 3. Flow diagram of the graphical DOS-version of the T.D.S. package.


(a

E uibiat TransItions Quit

3064.39 - 0200 - :, ;;g;

3019.49 - 0010 F2

2916.48 - 1000 Al

2838.20 - 0101 c F’ 2846.08 F2 2830.31

I I 3000 : 0000 1 0000 : 0000 1 0000 1 0000 : 0000 : Mel

:04 13CD4 CF4 28SIH4 29SIH4 30SIH4 28SIF4

3LYAD STRUCTURE : VIBRATIONAL QUANTUM NUMBERS Ground State (0000) Bending Dyad (0100/0001~ Bending Triad (0200/0101/0002) Stretching Dyad (1000/0010) Bending Tetrad (0300/0201/0102/0003) Bending/Stretohing Tetrad (1100/1001/0110/0011)

Stretchi&'Triad (2000/1010/0020)

slated topic(s): Available predictions

VIB.DEGENERACY

BASIC INFORMATIONS ABOUT THE 28SiH4 lf0LECUI.E ____________________~~~~~~~~~~~~~~~~~~~~~~~_~_ ilane 28SiH4 Tetrahedral Symmetry quilibrium Si-H bond length Ro = 1.482 Angstrom nertia Constant Bo = 2.859 on-l

nperturbed band center = J=O level : t-&U1 Stretching (Al) 2186.87 on-l nu2 Bending (E) 970.93 cm-l nu3 g~;~d&ns :;I?{ 2189.18 cm-l IR active nu4 913.46 cm-l IR active

Fig. 4. (a) VIBRATION LEVELS screen with a ZOOM option at the central window. (b) The option MOLECULE at VIBRATION LEVELS screen, providing basic information (central window) and access

to the option AVAILABLE PREDICTIONS.


or set of levels and ask for vibration-rotation energies [Fig. 5(a)] and resonance mixing coefficients of wavefunctions (proportional to dashes in different colors for level patterns) using the option

Z&+0,* The same information in a numerical form is provided by the option T/IEW. Its sub-option SET FILTER/observed only displays those v&rot levels which were accessible in various experimental studies carried out so far. Figure 5(b) demonstrates that experimental information is much less complete compared to that available from T.D.S. The option STARK runs calculations of Stark-splittings once an external electric field is specified.

Starting from the energy level picture the user can inquire for any accessible transition between vib-rot levels of chosen vibrational states of polyads (option TRANSITIONS). He is guided by the program. After both upper and lower sets of states, as well as the type of needed transition (ZR/MW/Raman), have been specified the system initiates the calculation of the spectrum for a chosen temperature. The calculated stick spectrum is displayed in Spectrum survey window either in graphical [Fig. 6(a)] or numerical mode [Fig. 6(b)] VZEW option. Logarithmic scale for intensities in the stick-mode is available.

Together with calculated frequencies and intensities the column Obs-Calc and estimated precision of theoretical predictions (both in mK = 0.001 cm-‘) are presented [Fig. 6(b)]. Empty spaces in Obs-Calc column correspond to predicted lines, which have not been fitted or measured so far. Such lines correspond to red sticks in the picture of survey spectrum whereas fitted (observed) lines correspond to black sticks. The graphical mode offers a swift possibility to magnify a scale (ZOOM-IN option). The marked area in Fig. 6(a) is to be immediately displaced in an additional window in more detail. This is especially convenient for the investigation of dense spectral ranges, Q-branches, hot bands and so on.

After the required spectral range has been chosen by the ZOOM-IN option, one may run spectrum calculations (the command PROFILE) with 3 choices for the form of the spectral contour (options GAUSS, LORENTZ, and VOZGT). The example of a plot for the absorption coefficient is presented in Fig. 7(a). For IR and MW transitions, one can use the TRANSMITTANCE option to get colored plots of the type given at Fig. 7(b).

The collisional pressure broadening parameter, the pressure value, and the optical pathlength (for transmittance) are to be specified in the SET PARAMETERS option.

BANDS screen

This screen was designed for users which have no special interest in molecular quantum ro-vibrational states and are motivated mostly by applications. Starting from this screen one can make the same simulations of spectra as described above, through a dialog with the system in a different way, but also to get access to additional information (advanced statistics, spectra of gaseous mixtures, and two-photon laser excitations). The BANDS screen allows one to display bands available from the database, to display spectroscopic parameters for selected bands, and to calculate spectra for various molecules or mixtures of molecules and for different transition types, under desired physical conditions.

This screen contains several menus (Fig. 8). The menu in the left part of the window displays the list of molecules included in the database. The last item of this menu is Mixture. If this item has been chosen the Mixture composition dialog box appears. Using this dialog box, one can give concentrations for different molecules in the mixture. The menus in the right part of the window displays the set of available transition types.

When both molecule and transition type are chosen, an information window appears. This window informs the user about molecules, concentrations and transition type chosen. Then a BANDS OF.. . window appears. It contains the number of calculated lines in each band for the fixed intensity cut-off, the band spectral coverage, and the band intensity. Using this window the user can select bands or display spectroscopic parameters or statistics. The option STATISTICS is available both in graphical [Fig. 9(a)] and numerical form [Fig. 9(b), the command VIEW].

The graphical Statistics window displays the number of fitted experimental data [histogram and right-hand side numbers of Y-axis in Fig. 9(a)] as well as the standard deviation of the fit [upper curve and left-hand side units in Fig. 9(a)], and the theoretical estimate of the model accuracy (lower curve) vs the rotational quantum number J. In the presented example, the methane v4 band,

T.D.S. spectroscopic databank for spherical tops

(b:

Evr-BJCJ+ll.crwl

---=E

2200

-I

2100 _ --

-E.=;;

2000 -I

I== E -=3 ------_=

- = =;=csr- -_-== 1900

-13 --

, I , I I

J

” 5 10 15 20 26

Md

Fig. 5. The option E vib-ror, showing vibration-rotation energy levels for Pentad of methane versus J quantum number. Different colored fractions of dashes (at VGA monitor) indicate the extent of a mixing

of wave-functions due to resonance interactions. (a) Calculated levels, (b) Observed levels only.

468 VL. G. TYUTEKEV et al

0.6

Infrared stick spectrum in natural scale

Intensity, arbitrary

2050 2100 ,111 Freq, cm-l

(b)

300 0101-0000: 1 2061.936369 -0.069 0.264 1. 0101-0000: 1 2071.953940 0.375 1. 0010-0000: 1 2235.658267 -5.166 0.267 6. 0002-0000: 1 1959.042629 0.570 0.220 2.0592E-006 0002-0000: 1 1971.194711 0.365 4.6763E-006 0101-0000: 1 2062.553187 -0.088 0.305 7.4472E-005 0101-0000: 1 2072.685292 0.379 2.0996E-006 0200-0000: 1Fl 8 2 F2 1 2172.591760 0.630 8.4820E-007

200 0010-0000: 1 2235.651728 1.371 0.267 4.1595E-003 0002-0000: 1 1973.753986 0.814 0.219 1.6582E-005 0002-0000: lF2 2 1 Fl 1 1980.614046 0.366 3.6008E-006 0101-0000: lF2 3 1 Fl 1 2075.652404 -0.704 0.268 7.8995E-005 0101-0000: lF2 4 1 Fl 1 2081.983467 0.382 7.0600E-006 0200-0000: lF2 5 1 Fl 1 2183.110427 0.712 3.41983-007 0010-0000: lF2 6 1 Fl 1 2244.609204 0.196 0.274 4.4556E-003

100 0002-0000: 2Al 1 3 A2 1 1948.328423 4.373lE-005 0002-0000: 2Al 2 3 A2 1 1969.546022 1.7693E-005 0101-0000: 2Ai 3 3 A2 1 2056.053609 0.333 1.5784E-004 0200-0000: 2Al 4 3 A2 1 2167.684475 0.670 7.5505E-006 0010-0000: 2Al 5 3 A2 1 2231.112999 -0.599 0.268 8.8739E-003

: ’ I : 1 1 1 L 0000 0000 non0 0000 a000 0000 oouo 1 0000 1 MO1

1 CF4 2ESIH4 29SIH4 30SIH4 2SSIF4 70GEH4 72GEH4 73GEH4

Fig. 6. The option TRANSITIONS (results at the central window) as run from LIBRA nONAL LEVELS screen (behind). (a) Graphical display. Survey stick-spectrum in the logarithmic scale. Black area is marked for ZOOM-IN command. (b) Numerical display (C’IEW command). Obs-Calc and Std. Dev. are in

mK = 0.001 cm ‘. Other units are given in Section 6.


(4

(b)

1000

0

-

Inknsity, cm-2%~1

\ Frca, cm-1

6000

1000

0

I uib,cm-1

0.6

0.4

0.2

0

Transmittance -

Frca, cm-l

Fig. 7. Plots from the PROFILE command, after zooming of a Q-branch at previous spectrum survey [Fig. 6(a)]. (a) Example of a plot for absorption coefficient (VOIGT option). (b) Example of a

transmittance function (TRANSMITTANCE option).

470 VL. G. TYLTEREV et al

M 0lecules.

12CHJ

13CH4

12CD4

13tn4

CF4

28SIH4

2YSIH4

3OSIH4

2BSIF4

70GEH4

72GEH4

73GEH4

74GEH4

7SGEH4

llSStQH4

SF6

i3CD4 0.87

Transition type: Infrared

Transitions:

Linear absorcntion

Laser excitation

a1 UP - Low #Lines Frera range,cm-1 Intensity Int.Units

0100-0000 : 2594 1257.4 - 1836.7 8.5E-001 cm-2*atn-1 0001-0000 :

* 0200-0000 : 746 2852.5 - 3272.9 4.2E-001 ::-2*atm-1 * 0101-0000 - 3391 2490.6 3234.5 6.8E+OOO cm-2*atm-1 * 0002-0000 : 1406 2144.5 - 2915.4 9.2E-001 cm-2*atm-1

1000-0100 : 6: 1185.7 - 1223.6 O.OE+OOO cm-2*atm-1 0010-0100 : 1459.4 - 1606.9 2.OE-004 cm-2+atm-1 0010-0001 : 265 1471.1 - 1945.3 l.lE-002 cm-2*atm-1 0200-0100 : 1390.9 - 1550.9 O.OE*OOO cm-2*atm-1 0101-0100 : 9:; 1162.1 - 1378.9 l.OE-001 cm-2*atm-1 0101-0001 : 13 1396.5 - 1561.5 O.OE+OOO cm-2*atm-1 0002-0001 : 1351 1164.0 - 1365.0 7.4E-001 cm-Z+atm-1

Fig. 8. BANDS screen. The picture corresponds to the choice of Mixfure item in the MOLECULE window and of Infrared item in the TRANSITIONS window. The central BANDS OF window displays a

fraction of the list of bands for the second item in the mixture (‘“CH,). available from T.D.S.

the standard deviation of the line position calculations is 0.00006cm ’ (which is of the order of experimental accuracy); line intensities for this band were fitted with r.m.s. residual <3”/0.

The menu in the right part of the BANDS screen (Fig. 8) offers a possibility to switch between linear absorption processes and laser excitation processes. The option TWO-PHOTON (available in the numerical mode only) provides a spectrum survey for two-photon transitions. An example of a calculated stick-survey for Raman transitions in logarithmic scale is presented in Fig. 10(a). About 90% of these predicted lines are “red” i.e., they have not yet been measured. An example

of synthetic Raman spectrum is given in Fig. IO(b). The window SUMMARY provides the supplementary information concerning basic features of

the T.D.S. package, distinctions from HITRAN or GIESA, references, hardware requirements, authors and so on. The example giving an idea of T.D.S.-team involvement is presented in Fig. 11.

Working with the T.D.S. package consists essentially of sequences of interactive manipulations with a set of graphic tools: windows, menus, viewers, etc. All screens offer context-sensitive help facilities. For the full description of tools and operations we refer to the User Manual.

5. AVAILABLE SPECTROSCOPIC INFORMATION

A detailed presentation of all data available from T.D.S., experimental origins used in a data reduction, as well as a complete reference list are beyond the scope of the present paper and will be presented separately (Champion et a1’9). The reader is referred to original papers in order to get more information for experimental high-resolution studies and data reductions of spherical top molecules. Just note that r.m.s. for positions are generally ranging from IO--” to a few lO_~‘cm ’


(4

Molecule 12CH4. Infrared transition biOl -0000. Fitted freqwncier.

3OSI

c

E,cm-1 I Num.fit.data(grecn bars) I Estimated theor.accwawIblucl I Std.deuiatienfrcdl 2881 0.00035 - - I 70GE -I

TransRbns:

3032.0 1.4E-002 cm-2*atm-1

0201-0100 : 2817.1 - 2817.1 O.OE+OOO em-2*atm-1 0102-0001 : 2824.0 - 2824.0 O.OE+OOO cm-Ziatm-1

MOkUkS: Transitionr:

0.000000 0.000057 0.000001 0.000051 0.000002 0.000050 0.000003 0.000049 0.000005 0.000057 0.000008 0.000057 0.000014 0.000072 0.000021 0.000072 0.000033 0.000076 0.000049 0.000100 0.000072 0.000073 0.000102 0.000142

0101-0001 : 84 1397.7 - 1661.9 3.9E-004 cm-2*atm-1 0002-0001 : 1364 1168.3 - 1439.8 7.1E-001 cm-2*atm-1 0110-0100 : 23 2970.7 - 3032.0 1.4E-002 cm-P*atn-1 0011-0001 : 2973.1 - 3037.0 7.X-002 cm-2+atm-1 0201-0100 :

; 2817.1 - 2817.1 O.OE+OOO om-lratm-1

0102-0001 : 2824.0 - 2824.0 O.OE+OOO cm-?*atn-1

- ml

n

d -

Fig. 9. STATISTICS option for vq band of methane (central windows) as run from BANDS screen. Provides number of obs. lines, estimations for the model accuracy, and r.m.s. of fitting (versus rotational

quantum number J). (a) Graphical display. (b) Numerical display (VIEW command).


Transitions:

i?; 131

12

9 28: 29: 301 28: ?o( 72t 731 74t 76l 111 SF1 Mi, -

0.6

log1 O(lntenr+l I, arbitrary

1, Freq, cm-l

Mel

12[ 1x 12X

! 282 295 30: 28s 7oc 72C 73c 746 76C 11E SFf Mix

Transitions: - .._... _. ion

Intensiw, arbitrary

1980 1970 1960 1990 2000

Fig. 10. Example of calculated Raman spectra (central windows) as run from BANDS screen (behind) by RAMAN command in the TRANSITION window. (a) Survey stick-spectrum in the logarithmic scale. (b) Simulation of spectrum with the PROFILE command (LORENTZ option) after a zoom had been done

in the survey spectrum (a).


TOMSK DIJON SPECTROSCOPY project

a

J.P.Champion Laboratoire SMIL

Universite de Bourgogne DIJON, FRANCE

ViGTyuterev LTS Laboratory

Institute of Atmospheric Optics TOMSK, RUSSIA

TDS TEAM MAIN INVOLVEMENT

Y.L.Babikov J.P.Champion J.C.Hiiico M.Loete A.NikiUn V.i.Perevaiov CPierre GPicrre S.A.Tashkun VI.G.Tyuterev Ch.Wenger

LTS SMIL SMIL SMIL LTS LTS

SMIL SMIL LTS LTS

SMIL

DOS Software Package Design Hamiltonian ModsiisaUon -Data Reduction Methane intensity Analysis and Data Reduction Transitlon Moment Modeiisation -Stark Effect Software and invariant Parameter DeterminaUon Transition MomentTheory Siiane Frequency Analysis - Bibilography Spherlcai Tops Involved in Laser Spectroscopy Software for fitting and formal calculations Reduced Hamiitonians and Invariant Parameters UNlX Software Design and Resources Management

This Package benefited from many other contributors among which experimentalists are gratefully acknowledged for provldlng us with wealth of valuable high resolution data:

[see the next page for names]

Fig. 11. Extract from the window SUMMARY.

for IR and Raman fitted transitions. R.m.s. for MW fitted frequencies are within 5&500 MHz. The relative precisions of the fitted IR intensities are of the order of 3-20%.

The number of related experimental studies is rather large. The reader is referred to the publications of those experimentalist names gratefully cited in the Acknowledgements (see also recent review for methane spectra by Brown et a13’ and references therein, and reviews3”2 on Raman spectra).

A summary of predictions available from T.D.S. is presented in Table 2. The following explanation should be made concerning notations used in this Table. Dip: dipolar

transitions (Infrared, Millimeter or Microwave). Raman: isotropic transitions (same polarizations for pump and probe beams). Two-photon: transitions calculated with two photons of equal frequency? ( “CO2 laser lines).

Definitions for vibrational band assignment are given in Table 1. Predictions include all transitions (within the range O-J,,,,,) for which line strength (in the temperature range O-T,,, K) can exceed Smin.

Column headings in numerical mode

Band-identification of upper and lower vibrational levels. Upper state-Upper state JCN identification, three column sequence:

J-rotational quantum number; IC-rovibrational symmetry; N-sequential number for given J and symmetry.

Lower state-Lower state JCN identification; same definition as above. Freq-Transition frequency (cm-’ or GHz).

TFor other multiphoton processes contact G. Pierre (SMIL).


Table 2. Summary of predictions available from T.D.S. (October 1993 update).

8and Syatam Tr Type Fmin-RU Ju Smin R286TmxNumber of linea

%i,

-_____-_____________~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

cs <- cs Dip O-7763 GIJZ 2s l.d-7 170 1000 SO8

Dyad <- Gs Dip 887-1840 30 l.d-5 2400001000 7688

Dyad <- DYad Dip m-17998 G&z 20 1.6-7 150 1000 3710

Pentad <- GS Dip 2163-3270 2s l.d-4 SlWO 1000 8769

Pentad <- GS Rpppur 2312-3075 18 l.d-3 a.u. 7900 IWO 3411

pentad <- Dyad Dip lle8-1847 1s S.d-4 IB 1000 3247

pentad <- Pentad Dip 7-18808 eb 12 S.d-8 1 IWO 7758

cs <- cs Dip o-7763 ak 28 1.6-7 170 IOW 48e

nyad <- CS Dip 803-1836 30 l.d-5 2300001000 7576

Dyad <- m Dip 11-18211 G&c 20 l.d-7 160 1000 3782

Pentad <- GS Dip 2144-3272 2s l-d-4 480001000 8038

Pantad <- GS Ramn 2404-308s 18 1.6-3 a.u. 8000 1000 3734

Pentad <- Dyad Dip 1162-IQ45 1s 5.d-4 la 1000 2674

Gs <- Gs Dip o-4705 Gm 30 l.d-8 270 1000 872

Dyad <- Gs Dip 787-1270 2s l.d-4 4700 1000 5514

Dvaa <- Dvaa Dip 8-10108 Ck 25 l.d-8 400 1000 6803

Pentad C- GS Dip 1835-a 2s 1.6-3 760 1000 3991

Pentad <- CS Rpmn IESE-2238 18 l.d-2 a.u. 2100 IWO 4898

Pentad <- Dyad Dip 893-1088 20 l.d-3 7.5 800 2473

Gs <- Gs Dip o-4705 Gm 30 l.d-8 270 1000 86s

w <- cs Dip 812-1251 25 l.d-4 4700 1WO SOW

Dvla <- Dvad Dip 11-10303 Glk 25 l.d-8 480 1000 6s77

Pentad <- GS Dip 1828-2393 2s 1.6-3 7!30 1000 3615

continued opposite


Table 2-continued

m¶tmd *- Gs bmn 1878-2204 10 l.d-2 a.~. 2WO 1000 4504

FWlf&+D$WI Dip SW-1042 20 l.d-3 86002494

B_Dyad+cS Dip 7m-1040 20 l.d-2 a.~. 770 1000 1483

s_Dyad+GS Dip 203&-2177 12 1. a.u. cm00 1000 101a ____~___~___________~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

"W4

____________________~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

B_Dytul+GS Dip 726-1040 20 l.d-2 a.u. 770 1000 1817

sJyad+cs Dip 2035-2177 12 1. a.u. so0 1000 1004

Gs <- Gs Dip

B_Dpd+cS Dip

BJyad + BJyad Dip

B_Triad <- CS Dip

B-triad <- BJIyad Dip

B-Tetrad (- GS Dip

sJyad+GS Dip

Sm <- S_Dyad Dip

s_Dyad+Gs

s_Triad <- Gs Dip

o-Boo0 Glk

800-1200

o-1OOoO c&z

1600-1800

820-1002

2500-3oso

2040-2300

o-4000 Gm

216s2180

4170-44w

4. d-8 1000

3.6-l a.u. 1000

4.d-8

l.d+l a.~. 100

3.d-1 a.~. 40

l.d-2 8.~. go00

5. 8.U. 660

9.6-7 l .u. 560

5.6-3 a.u. 2400

5. l .u. 2400

Gs Linmr Stark Effect 28

B.Jmd Lilwrr Stark EfYect 20

________~_____~___~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~--

%I4

_________~__________~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

GS + CS Dip O-WOO Qk 18 4.6-7 loo 380 242

B_Dyul+G2 Dip BDO-1200 la 3.0 au. loo 380 284

B&ad + B_Dymd Dip 0-10000 Qlz 17 4.6-7 32380 810

sJyad+GS Dip 2080-2300 18 8.0 a.u. 64 380 Be0

s-x-Gs Run 217s2190 1s 8.6-2 8.u. 220 350 809

continued overleaf

476

Table 2-continued

s&ad <- s_Dyad

VL. G. TYUTEREV et al

DIP O-2700 aiz IS 1.0 a.u. 833BOm2

------___---_____-__~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

%I,

_____-______________~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

GS <- GS Dip 0-22OOGk 18 4.d-7 100 330 242

B&ad <- Cs Dip 810-1100 IS 3.0 a.u. 103 350 880

BJIyad <- BJlyad Dip o-7OOOGih 17 4.d-7 38350 818

E_Dyad<-GS Dip 207522SO 18 8.0 a-u. 88350 882

s_Dyad+G8 Run 2175-2190 1s 8.d-2 a.~. 220 380 881

SJJyad <- SJIyad Dip 0-27OOGk 18 1.0 a.u. 100 350 970

____________________~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

“SiF,

____________________~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~_~~~~~~~~~~~~

GS <- GS Dip MO-24OG& 40 S.d-11 a.u. 100 380 812

0010 <- GS Dip 1024-1038 51 l.d-2 a.u. 100 390 3281

0010 e- 0100 Dip 30-700 Gk 40 8.d-11 a.u 2000 350 8108

____________________~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

'%nH,

____________________~~~~~~~~~~~~~~~~~~~~~~~~~~~~~__~~~~~~~~~~~~~~~~~~~~~~~~

c;6 (- GS Dip o-SO00 Gk 20 l.d-7 490350 348

B_Dyad+GS DIP 700-850 27 IO. a.u. 420 380 1868

B_Dyad <- B_Dyul Dip o-7SOO cb 20 l.d-7 1200 250 4lB8

E_Dyad+GS Dip 1828-1870 14 IO. a.u. 1200 280 1049

s_pyad+G8 Run mm-lm8 14 l.d-2 a.u. 1400 350 583

____________________~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

5 ____________________~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

0010 <- GS Dip 28-28Ttk 88 l.d-2 a.~. 100 350 II!328

w20<-GS Two-photon 28-2STHz 80

w30<-CS DIP 2817-2880 32 l.d-1 a.u. 27 350 11028

____________________~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The tsgeratare depadence of line q trengtha for SF 18 e

arbitrary

(M part1tic.n fulhlon included).

Units and notations

Line Position Units: cm-' (or GHZ).

Llne Strength Units: mm2 atm-' (or a.~. = Arbitrary Units).

Smin: Line Strength Threshold.

RasB: Line Strength Fknge at 298 K (2228 - (Smax at 298K) / Smin).


Obs-Calc-Observed minus calculated frequency ( 10m3 * cm-’ or MHz). Std. Dev-Individual standard deviation of frequency (lo-’ * cm-’ or MHz). Intensity-Transition intensity [cm 2 * atm-’ at the temperature specified (default is

296 K) or arbitrary units].

Column headings for two-photon table

Band-Identification of upper and lower vibrational levels. Frequency-Transition frequency (GHz).

Intensity-Transition intensity [cmm2 - a&n-’ or arbitrary units]. Transition-ID-Transition assignment: BLJ IN LC UN, where

B-branch (0, P, Q, R, or S); W-lower rotational quantum number;

LN-lower sequential number for given J and symmetry; LC-lower rovibrational symmetry; UN-upper sequential number for given J and symmetry.

Laser-Line-Laser line identification F-LaserF-Difference between transition frequency and laser frequency (MHz).

6. HARDWARE AND SOFTWARE REQUIREMENTS

The T.D.S. DOS-version is designed for: PC/AT Compatible with Math Co-processor, series 80386 or higher; DOS 3.0 or later version, Microsoft compatible mouse;? 20 Mbyte Hard Disk (or more for data storage depending on user’s specific needs); 1.44 Mbyte 3.5” or 1.2 Mbyte 5.25” Diskette Drive (Software installation and Data Input); and a majority of Laser Printers, Ink-Jet printers or Graphics Dot Matrix Printers which are suitable for hardcopy outputs.

7. CONCLUSION

Applications for T.D.S. may include:

Education /Training. In molecular physics, quantum chemistry, physical chemistry, laser physics. There exists a certain “barrier” in understanding spherical top spectra because of sophisticated

symmetry considerations, tensorial formalism, and specific labelling of states and transitions. We hope that the T.D.S. databank will serve as a tool facilitating the access to high resolution spectroscopic results on spherical tops. The user can choose any type of accessible transition between molecular state explicitly displayed on the screen and to make a calculation of associated spectra (under conditions significantly wider than standard laboratory conditions) without any knowledge of tetrahedral formalism or even of selection rules.

More sophisticated applications may rise from experience. Spectroscopic Applications. Analysis, laser spectroscopy, atmospheric optics, optical standards,

spectroscopic atlases. Environment Studies. Atmospheric physics (remote sensing), data supply for specific databases

(HITRAN, GEISA etc.). Photochemistry. Laser excitation, multiphoton processes. Demonstration DOS-versions of T.D.S. package (including the automatized version which runs

itself and shows “movies” of all successive options one after another) will be available through an “electronic publication” (in preparation) or by request from the authors.

Future developments

The T.D.S. data bank will be periodically updated when new analyses are performed. In the near future, recent results in the pentad reanalysis2’ of 12CH4 will be included as well as low J data on the upper polyads (o&ad, tetradecad) of this molecule. Also recent analyses33 of the lower states of CF, will be incorporated.

tAl1 commands of the T.D.S. package may be equally performed either using the mouse or the keyboard.

418 VL. G. Tvuwanv et al

We plan to extend the T.D.S. databank to other types of molecules, primarily to symmetric and asymmetric top isotopic modifications of the present family of molecules. Also the implementation of extended version for MS Windows and X Window system on UNIX Workstations is planned. The possibility of importing experimental spectra into the program to be compared with synthetic spectra will be implemented in the Windows-version.

A complete library of FORTRAN (ANSI 77) programs is being tested on SUN, HP and IBM workstations for providing a complementary tool of the present PC package in the field of spherical tops. This software is designed to allow the user to make predictions of spectra under various conditions controlled by a few standard parameters. It comprises a single UNIX command “STDS” with seven parameters following the simple syntaxt: STDS molecule/polyad Jmax Fmin

Fmax Tvib Trot Smin,

where molecule/polyad specifies the name of the file containing all spectroscopic information needed to calculate the spectrum of the desired molecule and polyad (essentially Hamiltonian and Transition effective parameters). Jmax is the maximum value of the angular momentum. Fmin and Fmax specify the lower and upper frequency limits. Tvib and Trot specify the vibrational and rotational temperatures, respectively. Smin is the intensity lower limit of the calculated spectrum.

The limitation of these programs are of two kinds: The first limitation is fundamental; although extrapolations to high J values are generally technically possible, the physical reliability of the predictions has to be carefully examined in each situation. The second limitation is related to hardware configuration: complex band systems may involve quite numerous lines arising from perturbation allowed transitions. In such cases, setting Smin = 0, for instance can generate very large files. Similarly setting relatively large Jmax can lead to time consuming calculations.

All questions and suggestions can be addressed by E-mail to:

[email protected] data included;

[email protected] DOS software.

Acknowledgemenfs-We would like to emphasize that this Package benefited from many contributors among whom experimentahsts W. Acef, A. Bauder, M. Bogey, H. Berger, D. Bermejo, C. Borde, L. R. Brown, H. Burger, C. Chardonnet, J. L. Destombes, H. Dreizler, G. Guelachvili, L. Henry, W. Kreiner, V. M. Krivtsun, B. Lavorel, G. Millet, J. Reuss, H. W. Schrotter, J. Steinfield, M. Takami, and A. Valentin are gratefully acknowledged for providing us with a wealth of valuable high-resolution data. The T.D.S. project was supported by: CNRS France and Russian Academy of Sciences (Scientific Cooperation Agreement 1.25), Region Bourgogne (grant for computer equipment) and IOA SO RAN (internal research grant). VI. G. T. thanks the Alexander von Humboldt Foundation for the support of the research in 1992 and CNRS (France) for the support of the research in 1993.

1.

2.

3. 4.

5. 6. 7. 8. 9.

10. 11. 12.

REFERENCES

L. S. Rothman, R. P. Gamache, R. H. Tipping, C. P. Rinsland, M. A. H. Smith, D. C. Benner, V. Malathy Devi, J. M. Flaud, C. Camy-Peyret, A. Perrin, A. Goldman, S. T. Massie, L. R. Brown, and R. A. Toth, JQSRT 48, 469 (1992). N. Husson, B. Bonnet, A. Chedin, A. A. Chursin, V. F. Golovko, and Vi. G. Tyuterev, JQSRT 52, 314, 425 (1994). L. R. Brown, C. B. Farmer, C. P. Rinsland, and R. A. Toth, Appl. Opt. 23, 5154 (1987). 0. K. Voitsekhovskaya, N. N. Trifonova, and A. V. Rozina, Information System for High-Resolution Spectroscopy, Nauka, Novosibirsk (1988). In Russian. J. P. Champion, Can. J. Phys. 55, 1802 (1977). J. P. Champion and G. Pierre, J. molec. Spectrosc. 79, 255 (1980). M. Loete, Can. J. Phys. 61, 1242 (1983). J. C. Hilico, M. Loete, and L. R. Brown, J. molec. Spectrosc. 111, 119 (1985). J. P. Champion, M. Loete, and G. Pierre, in The Spectroscopy of the Earth’s Atmosphere and Interstellar Medium, K. N. Rao and H. Weher, Eds., Academic Press, New York, NY (1992). Vl. G. Tyuterev and V. I. Perevalov, Chem. Phys. Lett. 74, 494 (1980). V. I. Perevalov and VI. G. Tyuterev, J. mofec. Spectrosc. %, 56 (1982). E. I. Lobodenko, 0. N. Sulakshina, V. I. Perevalov, and VI. G. Tyuterev, J. molec. Spectrosc. 126, 159 (1987).

tMore detail about this tool can be obtained by anonymous ftp or electronic mail at the following addresses: [email protected]/[email protected].


13. V. I. Perevalov, Vl. G. Tyuterev, and B. I. Zhilinskii, J. mofec. Spectrosc. 103, 147 (1984). 14. V. I. Perevalov, Vl. G. Tyuterev, and B. I. Zhilinskii, J. mofec. Spectrosc. 111, 1 (1986). 15. Yu. S. Makushkiu and Vl. G. Tyuterev, The Methods of Perturbation Theory and Effective Hamiltonians

in Molecular Spectroscopy, Nauka, Novosibirsk (1984). In Russian. 16. B. I. Zhilinskii, V. I. Perevalov, and Vl. G. Tyuterev, Method of Irreducible Tensorial Operators in the

Theory of Molecular Spectra, Nauka, Novosibirsk (1987). In Russian. Translated in French by J. L. Cambefort, SMIL, Dijon, France.

17. Vl. G. Tyuterev, J. P. Champion, G. Pierre, and V. I. Perevalov J. mofec. Specirosc. 105, 113 (1984). 18. Vl. G. Tyuterev, J. P. Champion, G. Pierre, and V. 1. Perevalov, J. molec. Spectrosc. 120, 49 (1986). 19. Vl. G. Tyuterev, J. P. Champion, and G. Pierre, Molec. Phys. 71, 995 (1990). 20. B. Lavorel, G. Millot, Q. L. Kou, G. Guelachvili, K. Bouzouba, P. Lepage, VI. G. Tyuterev, and G. Pierre,

J. molec. Spectrosc. 143, 35 (1990). 21. J. C. Hilico, J. P. Champion, S. Tuomi, Vl. G. Tyuterev, and S. A. Tashkun, J. molec. Spectrosc. (1994). 22. V. I. Perevalov, 0. N. Lyulin, Vl. G. Tyuterev, and M. Loete, J. molec. Spectrosc. 149, 15 (1991). 23. Yu. L. Babikov, S. A. Tashkun, Vl. G. Tyuterev, J. P. Champion, J. M. Jouvard, G. Pierre, and C.

Wenger, XZZth Conf. on High Resolution i.r. Spectrosc., Paper L16, Prague (1992). 24. G. Pierre, A. Valentin, and L. Henry, Can. J. Phys. 64, 341 (1986). 25. H. Prinz, W. A. Kreiner, and G. Pierre, Can. J. Phys. 68, 551 (1990). 26. J. P. Champion, J. C. Hilico, and L. Brown, J. molec. Spectrosc. 133, 244 (1989). 27. M. Oldani, A. Bauder, M. Loete, J. P. Champion, G. Pierre, J. C. Hilico, and A. G. Robiette, J. molec.

Spectrosc. 113, 229 (1985). 28. L. R. Brown, M. Loete, and J. C. Hilico, J. mol. Spectrosc. 133, (1989). 29. J. P. Champion, J. C. Hilico, M. Loete, G. Pierre, Vl. G. Tyuterev, and S. A. Tashkun, Spectrochim. Acta

A, to be published. 30. L. R. Brown, J. S. Margolis, J. P. Champion, J. C. Hilico, J. M. Jouvard, M. Loete, C. Chakerian Jr.,

G. Tarrago, and D. Chris Benner, JQSRT 48, 617 (1992). 31. H. W. Schrotter, H. Frunder, H. Berger, J. P. Boquillon, and G. Millot, in Advances in Non-linear

Spectroscopy, Wiley, New York, NY (1988). 32. B. Lavorel, G. Millot, M. Rotger, G. Rouille, H. Berger, and H. W. Schrotter, J. molec. Structure 237,

49 (1992). 33. A. Nikitin, T. Gabard, J. P. Champion, G. Pierre, A. G. Robiette, and A. Pine, 49th Symp. on Mofec.

Spectrosc., Columbus, OH (1994) and paper in preparation.

Documents

T.D.S. spectroscopic databank for spherical tops: DOS version