Ribeaud's program for Stark coefficients in an asymmetric rotor

       This program uses the Golden and Wilson treatment for an asymmetric top without nuclear quadrupole coupling, J.Chem.Phys. 16, 669 (1948), and as summarized in Gordy&Cook, 3rd ed., pp.468-477. Stark coefficients for first, second and mixed order components are calculated if you know how to read the output! The best I can do to help you is by providing below a scanned version of a hand annotated copy of the output (from about 1978) that survived in my archives.

       NOTE: this program is kept here for various historical reasons, whereas it is recommended that the program QSTARK is used for current research applications.

STARK.FOR The listing.  A header has been added to the original source, which explains the structure of the data file. The data is taken from file STARK.DAT and output is appended to file STARK.RES
STARK.DAT Test data for kappa=-0.5 and alpha=0.5 (see the Golden&Wilson paper)
STARK.RES Results file for the data above, which can be compared with the Golden&Wilson table of A,B coefficients. Note that there is a known bug in the coefficients for the 000 and 101 states.
STARK.JPG Scanned version of a hand annotated copy of the output to serve as rudimentary documentation.

Back to the table of programs





Stark coefficients for an asymmetric rotor (modification of program STARK by H.M.Pickett)

        This is a modified version of the program STARK.F written by H.M.Pickett. Like its predecessor, SZK is a postprocessing program working on output from the SPFIT/SPCAT package.  The program calculates the same quantities as STARK, but it takes its data from an .STR file produced by a prior run of SPCAT.  The .STR file contains in the second column the reduced transition dipole matrix element which is equal to the square root of the linestrength. This is the basis for evaluating the Golden&Wilson type Stark coefficients as defined in J.Chem.Phys. 16, 669 (1948). The .STR file is produced by setting STRFLAG in the .INT file to 1 (i.e. the tens digit in the first number in the top line has to be 1). The output from SZK is written to an .STK file.

        Modifications to Pickett's original are as stated at the top of the listing and have gone mainly into producing what is hopefully self-explanatory output. Only the coefficients for the energy levels are calculated so that those for the observed transitions have to be set up by hand. Note that with this version the coefficients should be calculated by setting only one of the three possible dipole moment components to unity - if several components contribute to the Stark shift then results from two or three such separate runs of SPCAT and SZK should be combined.

SZK.FOR The listing.  Input is from files xxx.STR and xxx.INT (the comment) and the output is written to xxx.STK
SZK.EXE Executable for Windows
SO2.STK Specimen results for SO2 to compare with the Gordy&Cook test case, p.474 (3rd Ed.). This file is generated by first running SPCAT, which requires files SO2.VAR and SO2.INT, then running SZK on the results.
H2OHF.STK Results file for H2O..HF, which shows the appearance of mixed order output - this can be compared with J.Chem.Phys. 78, 2910 (1983)

Back to the table of programs





To fit and to predict Stark shifts for a rotor with up to one quadrupolar nucleus by direct matrix diagonalization for each value of the electric field

        The incentive for writing this program came from the necessity to deal with Stark shifts measured in FTMW work on quadrupolar molecules.   The available field strength is quite low so such shifts fall into the inconvenient intermediate field regime. The only robust solution is through matrix diagonalization, which has to be carried out for each combination of field and MF (the quantisation used is J, K+1, K-1 ,F, MF).  QSTARK has been developed from Q2FIT and irreducible tensor matrix elements for quadrupolar coupling are from that program.  The matrix elements of HE are from:

        H.P.Benz, A.Bauder, Hs.H.Gunthard, J.Mol.Spectrosc. 21, 156 (1966). 

        An extension of QSTARK to the two quadrupole case is in progress.  Note that most of the internal workings from Q2FIT remain intact, including lack of factorisation so that matrix sizes and execution times may in some cases become considerable.  Some features:

  • Calculation for linear, symmetric, and asymmetric rotors, with zero or one quadrupolar nuclei
  • All of the observed Stark shifts can be included in one data set (if the field calibration is good enough) - for example for asymmetric tops without quadrupolar nuclei it is possible to fit second order and mixed order shifts simultaneously
  • The fit can be made either directly to frequencies or to frequency differences
  • It is possible to fit either the effective electrode separation (calibration) or the dipole moment components and, if desired, any of the remaining constants in the Hamiltonian - the latter allows enhanced determination of spectroscopic constants from Stark shift perturbations
  • All types of ΔM transitions can be fitted: 0 and 1
  • Fit can be weighted according to estimated measurement errors
  • It is possible to calculate and plot the behaviour of selected Stark components with the electric field. The program can produce simple diagnostic ASCII plots in the standard output file, as well as appropriate files for the gle program, and thus to obtain higher quality PDF etc. output.
  • Experimental measurements can be plotted on top of predictions (these are placed in a simple two column file of voltages and frequencies during a fitting run, and this file is reused during a subsequent predictive run)
  • It is possible to plot predicted Stark lobe behaviour as a linear or quadratic function of applied voltage or electric field
  • Separating blank lines and comments can be embedded between the measured frequencies and will be echoed to the output if required, and the number of transitions declared in the data can also be automatically counted by the program

       The recommended paper for citing the the use of QSTARK is:

  • Z.Kisiel, J.Kosarzewski, B.A.Pietrewicz, L.Pszczolkowski, Chem. Phys. Lett. 325, 523-530 (2000).

       Known bugs:

       The program calculates correct energies but is known to run into labelling problems when the off-diagonals in the H matrix become sufficiently large. Thus indices may be incorrectly assigned to the eigenvalues. Known instances of such behaviour are:

  • first order Stark effects in symmetric tops
  • highly perturbing states in asymmetric tops
  • high field calculations when μc is non-zero and QSTARK switches to the complex H matrix formulation

       Extensive dump output, as controlled by the IDUMP parameter, allows checking of the internal workings in order to obtain a more detailed insight into such behaviour.

QSTARK.FOR The listing.  There is much documentation at the top of this listing, including a detailed description of the input file.  The recommended extension for the input data files is .Q


Compile with any 32-bit compiler, remembering to use the appropriate option for static allocation of variables (e.g. -static with f77, or -Qsave with Intel Visual Fortran)

Some compilers (e.g. f77) may treat the backslash '\' character in strings as a command to generate special characters. This will affect the proper generation of xtitle and ytitle lines in the .GLE file. If this is the case replace '\' by '\\'.

QS.EXE Executable for the Windows system..

The program now uses dynamic dimensioning so it is only limited by the memory available for its execution.

  Sample fits
OCS.Q Data set for the standard calibration molecule, set up to determine the electrode spacing. Note the use of asymmetric rotor quantum numbers, annotations between lines of the dataset, automatic line counting, and simultaneous fit of ΔM=0 and ΔM=1 transitions.
OCS.RES Abbreviated results file for the above. For supersonic expansion, cavity-FTMW spectroscopy there are practical limits on the magnitude of the applied electric field so that Stark shifts are typically less than 1 MHz. This results in only moderate precision of calibration.
MECN.Q MEI.Q Data sets for the two calibration molecules used in Warsaw. Larger dipole moments allow measurement of considerably larger Stark shifts for available electric fields than is the case for OCS.
MECN.RES MEI.RES Results files for the above. Note the improved precision in the determination of the cell constant and good correspondence between the two determinations.
ISOX.Q The data for isoxazole from S.McGlone and A.Bauder, J.Chem.Phys. 109, 5383 (1998), in addition to the two dipole components the two poorly known quadrupole components are to be fitted
ISOX.RES Results for the above - only an approximate version of intermediate field analysis was used in the original paper, and appreciable improvement is apparent.   Note that there are some problems in eigenvalue assignment near line 44 - the scheme in the program is over simplistic and fails, it will hopefully be improved when a really trying case appears.
MEIK0.Q The MBER data for the J=1← 0 transition in CH3I from J.Mol.Spectrosc. 160, 351 (1993) - the paper in which earlier noise in the values of the dipole moment for methyl iodide was resolved
MEIK0.RES Results for the above.
W2HCL.Q FTMW data set for (H2O)2H35Cl consistent with Fig.4 in Chem.Phys.Lett. 325, 523 (2000)
W2HCL.RES Abbreviated results for the above
  Sample predictions
W.Q Data set for (H2O)2H35Cl similar to W2HCL.Q above adapted to produce the basis for Fig.4 in Chem.Phys.Lett. 325, 523 (2000).

Each of the six bottom lines specifies a Stark lobe for which calculated points should be generated, and defines the voltage range, the number of points to be calculated and the point distribution (whether linear or quadratic). The last line also defines the Stark shift range of the plots.

EXP.DAT The optional data file containing measured data points to be superimposed on the Stark component plot.
W.RES The main output file produced by QSTARK from the above data, containing blocks of calculated points for the Stark components, as well as a simple ASCII pseudoplot at the bottom.

The same run of QSTARK also produces files EXPTPLOT.DAT, W.GLE and six files W1.DAT,...,W6.DAT.

W.PS The PostScript diagram generated by running gle on the data above using the command: gle_ps (for gle4.0.7)
W1.PS The PostScript plot obtained by changing "The number of iterations" parameter in W.Q above from -2 to -11. In this case the plot is in portrait orientation and is of frequency against voltage.

Back to the table of programs