CCP6 SBE User manual
 
 
                       Jeremy M. Hutson
 
 
                   Department of Chemistry,
       University of Durham, Durham, DH1 3LE, England
 
 
                      and Sheldon Green
 
 
NASA Institute for Space Studies, Goddard Space Flight Center,
          2880 Broadway, New York, NY 10025, U.S.A.
 
 
 
   SBE is a postprocessor for the MOLSCAT program, for
calculating various effective cross sections for atom-diatom
systems from the S matrices produced in close-coupling
calculations. It processes S matrices stored on MOLSCAT's
ISAVEU channel, and is capable of calculating (among others)
the effective cross sections appearing in:
 
1) Sound absorption
2) Thermal diffusion
3) Shear viscosity
4) Nuclear magnetic relaxation (NMR)
5) Depolarized Rayleigh (DPR) light scattering
6) Senftleben-Beenakker effects (SBE) (the effects of magnetic
fields on transport properties).
 
The SBE program does not calculate cross sections for infrared
                     ___
and Raman pressure broadening and shifting, which involve
pairs of S matrices at different total energies; however,
there are internal options within MOLSCAT which allow these
cross sections to be evaluated.
 
   The present version of the SBE program can deal only with S
matrices for MOLSCAT's collision types ITYPE = 1, 2 and 7. It
cannot cope with diatom-diatom or atom-nonlinear molecule
collisions, and does not allow for any decoupling
approximations.
 
   SBE is written in near-standard FORTRAN 77. Versions of the
program are available for VAX/VMS, IBM (FORTRAN VS) and CRAY
computers.
 
   The effective transport and relaxation cross sections may
be defined in several different ways, with different
normalisations. Liu et al. [1] have given one set of
definitions, while a rather different set have been defined by
Fitz et al. [2]. Other authors have used definitions different
from both these. The current version of SBE generates cross
sections in the Liu et al. definition, but it does this by
first evaluating equation (2.37) of Fitz et al. [2] and then
converting to the Liu et al. definition using a FORTRAN
FUNCTION called CFACT. It would be very straightforward to
modify this if required.
 
   The SBE program is controlled mainly by the information in
the S matrix save file output by MOLSCAT (MOLSCAT's channel
ISAVEU). SBE also reads information from channel 5; in
general, this controls which energies are to be selected from
the ISAVEU file, and which cross sections are to be
calculated. The channel 5 input is in NAMELIST format, and the
variables read are as follows:
 
NCALC  The number of energies for which cross section
       calculations are to be performed. See ICALC to specify
       the particular energies required.
 
ICALC  A list of integers which indexes the energies required
       in MOLSCAT's ENERGY array. ICALC defaults to
       1,2,3,4...NCALC: that is, the first NCALC energies in
       the S matrix save file.
 
ISU    FORTRAN channel number on which the S matrix save file
       (MOLSCAT's ISAVEU file) is read. Defaults to 12.
 
MXSIG  If MXSIG is greater than zero, only cross section
       matrix elements between the lowest MXSIG rotational
       levels will be calculated. Since high j cross sections
       can be very expensive to evaluate, judicious use of
       this parameter can save a lot of computer time.
 
NKSET  The number of different cross sections which are to be
       calculated for each energy. See KSET to specify the
       particular cross sections required.
 
KSET   Array specifying a set of 5 angular momentum quantum
       numbers for each cross section required. In the
       notation of Fitz et al. [2], these are Kl', Kj', Kl, Kj
       and K. The default values are
 
 
       Kl' Kj' Kl  Kj   K    Liu et al.       Observable
 
        0   0   0   0   0   sigma(zeta)    Sound absorption
        1   0   1   0   1   sigma(eta,1)   Thermal diffusion,
                                           Shear viscosity
        2   0   2   0   2   sigma(eta,2)   Shear viscosity
        0   1   0   1   1   sigma(v)       NMR
        0   2   0   2   2   sigma(T)       NMR, DPR
        2   0   0   2   2   sigma(eta,T)   Viscomagnetic SBE,
                                           Flow birefringence
        0   2   2   0   2   sigma(T,eta)   Viscomagnetic SBE,
                                           Flow birefringence
        1   0   1   2   1   \
        1   2   1   2   1   |        Thermal conductivity SBE
        1   2   1   2   2   |
        1   2   1   2   3   /
 
       A tabulation of references for the formal expressions
       for the various cross sections, and their relationships
       to the experimental observables, has been given by
       Hutson and McCourt [3].
 
IPLOT  If IPLOT is greater than zero, the program reads an
       additional NAMELIST block &PLOT, and does some
       plotting. However, since the actual plotting routines
       are implementation dependent, this feature is not
       supported in the distribution version.
 
   In this version, the user has no control over the range of
JTOT included in the cross sections; the program simply does
calculations for all the S matrices it finds in the input save
file.
 
   The SBE program also outputs (on channel 7) a formatted
file containing details of the individual contributions to the
cross sections. This file may be processed by an additional
program (RESUM), available from J.M. Hutson on request, if
partial opacities (rather than integral cross sections) are
required. However, for production runs, the output on channel
7 is not useful. Since it can be VERY large, it is best to
send it to a dummy device rather than a file if possible.
 
 
Debugging
_________
 
   The code has been extensively used for calculating cross
sections for rare gas - H2 collisions, and is reliable for
atom - homonuclear diatom systems. In its present form, it has
not been tested for collisions involving heteronuclear
molecules: it is believed to be correct for that case also,
but it needs checking. If any user undertakes this, please
send details to J.M. Hutson.
 
 
Timing
______
 
   The SBE program does a very large amount of angular
momentum algebra, and the computer time required is not
negligible compared to that for the scattering calculation
itself. Indeed, the SBE calculation may dominate when large j
cross sections are required (perhaps even for j=4). The time
required by SBE MUST be taken into account when contemplating
a large calculation.
 
   Although a CRAY version of SBE is available, it should be
noted that the operations performed by this program are almost
completely unvectorisable. In order to use the available
machines efficiently, it is thus probably desirable to perform
the SBE calculation on an machine other than a vector processor.
 
References
__________
 
[1]  W.-K. Liu, F.R. McCourt, D.E. Fitz and D.J. Kouri,
     J. Chem. Phys. 71, 415 (1979).
 
[2]  D.E. Fitz, D.J. Kouri, D. Evans and D.K. Hoffman,
     J. Chem. Phys. 74, 5022 (1981).
     D.E. Fitz, D.J. Kouri, W.-K. Liu, F.R. McCourt, D. Evans
     and D.K. Hoffman, J. Phys. Chem. 86, 1087 (1982).
 
[3]  J.M. Hutson and F.R. McCourt, J. Chem. Phys. 80, 1135
     (1984).
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
SBE User Manual               4                 2 October 1985