** LABEL** -
Title for run (up to 80 characters). Note that this must appear
in the data file as a literal string enclosed in quotation
marks, e.g.

`LABEL='TEST RUN'`

** URED** -
Reduced mass for collision, m1*m2/(m1+m2), in atomic mass units
(mass of carbon-12 is 12.0)

** INTFLG** -
Selects propagator to be used (see
Section 1.3 above)

** LASTIN** -
(default 1).
If

`LASTIN`

is set to 1, the run will terminate after
the current scattering calculation is complete. If
`LASTIN`

is 0, another complete set of data will be
read once this set has been processed.** ICONV** -
(default 0).
If

`ICONV`

is set to 1 on input, NAMELIST block
`&CONV`

(see Section
6) will be read and the program will perform automatic
convergence testing with respect to step size,
`RMIN`

, `RMID`

or `RMAX`

(see
Section 2.12). If
`ICONV=0`

(the default), NAMELIST block
`&CONV`

is not read.** MXSIG**
(default 0). By default, MOLSCAT will accumulate total
cross sections between every pair of levels in the basis
set, including closed channels. This uses a fairly large
amount of storage, and is often not required. If

`MXSIG`

is set to a positive integer, only cross sections
between the first `MXSIG`

levels will be calculated.** LMAX, MMAX** -
(default 0). For IOS calculations, these are the highest
L and M values for which generalized IOS cross sections,
Q(L,M,M') will be accumulated. For

`ITYPE=103`

(see
Section 3.3), `LMAX`

and `MMAX`

identify the maximum L for rotors 1 and 2
respectively.
** IRSTRT**
(default 0).
If not zero requests that a calculation be restarted from saved
S-matrices on unit

`ISAVEU`

(see
Section 2.5).
`IRSTRT=3`

restarts after the last `(JTOT,M,INRG)`

-set found on `ISAVEU`

.
`IRSTRT=2`

restarts after the last `ISAVEU`

; similarly,
`IRSTRT=1`

restarts after a completed
`JTOT`

block. If `IRSTRT=-1`

, the program
tries to restart at `JTOT=JTOTL`

taken from the
current `&INPUT`

data. This option is useful if a
job terminates abnormally; it can also be used to change
tolerances in the propagator or to switch to a different
propagator.
The amount of printed output produced by MOLSCAT is controlled
by the integer variable `PRNTLV`

(default 0);
sensible values of `PRNTLV`

vary from 1 (when only
total cross sections are required) to 35 (when debugging).
`PRNTLV=3`

prints out some information about each
set of coupled equations solved, and complete S-matrices are
printed out if `PRNTLV=11`

or more. Voluminous
debugging output starts appearing at `PRNTLV=15`

.

The number of page throws generated is controlled by the
parameter `ITHROW`

(default 0). If
`ITHROW=1`

, each new S-matrix calculation starts on a
new page.

The printing of total and partial cross sections is controlled
by the parameter `ISIGPR`

(default 0). This must be
set to 1 if printing of cross sections is required (2 to get
coupled states cross sections which are incomplete owing to
missing m-values).

MOLSCAT has built-in loops over total angular momentum
`JTOT`

and "symmetry" type `M`

. The loop
over `JTOT`

is controlled by the three input
variables `JTOTL`

, `JTOTU`

and
`JSTEP`

; the program will loop from
`JTOTL`

to `JTOTU`

in steps of
`JSTEP`

. Note that the orbital angular momentum label
appearing in various decoupling schemes is treated as a total
angular momentum for this purpose.

If total cross sections are required, there is an alternative
form of input flagged by the value ```
JTOTU .ge.
999999
```

(or `JTOTU .lt. JTOTL`

); this
alternative is obtained by the default values. The end of the
loop over `JTOT`

is then controlled by the variables
`DTOL, OTOL`

and `NCAC`

: `JTOT`

will start at `JTOTL`

and be incremented by
`JSTEP`

until `NCAC`

(default 4)
successive `JTOT`

values each contribute less that
`DTOL`

(default 0.3) to any diagonal cross section
matrix element and less than `OTOL`

(default 0.005)
to any off-diagonal cross section. (Note that MOLSCAT always
gives cross sections in units of square Angstroms.) This option
should be used with care, since you must be sure that the
calculation will converge before the job runs out of time. Note
that elastic cross sections usually converge very much more
slowly than inelastic ones.

The loop over symmetry types ("parity cases") `M`

is
used differently for different decoupling schemes. For
close-coupling, `M`

takes values 1 and 2 for odd and
even parity label respectively. (For `ITYPE=3`

, if the two
linear molecules are identical `M`

is further
subdivided into exchange symmetries.) For coupled states
calculations, `M-1`

is the body-fixed projection
quantum number. Under normal circumstances, MOLSCAT generally
loops over all possible values of `M`

for the
coupling case concerned (see, however,
Section 3.10). If the input
variable `MSET`

is non-zero (default 0), MOLSCAT will
skip all calculations except for `M=MSET`

. This
option is particularly useful for resonance searches (see
Section 2.10) and convergence
checking (see Section 6). If
`MHI`

is also non-zero (default 0), calculations are
performed for the range of ```
M values from
```

`MSET`

to `MHI`

.

The total energies (total energy equals collision kinetic energy
plus asymptotic channel energy) at which scattering calculations
are performed are controlled by the array `ENERGY`

and the variables `NNRG, NTEMP, TEMP, DNRG, EUNITS`

and `EUNITC`

. If `DNRG=0.0`

(the
default), calculations will be performed for the
`NNRG`

energies listed in the `ENERGY`

array. If `DNRG`

is not 0.0, calculations will be
performed at `NNRG`

equally spaced energies,
`DNRG`

apart, starting at `ENERGY(1)`

.
The maximum allowed value of `NNRG`

is currently 100.

The units of `ENERGY`

and `DNRG`

are
determined by the integer variable `EUNITS`

(default
1) or by the `character*4`

variable
`EUNITC`

(default is blanks)
as follows:

EUNITS = 1 or EUNITC = 'CM' 1/cm EUNITS = 2 or EUNITC = 'K' Kelvin EUNITS = 3 or EUNITC = 'MHZ' MHz EUNITS = 4 or EUNITC = 'GHZ' GHz EUNITS = 5 or EUNITC = 'EV' eV EUNITS = 6 or EUNITC = 'ERG' erg EUNITS = 7 or EUNITC = 'AU' Hartrees EUNITS = 8 or EUNITC = 'KJ' kJ/mol EUNITS = 9 or EUNITC = 'KCAL' kcal/mol

If a nonblank character string (length 4 or less) is input via
`EUNITC`

, it will override any value input via
`EUNITS`

, and an attempt will be made to match one of
the allowed units and set the conversion factor. This matching
is insensitive to case and extraneous characters are generally
ignored, so that `EUNITC='1/CM'`

has the same effect
as `EUNITC='cm-1'`

or `EUNITS=1`

.
Likewise, both `EUNITC='e.v.'`

and
`EUNITC='eV'`

cause conversion from electron volts.

The input energies are converted immediately into 1/cm using the appropriate conversion factor, and all energies subsequently printed by MOLSCAT are in 1/cm.

There are special interpretations of the `NNRG`

and
`ENERGY`

parameters which may be invoked when

- Searching for resonances
- Calculating line broadening cross sections.

These are described separately in Section 2.9 and Section 2.10.

An alternative form of input is available to facilitate
Boltzmann averaging of cross sections using Gaussian quadrature.
This is controlled by the array `TEMP`

and the
variables `NTEMP`

and `NGAUSS`

. If
`NTEMP`

is greater than 0 (default 0), scattering
calculations are performed at energies corresponding to
`NGAUSS`

point Gaussian quadratures for the
`NTEMP`

different temperatures (in Kelvin) in the
`TEMP`

array. The maximum allowed values are
`NTEMP=5`

and `NGAUSS=6`

. Note that
Gaussian quadrature is not a very reliable way of thermally
averaging some types of cross sections, and use of this option
is generally not recommended.

In addition to its main printed output on channel 6, MOLSCAT can
also write out a file containing S-matrices for subsequent
processing by another program (for example, in the calculation
of differential cross sections or transport cross sections).
This option is invoked if `ISAVEU`

is not 0 (default
0), and the S-matrices are then written to channel
`ISAVEU`

.

Early versions of the program saved this in formatted card image
files with format statements as indicated below. From MOLSCAT
version 11 onwards (June 92), the data are saved in unformatted
(binary) files which provide better precision, use less space,
and reduce the conversion overhead. In the binary files the data
enumerated below are written in the same order, as single
(logical) records (i.e. single unformatted `WRITE`

statements), except for (7), which is described more fully
below. Beginning with version 14 (Aug 94) `NOPEN`

is
found in record (5) rather than in (6).

Contents of the `ISAVEU`

file are as follows:

`LABEL,ITYPE,NLEV,NQN,URED,IP (A80/3I4,F8.4,I4)`

`LABEL`

is the title of run; character length 80.`ITYPE`

specifies the collision type.`NLEV`

is the number of levels in the angular basis set.`NQN`

is the number of (quantum) descriptors per level.`URED`

is the reduced mass in atomic mass units.`IP`

is the MOLSCAT version number (14 in this version).

`((JLEV(I,J),I=1,NLEV),J=1,NQN) (20I4)`

`JLEV(ILEV,J)`

are the quantum numbers of level`ILEV`

. The meaning depends on`ITYPE`

; see Section 3.`NLEVEL,(ELEVEL(I),I=1,NLEVEL) (I4/(5E16.8))`

Number and values of the asymptotic level energies (1/cm).`NNRG,(ENERGY(I),I=1,NNRG) (I4/(5E16.8))`

Number and values of the scattering energies (1/cm).`JTOT,INRG,EN,IEXCH,WT,M,NOPEN (2I4,E16.8,I4,E16.8,I4)`

These describe a single scattering calculation:`JTOT`

is the total angular momentum.`INRG`

is the index of the energy in the list in 4.).`EN`

is the total energy (1/cm);it should equal`ENERGY(INRG)`

.`IEXCH`

is the exchange parity for identical molecules:`IEXCH=0`

no exchange symmetry;`IEXCH=1`

odd exchange symmetry;`IEXCH=2`

even exchange symmetry`WT`

(if nonzero) is a statistical weight of this`JTOT, M`

.`M`

is the serial index of the symmetry block.`NOPEN`

is the number of open channels in the S-matrix. (Note: beginning in version 14 (Aug 94)`NOPEN`

has been moved from record (6) to record (5), and programs which process saved S-matrices should check the value of`IP`

in record (1) to determine the expected format.)

`(LEV(I),L(I),WV(I),I=1,NOPEN) (I4/(2I4,E16.8))`

`LEV(I)`

is a pointer to`JLEV`

(see above) for the basis set in channel`I`

.`L(I)`

is the orbital angular momentum for channel`I`

.`WV(I)`

is the wavevector of channel`I`

(1/Angstroms).

- (
`SREAL(I),I=1,NSQ),(SIMAG(I),I=1,NSQ) (5E16.8)`

`NSQ=NOPEN*NOPEN`

`SREAL(I)`

and`SIMAG(I)`

are the real and imaginary parts of the S-matrix elements, listed in FORTRAN storage order for the`NOPEN*NOPEN`

matrices`SREAL`

and`SIMAG`

. In unformatted files (version 11 and later),`SREAL`

and`SIMAG`

are each written as a single record, listing only the lower triangle,

`((S(I,J),J=1,I),I=1,NOPEN)`

These arrays are written by calls to subroutine`SWRITE`

, and it is recommended that entry`SREAD`

in that routine can be used to read the records for subsequent processing.

Records 5.), 6.) and 7.) are repeated for each S-matrix
calculated, looping over `INRG`

(innermost),
`M`

and `JTOT`

(outermost):

JTOT = JTOTL,JTOTU,JSTEP M = 1,MXPAR INRG = 1,NNRG ... 5.), 6.), 7.) ... END LOOP

`MXPAR`

depends on `ITYPE`

. Note that not
every S-matrix will necessarily exist. S-matrices may be missing
from the file because there are no open channels for that
energy, because it was skipped owing to
`IFEGEN.gt.1`

in a
pressure broadening calculation, or because there was an error
or convergence failure in the calculation.

The S-matrix output file is not supported for IOS calculations, and the output that can be generated for some cases is probably not generally useful.

The option to write out partial cross sections to a separate file is not implemented in this version of MOLSCAT, but could be resuscitated if necessary.

If `ISIGU`

is greater than 0 (default 0), MOLSCAT
will maintain a (direct access) file containing accumulated
cross sections on channel `ISIGU`

. This file is
updated for each energy after each complete `JTOT`

,
so it contains valid information about the run so far even if
the program terminates abnormally.

All the propagators have options to save energy-independent
matrices on a scratch file to save computation at subsequent
energies. This is particularly advantageous for the R-matrix and
`VIVS`

propagators. If `ISCRU .gt. 0`

(default 0), this save file is created on channel
`ISCRU`

and used for any subsequent energies. It can
be large.

Note that this option saves CPU time at the expense of disc I/O.
It is usually advantageous for the R-matrix, `VIVS`

,
quasiadiabatic and hybrid Airy propagators if `NNRG`

is not 1, but for the DeVogelaere and basic log-derivative
propagators it may not save resources overall unless the
potential itself is very expensive to calculate. This is
particularly true on fast machines such as CRAYs. Note, however,
that `ISCRU .gt. 0`

saves considerable time for
single-channel IOS cases with `INTFLG=6`

, since the
computer time for these is usually dominated by potential
evaluations.

When searching for and characterising resonances, a propagator scratch file created in one run may be used in a subsequent run to save work. This is described in Section 2.10 below.

The propagator scratch file option is not implemented in the parallel version of MOLSCAT.

Calculations for pressure
broadening (line shape) cross sections are controlled by the
following variables in the `&INPUT`

data:
`NLPRBR`

(synonym is `IFLS`

),
`IFEGEN, LINE`

and `LTYPE`

.

Calculations are supported
for `ITYPE`

= 1, 2, 3, 5, 6, 7, 11, 12, 15, 16, 17, 21, 22, 25, 26, 27, 31, 101,
and 105. The pressure broadening option is invoked if `NLPRBR .gt. 0`

on input (default 0); the value of `NLPRBR`

specifies the number of
spectroscopic lines for which pressure broadening calculations are to
be carried out. The lines themselves are specified by the array `LINE`

, of
4*NLPRBR elements. Each successive quartet of elements of `LINE`

indexes the
rotor levels involved in the transition, according to the elements of the
`JLEVEL`

array described in Section 3. The 4 values indicate JA, JB, JA', JB',
where JA-JB is the spectroscopic transition and the primes indicate post-
collision values. Note that the "diagonal" values JA=JA' and JB=JB' describe
widths and shifts of isolated lines, and off-diagonal values describe
collisional transfer of intensity.

Pressure broadening calculations require S-matrix elements involving the
initial and final (spectroscopic) levels at the same kinetic (not total)
energy. Generation of the necessary total energies is facilitated by the input
parameter `IFEGEN`

. If `IFEGEN .gt. 0`

(default 0), the program will treat the
input `ENERGY`

values as kinetic energies, and generate the necessary total
energies for the lines requested. If `IFEGEN`

is 0, only those requested
lines which can be constructed from the total energies actually specified by
`NNRG, ENERGY`

will be calculated. Through version 13 of MOLSCAT, input values
of relative kinetic energies in `ENERGY`

were retained in the the list of
generated total energies whether they were needed for a requested pressure
broadening calculation or not; beginning with version 14 only total energies
needed for the requested pressure broadening calculations are retained.
Further, beginning with version 14, specifying `IFEGEN .gt. 1`

will suppress
calculations for individual `JTOT, INRG, M`

("parity case") which do not
contribute S-matrices needed for the requested pressure broadening.
**Warning:**
some subset of the state-to-state cross sections may be incorrect (missing
some partial wave/parity contributions) if this last option is used.

The tensor order of the spectroscopic transition (i.e., 1 for dipole
transitions, 0 for isotropic Raman scattering) is specified in the input array
`LTYPE`

. If the default value (-1) is found, `LTYPE`

is calculated from `ABS(JA-JB)`

.

Scattering resonances and predissociating states of Van der
Waals molecules appear as characteristic features in the
energy-dependence of S-matrices. In MOLSCAT, a run
to find or characterise a resonance is flagged by setting the
parameter `KSAVE .gt. 0`

(default 0). This option is
**not** supported for IOS calculations
(`ITYPE`

.gt. 100). Setting `KSAVE .gt. 0`

has principal effects:

- The S-matrix eigenphase sum is calculated at each energy,
and a short summary of the eigenphase sums is written to
channel
`KSAVE`

. - The output to channel
`ISAVEU`

is modified to be suitable for use with the program`RESFIT`

. S-matrices, K-matrices and eigenphase sums are written to channel`ISAVEU`

unformatted.

A MOLSCAT run to characterise a resonance must deal
with only one total angular momentum `JTOT`

and
symmetry type `M`

in a given run. Thus,
`JTOTL`

and
`JTOTU`

must be the same, and the parameter
`MSET`

must be set greater than 0 to select the
particular symmetry type required.

A special option is available to assist with searching for narrow resonances.
If `NNRG`

is given as a negative integer of the form -5*N, with N integral and
the energies themselves specified by `ENERGY(1)`

and `DNRG`

, MOLSCAT will perform N
groups of 5 equally spaced calculations. After each group, the program will
try to interpret the 5 eigenphase sums as the "tail" of a resonance, and
estimate the position of the resonance centre. This estimate is then used as
the starting point for the next group of 5 energies. This option can be useful
in searching for a resonance if a reasonably good estimate of its energy is
already available, and may succeed in converging on a narrow resonance from as
far as 10**5 widths away. However, convergence is **not** guaranteed, and it is
not usually useful to do more than 3 sets of 5 energies in a single run.

Resonance search calculations should usually be done with either
the R-matrix propagator or one of the modified log-derivative
propagators, since many different energies are always necessary.
It is thus always desirable to use the `ISCRU`

option
to save energy-independent matrices on a scratch file. For the
special case of resonance searches, with `JTOTU=JTOTL`

and `MSET .gt. 0`

, the
`ISCRU`

file from one run may be used as input for
the next run at a different set of energies. This option is
invoked by setting `ISCRU`

negative for the
subsequent run(s); the program then expects to find a suitable
input file on channel |`ISCRU`

|. It reads the header
on this file to check that it contains valid information, and
then proceeds with "subsequent energy" calculations for all the
energies requested.

Atom - surface scattering calculations are not plagued by
complications arising from total angular momentum and parity.
MOLSCAT uses the internal loops over
`JTOT`

and `M`

to loop over the polar
angle theta (measured from the surface normal) and the azimuthal
angle phi (measured relative to the surface reciprocal lattice
vector g1). The loop over theta is controlled by the input
parameters `JTOTL, JTOTU, JSTEP, THETLW`

and
`THETST`

, while that over phi is controlled by
`MXPHI, PHILW`

and `PHIST`

. The logic used
is equivalent to:

DO 840 JTOT = JTOTL,JTOTU,JSTEP THETA = THETLW + THETST*JTOT DO 830 M = 1,MXPHI PHI = PHILW + PHIST*(M-1) .. .. Scattering calculation for angles THETA, PHI .. .. 830 CONTINUE 840 CONTINUE

Note that, for surface scattering, subsequent energies have a rather
non-intuitive meaning, because the threshold energies (K+G)**2 depend on the
parallel component of the momentum K. MOLSCAT interprets subsequent energies
as having the **same** parallel momentum as the first energy, but a different
perpendicular momentum. This corresponds to a change in the polar angle as
well as the scattering energy.

Convergence of coupled channel calculations with respect to integration range and step size is very important; lack of convergence can give very poor results, whereas unnecessarily conservative tolerances can waste large amounts of computer time. It is always advisable to conduct careful step size convergence tests on a small basis set before embarking on any major set of calculations with MOLSCAT.

MOLSCAT operates with units of lengths specified by RM, which is
set in subroutine `POTENL`

(see
Section 5) and which may be input via
the `&POTL`

data set (see
Section 4).

Variables which control the integration, such as
`RMIN`

, `RMAX`

, etc. (described below) are
in units of `RM`

. Note that `RM`

itself is
specified in units of Angstroms, and users might find it
convenient to have all distances in Angstroms by setting
`RM=1.0`

. As another example, to specify all
distances in bohr radii (atomic units) one should specify
`RM=0.529177`

.

The mechanisms used to choose the starting and finishing points
for integrating the coupled equations are the same for all
propagators. In the simplest case, the input variables
`RMIN`

(default 0.8) and `RMAX`

(default
10.0) are supplied and used exactly as input. (Note that the
default values are appropriate when `RM`

is
approximately the distance of the potential minimum.) However,
in certain circumstances `RMIN`

and `RMAX`

are modified from their input values:

1) If `IRMSET .gt. 0`

on input (default 9), the
program will estimate a suitable distance to start propagating,
using the criterion that the wavefunction amplitude in all
channels should be less than 10**(-IRMSET) at the starting
point. A crude semiclassical estimate of the wavefunction is used to make
this estimate, which is calculated separately for each `JTOT, M`

(at the
first energy only).

2) If there is a centrifugal barrier present, the program checks
that all open channels are classically accessible at the
`RMAX`

requested, for all energies in the
`ENERGY`

list. If necessary, `RMAX`

is
increased to the value of `R`

at the furthest
classical turning point found in the centrifugal potential for
any energy. However, `RMAX`

is never decreased from
the input value. For special purposes, this action can be
suppressed by setting `IRXSET=0`

on input (default
1). However, this is not recommended for general cross section
calculations.

Thus, the input value of `RMAX`

is the smallest
distance at which the propagator may terminate. The DeVogelaere
and R-matrix propagators also check some aspects of convergence
internally, and may propagate beyond `RMAX`

under
certain circumstances.

It should be noted that propagating out to the centrifugal
turning point is **not** necessarily adequate, particularly
when calculating elastic integral cross sections or line shift
cross sections. It is also important to realise that a value of
`RMAX`

which is adequate for low `JTOT`

may not be adequate for high `JTOT`

, and that
calculations using too small a value of `RMAX`

may
appear to be converged with respect to the partial wave sum when
they are not actually converged.

The DeVogelaere and the basic log-derivative propagators are
wavefunction-following methods, and use a constant step size controlled by the
parameter `STEPS`

(default 10.0). This is interpreted as the number of steps per
half-wavelength for the open channel of highest kinetic energy in the
asymptotic region. A value between 10 and 20 is usually adequate, unless the
depth of the potential well is large compared to the scattering energy.

The two modified log-derivative propagators are actually potential-following
methods, but they nevertheless use the same mechanism (`STEPS`

) to determine
step size, for compatibility with the basic log-derivative code. For these
propagators, values of `STEPS`

around 5.0 are usually adequate.

The R-matrix and `VIVS`

propagators are potential-following methods, so the de
Broglie wavelength is less important. Instead, the required initial step size
is input explicitly in the variable `DR`

(default 0.02). However, in both
propagators the step size may subsequently be modified, as described for the
individual propagators below.

**STABIL** -
The DeVogelaere method is potentially unstable in a
classically forbidden region, because the exponential
growth of closed channel wavefunctions can lead to a
loss of linear independence of the solutions. To avoid
this, the DeVogelaere propagator re-imposes linear
independence every `STABIL`

steps. The default (5.0) is
usually adequate.

**STEST** -
is a tolerance parameter used for two purposes:

- The K-matrix obtained by matching to the asymptotic
boundary conditions should be exactly symmetric,
but this is never the case because of numerical
rounding errors. The program counts and prints
out the number of pairs of symmetry-related off-
diagonal elements which differ by more than
`STEST`

. - The S-matrix is calculated at successive values of R,
starting at
`RMAX`

and incrementing by approximately half a wavelength each time. This is repeated until two successive S-matrices differ by no more than`STEST`

in any element, up to a maximum of 20 attempts.

** RMID** -
(default 9999.0). For

`R .lt. RMID`

, the R-matrix propagator
uses a constant step size of `DR`

. For `R .gt. RMID`

, the step
size is `DR*R/RMID`

, so that larger steps are taken in the
long-range region. If `RVFAC`

is set greater than the default
value of 0.0, `RMID`

is set automatically to `RVFAC*RTURN`

,
where `RTURN`

is an estimate of the position of the classical
turning point, calculated for each `JTOT`

and parity case.
(`RVIVAS`

is a synonym for `RMID`

.)
** SHRINK** -
If the integer variable

`SHRINK`

is 1 on input (the default),
the R-matrix propagator will monitor closed channels in
the long range region and accumulate a phase integral for
each. If a semiclassical estimate based on this phase
integral indicates that the wavefunction amplitude in the
channel concerned has dropped below 10**(-IRMSET), the
channel will be removed from the basis set for the
remainder of the propagation.
** VTOL** -
controls a convergence criterion applied to the
eigenvectors of the potential matrix (default

`VTOL=1.D-6`

). The R-matrix propagator willnot
attempt to apply boundary conditions until the eigenvector
is a (permuted) unit matrix to within tolerance `VTOL`

for two successive steps. This test is applied only to
eigenvectors which are asymptotically non-degenerate.
** MAXSTP** -
is the largest number of steps allowed for the R-matrix
propagator (default 10000). If convergence has not been
achieved after this many steps, the program prints an
error message and exits.

** RVIVAS** -
(default 9999.0) is the distance at which the switchover from
the log-derivative method to

`VIVS`

takes place (but
see also `RVFAC`

below). A value of
`RVIVAS`

just inside the potential minimum is usually
most efficient. If `RVIVAS`

is more than
`RMAX`

, the entire propagation will use the
log-derivative method; however, the preferred method of
achieving this effect is to use `INTFLG=5`

, since
this uses considerably less storage. Conversely, if
`RVIVAS`

is less than `RMIN`

, the entire
propagation will use `VIVS`

(not recommended). It
must be remembered that MOLSCAT itself may adjust
`RMIN`

and `RMAX`

as described above;
`RVIVAS`

can if necessary be set to a large negative
or positive number to ensure the desired effect.
(`RMID`

is a synonym for `RVIVAS`

.)
** RVFAC** -
(default 0.0). If

`RVFAC .gt. 0.0`

,
`RVIVAS`

is adjusted automatically for each
`JTOT`

/ parity case, to be `RVFAC`

times
an estimate of the classical turning point. A value of
`RVFAC`

around 1.1 is usually suitable, and is
recommended for cross section calculations using
`INTFLG=4`

.
The log-derivative propagator has no variable parameters except
`STEPS`

, which determines the step size as described
above. However, control of the `VIVS`

propagator is
quite complicated. `VIVS`

operates with both a
variable interval length and a variable step length. A single
diagonalising transformation is used over the whole of each
interval, which may consist of several steps. The algorithms
used to determine interval and step sizes will be discussed
separately.

The step size and interval size algorithms used by
`VIVS`

attempt to take the longest step which will
give the required accuracy at each point in the integration.
However, the optimum step size at one scattering energy is not
necessarily safe at another, and `VIVS`

can sometimes
give problems if the groups of energies in a particular run are
not chosen with care. In particular, one should avoid: 1) A
first energy which is close to (or above) a channel threshold
and a subsequent energy which is far below it. 2) A first energy
which is far above a channel threshold and a subsequent energy
which is close to it.

** TOLHI** -

`VIVS`

accumulates perturbation corrections to the
wavefunction as it propagates, and uses these to
obtain a suitable length for the next interval.
The input parameter `DR`

described above is used as
the size of the first interval, and subsequent
interval lengths are obtained using the input tolerance
`TOLHI`

(default 0.001); the criterion is that some
functional, t, of the perturbation corrections should be
not greater than `TOLHI`

over any interval. Within an
interval, t is checked against `TOLHI`

at each step, and
a new interval is started (with a new diagonalising
transformation) if it appears likely to exceed `TOLHI`

over
the next step.
Each interval is divided into `IALPHA`

steps (default
`IALPHA=6`

). Within an interval, the step sizes
increase geometrically, with each step being a factor alpha
larger than the previous one. The quantity alpha may be
specified in either of 2 ways:

- If the logical input parameter
`IALFP`

is`.FALSE.`

(the default), alpha increases linearly from`ALPHA1`

(default 1.0) at the starting point for`VIVS`

to`ALPHA2`

(default 1.5) at`RMAX`

. - If
`IALFP`

is`.TRUE.`

on input, the program starts with an initial value of`ALPHA1`

, and adjusts this as it propagates.`ALPHA2`

is then not used.

A useful special option is obtained by setting `IALPHA=0`

on input. Intervals then consist of a variable number
of steps, and the decision to start a new interval is based
solely on the magnitude of the perturbation corrections; a new
interval is started (and a new diagonalising transformation
obtained) whenever the quantity t approaches `TOLHI`

.
The initial step size is taken from `DR`

, and
subsequent steps use a criterion based on `TOLHI`

.

The `IALPHA=0`

option can be very efficient, and
often requires remarkably few intervals/steps to produce
converged results.

There are several logical input variables which control the
extent to which `VIVS`

calculates and uses
perturbation corrections to the wavefunction. The three
variables `IV, IVP`

and `IVPP`

(defaults
`.TRUE., .FALSE.`

and `.FALSE.`

,
respectively) control the calculation of perturbation
corrections due to the potential itself (`IV`

)
and to its first (IVP) and second (IVPP) derivatives.
The perturbation corrections thus calculated are used in
calculating interval sizes, but are included in the wavefunction
only if `IPERT`

is `.TRUE.`

(the default).
If `ISHIFT`

is `.TRUE.`

(default
`.FALSE.`

), the second derivative is used to shift
the reference potential to give the best fit to the true
potential.

For production runs, `IV, IVP, IVPP, IPERT`

and
`ISHIFT`

should usually all be `.TRUE.`

.
This may be forced by setting `IDIAG = .TRUE.`

, which
overrides any `.FALSE.`

values for the individual
variables.

If `IVP, IVPP`

or `ISHIFT`

is set,
`VIVS`

will require radial derivatives of the
potential. These are supplied properly for simple potentials by
the standard version of `POTENL`

described below, but
for some potentials they can be difficult to evaluate. In this
case, the input variable `NUMDER`

may be set
`.TRUE.`

, in which case the necessary derivatives are
calculated numerically, and `POTENL`

is never called
with `IC .gt. 0`

(see Section 5).

** ISYM** -
(default

`.TRUE.`

). If `ISYM`

is
`.TRUE.`

, the R-matrix is forced to be symmetric at
the end of each interval. This is usually advisable for
production runs.
** XSQMAX** -
(default 1.D4) controls the application of perturbation
corrections to deeply closed channels. If a channel is locally
closed by more than

`XSQMAX`

reduced units,
perturbation corrections for it are not calculated. The default
should be adequate.
The only relevant input variables are `RMIN`

,
`RMAX`

and `STEPS`

as described at the
beginning of this section.

The modified log-derivative (`INTFLG=6`

) propagator
is used from `RMIN`

to `RMID`

. In
general, values of `RMID`

somewhat beyond the
distance of the minimum are recommended. If ```
RVFAC .gt.
0.0
```

on input, `RMID`

is calculated as
described above; values of 1.2 to 1.4 are generally useful. If
`RMID`

is less than `RMIN`

, or if it is
determined that `RMID-RMIN`

is smaller than one step,
the log-derivative propagator will be skipped. The step size
for this propagator is controlled by `STEPS`

as
described above unless `IABSDR`

(default 0) is set to
1, in which case the step size is taken from the input `DR`

.

The Airy propagator is used to propagate from `RMID`

to `RMAX`

. If `RMID`

is greater than
`RMAX`

this propagator is not called. By default the
initial step size is taken as the value calculated for the
modified log-derivative part, but it can be further controlled
by the following variables.

** DRAIRY** -
(default -1.0) can be used to input an absolute step
size. If

`DRAIRY`

is less than zero, the initial step
size is taken from the log-derivative propagator.
** TOLHI** -
(default 0.001).
If less than 1, the propagator uses this as a tolerance to
adjust the step size (by a perturbation method) to try to
maintain this accuracy. If greater than 1, the step size is
increased by this factor in each interval. Values around 1.03
to 1.07 are generally useful.

** POWRX** -
(default 3).
If

`TOLHI`

is less than 1, this is the inverse power
used in estimating the step size from perturbation calculations.
The default value is usually adequate.
The `INTFLG=-1`

propagator is suitable only for
single channel cases and is used almost exclusively for IOS
calculations. It does the WKB integral
for the phase shift by Gauss-Mehler quadrature. It is controlled by
input variables `NGMP`

and `STEST`

** NGMP** -
Dimension 3. N-point Gauss integration is done starting
with

`N=NGMP(1)`

, incrementing by
`NGMP(2)`

, until `NGMP(3)`

.
Starting with the 2nd pass the phase shift is compared
with the previously calculated value until it has
converged to within a tolerance specified by `STEST`

.
** STEST** -
(default 0.0001) is the convergence tolerance for the
WKB phase shift; values on the order of 0.001 are probably
more suitable than the default value.

Forward to Section 3

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