FMS: Full multiple scattering

 

This module carries out a full multiple scattering XANES calculation for a cluster centered on the absorbing atom. Thus all multiple-scatteing paths within this cluster are summed to infinite order. This is useful for XANES calculations, but usually cannot be used for EXAFS analysis. FMS loses accuracy beyond , which is typically about 4 Å since the muffin-tin radius is typically about 1 Å.

 FMS    rfms lfms2    (Standard)

Compute full multiple scattering within a sphere of radius rfms centered on the absorbing atom. If you don't use FMS card, the multiple scattering path expansion is used.

rfms is the cluster radius used in all modules but POT. Specifically is is used for in the LDOS, FMS, and as the lower limit of pathfinder calculations. Typically a converged XANES calculation requires about 50-150 atoms in a cluster. The FMS module sums all MS paths within the specified cluster. The number of atoms in this cluster is limited to 87 by default, but one can manually increase the dimension parameter nclusx in the ancilliary FEFF8 source code file 'dim.h' to alter the maximum cluster size. If there are more than nclusx atoms within the specified cluster size, FEFF will reduce the cluster size and issue a warning.

For EXAFS analysis one typically calculates to k=20, but FMS results are not accurate at high energies. Thus if you are running FEFF8 for EXAFS you should not use FMS and XANES cards. It is, however, desirable to calculate self-consistent potentials even for EXAFS calculations as in the example below:

   *calculate EXAFS with SCF potentials and paths to R=6 angstroms
   CONTROL  1  1  1  1  1  1
   *FMS
   SCF   3.1
   RPATH 6.0
   EXAFS

If the value of RPATH as described in Section 2.6 is greater than rfms, the pathfinder will look for paths which extend beyond the cluster used for the FMS and add them to the FMS calculation of the DOS and XANES:

where at least one atoms i in the path is outside the FMS cluster and the value of RPATH is the maximum half path length for LDOS, FMS and pathfinder modules.

The MS expansion sometimes does not converge well in the XANES energy region. Thus one should avoid adding paths for LDOS and XANES, and RPATH should be less than rfms. Adding single scattering path only (NLEG 2) usually works well to check the convergence of FMS. But adding double scattering (NLEG 3) often leads to very bad results in XANES. Thus RPATH is useful for EXAFS or for XANES only when the path expansion is stable.

The optional lfms2 argument is a logical flag which defines how the FMS is done, similar to the flag lfms1 in the SCF card. With the default value of 0 (appropriate for solids), the FMS is calculated for a cluster of size rfms around each representative unique potential. With lfms=1 (appropriate for molecules), FMS is done only once for a cluster of size rfms around absorbing atom only. The proper use of this flag can lead to a considerable time savings.

For example, if you calculate FMS for a molecule smaller than 40 atoms, there is no need to invert matrices, and will reduce time for calculations by factor (), where nph is a number of unique potentials listed in POTENTIAL card).

A typical use of the FMS card uses , for example,

     FMS  6.0     ! for XANES and LDOS need about 100 atom cluster
     RPATH 8.0    ! usually use rpath < rfms
     NLEG  2      ! adds 2 leg paths between 6 and 8 angstroms

For molecules of less than 30 atoms of radius 4.0 Å we suggest using , as in

     FMS  5.0 1
     RPATH  -1

 DEBYE    temp thetad [idwopt]    (Useful)

See the full description in Section 2.8. The temperature effect on FMS is approximated by multiplying each free propagator by , which leads to the correct DW factors for single scattering. The DW factors for multiple scattering are not exact, but their contribution is reduced both by thermal factors and by the mean free path. Also if you are running the FMS module, then you can obtain only XANES and this approximate treatment of thermal effect on XANES is probably adequate.