$RADIAL group                (relevant only to atoms)
 
   This input data governs the computation of radial
expectation values (r) and  for atomic orbitals.  The
atomic wavefunctions can be any SCFTYP except UHF.  The
atomic calculation should preserve radial degeneracy in p,
d, or f shells, so UHF is not allowed, and furthermore,
many atoms will require GVB or MCSCF inputs (see the
'Further References' section about doing atomic SCF).  It
is OK to use core potentials (MCP or ECP) or to apply
scalar relativistic effects, so long as the calculation
preserves degeneracy 2l+1 in every occupied shell.
 
   One should keep in mind that there is some arbitrariness
in how different SCFTYPs canonicalize orbitals, so that
individual orbitals may vary, for exactly the same total
wavefunction.  For example, ROHF orbitals within the doubly
occupied set of orbitals change as a function of the A and
B canonicalization inputs (see 'Further References').
Similar comments apply to orbitals from GVB or MCSCF.
 
   It is recommended that you do two runs, first to check
if radial degeneracy is maintained (equal eigenvalues for
all three p, or all five d orbitals).  This preliminary run
will help count which orbitals lie in degenerate shells,
for MEMSH below.  The quality of the numerical radial
integration can be assessed from its closeness to 1.0.
Radial wavefunctions can be printed, as an option.  There
are no defaults provided for the first three keywords,
which are required inputs, if this group is given.
 
NSHELL - number of atomic shells to be computed
 
IDEGSH - an array of NSHELL values, giving the degeneracy
         of each shell (1, 3, 5, or 7)
 
MEMSH  - an array containing the sum of all IDEGSH values,
         listing the members of each shell.
 
RMAX   - maximum radius to be considered, in Bohr.  The
         default is most appropriate for valence orbitals,
         which for bottom row elements may extend to five
         Angstrons (default=10.0).  Inner shell orbitals
         may require input of a smaller RMAX, to move some
         of the tick marks closer to the nucleus.
 
NTICKS - radial increment is RMAX/NTICKS, so the default
         step size is 0.01 Bohr (default NTICKS=1001)
 
PRTRAD - flag to print each shell's radial wavefunction at
         every radial tick mark (default is .FALSE.)
 
The following example uses a basis that is too small to be
converged, printing radial expectation values for manganese
as 1s=0.0615, 3p=0.9156, 4s=3.4027, and 3d=1.1095:
 
 $contrl scftyp=rohf mult=6 ispher=1 $end
 $guess  guess=huckel norder=1
         iorder(10)=15,10,11,12,13,14 $end
 $basis  gbasis=n31 ngauss=6 $end
 $scf    rstrct=.true. $end
 $radial nshell=4 idegsh(1)=1,3,1,5
         memsh(1)=1,  7,8,9,  10,  11,12,13,14,15 $end
 $data
Mn atom...(4s)2(3d)5...6-S...spherical harmonics
Dnh 2
 
Mn 25.0
 $end
 
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