$RADIAL group                (relevant only to atoms)                           
   This input data governs the computation of radial                            
expectation values  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                          
Mn atom...(4s)2(3d)5...6-S...spherical harmonics                                
Dnh 2                                                                           
Mn 25.0                                                                         

generated on 7/7/2017