Example: Spin-Orbit SFO analysis: TlH
*************************************

"Download TlH_SO_analysis.run"

   #! /bin/sh


   # Application of the Spin-Orbit relativistic option (using double-group
   # symmetry) to TlH with a detailed analysis of the spinors in terms of SFOs
   # (Symmetrized Fragment Orbitals).

   # In order to get the population analysis, one should have one scalar
   # relativistic fragment, which is the whole molecule. The SFOs in this case are
   # the scalar relativistic orbitals, which are already orthonormal, because one
   # has only one fragment which is the whole molecule.

   AMS_JOBNAME=Scalar $AMSBIN/ams <<eor
   System
     atoms
        Tl       0.0             0.0             0.0
        H        0.0             0.0             1.870
     end
   end

   Task SinglePoint

   Engine ADF
     title TlH, scalar relativistic zora
     beckegrid
       quality good
     end
     eprint
       sfo eig ovl
     end
     basis
       core None
       type TZ2P
       CreateOutput Yes
     end
     print SFO
     relativity
       level scalar
       formalism ZORA
     end
     xc
       gga BP86
     end
   EndEngine

   eor

   # In order to get the population analysis, one should have one scalar
   # relativistic fragment, which is the whole molecule, which is TlH in this case.

   AMS_JOBNAME=SpinOrbit $AMSBIN/ams <<eor
   System
     atoms
        Tl       0.0             0.0             0.0    adf.f=TlH
        H        0.0             0.0             1.870  adf.f=TlH
     end
   end

   Task SinglePoint

   Engine ADF
     title TlH from fragment TlH,  with SpinOrbit coupling
     beckegrid
       quality good
     end
     eprint
       sfo eig ovl
     end
     fragments
        TlH Scalar.results/adf.rkf
     end
     print SFO
     relativity
       level spin-orbit
       formalism ZORA
     end
     xc
       gga BP86
     end
   EndEngine

   eor

   # The output gives something like:
   # ================================================================================
   # 
   #  =======================
   #  Double group symmetry :  *   J1/2  *
   #  =======================
   #                                        ===  J1/2:1 ===
   #  Spinors expanded in SFOs
   # Spinor:             21               22               23               24
   #  occup:            1.00             1.00             1.00             0.00
   #  ------            ----             ----             ----             ----
   #  SFO SIGMA
   #    13.alpha:   0.7614+0.0000i   0.0096+0.0000i   0.0052+0.0000i  -0.0006+0.0000i
   #    14.alpha:   0.0154+0.0000i  -0.9996+0.0000i   0.0208+0.0000i  -0.0077+0.0000i
   #    15.alpha:  -0.0146+0.0000i   0.0185+0.0000i   0.9849+0.0000i   0.1625+0.0000i
   #  SFO PI:x
   #     8.beta :   0.4578+0.0000i   0.0091+0.0000i   0.0112+0.0000i   0.0030+0.0000i
   #     9.beta :   0.0005+0.0000i  -0.0074+0.0000i  -0.1119+0.0000i   0.6910+0.0000i
   #  SFO PI:y
   #     8.beta :   0.0000+0.4578i   0.0000+0.0091i   0.0000+0.0112i   0.0000+0.0030i
   #     9.beta :   0.0000+0.0005i   0.0000-0.0074i   0.0000-0.1119i   0.0000+0.6910i
   #
   # ================================================================================

   # Left out are a lot of small numbers. The meaning is that a spinor of J_z=1/2
   # symmetry can have SIGMA and PI character, for example, the 21st spinor with
   # occupation number 1.0, is approximately (21 J_z=1/2) = 0.76 (13 SIGMA alpha) +
   # 0.46 (8 PI:x beta) + i 0.46 (8 PI:y beta)

   # Next in the SFO contributions per spinor the real and imaginary spin alpha
   # part and real and imaginary spin beta part are all summed together to give a
   # percentage of a certain SFO. are summed. For example the 21st spinor has
   # almost 60% (13 SIGMA) character.

   # ======================================
   #
   # SFO contributions (%) per spinor
   # Spinor:      21     22     23     24

   # occup:      1.00   1.00   1.00   0.00
   # ------      ----   ----   ----   ----

   # SFO SIGMA
   #     13:    57.97   0.01   0.00   0.00
   #     14:     0.02  99.92   0.04   0.01
   #     15:     0.02   0.03  97.01   2.64
   # SFO PI:x
   #      8:    20.96   0.01   0.01   0.00
   #      9:     0.00   0.01   1.25  47.75
   # SFO PI:y
   #      8:    20.96   0.01   0.01   0.00
   #      9:     0.00   0.01   1.25  47.75
   #
   # ======================================


