#! /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.

$ADFBIN/adf <<eor
title   TlH, scalar relativistic zora
BeckeGrid
 quality good
End
EPRINT
  SFO eig ovl
END
relativistic scalar zora
ATOMS
  Tl       0.0             0.0             0.0
  H        0.0             0.0             1.870
end
Basis
  Type TZ2P
  Core None
end
xc
  GGA BP86
end
PRINT SFO
eor

mv TAPE21 TlH.t21

# 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.

$ADFBIN/adf <<eor
title   TlH from fragment TlH,  with SpinOrbit coupling
BeckeGrid
 quality good
End
EPRINT
  SFO eig ovl
END
relativistic spinorbit zora
ATOMS
  Tl       0.0             0.0             0.0    f=TlH
  H        0.0             0.0             1.870  f=TlH
end
fragments
  TlH     TlH.t21
end
xc
  GGA BP86
end
PRINT SFO
eor

mv TAPE21 TlH_spinorbit.t21

# 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
#
# ======================================