Example: Spin-Orbit SFO analysis: TlH

Download TlH_SO_analysis.run

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
end input
eor

mv TAPE21 t21.TlH

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
end input
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