Example: Spin-Orbit coupling: Bi and Bi2¶

#! /bin/sh


# Application of the Spin-Orbit relativistic option (using double-group
# symmetry) to Bismuth (atom and dimer).

# For comparison with the full double-group calculation, the 'standard'
# unrestricted calculation on Bismuth is carried out, using the scalar
# relativistic option.

# A net spin polarization of 3 electrons is applied (key charge).

AMS_JOBNAME=Bi_SR $AMSBIN/ams <<eor
System
  atoms
     Bi   0.000000      0.000000      0.00000000
  end
end

Task SinglePoint

Engine ADF
  title Bi unrestricted
  beckegrid
    quality good
  end
  basis
    core None
    type TZ2P
    CreateOutput Yes
  end
  relativity
    level scalar
    formalism ZORA
  end
  spinpolarization 3
  unrestricted
  xc
    gga becke perdew
  end
EndEngine
eor


# The CHARGE key, in conjunction with the UNRESTRICTED key is used to specify
# that 3 electrons must be unpaired (second value of the CHARGE key), while the
# system is neutral (first value of the CHARGE key).

# Next we do a Spin-Orbit calculation on the Bismuth atom.

# Note that it is a 'unrestricted' run using the noncollinear approximation, and
# SYMMETRY NSOYM. The electronic charge density is spin-polarized.

AMS_JOBNAME=Bi_SO $AMSBIN/ams <<eor
System
  atoms
     Bi   0.000000      0.000000      0.00000000
  end
end

Task SinglePoint

Engine ADF
  title Bi spinorbit unrestricted noncollinear
  beckegrid
    quality good
  end
  basis
    core None
    type TZ2P
    CreateOutput Yes
  end
  relativity
    level spin-orbit
    formalism ZORA
    spinorbitmagnetization noncollinear
  end
  symmetry nosym
  unrestricted
  xc
    gga becke perdew
  end
EndEngine
eor


# Because an all electron basis set is used, the bond energy is huge, due to the
# very large higher order spin-orbit effect on the 2p orbitals.

# == Bi2 dimer ==

# Now we turn to the dimer Bi2: a series of Single Point calculations, all with
# the same inter atomic distance.

# First the scalar relativistic run.

AMS_JOBNAME=Bi2_SR $AMSBIN/ams <<eor
System
  atoms
     Bi       0.0             0.0             1.33
     Bi       0.0             0.0            -1.33
  end
end

Task SinglePoint

Engine ADF
  title Bi2, scalar relativistic
  beckegrid
    quality good
  end
  basis
    core None
    type TZ2P
    CreateOutput Yes
  end
  relativity
    level scalar
    formalism ZORA
  end
  xc
    gga becke perdew
  end
EndEngine
eor

# The calculated scalar relativistic atomization energy will be close to 2.74
# eV. This is the bond energy of the dimer minus 2 times the bond energy of the
# unrestricted scalar relativistic atom.

# The result file tape21 is used as reference in subsequent calculations: run
# the spin-orbit case starting from the just completed dimer calculation as a
# fragment. The resulting 'bonding energy', ie the energy w.r.t. the scalar
# relativistic ZORA dimer, gives directly the effect of the full-relativistic
# ZORA versus the scalar relativistic ZORA option: the energy is lowered by huge
# amount, again mainly due to the large spin-orbit effect on the 2p orbitals.

AMS_JOBNAME=Bi2_SO_frag $AMSBIN/ams <<eor
System
  atoms
     Bi    0.0    0.0    1.33  adf.f=Bi2
     Bi    0.0    0.0   -1.33  adf.f=Bi2
  end
end

Task SinglePoint

Engine ADF
  title Bi2 from fragment Bi2,  with SpinOrbit coupling
  beckegrid
    quality good
  end
  fragments
     Bi2     Bi2_SR.results/adf.rkf
  end
  print SpinOrbit
  relativity
    level spin-orbit
    formalism ZORA
  end
  xc
    gga becke perdew
  end
EndEngine
eor


# If one looks at the SFO analysis in the output of this calculation, one can
# observe that a first-order spin-orbit splitting of the scalar relativistic
# fragment orbitals is a good approximation to many of the calculated valence
# spinors.

# A final consistency check: run the spin-orbit dimer from single-atom
# fragments. The bonding energy should equal the sum of the bonding energies of
# the previous two runs: scalar relativistic dimer w.r.t. single atom fragments
# plus spin-orbit dimer w.r.t. the scalar relativistic dimer.

AMS_JOBNAME=Bi2_SO $AMSBIN/ams <<eor
System
  atoms
     Bi       0.0             0.0             1.33
     Bi       0.0             0.0            -1.33
  end
end

Task SinglePoint

Engine ADF
  title Bi2 from atomic fragments, SpinOrbit coupling
  beckegrid
    quality good
  end
  basis
    core None
    type TZ2P
    CreateOutput Yes
  end
  print SpinOrbit
  relativity
    level spin-orbit
    formalism ZORA
  end
  xc
    gga becke perdew
  end
EndEngine
eor


# The calculated spin-orbit coupled relativistic atomization energy will be
# close to 2.18 eV. This is the bond energy of the dimer minus 2 times the bond
# energy of the unrestricted non-collinear spin-orbit coupled relativistic atom.
# Note that one has to subtract huge numbers.