Bi and Bi₂: Spin-Orbit

 

Sample directory: adf/SO_Bi2/

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

To prepare for the relativistic calculations, the dirac program is applied to generate the relativistic core potential for the Bismuth atom with a frozen core up to the 5p shell.

$ADFBIN/dirac -n1 < $ADFRESOURCES/Dirac/Bi.5p

mv TAPE12 t12rel

The next step is the creation of the restricted Bismuth atom (scalar relativistic).

The GGA (Becke-Perdew) facility is used for consistency with the calculations to follow, but is not necessary per se to carry out the subsequent calculations.

$ADFBIN/adf <<eor
create Bi  file=$ADFRESOURCES/TZP/Bi.5p
xc
  LDA vwn
  GGA  becke perdew
end
relativistic scalar
corepotentials  t12rel  &
Bi     1
end
end input
eor

mv TAPE21 t21Bi

Note that usage of the block form for the CorePotentials key would not have been necessary here. We could as well have used:

corepotentials t12rel

instead of

corepotentials  t12rel  &
Bi     1
end

Bi: single atom

For comparision 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).

$ADFBIN/adf <<eor

title Bi unrestricted

integration 4.0

xc
  LDA vwn
  GGA  becke perdew
end

relativistic scalar
corepotentials  t12rel  &
Bi    1
end

ATOMS
Bi   0.000000      0.000000      0.00000000
end

fragments
Bi t21Bi
end

unrestricted

charge 0 3

end input
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 'restricted' run (the key unrestricted is not used). The double-group symmetry orbitals are, like the single-group ones in a non-SpinOrbit calculation, degenerate, allowing 2 electrons in each spatial orbital. These are equally occupied (using fractional occupations if necessary) and the electronic charge density is not spin-polarized.

$ADFBIN/adf <<eor
title Bi spinorbit

integration 4.0

xc
  LDA vwn
  GGA  becke perdew
end

relativistic spinorbit
corepotentials  t12rel  &
Bi    1
end

ATOMS
Bi   0.000000      0.000000      0.00000000
end

fragments
Bi t21Bi
end

end input
eor

Comparison of the bonding energy (w.r.t. the create restricted atom) for the scalar relativistic and spin-orbit runs respectively show that application of the spin-orbit operator lowers the energy by approximately 1.1 eV.

In the previous run default occupations were used: the occupations were determined from the aufbau principle during the first few scf iterations.

The following is an excited state calculation: occupation numbers are specified in input and by comparison with the result from the previous run we see that one electron has been promoted from a p1/2 to a p3/2 orbital.

$ADFBIN/adf <<eor
title Bi spinorbit, specified occupations

PRINT SpinOrbit

integration 4.0

xc
  LDA vwn
  GGA  becke perdew
end

relativistic spinorbit
corepotentials  t12rel  &
Bi    1
end

ATOMS
Bi   0.000000      0.000000      0.00000000
end

fragments
Bi t21Bi
end

charge 0

occupations
 s1/2  2
 p1/2  1
 p3/2  2
 d3/2  4
 d5/2  6
end

end input
eor

The PRINT key (here with argument SPINORBIT) controls output printing. Here it induces the printing of some extra information about the relativistic double group symmetry 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.

$ADFBIN/adf <<eor
title   Bi2, scalar relativistic

integration 4.0

relativistic scalar
corepotentials  t12rel  &
Bi    1
end

ATOMS
Bi       0.0             0.0             1.33
Bi       0.0             0.0            -1.33
end

fragments
Bi     t21Bi
end

xc
  LDA vwn
  GGA  becke perdew
end

end input
eor

mv tape21 t21Bi2

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 dimer, gives directly the effect of the full-relativistic versus the scalar relativistic option: the energy is lowered by 2.3 eV.

$ADFBIN/adf <<eor
title   Bi2 from fragment Bi2,  with SpinOrbit coupling

PRINT SpinOrbit
 
integration 4.0

relativistic spinorbit
corepotentials  t12rel  &
Bi    1
end

ATOMS
Bi    0.0    0.0    1.33  f=Bi2
Bi    0.0    0.0   -1.33  f=Bi2
end

fragments
Bi2     t21Bi2
end

xc
  LDA vwn
  GGA  becke perdew
end

end input
eor

rm TAPE21 logfile

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.

$ADFBIN/adf <<eor
title   Bi2 from atomic fragments, SpinOrbit coupling

PRINT SpinOrbit
 
integration 4.0

relativistic spinorbit
corepotentials  t12rel  &
Bi    1
end

ATOMS
Bi       0.0             0.0             1.33
Bi       0.0             0.0            -1.33
end

fragments
Bi     t21Bi
end

xc
  LDA vwn
  GGA  becke perdew
end

end input
eor

Copyright Terms of UsePrivacy Policy