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
