Example: Core-electron binding energies (CEBE): NNO¶
ADF is well suited for calculating Core Electron Binding Energies (CEBEs). In this example it is shown how one can differentiate between the 1s CEBEs of the two non-equivalent nitrogen atoms in N2 O, using a delta-SCF technique. It starts with a regular calculation that has the purpose of preparing a reference TAPE21 file for the NNO molecule, which will later be useful in the energy analysis. The result file is saved to t21.NNO.
The same GGA functional is specified throughout the run. The amount of output is reduced by using some print keys.
The prepare the nitrogen atom with a core hole (restricted) will be used as a fragment later. This enables selection of where the core hole should be.
$ADFBIN/adf -n1 << eor title N atom core hole ATOMS N 0.0 0.0 0.0 end Basis Type TZ2P Core None end xc gradients pw86x pw91c end numericalquality good occupations s 1 2 p 3 end end input eor mv TAPE21 t21.N_ch
Now perform the restricted ground state molecule for analysis later. The TAPE21 result file is saved.
$ADFBIN/adf << eor title NNO noprint sfofragpop fragsfo xc gradients pw86x pw91c end numericalquality good ATOMS N 0.0 0.0 -1.1284 N 0.0 0.0 0.0 O 0.0 0.0 1.1841 end Basis Type TZ2P Core None createoutput None end end input eor mv TAPE21 t21.NNO
Next follow two sets of almost identical calculations in which a 1s electron is removed from one or the other N atom (please note that the deepest s level is associated with the 1s of the oxygen atom). The molecular NNO result file is used as fragment. An unrestricted calculation is done and a positive charge is specified. The final result file for the molecule with the core hole is saved. Then another calculation is done to conveniently obtain the energy with respect to the normal molecule. This is repeated for a core hole on the other N atom.
$ADFBIN/adf <<eor title NNO unrestricted core hole noprint sfofragpop fragsfo ATOMS N 0.0 0.0 -1.1284 f=N_ch N 0.0 0.0 0.0 O 0.0 0.0 1.1841 end xc gradients pw86x pw91c end numericalquality good Basis Type TZ2P Core None createoutput None end fragments N_ch t21.N_ch end unrestricted charge 1 1 occupations sigma 1 1 1 4 // 1 0 1 4 pi 4 // 4 end end input eor mv TAPE21 t21.NNO.unr1
In the second calculation the result file of one of the unrestricted NNO calculations is used as restart file, which ensures that the hole stays at its place, because the starting density is already correct. The result file t21.NNO for the normal NNO calculation is specified as fragment to serve as an energy reference. The final Bonding Energy printed by ADF indicates what the CEBE is. However, please check Chong, D.P. Accurate DFT Calculation of Core-Electron Binding Energies in Reviews in Modern Quantum Chemistry, A Celebration of the Contributions of R.G. Parr, edited by K.D. Sen (World Scientific Publishing Co., Singapore), 1106-1139 (2002) for more detailed information on Core-Electron Binding Energies. This reference also contain information on empirical corrections that may have to be made on the final numbers.
$ADFBIN/adf <<eor title NNO unr. core hole noprint sfofragpop fragsfo xc gradients pw86x pw91c end numericalquality good restart NNO.unr1.t21 ATOMS N 0.0 0.0 -1.1284 f=NNO N 0.0 0.0 0.0 f=NNO O 0.0 0.0 1.1841 f=NNO end fragments NNO NNO.t21 end unrestricted charge 1 1 occupations sigma 1 1 1 4 // 1 0 1 4 pi 4 // 4 end end input eor
Similarly, one could easily have prepared an oxygen with a core hole and determined the CEBE of the oxygen 1s atom.