Projection on Atomic Orbitals, Population Analysis, etc.

Some popular analysis methods from conventional quantum chemistry programs using local (gaussian) basis sets, e.g. Mulliken-style population analysis are not directly possible in plane wave calculations. However they can be approximated by first projecting the wavefunction on an (minimal) atomic basis set.

&PROP
 PROJECT WAVEFUNCTION
 POPULATION ANALYSIS MULLIKEN
&END

By default CPMD projects on a minimal Slater basis set that is included into the executable and also used to construct the initial atomic guess. The represent the atomic wavefunction of the valence state from an all-electron calculation, It is, however, more consistent to project on the atomic pseudowavefunctions that were used to generate the pseudopotential (which are encoded into numerical pseudopotential files). For that we have to add a &BASIS section:

&BASIS
 PSEUDO AO 2
  0 1
 PSEUDO AO 1
  0
&END

This instructs CPMD to read two wavefunctions from the first pseudopotential file (O_MT_PBE.psp): one s-type and one p-type and only one s-type function from the second pseudopotential file (H_MT_PBE.psp). The is reflected in the output when the internal atomic basis in constructed:

 GENERATE ATOMIC BASIS SET
      O        PSEUDO ATOMIC ORBITALS
        L VALUE=S                      OCCUPATION= 2.00
        L VALUE=P                      OCCUPATION= 4.00
      H        PSEUDO ATOMIC ORBITALS
        L VALUE=S                      OCCUPATION= 1.00

Please note that projecting on a larger than minimal basis set has little meaning, since the projection will be incomplete anyways due to the different nature of plane wave and local basis sets. This incompleteness of the projection is also indicated in the output and should be taken into account when interpreting the results.

 WAVEFUNCTIONS IN ATOMIC ORBITAL BASIS

      ORBITAL      1       2       3       4
  COMPLETNESS    0.990   0.981   0.987   0.989
  OCCUPATION     2.000   2.000   2.000   2.000
  1   O  S      -0.871   0.000   0.389   0.000
         Px      0.000  -0.723   0.000   0.000
         Pz      0.000   0.000   0.000   0.995
         Py     -0.145   0.000  -0.865   0.000
  2   H  S      -0.095  -0.332  -0.163   0.000
  3   H  S      -0.095   0.332  -0.163   0.000

 POPULATION ANALYSIS FROM PROJECTED WAVEFUNCTIONS

       ATOM          MULLIKEN        LOWDIN       VALENCE
   1     O             -0.902        -0.663         1.435
   2     H              0.503         0.384         0.728
   3     H              0.503         0.384         0.728
  UNASSIGNED CHARGE     0.105         0.105

 MAYER BOND ORDERS FROM PROJECTED WAVEFUNCTIONS

           1  O    2  H    3  H
   1  O   0.000   0.717   0.717
   2  H   0.717   0.000   0.010
   3  H   0.717   0.010   0.000

The output shows, that based on the projection additional properties can are calculated, e.g. atomic charges and bond orders. Of course, the accuracy of these numbers depends on the reliability of the projection.