Populations, Charge analysis
Mulliken populations
Mulliken populations are based
on the elementary atomic basis functions (bas).
The individual BAS populations are
printed together with summaries of the populations in all basis functions with
the same angular moment quantum number on the same atom.
A final summary is obtained by adding all functions on each atom, yielding the
atom-atom populations. The atom-atom populations per
l-value can be obtained if the key EXTENDEDPOPAN is included.
The atomic gross charges are derived from the net and
the overlap populations in the usual way.
In addition, a population analysis may be given of individual MOs (by default this is suppressed). See
the EPrint keys SCF (option mopop) and orbpop.
Hirshfeld charges
Of the three methods applied in adf
to compute charges (Mulliken, Hirshfeld, Voronoi) we recommend the Hirshfeld analysis
[125,
126] and the analysis based
on Voronoi deformation density (VDD) charges
[109,
127], see below. The
fragments to which the Hirshfeld charges apply are enumerated in the early
geometry part of the output file, where for each fragment the numbers of the
atoms are given that belong to the fragment.
The sum of the Hirshfeld charges may not add up to the analytical net total
charge of the molecule. Any deviation from this is caused by numerical
integration precision (small effect) and the neglect of long-distance terms
that adf uses to speed up the
integral evaluations. This approximation does not affect very much the energy
and molecular orbital properties, but it does show up in the
sum-of-charges somewhat more. It does not indicate an error (unless the
deviation is really large, say in the order of 1‰ of the total number of
electrons).
Voronoi Deformation Density (VDD) Charges
The VDD method is based on the deformation density and a rigorous partitioning of space into non-overlapping atomic areas, the so-called Voronoi cells [109, 127, 128]. The Voronoi cell of an atom A is the region in space closer to nucleus A than to any other nucleus (cf. Wigner-Seitz cells in crystals). The VDD charge of an atom A monitors the flow of charge into, or out of the atomic Voronoi cell as a result of 'turning on' the chemical interactions between the atoms. The VDD method summarizes the three-dimensional deformation density on a per-atom basis. It is conceptually simple and affords a transparent interpretation based on the plausible notion of charge redistribution due to chemical bonding, i.e. the gain or loss of charge in well-defined geometrical compartments of space. For the use of VDD in analyzes involving molecular fragments, see Ref. [129].
In the same fashion as for the Hirshfeld analysis, a summation over all atoms is given which should yield zero (for a neutral molecule). The deviation from zero is caused by numerical integration and by neglect-of-long-distance-terms; the same remarks apply as for the Hirshfeld analysis above.
Multipole Derived Charges (MDC)
This charge analysis uses the atomic multipoles (obtained from the fitted density) up to some level X, and reconstructs these multipoles exactly (up to level X) by distributing charges over all atoms. The SCF should have converged for a meaningful MDC analysis.
Mayer Bond orders
The Mayer bond order between two atoms is calculated from the density and the overlap matrices (key EXTENDEDPOPAN), see Ref. [140]. See for Mayer bond orders and alternative definitions of bond orders also the key BONDORDER.
