Keyword

Options:

MULLIKEN | A Mulliken population analysis is performed. This is the default. | ||

LOEWDIN | A Löwdin population analysis is performed. | ||

BADER | A Bader population analysis is performed. | ||

NBO | Create input file for an NBO analysis. | ||

BECKE | Real space is partitioned into overlapping (fuzzy) Becke cells. | ||

HIRSHFELD | Real space is partitioned into overlapping Hirshfeld cells. | ||

VORONOI | Real space is partitioned into non-overlapping Voronoi cells. |

SCF | The SCF density is used for the Hirshfeld weights. Only meaningful for the HIRSHFELD option. | ||

ITERATIVE | The Hirshfeld weights are refined iteratively. Only meaningful for the HIRSHFELD option. | ||

FRACTIONAL | Same as the ITERATIVE option but separates and spin densities. Only meaningful for the HIRSHFELD option. | ||

DEFORMATION | The deformation density is analyzed. Only meaningful for the BECKE, HIRSHFELD and VORONOI options. | ||

FULL | More information is printed. |

For all population analyses, deMon2k calculates atomic charges and, in the case of open-shell systems, atomic spin populations. From the orbital-based population analysis of Mulliken [262] or Löwdin [263], the bond order [264] or valence matrix [267] is calculated as well (closed-shell systems only) with the option FULL. In the case of the Bader population analysis [38], the critical points of the electron density and the molecular graph are also calculated. These quantities can be visualized with VU [41] using the

With the options BECKE, HIRSHFELD or VORONOI a topological atom-in-molecule (AIM)
analysis of the electronic density is performed. The electronic density,
is integrated numerically on a fixed grid of points. By selecting the BASIS or AUXIS
option of the TOPOLOGY keyword (see 4.10.2), the user triggers the analysis
of the Kohn-Sham density (BASIS) or of the auxiliary density (AUXIS). By default the
Kohn-Sham density is used for all topological analyses. The quality of the integration
grid is also set with the TOPOLOGY keyword using the options COARSE, MEDIUM, FINE or
REFERENCE. The DEFORMATION option of the POPULATION keyword triggers the analysis of
the deformation density,
, defined as:

(38) |

Voronoi:

(39) |

Becke:

(40) |

Hirshfeld:

The cell function
of the BECKE weights is defined by a "soft" step
function in terms of the elliptic coordinates defined as [269]:

(42) |

As can be seen from Eq. (4.32) the atomic Hirshfeld weights are always calculated from the auxiliary densities, independent of whether the Kohn-Sham or auxiliary density is partitioned. For the reference densities in Eq. (4.32) 4 different options are available. By default spherically averaged neutral atom densities are used to calculate the atomic Hirshfeld weights. This is the standard Hirshfeld scheme from the literature [265]. With the SCF option of the POPULATION keyword is calculated from the atomic SCF auxiliary densities. With the ITERATIVE option of each atom is calculated from a spherically averaged ion with the current charge of the atom (see Eq. 19 of Ref. [266]). Note that this approach is computationally more involved than the standard Hirshfeld scheme because it requires repetitive integration of the electronic density over the grid. The tolerance criteria and the maximum number of iterations are set by the TOPOLOGY keyword options TOL and MAX, respectively. The iterative Hirshfeld scheme produces higher partial charges in absolute value than the standard one and is also applicable to ionic molecules. Moreover the arbitrariness in the definition of the reference densities of the standard Hirshfeld approach is removed with the iterative version. In open-shell molecules either the density or the spin densities can be refined iteratively according to scheme that was just discussed. This selection is triggered by the options ITERATIVE or FRACTIONAL, respectively. Therefore, the input lines,

POPULATION HIRSHFELD ITERATIVE

and

POPULATION HIRSHFELD FRACTIONAL

yield the same iterative Hirshfeld charges for closed-shell molecules but different charges for open-shell molecules.