[-]stw  filename


"Stewart atoms are the unique nuclear-centered spherical functions whose sum best fits a molecular electron density in a least-squares sense (Gill, P. M. W.)".[1 Gill, P. M. W.
J. Phys. Chem. 1996, 100, 15421-15427.
, 2Gilbert, A. T. B.; Lee, A. M.; Gill, P. M. W.
J. Mol. Struct. (Theochem) 2000, 500, 363-374.
] Least-squares refinements of experimental and theoretical structure factors in reciprocal space (as done by VALRAY and XD) and ED's in real space (as done by PAMoC) provide a set of pseudoatom populations in the form of spherical harmonics tensors, that can be easily converted into traceless cartesian moments by a linear transformation. However a volume integration is needed to evaluated unabridged cartesian moments as well as a number of other atomic properties of common interest. This can be achieved by means of keyword stw.


This keyword enters the pathname to an archive file on disk which contains Stewart pseudoatom properties evaluated by PAMoC through 3D volume integration. If the file does not exist, then PAMoC provides to create it and to fill it with newly calculated properties. If the file exists, but it is empty or uncomplete, PAMoC calculates the missing properties, that will be stored on the file until it is complete. Once all properties have been calculated or if the file exists and is complete, PAMoC retrieves the data on file and prints them on the output file with a clear, structured and self-explaining lay-out of the text.

The archive file contains the following integral properties for each nuclear centre:

1.population pa = ∫ ρa(ra) d3ra
2.dipole ma = ∫ ρa(rara d3ra
3.quadrupole ma(2) = ∫ ρa(rara2 d3ra
4.octupole ma(3) = ∫ ρa(rara3 d3ra
5.hexadecapole ma(4) = ∫ ρa(rara4 d3ra
6.volume Va = ∫ δρ0[ρa(ra)] d3ra   where   δρ0[ρa(ra)]  = 1  if  ρa(ra)  ≥ ρ0  and 0 otherwise.
7.laplacian energy La = −¼∫ ∇2ρa(ra) d3ra
8.<ra2> <ra2> = ∫ ρa(ra) ra2 d3ra
9.Shannon entropy Sa = −∫ ρa(ra) ln ρa(ra) d3ra
10.electric potential φa(Ra) = −∫ ρa(r'a) |r'a|−1 d3r'a
11.electric field Ea(Ra) = −∫ φa(r'ad3r'a  = −∫ ρa(r'a) |r'a|−3 r'a d3r'a
12.electric field gradient EFGa(Ra)  = −∫ ρa(r'a) [ |r'a|−5 r'a2  − |r'a|−3 I ] d3r'a
13.source function self-contribution to the ED at nuclear centre Sa(Ra) = −(1/4π) ∫ ∇2 ρa(r'a) |r'a|−1 d3r'a
Kinetic-energy density funtionals
13.2nd order gradient expansion formula, Kirzhnits (1975)  
13.Lee-Yang-Parr (LYP, 1988)  
Exchange-energy density funtionals
13.Perdew-Wang '91  
13.Modified Perdew-Wang 1991  
13.Gill 1996  
13.Perdew-Wang '86  
13.Lacks and Gordon '93  
Correlation-energy density funtionals
13.LYP version of Colle-Salvetti formula  
Electron localization functions
13.ELF, Tsirelson  
Related Keywords


  1. "Extraction of Stewart Atoms from Electron Densities"
    Gill, P. M. W.
    J. Phys. Chem. 1996, 100, 15421-15427.
  2. "Methods for constructing Stewart atoms"
    Gilbert, A. T. B.; Lee, A. M.; Gill, P. M. W.
    J. Mol. Struct. (Theochem) 2000, 500, 363-374.