Integration over atomic basin

The integration over atomic basins is the most time consuming task in AIM2000. The integrals runs over three coordinates:

The first aspect, a user has to think about, is the use of symmetry which can very much accelerate the integration process. After the atom is chosen in the Control View, a special atomic coordinate system is constructed which allows optimal use of symmetry in the integration. The axis of this system are displayed in 3DView. The coordinates of all atoms of the molecule in the atomic coordinate system are displayed in the list box on the right hand side of the dialog.

You can now enter the borders of the Phi-integration under lower and upper borders in the Phi-integration (degrees) using the spin-buttons. The angle Phi is measured around the z-axis with Phi = 0 in the xz-plane.

Beneath the spin-buttons, a factor is shown by which the integration results are multiplied, e.g. 2*Pi if the upper and lower border of the Phi-integration are equal (rotational symmetry) or 4 if Phi runs from 0 to 90 degrees. The program presets this factor after the integration borders are chosen, but the user can overwrite this value.

The third value the user has to enter (in case a natural coordinate system is used) is the radius of the sphere around the nucleus where a polar coordinate system can be used for integration. This sphere must be totally inside the atomic basin!

Buttons of the dialog:

All results are displayed in the lower list-box of the dialog. For comments on the integrated functions and properties see Basin Properties.