Integration over atomic basin

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

• in a natural coordinate system: s along a gradient path, and the angles Theta and Phi which define a path on the Beta-Sphere around the nucleus.
• in a radial coordinate system: s along a ray, and the angles Theta and Phi.

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:

• Integration inside Beta-Sphere: Only integration inside the sphere in polar coordinates is performed.
• Integration in natural coordinates: Integration is performed according to the settings of the above values in natural coordinates.
• Integration in radial coordinates: Integration is performed in a radial coordinate system with determination of interatomic surfaces. This integration method is usually much slower than the other one and constitutes a kind of "brute force" procedure.
• Options: Displays an options-dialog to manipulate the settings of the integration procedures.
• Functions: brings you to the Basin Properties dialog
• Delete Results: existing integration-results are removed.
• OK: close 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.