Counting nodal surfaces in molecular orbitals: Elimination of artificial nodes

The nodal surfaces of a molecular orbital (MO) provide significant information about electronic structure. For example, antibonding can be identified by the existence of a nodal surface between two atoms. This paper sets out an algorithm for finding nodal surfaces in an MO. Unfortunately, when a non-orthogonal basis set expansion is used (e.g., contracted Gaussian-type functions (CGTFs)), the calculated MOs may contain nodal surfaces that are artifacts of the method of calculation. These artifacts are obstacles to any algorithmic counting of nodal surfaces, so it is important to eliminate them. We present a simple method for eliminating artificial nodes by introducing a radius r_fbd. Nodes outside a sphere of radius r_fbd are considered to be artifacts and are eliminated. The radius r_fbd is determined from the radial distributions of the respective CGTFs that constitute the MO under consideration. The space outside the sphere of r_fbd is called the forbidden space, and the charge distribution is set to zero in that space. We illustrate this method by analyzing nodal surfaces in the Li atom, Be atom, Zn atom, H2O molecule, and formaldehyde.