Related Experiment Video
Updated: May 11, 2026

Finite Element Analysis Model for Assessing Expansion Patterns from Surgically Assisted Rapid Palatal Expansion
Published on: October 20, 2023
Improved partition-expansion of two-center distributions involving Slater functions
Rafael López1, Guillermo Ramírez, Ignacio Ema
1Departamento de Química Física Aplicada, Facultad de Ciencias C-XIV, Universidad Autónoma de Madrid, Madrid, Spain. rafael.lopez@uam.es
Abstract:
The calculation of the electronic structure of large systems is facilitated by the substitution of the two-center distributions by their projections on auxiliary basis sets of one-center functions. An alternative is the partition-expansion method in which one first decides what part of the distribution is assigned to each center, and next expands each part in spherical harmonics times radial factors. The method is exact, requires neither auxiliary basis sets nor projections, and can be applied to Gaussian and Slater basis sets. Two improvements in the partition-expansion method for Slater functions are reported: general expressions valid for arbitrary quantum numbers are derived and the efficiency of the procedure is increased giving analytical solutions to integrals previously computed by numerical quadrature. The efficiency of the new version is assessed in several molecules and the advantages over the projection methods are pointed out.
Related Concept Videos
Extraction: Partition and Distribution Coefficients
For extracting a solute from an aqueous phase into an organic...
Applications of Integration to Probability Density Functions
Routh-Hurwitz Criterion II
The first scenario occurs when a singular zero appears in the first column of the Routh table. This situation creates a division by zero issues. To resolve this, a small positive or negative number, denoted as epsilon (∈), is substituted for the zero. The stability analysis proceeds by assuming a sign for ∈. If ∈ is positive, any sign change in the first column of the Routh...
Divergence and Stokes' Theorems
Slant Asymptotes
Singularity Functions for Shear
