New development of numerical gridbased methods
The electronic structures and dynamics in atoms and molecules are governed by
the Coulomb potential. For numerical simulations, it requires to treat the
short and longrange behaviors of the Coulomb potential with dense local
refinement and large spatial dimension. To attack the Coulomb potential in
allelectron calculations of polyatomic molecules, I have developed new
numerical gridbased methods: Voronoicell finite difference (VFD) method and
timedependent VFD method. In contrast to the ordinary finite difference
method with regular uniform grids, the VFD method can accommodate any types of
grid distributions, so called unstructured grids, with the help of
geometrical adaptivity of the Voronoi diagram, while it retains simplicity of the finite difference method. Nonuniform and highly adaptive
multicenter molecular grids are constructed by a combination of spherical
atomic grids centered at nuclear positions. The new methods have been applied
to solve densityfunctional theory (DFT) [1] and
timedependent DFT (TDDFT) [2] equations for accurate
electronic structure and dynamics calculations of polyatomic molecules on
multicenter molecular grids.

Voronoi diagram on unstructured grids.

Related Publications
 SangKil Son, Voronoicell finite difference method for accurate electronic structure calculation of polyatomic molecules on unstructured grids, J. Comput. Phys. 230, 2160–2173 (2011) [BibTeX][pdf][abstract]doi:10.1016/j.jcp.2010.12.012
 SangKil Son and ShihI Chu, Theoretical study of orientationdependent multiphoton ionization of polyatomic molecules in intense ultrashort laser fields: A new timedependent Voronoicell finite difference method, Chem. Phys. 366, 91–102 (2009) [BibTeX][pdf][abstract]doi:10.1016/j.chemphys.2009.09.006
Oral Presentations
 SangKil Son and ShihI Chu, Multielectron Effects on Strongfield Multiphoton Ionization of Polyatomic Molecules in Kansas Physical Chemistry Symposium (University of Kansas, Lawrence, Kansas, November 7, 2009) [oral presentation] [BibTeX][slide: 3Mb][abstract]
 SangKil Son, Theoretical study of strongfield multiphoton ionization of polyatomic molecules: a new timedependent Voronoicell finite difference method in CFEL Seminar (CFEL, DESY, Hamburg, Germany, July 23, 2010) [oral presentation] [BibTeX][pdf][slide: 6Mb][abstract][link]
