3rd Floor Classroom/3-Flatiron Institute (162 5th Avenue)
3rd Floor Classroom/3-Flatiron Institute
162 5th Avenue
40
Description
Title: An Application of Hierarchical Matrices to Quantum Chemistry
The continuous fast multipole method (CFMM) is well known for its asymptotically linear complexity for constructing the Coulomb matrix in quantum chemistry. However, in practice, CFMM must evaluate a large number of interactions directly, being unable to utilize multipole expansions for interactions between overlapping continuous charge distributions. Instead of multipole expansions, we propose a technique for compressing the interactions between charge distributions into low-rank form, resulting in significantly fewer interactions that must be computed directly. We apply the H2 hierarchical matrix representation to the electron repulsion integral (ERI) tensor with Gaussian basis sets to rapidly calculate the Coulomb matrices in Hartree-Fock and density functional theory calculations. The hierarchical matrix approach has very modest storage requirements, allowing large calculations to be performed in memory without recomputing ERIs. Like CFMM, the hierarchical matrix approach is asymptotically linear scaling, but the latter requires severalfold less memory (or severalfold less computation, if quantities are computed dynamically) due to being able to efficiently employ low-rank approximations for significantly more blocks.
If you would like to attend, please email crampersad@flatironinstitute.org for the Zoom details.
