Date: November 13(Tue.), from 16:00
Place: Main building, room 213
Lecturer:
James S. M. Anderson (Univ. of Tokyo)
Title:
GKCI Approach for Solving the Electronic and Nuclear Schroedinger Equation
Abstract:
Achieving high accuracy in both electronic and nuclear structure computations
is a priority when developing a structure method. The full configuration interaction (Full-CI)
method achieves the highest accuracy within a model space, but is very computationally
expensive (exponential scaling). Full-CI is a robust method that can be used with any Hamiltonian.
It does not take advantage of the inherent smoothness associated with the solutions
to the electronic and nuclear structure Hamiltonians. In the nuclear structure problem
simplicity arises from every nucleon being identical (in the isospin formalism),
and that the Hamiltonian only contains one- and two-body symmetric operators
(though three-body operators are becoming more prominent). The same is true in the electronic structure problem.
Our approach takes into account these symmetries that are neglected in the Full-CI approach.
Results from Griebel[1] and others[2-4] in the mathematics of complexity literature show
how one may construct a truncated Full-CI that has polynomial scaling but maintains Full-CI accuracy
(at least within the large model space limit). We refer to this approach as GK-CI.[5]
A special case of the method is similar to the no-core shell model. In this presentation
the mechanics of the approach will be explained as well as preliminary results.
References
1. M. Griebel and S. Knapek, Constr. Approx. 16, 525 (2000).
2. H. Bungartz and M. Griebel, Acta Numer. 13, 147 (2001).
3. G.W. Wasilkowski and H. Wozniakowski, Found. Comput. Math., 5, 240 (2005)
4. S.A. Smolyak, Dokl. Akad. Nauk 4, 240 (1963)
5. J.S.M. and P.W. Ayers, J. Chem. Phys., J. Chem. Phys. Submitted (2011).