Correlations in sequences of generalized eigenproblems arising in Density Functional Theory

Details Correlations in sequences of generalized eigenproblems arising in Density Functional Theory Correlations in sequences of generalized eigenproblems arising in Density Functional Theory

2011-08-12

arxiv.org/abs/1108.2594v2

Physics

Computational Physics

11 Pages and 6 figures. Added references, appendix and figures. Accepted for publication by Computer Physics Communications

Scientific paper

Density Functional Theory (DFT) is one of the most used ab initio theoretical frameworks in materials science. It derives the ground state properties of a multi-atomic ensemble directly from the computation of its one-particle density \nr .In DFT-based simulations the solution is calculated through a chain of successive self-consistent cycles; in each cycle a series of coupled equations (Kohn-Sham) translates to a large number of generalized eigenvalue problems whose eigenpairs are the principal means for expressing \nr. A simulation ends when \nr\ has converged to the solution within the required numerical accuracy. This usually happens after several cycles, resulting in a process calling for the solution of many sequences of eigenproblems. In this paper, the authors report evidence showing unexpected correlations between adjacent eigenproblems within each sequence. By investigating the numerical properties of the sequences of generalized eigenproblems it is shown that the eigenvectors undergo an "evolution" process. At the same time it is shown that the Hamiltonian matrices exhibit a similar evolution and manifest a specific pattern in the information they carry. Correlation between eigenproblems within a sequence is of capital importance: information extracted from the simulation at one step of the sequence could be used to compute the solution at the next step. Although they are not explored in this work, the implications could be manifold: from increasing the performance of material simulations, to the development of an improved iterative solver, to modifying the mathematical foundations of the DFT computational paradigm in use, thus opening the way to the investigation of new materials.

Affiliated with

Also associated with

No associations

Rating

Correlations in sequences of generalized eigenproblems arising in Density Functional Theory does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Correlations in sequences of generalized eigenproblems arising in Density Functional Theory, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Correlations in sequences of generalized eigenproblems arising in Density Functional Theory will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-16150