# NTPoly Application: Density-Functional Pertubation Theory

Recently, a very interesting paper by Honghui Shang of the Chinese Academy of Sciences has appeared in Computer Physics Communications. This paper presents an efficient method for computing the response density matrix for density-functional pertubation theory. In order to demonstrate their method, they utilized the NTPoly library.

Shang, Honghui, WanZhen Liang, Yunquan Zhang, and Jinlong Yang. “Efficient parallel linear scaling method to get the response density matrix in all-electron real-space density-functional perturbation theory.” Computer Physics Communications 258 (2020): 107613.

Density-Functional Perturbation Theory is a method to compute response properties of systems such as polarizability, vibrational frequencies, etc. The authors describe how Density Matrix Purification can be used as a replacement for the typical approach which requires the eigenvectors and eigenvalues of the Hamiltonian. They utilized the sparse-matrix sparse-matrix routine implemented in NTPoly via the ELSI interface to implement this approach. The authors examined closely what parameters are needed to get good accuracy without sacrificing too much performance. To test the performance of their method, the authors deployed the code on the Tianhe-2 supercomputer and performed tests with up to 25,200 cores. Despite the fact that NTPoly has never been tuned for such a machine, the code showed excellent scalability.