Efficient Algorithms for Estimating the Absorption Spectrum within Linear Response TDDFT

Jiri Brabec, Lin Lin, Meiyue Shao, Niranjan Govind, Chao Yang, Yousef Saad, Esmond G. Ng

Research output: Contribution to journalArticlepeer-review

34 Scopus citations


We present a special symmetric Lanczos algorithm and a kernel polynomial method (KPM) for approximating the absorption spectrum of molecules within the linear response time-dependent density functional theory (TDDFT) framework in the product form. In contrast to existing algorithms, the new algorithms are based on reformulating the original non-Hermitian eigenvalue problem as a product eigenvalue problem and the observation that the product eigenvalue problem is self-adjoint with respect to an appropriately chosen inner product. This allows a simple symmetric Lanczos algorithm to be used to compute the desired absorption spectrum. The use of a symmetric Lanczos algorithm only requires half of the memory compared with the nonsymmetric variant of the Lanczos algorithm. The symmetric Lanczos algorithm is also numerically more stable than the nonsymmetric version. The KPM algorithm is also presented as a low-memory alternative to the Lanczos approach, but the algorithm may require more matrix-vector multiplications in practice. We discuss the pros and cons of these methods in terms of their accuracy as well as their computational and storage cost. Applications to a set of small and medium-sized molecules are also presented.

Original languageEnglish (US)
Pages (from-to)5197-5208
Number of pages12
JournalJournal of Chemical Theory and Computation
Issue number11
StatePublished - Nov 10 2015

Bibliographical note

Publisher Copyright:
© 2015 American Chemical Society.


Dive into the research topics of 'Efficient Algorithms for Estimating the Absorption Spectrum within Linear Response TDDFT'. Together they form a unique fingerprint.

Cite this