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Title: Efficient Algorithms for Estimating the Absorption Spectrum within Linear Response TDDFT

Journal Article · · Journal of Chemical Theory and Computation
 [1];  [2];  [1];  [3];  [1];  [4];  [1]
  1. Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
  2. Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Univ. of California, Berkeley, CA (United States)
  3. Pacific Northwest National Lab. (PNNL), Richland, WA (United States)
  4. Univ. of Minnesota, Minneapolis, MN (United States)
+ Show Author Affiliations

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.

Research Organization:
Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
Sponsoring Organization:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
Grant/Contract Number:
AC02-05CH11231
OSTI ID:
1378640
Journal Information:
Journal of Chemical Theory and Computation, Vol. 11, Issue 11; ISSN 1549-9618
Publisher:
American Chemical SocietyCopyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 28 works
Citation information provided by
Web of Science

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Cited By (3)

S erenity : A subsystem quantum chemistry program journal January 2018
Modeling L 2,3 -edge X-ray absorption spectroscopy with linear response exact two-component relativistic time-dependent density functional theory journal June 2019
Relativistic four-component linear damped response TDDFT for electronic absorption and circular dichroism calculations journal November 2019

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