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Tensor Decomposition in Vibrational Coupled Cluster Response Theory

Banff International Research Station for Mathematical Innovation and Discovery

I will discuss the integration of the tensor decomposition idea in the context of calculation of vibrational coupled cluster (VCC) wave functions and VCC response functions. Traditionally explicit quantum calculations for molecules with more than a few atoms is hampered by the curse of dimensionality leading to an explosion in complexity with system size. This includes both the fast increase in computational cost per quantum state with increasing system size, as well as the problem of the explosion in the number of available quantum states in relevant energy ranges. I will describe how response functions can be used to calculate vibrational spectra (IR or Raman) without the need for calculation of eigenstates, but requiring instead solution of complex linear response equations. On the other hand, a pole and residue search of the response function shows, that if needed, explicit state-by-state information can be obtained through solving response eigenvalue equations. The complex linear equation and real eigenvalue equations can in turn be solved by iterative methods. I will show how one iteratively can build up a subspace consisting of vectors that are stacked decomposed tensors. I will hereunder describe current progress in exploiting the computational advantages of the tensor decomposition in the transformations required for the iterative algorithms. Implementations have been made using the stanard canonical tensor decomposition format. (CP: CANDECOMP/PARAFAC). Numerical studies illustrate the theoretical concepts.

Mathematics; Quantum theory; Partial differential equations; Applied computer science

video/mp4

Author affiliation: Aarhus University

2016-07-27

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/58561

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/