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An adaptive multiscale bond order dissection ANOVA approach for efficient electronic structure calculations Griebel, Michael


We present a multi--scale decomposition approach for the efficient approximate calculation of the electronic structure problem for molecules. It is based on a dimension-wise decomposition of the space the underlying Schroedinger equation lives in. This decomposition is similar to the ANOVA-approach (analysis of variance) which is well-known in statistics. It represents the energy as a finite sum of contributions which depend on the positions of single nuclei, of pairs of nuclei, of triples of nuclei, and so on. Under the assumption of locality of electronic wave functions, the higher order terms in this expansion decay rapidly and may therefore be properly truncated. Furthermore, additional terms are eliminated according to the bonding structure of the molecule. This way, only the calculation of the electronic structure of local parts, i.e. small subsystems of size $k$ of the overall system, is necessary to approximate the total ground state energy. This is approximately done by e.g. the HF-approach, DFT, CI, CC or MP2. This decomposition approach is combined with rising the number $p$ of approximation functions in the discretization of the $k$-sized subsystems. Then, it turns out that a sparse grid-like approach in the parameters $k$ and $p$ results in a very fast and parallel solution procedure which allows to treat huge bio-molecules in decent run time and results in excellent approximations. Furthermore, our new approach can be used in an adaptive sparse-grid fashion which speeds up things even further. This is joint work with J. Hamaekers and R. Chinnamsetty.

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