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Comput."],"published-print":{"date-parts":[[2017,1]]},"abstract":"<jats:p>We consider the Born--Oppenheimer approximation of the Schr\u00f6dinger equation for two hydrogen atoms in the case of large separation distances. We show that the Feschbach--Schur perturbation method can be used to solve the problem for the difference between a given separation and infinite separation. This leads to a simplified problem which can be solved iteratively. We show that this iteration converges for sufficiently large separation distances and we solve the arising sequence of six-dimensional PDEs with a finite element method in combination with low-rank tensor techniques to make the computations tractable. In particular we show how the discretized problems can be represented and solved in the tensor-train format. Since the storage and computational complexity of this format scale linearly in the dimension, a very large number of grid points can be employed, which leads to accurate approximations of the ground-state energy and ground-state wavefunction. Various numerical experiments show the performance and accuracy of this method.<\/jats:p>","DOI":"10.1137\/15m102808x","type":"journal-article","created":{"date-parts":[[2017,2,28]],"date-time":"2017-02-28T11:36:08Z","timestamp":1488281768000},"page":"B190-B220","source":"Crossref","is-referenced-by-count":8,"title":["Using the Tensor-Train Approach to Solve the Ground-State Eigenproblem for Hydrogen Molecules"],"prefix":"10.1137","volume":"39","author":[{"given":"Alexander","family":"Veit","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"L. Ridgway","family":"Scott","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2017,2,28]]},"reference":[{"key":"atypb1","unstructured":"I. Anapolitanos,\n                      On van der Waals Forces\n                      , Ph.D. thesis, University of Toronto, 2011."},{"key":"atypb2","unstructured":"M. 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