RESEARCH ARTICLE Tensor Representation Techniques in post-Hartree Fock Methods: Matrix Product State Tensor Format
Udo Benedikt, Henry Auer, Mike Espig, Wolfgang Hackbusch, Andrew L. Alexander · 2013
;In this proof-of-principle study, we discuss the application of various tensor representation formats and their implications on memory requirements and computational eort for tensor manipulations as they occur in typical post Hartree-Fock methods. A successive tensor decomposition / rank reduction scheme in the matrix product state (MPS) format for the two electron integrals in the AO and MO basis and an estimate of the t2 amplitudes as obtained from MP2 are described. Furthermore, the AO-MO integral transformation, the calculation of the MP2 energy and the potential usage of tensors in low rank MPS representation for the tensor contractions in CC theory are discussed in detail. We are able to show that the overall scaling of the memory requirements is reduced from the conventional N 4 scaling to approximately N 3 and the scaling of computational eort for tensor contractions in post-HF methods can be reduced to roughly N4 while the decomposition itself scales as N5. While ecient algorithms with low prefactor for the tensor decomposition have yet to be devised, this Ansatz oers the possibility to nd a robust approximation with low scaling behaviour with system and basis set size for post Hartree Fock ab initio methods.