Method Development and Tensor Decomposition Approaches for the Solution of the Schrödinger Equation

Tensor decomposition techniques are omnipresent in quantum chemistry - this starts from the RI approximation or Cholesky decomposition to approaches like Laplace-transform MP2 up to DMRG. In the framework of this project, the potential of tensor decomposition methods for devising new approximations for electronic structure methods are explored in cooperation with
scientists from applied mathematics. While we have been able to show that the application of tensor decomposition techniques should be beneficial for methods like CCSDT or FCI, several technical and conceptual challenges have yet to be overcome.

K.-H. Böhm,A. A. Auer, M. Espig, Tensor representation techniques for full configuration interaction: A Fock space approach using the canonical product format, J. Chem. Phys., 144, 12. DOI: 10.1063/1.4953665, (2016).

U. Benedikt, K.-H. Böhm, A. A. Auer, Tensor decomposition in post-Hartree-Fock methods. II. CCD implementation. J. Chem. Phys., 139, 22, 224101 DOI: 10.1063/1.4833565, (2013).

Further work in method development has been focussed at automatic program generation projects or studies on core-correlation in DLPNO-CC.

M. Krupička, K. Sivalingam, L. Huntington, A. A. Auer, F. Neese, A toolchain for the automatic generation of computer codes for correlated wavefunction calculations, Comput. Chem., 38, 1853– 1868. DOI: 10.1002/jcc.24833, (2017).

G. Bistoni, C. Riplinger, Y. Minenkov, L. Cavallo, A. A. Auer, F. Neese, Treating Subvalence Correlation Effects in Domain Based Pair Natural Orbital Coupled Cluster Calculations: An Out-of-the-Box Approach, J. Chem. Theory Comput., 13, 7, 3220-3227, (2017).