Computational Chemistry, Contributed Talk (15min)

Pushing the limits of the Density Matrix Renormalization Group: from vibrational spectroscopy to quantum dynamics

A. Baiardi1, M. Reiher2
1Laboratorium für Physikalische Chemie, ETH Zürich, Switzerland, 2Laboratory of Physical Chemistry, ETH Zurich

Simulation methods based on tensor factorizations, such as the density matrix renormalization group (DMRG) [1,2], are currently reshaping the limits of wave function-based quantum chemical algorithms. Tensor-based methods provide very compact parameterizations that can encode many-body wave functions by taming the high computational cost of Full Configuration Interaction and, therefore, enable large-scale exact quantum simulations. Chemical applications of DMRG have focused so far on time-independent electronic problems. In the present contribution, we show the potentiality of DMRG beyond this application field, by focusing on three simulation targets.
We first introduce the vibrational DMRG theory [3,4] to calculate the exact anharmonic vibrational energies of large molecular systems. Then, we apply DMRG to solve the time-dependent (TD) Schrödinger and show that the resulting algorithm, namely TD-DMRG [5,6], can accurately simulate ultrafast molecular processes occurring on multiple time-scales. Finally, we present an explicitly correlated DMRG variant, the transcorrelated DMRG (tc-DMRG) [7] that relies on the transcorrelated method [8] and enhances the accuracy of conventional DMRG for strongly-correlated molecules.



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[2] A. Baiardi, M. Reiher, J. Chem. Phys., 2020, 152, 040903.
[3] A. Baiardi, C. J. Stein, V. Barone, M. Reiher, J. Chem. Theory Comput., 2017, 13, 3764–3777.
[4] A. Baiardi, C. J. Stein, V. Barone, M. Reiher, J. Chem. Phys., 2019, 150, 094113.
[5] A. Baiardi, M. Reiher, J. Chem. Theory Comput. 2019, 15, 3481–3498.
[6] A. Baiardi, ArXiv e-prints, 2020, 2010.02049.
[7] A. Baiardi, M. Reiher, J. Chem. Phys., 2020, 153, 164115.
[8] S. F. Boys, N. C. Handy, Proc. R. Soc. A Math. Phys. Eng. Sci., 1969, 310, 43–61.