Computational Chemistry, Contributed Talk (15min)

CC-023

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

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.

**References**:

[1] S. R. White, *Phys. Rev. Lett.*, **1992**, 69, 2863–2866.

[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.