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EPJ Web of Conferences

A new method to calculate ultrafast electron dynamics in molecules based on matrix product states

Lars-Hendrik Frahm, Daniela Pfannkuche

Published Jan 1, 2019• 0 citations
Publisher

Abstract

We propose a new method to describe electron dynamics in molecules on the scale of femtoseconds. It is based on factorizing the electronic wave function into a matrix product state and using this factorization to solve the time dependent Schrodinger equation.
DOI
10.1051/epjconf/201920503009

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Ultrafast dynamics in chemical systems provide a unique access to fundamental processes at the molecular scale. A proper description of such systems is often very challenging because of the quantum nature of the problem. The concept of matrix product states (MPS), however, has proven its performance in describing such correlated quantum systems in recent years for a wide range of applications. In this work, we continue the development of the MPS approach to study ultrafast electron dynamics in quantum chemical systems. The method combines time evolution schemes, such as fourth-order Runge-Kutta and Krylov space time evolution, with MPS, in order to solve the time-dependent Schrödinger equation efficiently. This allows for describing electron dynamics in molecules on a full configurational interaction (CI) level for a few femtoseconds after excitation. As a benchmark, we compare MPS-based calculations to full CI calculations for a chain of hydrogen atoms and for the water molecule. Krylov space time evolution is in particular suited for the MPS approach, as it provides a wide range of opportunities to be adjusted to the reduced MPS dimension case. Finally, we apply the MPS approach to describe charge migration effects in iodoacetylene and find direct agreement between our results and experimental observations.
Recent advances in experimental techniques have enabled precise characterization of fundamental nonadiabatic and even electronic dynamics in molecules, on ultrafast time scales reaching femtosecond to attosecond resolution. However, accurate theoretical simulation of these ultrafast chemical dynamics processes in large systems remains challenging, largely due to the overwhelming number of degrees of freedom (DoFs) and the pronounced many-body correlations. In recent years, by leveraging efficient decomposition schemes for high-dimensional wave function and operator tensors, the time-dependent density matrix renormalization group (TD-DMRG) has emerged as a powerful and accurate quantum dynamics method for simulating nonadiabatic and electron dynamics in large chemical systems, in conjunction with realistic electron/exciton-vibration/phonon models or ab initio quantum chemistry many-electron Hamiltonians. This review outlines the fundamentals of TD-DMRG for chemical dynamics, covering matrix product state/operator (MPS/MPO) frameworks and algorithms from ground-state calculations to time evolution. We discuss thermal/environmental effects and compare TD-DMRG with other tensor network methods such as multiconfiguration time-dependent Hartree (MCTDH) and multilayer MCTDH (ML-MCTDH). Demonstrated applications include simulations of pyrazine absorption, singlet fission in rubrene crystal, and charge migration in chloroacetylene cation. These show TD-DMRG’s capability for modeling complex ultrafast processes from femtoseconds to attoseconds with controlled accuracy.