Electron Dynamics with the Time-Dependent Density Matrix Renormalization Group

Abstract

In this work, we simulate the electron dynamics in molecular systems with the Time-Dependent Density Matrix Renormalization Group (TD-DMRG) algorithm. We leverage the generality of the so-called tangent-space TD-DMRG formulation and design a computational framework in which the dynamics is driven by the exact non-relativistic electronic Hamiltonian. We show that, by parametrizing the wave function as a matrix product state, we can accurately simulate the dynamics of systems including up to 20 electrons and 32 orbitals. We apply the TD-DMRG algorithm to three problems that are hardly targeted by time-independent methods: the calculation of molecular (hyper)polarizabilities, the simulation of electronic absorption spectra, and the study of ultrafast ionization dynamics.

47 pages, 11 figures

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• Second-order self-consistent field algorithms: from classical to quantum nuclei
• SCINE -- Software for Chemical Interaction Networks
• A multi-fragment real-time extension of projected density matrix embedding theory: Non-equilibrium electron dynamics in extended systems
• QCMaquis 4.0: Multi-Purpose Electronic, Vibrational, and Vibronic Structure and Dynamics Calculations with the Density Matrix Renormalization Group
• Simulating real-time molecular electron dynamics efficiently using the time-dependent density matrix renormalization group
• Adiabatic extraction of nonlinear optical properties from real-time time-dependent electronic-structure theory
• Real-time propagation of adaptive sampling selected configuration interaction wave function
• Enhanced Krylov Methods for Molecular Hamiltonians: Reduced Memory Cost and Complexity Scaling via Tensor Hypercontraction
• N-Mode Quantized Anharmonic Vibronic Hamiltonians for Matrix Product State Dynamics
• Solving intractable chemical problems by tensor decomposition