Matrix product state (MPS) is one efficient way to compress quantum states and reduce computational cost. This chapter presents the application of MPS framework as well as time-dependent density matrix renormalization group (tDMRG) variants in chemical systems. The elementary principles of MPS approaches are provided, including the basic concept of MPS and matrix product operator, the density matrix renormalization group method and tDMRG approaches based on the MPS/matrix product operator framework to solve the time-independent and dependent Schrödinger equation, respectively. Then, several examples of tDMRG applications in chemical systems investigated by the authors, including charge carrier dynamics in polymer chain, charge transfer and dissociation in organic systems, nonadiabatic dynamics of excited states S1/S2 in pyrazine molecule and singlet fission processes in organic systems, are displayed.
Matrix product state (MPS) is one efficient way to compress quantum states and reduce computational cost. This chapter presents the application of MPS framework as well as time-dependent density matrix renormalization group (tDMRG) variants in chemical systems. The elementary principles of MPS approaches are provided, including the basic concept of MPS and matrix product operator, the density matrix renormalization group method and tDMRG approaches based on the MPS/matrix product operator framework to solve the time-independent and dependent Schrödinger equation, respectively. Then, several examples of tDMRG applications in chemical systems investigated by the authors, including charge carrier dynamics in polymer chain, charge transfer and dissociation in organic systems, nonadiabatic dynamics of excited states S1/S2 in pyrazine molecule and singlet fission processes in organic systems, are displayed.
Electronic and/or vibronic coherence has been found by recent ultrafast spectroscopy experiments in many chemical, biological, and material systems. This indicates that there are strong and complicated interactions between electronic states and vibration modes in realistic chemical systems. Therefore, simulations of quantum dynamics with a large number of electronic and vibrational degrees of freedom are highly desirable. Due to the efficient compression and localized representation of quantum states in the matrix-product state (MPS) formulation, time-evolution methods based on the MPS framework, which we summarily refer to as tDMRG (time-dependent density-matrix renormalization group) methods, are considered to be promising candidates to study the quantum dynamics of realistic chemical systems. In this work, we benchmark the performances of four different tDMRG methods, including global Taylor, global Krylov, and local one-site and two-site time-dependent variational principles (1TDVP and 2TDVP), with a comparison to multiconfiguration time-dependent Hartree and experimental results. Two typical chemical systems of internal conversion and singlet fission are investigated: one containing strong and high-order local and nonlocal electron-vibration couplings and the other exhibiting a continuous phonon bath. The comparison shows that the tDMRG methods (particularly, the 2TDVP method) can describe the full quantum dynamics in large chemical systems accurately and efficiently. Several key parameters in the tDMRG calculation including the truncation error threshold, time interval, and ordering of local sites were also investigated to strike the balance between efficiency and accuracy of results.
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.
Abstract The simulations of spectroscopy and quantum dynamics are of vital importance to the understanding of the electronic processes in complex systems, including the radiative/radiationless electronic relaxation relevant for optical emission, charge/energy transfer in molecular aggregates related to carrier mobility in organic materials, as well as photovoltaic and thermoelectric conversion, light‐harvesting and spin transport, and so forth. In recent years, time‐dependent density matrix renormalization group (TD‐DMRG) has emerged as a general, numerically accurate and efficient method for high‐dimensional full‐quantum dynamics. This review will cover the fundamental algorithms of TD‐DMRG in the modern framework of matrix product states (MPS) and matrix product operators (MPO), including the basic algebra with respect to MPS and MPO, the novel time evolution schemes to propagate MPS, and the automated MPO construction algorithm to encode generic Hamiltonian. Most importantly, the proposed method can handle the mixed state density matrix at finite temperature, enabling quantum statistical description for molecular aggregates. We demonstrate the performance of TD‐DMRG by benchmarking with the current state‐of‐the‐art methods for simulating quantum dynamics of the spin‐boson model and the Frenkel–Holstein(–Peierls) model. As applications of TD‐DMRG to real‐world problems, we present theoretical investigations of carrier mobility and spectral function of rubrene crystal, and the radiationless decay rate of azulene with an anharmonic potential energy surface. This article is categorized under: Theoretical and Physical Chemistry > Statistical Mechanics Theoretical and Physical Chemistry > Reaction Dynamics and Kinetics Software > Simulation Methods
This paper is an introduction to a density matrix renormalization group method (DMRG) and its use in quantum chemistry. Firstly we define the term of strongly correlated systems and explain why the standard methods of quantum chemistry are not suitable for use with such systems. Then, motivated by the principle of locality, we introduce the wave function approximation in the form of matrix product state (MPS), its graphical representation and calculation of expectation values of operators. In the next section, we present the canonical form of MPS expansion and show its relationship to the algorithm of the DMRG method as a form of optimization of matrices in MPS in the sense of variational minimization of energy. Then, a brief overview is given to the properties of DMRG method, with its computational complexity and the resulting limitations, followed by a list of methods for inclusion of the remaining dynamical correlation. Finally, we provide example calculations on realistic, chemically interesting molecules.
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.
Substantial progress of the time-dependent density matrix renormalisation group (t-DMRG) method in the recent 15 years is reviewed in this paper. By integrating the time evolution with the sweep procedures in density matrix renormalisation group (DMRG), t-DMRG provides an efficient tool for real-time simulations of the quantum dynamics for one-dimensional (1D) or quasi-1D strongly correlated systems with a large number of degrees of freedom. In the illustrative applications, the t-DMRG approach is applied to investigate the nonadiabatic processes in realistic chemical systems, including exciton dissociation and triplet fission in polymers and molecular aggregates as well as internal conversion in pyrazine molecule.