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.
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.
Motion of charges at the atomic level is the fundamental mechanism for all chemical and biological processes in nature. Processes such as the photoelectric effect, molecular dissociation, and photosynthesis, are initiated by the electrons and the nuclei moving on the time scale of attoseconds to femtoseconds. Learning to control and steer these ultrafast dynamics is the objective of femtochemistry, where we have the vision to design artificial reactions and to engineer compounds with exceptional physical, chemical, or biological properties. The theoretical description of molecular systems is challenging however, due to the large number of degrees of freedom and the intrinsic quantum nature of the problem. A full quantum description of the molecules is far from feasible using today's computational resources. We need approximated models to resolve the ultrafast dynamics in molecules theoretically. Here we show, matrix product states (MPS) are particularly suited to describe ultrafast electron dynamics in molecules. Using the Hamburg CheMPS2 program developed for this thesis, we demonstrate the massive reduction of degrees of freedom when representing the many-body state by time-dependent MPS. In the context of ultrafast electron dynamics in molecules, we compare reduced density matrices and Green's functions obtained from the MPS approach with those from a completely correlated state. We see a reduction of the effective number of degrees of freedom by several orders of magnitude, while the error of the one-body reduced density matrix can be controlled to stay below 10% within a time frame of 3fs. This feature is shown for correlated systems such as the 10 site hydrogen chain, the hydrogen fluoride molecule, the water molecule, the ammonia molecule, and the methane molecule. Additionally, for the ionized iodoacetylene molecule, we observe electron dynamics that is in quantitative agreement with experimental reports. We pinpoint the performance of the MPS approach in resolving electron migration and demonstrate the vital role of correlations in this process. We expect the computationally efficient MPS based time evolution to enable accurate description of many phenomena involving electron dynamics in molecules hidden before. Still, the method can be expanded to describe phenomena including nuclear motion and explicit ionization processes.
Die Bewegung von Ladungen auf atomaren Skalen ist die grundlegende Ursache fur alle chemischen und biologischen Prozesse. Der photoelektrische Effekt, Dissoziation von Molekulen und Photosynthese sind nur einige Prozesse, die von einer Bewegung der Elektronen auf der Zeitskala zwischen Attosekunden und Femtosekunden ausgelost werden. Kontrolle uber diese ultraschnelle Dynamik zu gewinnen ist das Ziel der Femtochemie. In der Lage zu sein, die ultraschnelle Elektronenbewegung in Molekulen zu steuern, wurde es ermoglichen kunstliche Reaktionen hervorzurufen und damit Verbindungen mit neuartigen Eigenschaften zu schaffen. Eine theoretische Beschreibung solcher Prozesse ist allerdings sehr aufwendig, da Molekule viele Freiheitsgerade besitzen und sie intrinsisch quantenmechanisch sind. Eine komplett quantenmechanische Beschreibung wurde unsere heutigen Rechenkapazitaten bei Weitem ubersteigen. Daher brauchen wir Methoden, um dennoch Zeitabhangigkeit in Molekulen annaherungsweise zu beschreiben. In dieser Arbeit zeigen wir, dass eine solche Beschreibung mittels Matrixproduktzustanden (MPS) moglich ist. Mit dem eigens fur diese Arbeit entwickelten Hamburg CheMPS2 Programm demonstrieren wir die immense Reduzierung der Freiheitsgrade, wenn der Vielteilchenzustand durch einen zeitabhangigen MPS reprasentiert wird. Im Kontext von ultraschneller Elektronendynamik in Molekulen, vergleichen wir reduzierte Dichtematritzen sowie Greensche Funktionen zwischen dem MPS-Ansatz und einer komplett korrelierten Rechnung. Wir sehen eine Reduktion der Anzahl von effektiven Freiheitsgraden um mehrere Grosenordnungen, wobei der Fehler in der Einteilchen-Dichtematrix immer unter 10% innerhalb der ersten 3fs gehalten werden kann. Diese Eigenschaft weisen wir fur korrelierte Systeme, wie der Kette aus zehn Wasserstoffatomen, Fluorwasserstoff, das Wassermolekul, Ammoniak und Methan, nach. Zusatzlich wird Ladungsmigration in ionisiertem Iodoacetylene untersucht, wobei wir hier eine quantitative Ubereinstimmung mit experimentellen Daten erreichen. Wir spezifizieren in diesem System den Einfluss von Elektronenkorrelation und zeigen explizit, dass der MPS-Ansatz in der Lage ist diese aufzulosen. Wir erwarten, dass der sehr effiziente MPS-Ansatz zukunftig genutzt werden kann, um Ladungsmigrationseffekte zu beschreiben, die zuvor verborgen waren. Auch lasst sich der MPS-Ansatz noch zusatzlich erweitern, um beispielsweise Kernbewegungen oder Ionisierungsprozesse zu berucksichtigen.
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.
Dynamical electronic- and vibrational-structure theories have received a growing interest in the past few years due to their ability to simulate spectra recorded with ultrafast experimental techniques. The exact time evolution of a molecular system can, in principle, be obtained from the time-dependent version of full configuration interaction. Such an approach is, however, limited to few-atom systems due to the exponential increase of its cost with the system dimension. In the present work, we overcome this unfavorable scaling by employing the time-dependent density matrix renormalization group (TD-DMRG) which parametrizes the time-dependent wave function as a matrix product state. The time-dependent Schrödinger equation is then integrated with a sweep-based algorithm, as in standard time-independent DMRG. Unlike other TD-DMRG approaches, the one presented here leads to a set of coupled equations that can be integrated exactly. The resulting theory enables us to study real- and imaginary-time evolutions of Hamiltonians comprising more than 20 degrees of freedom that are challenging for current state-of-the-art quantum dynamics algorithms. We apply our algorithm to the simulation of quantum dynamics of models of increasing complexity, ranging from simple excitonic Hamiltonians to more complex ab initio vibronic ones.
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.
Revealing possible long-living coherence in ultrafast processes allows detecting genuine quantum mechanical effects in molecules. To investigate such effects from a quantum chemistry perspective, we have developed a method for simulating the time evolution of molecular systems based on ab initio calculations, which includes relaxation and environment-induced dephasing of the molecular wave function whose rates are external parameters. The proposed approach combines a quantum chemistry description of the molecular target with a real-time propagation scheme within the time-dependent stochastic Schrödinger equation. Moreover, it allows a quantitative characterization of the state and dynamics coherence through the l1-norm of coherence and the linear entropy, respectively. To test the approach, we have simulated femtosecond pulse-shaping ultrafast spectroscopy of terrylenediimide, a well-studied fluorophore in single-molecule spectroscopy. Our approach is able to reproduce the experimental findings [R. Hildner et al., Nat. Phys. 7, 172 (2011)], confirming the usefulness of the approach and the correctness of the implementation.