Multiconfiguration Time-dependent Hartree Method Research Articles

Charged ultralong-range Rydberg trimers

We show that the recently observed class of long-range ion-Rydberg molecules can be divided into two families of states, which are characterised by their unique electronic structures resulting from the ion-induced admixture of quantum defect-split Rydberg $n$P states with different low-field seeking high-$l$ states. We predict that in both cases these diatomic molecular states can bind additional ground state atoms lying within the orbit of the Rydberg electron, thereby forming charged ultralong-range Rydberg molecules (ULRM) with binding energies similar to that of conventional non-polar ULRM. To demonstrate this, we consider a Rydberg atom interacting with a single ground state atom and an ion. The additional atom breaks the system's cylindrical symmetry, which leads to mixing between states that would otherwise be decoupled. The electronic structure is obtained using exact diagonalisation over a finite basis and the vibrational structure is determined using the Multi-Configuration Time-Dependent Hartree method. Due to the lobe-like structure of the electronic density, bound trimers with both linear and nonlinear geometrical configurations of the three nuclei are possible. The predicted trimer binding energies and excitation series are distinct enough from those of the ion-Rydberg dimer to be observed using current experimental techniques.

Optimal Mode Combination in the Multiconfiguration Time-Dependent Hartree Method through Multivariate Statistics: Factor Analysis and Hierarchical Clustering.

The multiconfiguration time-dependent Hartree (MCTDH) method and its multilayer extension (ML-MCTDH) are powerful algorithms for the efficient computation of nuclear quantum dynamics in high-dimensional systems. By providing time-dependent variational orbitals and an optimal choice of layered effective degrees of freedom, one is able to reduce the computational cost to an amenable number of configurations. However, choices related to selecting properly the mode grouping and tensor tree are strongly system dependent and, thus far, subjectively based on intuition and/or experience. Therefore, herein we detail a new protocol based on multivariate statistics─more specifically, factor analysis and hierarchical clustering─for a reliable and convenient guiding in the optimal design of such complex "system-of-systems" tensor-network decompositions. The advantages of employing the new algorithm and its applicability are tested on water and two floppy protonated water clusters with large amplitude motions.

Rovibrational states calculations of the H2O-HCN heterodimer with the multiconfiguration time dependent Hartree method.

Water and hydrogen cyanide are two of the most common species in space and the atmosphere with the ability of binding to form dimers such as H2O-HCN. In the literature, while calculations characterizing various properties of the H2O-HCN cluster (equilibrium distance, vibrational frequencies and rotational constants) have been done in the past, extensive calculations of the rovibrational states of this system using a reliable quantum dynamical approach have yet to be reported. In this work, we intend to mend that by performing the first calculation of the rovibrational states of the H2O-HCN van der Waals complex on a recently developed potential energy surface. We use the block improved relaxation procedure implemented in the Heidelberg MultiConfiguration Time-Dependent Hartree (MCTDH) package to compute the states of the H2O-HCN isomer, from which we extract the transition frequencies and rotational constants of the complex. We further adapt an approach first suggested by Wang and Carrington-and supported here by analysis routines of the Heidelberg MCTDH package-to properly characterize the computed rovibrational states. The subsequent assignment of rovibrational states was done by theoretical analysis and visual inspection of the wavefunctions. Our simulations provide a Zero Point Energy (ZPE) and intermolecular vibrational frequencies in good agreement with past ab initio calculations. The transition frequencies and rotational constants obtained from our simulations match well with the available experimental data. This work has the broad aim to propose the MCTDH approach as a reliable option to compute and characterize rovibrational states of van der Waals complexes such as the current one.

Photodissociation dynamics and UV absorption spectrum of acetone oxide (CH3)2COO.

The photodynamics and B1A' ← X1A' absorption spectrum of acetone oxide, (CH3)2COO, are studied theoretically from first principles. The underlying adiabatic potential energy curves (and surfaces) are computed by a second-order multireference perturbation theory method and diabatized using a diabatization by ansatz scheme. To confirm the results, for selected geometries EOM-CCSD and XMS-RS2C calculations were also performed. The dynamical calculation rests on the multi-configuration time-dependent Hartree wavepacket propagation method. The experimental absorption spectrum is reproduced satisfactorily. This result serves to validate the Hamiltonian model built within the quasi-diabatic representation. Contrary to the smallest Criegee intermediate, CH2OO, it is found that the vibronic coupling between the B and C states of (CH3)2COO plays an essential role in reproducing the experimental absorption spectrum. Time-dependent electronic populations reveal a faster decay than for the smaller system CH2OO. This is interpreted in terms of the stronger coupling between the B and C states in the larger system leading to a shorter lifetime for the B state than in CH2OO.

Interaction-controlled impurity transport in trapped mixtures of ultracold bosons

We explore the dynamical transport of an impurity between different embedding majority species which are spatially separated in a double well. The transfer and storage of the impurity is triggered by dynamically changing the interaction strengths between the impurity and the two majority species. We find a simple but efficient protocol consisting of linear ramps of majority-impurity interactions at designated times to pin or unpin the impurity. Our study of this highly imbalanced few-body triple mixture is conducted with the multi-layer multi-configuration time-dependent Hartree method for atomic mixtures which accounts for all interaction-induced correlations. We analyze the dynamics in terms of single-particle densities, entanglement growth and provide an effective potential description involving mean-fields of the interacting components. The majority components remain self-trapped in their individual wells at all times, which is a crucial element for the effectiveness of our protocol. During storage times each component performs low-amplitude dipole oscillations in a single well. Unexpectedly, the inter-species correlations possess a stabilizing impact on the transport and storage properties of the impurity particle.

Open quantum dynamics of strongly coupled oscillators with multi-configuration time-dependent Hartree propagation and Markovian quantum jumps.

Modeling the non-equilibrium dissipative dynamics of strongly interacting quantized degrees of freedom is a fundamental problem in several branches of physics and chemistry. We implement a quantum state trajectory scheme for solving Lindblad quantum master equations that describe coherent and dissipative processes for a set of strongly coupled quantized oscillators. The scheme involves a sequence of stochastic quantum jumps with transition probabilities determined by the system state and the system-reservoir dynamics. Between consecutive jumps, the wave function is propagated in a coordinate space using the multi-configuration time-dependent Hartree method. We compare this hybrid propagation methodology with exact Liouville space solutions for physical systems of interest in cavity quantum electrodynamics, demonstrating accurate results for experimentally relevant observables using a tractable number of quantum trajectories. We show the potential for solving the dissipative dynamics of finite size arrays of strongly interacting quantized oscillators with high excitation densities, a scenario that is challenging for conventional density matrix propagators due to the large dimensionality of the underlying Hilbert space.

Unpredictable condensate–depletion dynamics in one-dimensional power-law traps

The dynamic depletion of a trapped one-dimensional Bose–Einstein condensate (BEC) that is driven by laser stirring is numerically explored using beyond mean-field methods. For this purpose, the multi-configurational time-dependent Hartree method for bosons (Alon et al 2008 Phys. Rev. A 77 033613) is applied. In order to induce the depletion, the BEC is excited by a negative Gaussian potential (dimple) whose depth is modulated with time. The BEC is examined in various trapping geometries, with different interactions, and the condensate depletion is recorded as a function of time. A general power–law trap is considered that can be experimentally generated and shaped by the holographic methods of Bruce et al (2011 Phys. Rev. A 84 053410). The chief goal is to explore the interplay between trapping geometry and interactions in defining the depletion dynamics. It is chiefly found, that the details of these depletion dynamics are unpredictable and determined by a combination of the principle dimple depth, trap, and interactions. One significant feature of this work is that quite a number of plateaus is reached in the aforementioned dynamics.

Vibronic coupling in the ground and excited states of the imidazole radical cation.

Vibronic interactions in the ground and two excited states of the imidazole radical cation, X2A″ (π-1), A2A' (nσ-1), and B2A″ (π-1), and the associated nuclear dynamics were studied theoretically. The results were used to interpret the recent photoelectron measurements [M. Patanen et al., J. Chem. Phys. 155, 054304 (2021)]. The present high-level electronic structure calculations employing, in particular, the single, double, and triple excitations and equation-of-motion coupled-cluster method accounting for single and double excitation approaches and complete basis set extrapolation technique for the evaluation of the vertical ionization energies of imidazole indicate that the A 2A' and B 2A″ states are very close in energy and subject to non-adiabatic effects. Our modeling confirms the existence of pronounced vibronic coupling of the A 2A' and B 2A″ states. Moreover, despite the large energy gap of nearly 1.3eV, the ground state X 2A″ is efficiently coupled to the A 2A' state. The modeling was performed within the framework of the three-state linear vibronic coupling problem employing Hamiltonians expressed in a basis of diabatic electronic states and parameters derived from ab initio calculations. The ionization spectrum was computed using the multi-configuration time-dependent Hartree method. The calculated spectrum is in good agreement with the experimental data, allowing for some interpretation of the observed features to be proposed.

Quantum Interference Paves the Way for Long-Lived Electronic Coherences.

The creation and dynamical fate of a coherent superposition of electronic states generated in a polyatomic molecule by broadband ionization with extreme ultraviolet pulses is studied using the multiconfiguration time-dependent Hartree method together with an ionization continuum model Hamiltonian. The electronic coherence between the hole states usually lasts until the nuclear dynamics leads to decoherence. A key goal of attosecond science is to control the electronic motion and design laser control schemes to retain this coherence for longer timescales. Here, we investigate this possibility using time-delayed pulses and show how this opens up the prospect of coherent control of charge migration phenomenon.

On the UV spectroscopy and photodynamics of octatetraene

The UV absorption spectrum of all-trans-octatetraene is reinvestigated theoretically, focussing on the strongly dipole-allowed – transition. The dynamical calculations rely on ab initio multistate CASPT2 (MS-CASPT2) computations of the underlying potential energy surfaces and coupling elements, and the multiconfiguration time-dependent Hartree (MCTDH) method for solving the time-dependent Schrödinger equation for the nuclear motion. The vibronic structure of the absorption band near 2700 Å is well reproduced, better than ever before by a purely ab initio approach. The C–C single bond and double bond stretching modes dominate the vibrational structure of the transition. While the latter resembles nearly harmonic motion on weakly coupled potential energy surfaces, the time-dependent calculations reveal a subpicosecond electronic population transfer from the state to the lower-lying state proceeding on a time scale of . The details of this internal conversion process and its relation to the conical intersection between the two excited states are discussed, paying particular attention to the impact of the – energy gap on the dynamics.

Nonadiabatic Vibrational Resonance Raman Spectra from Quantum Dynamics Propagations with LVC Models. Application to Thymine.

We present a viable protocol to compute vibrational resonance Raman (vRR) spectra for systems with several close-lying and potentially coupled electronic states. It is based on the parametrization of linear vibronic coupling (LVC) models from time-dependent density functional theory (TD-DFT) calculations and quantum dynamics propagations of vibronic wavepackets with the multilayer version of the multiconfiguration time-dependent Hartree (ML-MCTDH) method. Our approach is applied to thymine considering seven coupled electronic states, comprising the three lowest bright states, and all vibrational coordinates. Computed vRR at different excitation wavelengths are in good agreement with the available experimental data. Up to 250 nm the signal is dominated by the lowest HOMO → LUMO transition, whereas at 233 nm, in the valley between the two lowest energy absorption bands, the contributions of all the three bright states, and their interferences and couplings, are important. Inclusion of solvent (water) effects improves the agreement with experiment, reproducing the coalescence of vibrational bands due to CC and C=O stretchings. With our approach we disentangle and assess the effect of interferences between the contribution of different quasi-resonant states to the transition polarizability and the effect of interstate couplings. Our findings strongly suggest that in cases of close-lying and potentially coupled states a simple inclusion of interference effects is not sufficient, and a fully nonadiabatic computation should instead be performed. We also document that for systems with strong couplings and quasi-degenerate states, the use of HT perturbative approach, not designed for these cases, may lead to large artifacts.

Multilayer Multiconfiguration Time-Dependent Hartree Study on the Mode-/Bond-Specific Quantum Dynamics of Water Dissociation on Cu(111).

In this work, full-dimensional (9D) quantum dynamics calculations on mode-/bond-specific surface scattering of a water molecule on a copper (111) rigid surface are performed through the multilayer multiconfiguration time-dependent Hartree (ML-MCTDH) method. To easily perform the ML-MCTDH calculations on such a triatomic molecule-surface system, we first choose specific Jacobi coordinates as a set of coordinates of water. Next, to efficiently perform the 9D ML-MCTDH wavepacket propagation, the potential energy surface is transferred to a canonical polyadic decomposition form with the aid of a Monte Carlo-based method. Excitation-specific dissociation probabilities of H2O on Cu(111) are computed, and mode-/bond-specific dynamics are demonstrated by comparison with a probability curve computed for a water molecule in the ground state. The dependence of the dissociation probability of the initial state of H2O is studied, and it is found that the excitation-specific dissociation probabilities can be divided into three groups. We find that the vibrationally excited states enhance the dissociation reactivity of H2O, while the rotationally excited states hardly influence it.

Quantum dynamical study of inter-chain exciton transport in a regioregular P3HT model system at finite temperature: HJ vs H-aggregate models.

We report on quantum dynamical simulations of inter-chain exciton transport in a model of regioregular poly(3-hexylthiophene), rr-P3HT, at finite temperature using the Multi-Layer Multi-Configuration Time-Dependent Hartree method for a system of up to 63 electronic states and 180 vibrational modes. A Frenkel Hamiltonian of HJ aggregate type is used along with a reduced H-aggregate representation; electron-phonon coupling includes local high-frequency modes as well as anharmonic intermolecular modes. The latter are operative in mediating inter-chain transport by a mechanism of transient localization type. Strikingly, this mechanism is found to be of quantum coherent character and involves non-adiabatic effects. Using periodic boundary conditions, a normal diffusion regime is identified from the exciton mean-squared displacement, apart from early-time transients. Diffusion coefficients are found to be of the order of 3 × 10-3cm2/s, showing a non-linear increase with temperature.

Modelling ultrafast dynamics at a conical intersection with regularized diabatic states: An approach based on multiplicative neural networks

• Neural network (NN) potentials for quantum dynamics of cis–trans photoisomerization. • Multiplicative NNs adapted to regularized diabatic states at a conical intersection. • NN potentials match a sum-of-products form required by MCTDH wavefunction propagation. • Good agreement found for highly correlated dynamics with up to 13 degrees of freedom. Neural-network (NN) potentials are employed in conjunction with the Multiconfiguration Time-Dependent Hartree (MCTDH) method in order to simulate an ultrafast photoinduced cis–trans type isomerization process induced by a conical intersection. To this end, NN potentials are fitted to a diabatic potential of regularized diabatic states type [Köppel et al., J. Chem. Phys. 115, 2377 (2001)], which entirely relies on adiabatic potential information. Multiplicative NNs are employed which match the sum-of-products form of the multiconfigurational MCTDH wavefunction. Good agreement with the reference dynamics is obtained for simulations of the highly correlated dynamics with up to 13 degrees of freedom. This study contributes to developing NN methodologies suitable for photochemical dynamics at complex excited-state topologies.

Representation of Diabatic Potential Energy Matrices for Multiconfiguration Time-Dependent Hartree Treatments of High-Dimensional Nonadiabatic Photodissociation Dynamics.

Conventional quantum mechanical characterization of photodissociation dynamics is restricted by steep scaling laws with respect to the dimensionality of the system. In this work, we examine the applicability of the multi-configurational time-dependent Hartree (MCTDH) method in treating nonadiabatic photodissociation dynamics in two prototypical systems, taking advantage of its favorable scaling laws. To conform to the sum-of-product form, elements of the ab initio diabatic potential energy matrix (DPEM) are re-expressed using the recently proposed Monte Carlo canonical polyadic decomposition method, with enforcement of proper symmetry. The MCTDH absorption spectra and product branching ratios are shown to compare well with those calculated using conventional grid-based methods, demonstrating its promise for treating high-dimensional nonadiabatic photodissociation problems.

Artificial atoms from cold bosons in one dimension

We investigate the ground-state properties of weakly repulsive one-dimensional bosons in the presence of an attractive zero-range impurity potential. First, we derive mean-field solutions to the problem on a finite ring for the two asymptotic cases: (i) all bosons are bound to the impurity and (ii) all bosons are in a scattering state. Moreover, we derive the critical line that separates these regimes in the parameter space. In the thermodynamic limit, this critical line determines the maximum number of bosons that can be bound by the impurity potential, forming an artificial atom. Second, we validate the mean-field results using the flow equation approach and the multi-layer multi-configuration time-dependent Hartree method for atomic mixtures. While beyond-mean-field effects destroy long-range order in the Bose gas, the critical boson number is unaffected. Our findings are important for understanding such artificial atoms in low-density Bose gases with static and mobile impurities.

Breathing dynamics of the few-body Bose polaron in a species-selective harmonic trap

We perform an extensive numerical study on the breathing dynamics of a few-body Bose polaron setup in a one-dimensional species-selective harmonic trap. The dynamics is triggered by a quench of the impurity trap. The excitation of the background majority atoms is mediated via the majority-impurity interaction. The breathing spectrum is obtained for different numbers of majority particles, several values of the majority-component interaction strengths and trap ratios. It is further compared to the breathing spectrum of a particle-balanced few-body Bose-Bose mixture. In particular, for equal post-quench traps the employed protocol allows to couple states of different center-of-mass parity in contrast to species-symmetric trap quenches. Among the participating eigenstates we identify one having odd center-of-mass parity and even global parity. The breathing frequency induced by this state is a monotonically decreasing function of the coupling parameter. Importantly, in order to be observable it requires the entanglement between the species to be taken into account. We demonstrate this by comparing the numerically exact results obtained by means of the Multi-Layer Multi-Configuration Time-Dependent Hartree Method for Mixtures to the ones of a species mean-field ansatz. The entanglement-sensitive breathing frequency persists also for unequal post-quench traps where the center-of-mass cannot be decoupled. Finally, we analyze the impact of parity symmetry on the breathing dynamics by initializing a state of odd global parity. We evidence a striking resemblance to the ground state breathing dynamics.

How the Interplay among Conformational Disorder, Solvation, Local, and Charge-Transfer Excitations Affects the Absorption Spectrum and Photoinduced Dynamics of Perylene Diimide Dimers: A Molecular Dynamics/Quantum Vibronic Approach.

In this contribution we present a mixed quantum-classical dynamical approach for the computation of vibronic absorption spectra of molecular aggregates and their nonadiabatic dynamics, taking into account the coupling between local excitations (LE) and charge-transfer (CT) states. The approach is based on an adiabatic (Ad) separation between the soft degrees of freedom (DoFs) of the system and the stiff vibrations, which are described by the quantum dynamics (QD) of wave packets (WPs) moving on the coupled potential energy surfaces (PESs) of the LE and CT states. These PESs are described with a linear vibronic coupling (LVC) Hamiltonian, parameterized by an overlap-based diabatization on the grounds of time-dependent density functional theory computations. The WPs time evolution is computed with the multiconfiguration time-dependent Hartree method, using effective modes defined through a hierarchical representation of the LVC Hamiltonian. The soft DoFs are sampled with classical molecular dynamics (MD), and the coupling between the slow and fast DoFs is included by recomputing the key parameters of the LVC Hamiltonians, specifically for each MD configuration. This method, named Ad-MD|gLVC, is applied to a perylene diimide (PDI) dimer in acetonitrile and water solutions, and it is shown to accurately reproduce the change in the vibronic features of the absorption spectrum upon aggregation. Moreover, the microscopic insight offered by the MD trajectories allows for a detailed understanding of the role played by the fluctuation of the aggregate structure on the shape of the vibronic spectrum and on the population of LE and CT states. The nonadiabatic QD predicts an extremely fast (∼50 fs) energy transfer between the two LEs. CT states have only a moderate effect on the absorption spectrum, despite the fact that after photoexcitation they are shown to acquire a fast and non-negligible population, highlighting their relevance in dictating the charge separation and transport in PDI-based optical devices.

Predicting Molecular Photochemistry Using Machine-Learning-Enhanced Quantum Dynamics Simulations.

The processes which occur after molecules absorb light underpin an enormous range of fundamental technologies and applications, including photocatalysis to enable new chemical transformations, sunscreens to protect against the harmful effects of UV overexposure, efficient photovoltaics for energy generation from sunlight, and fluorescent probes to image the intricate details of complex biomolecular structures. Reflecting this broad range of applications, an enormously versatile set of experiments are now regularly used to interrogate light-driven chemical dynamics, ranging from the typical ultrafast transient absorption spectroscopy used in many university laboratories to the inspiring central facilities around the world, such as the next-generation of X-ray free-electron lasers.Computer simulations of light-driven molecular and material dynamics are an essential route to analyzing the enormous amount of transient electronic and structural data produced by these experimental sources. However, to date, the direct simulation of molecular photochemistry remains a frontier challenge in computational chemical science, simultaneously demanding the accurate treatment of molecular electronic structure, nuclear dynamics, and the impact of nonadiabatic couplings.To address these important challenges and to enable new computational methods which can be integrated with state-of-the-art experimental capabilities, the past few years have seen a burst of activity in the development of "direct" quantum dynamics methods, merging the machine learning of potential energy surfaces (PESs) and nonadiabatic couplings with accurate quantum propagation schemes such as the multiconfiguration time-dependent Hartree (MCTDH) method. The result of this approach is a new generation of direct quantum dynamics tools in which PESs are generated in tandem with wave function propagation, enabling accurate "on-the-fly" simulations of molecular photochemistry. These simulations offer an alternative route toward gaining quantum dynamics insights, circumventing the challenge of generating ab initio electronic structure data for PES fitting by instead only demanding expensive energy evaluations as and when they are needed.In this Account, we describe the chronological evolution of our own contributions to this field, focusing on describing the algorithmic developments that enable direct MCTDH simulations for complex molecular systems moving on multiple coupled electronic states. Specifically, we highlight active learning strategies for generating PESs during grid-based quantum chemical dynamics simulations, and we discuss the development and impact of novel diabatization schemes to enable direct grid-based simulations of photochemical dynamics; these developments are highlighted in a series of benchmark molecular simulations of systems containing multiple nuclear degrees of freedom moving on multiple coupled electronic states. We hope that the ongoing developments reported here represent a major step forward in tools for modeling excited-state chemistry such as photodissociation, proton and electron transfer, and ultrafast energy dissipation in complex molecular systems.

Analyzing Grid-Based Direct Quantum Molecular Dynamics Using Non-Linear Dimensionality Reduction.

Grid-based schemes for simulating quantum dynamics, such as the multi-configuration time-dependent Hartree (MCTDH) method, provide highly accurate predictions of the coupled nuclear and electronic dynamics in molecular systems. Such approaches provide a multi-dimensional, time-dependent view of the system wavefunction represented on a coordinate grid; in the case of non-adiabatic simulations, additional information about the state populations adds a further layer of complexity. As such, wavepacket motion on potential energy surfaces which couple many nuclear and electronic degrees-of-freedom can be extremely challenging to analyse in order to extract physical insight beyond the usual expectation-value picture. Here, we show that non-linear dimensionality reduction (NLDR) methods, notably diffusion maps, can be adapted to extract information from grid-based wavefunction dynamics simulations, providing insight into key nuclear motions which explain the observed dynamics. This approach is demonstrated for 2-D and 9-D models of proton transfer in salicylaldimine, as well as 8-D and full 12-D simulations of cis-trans isomerization in ethene; these simulations demonstrate how NLDR can provide alternative views of wavefunction dynamics, and also highlight future developments.