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.

Quantifying the Effect of Initial Fluctuations on Isospin-Sensitive Observables from Heavy-Ion Collisions at Intermediate Energies

Initial fluctuation is one of the ingredients that washes fingerprints of the nuclear symmetry energy on observables in heavy-ion collisions. By artificially using the same initial nuclei in all collision events, the effect of the initial fluctuation on isospin-sensitive observables, e.g., the yield ratio of free neutrons with respect to protons Nn/Np, 3H/3He yield ratio, the yield ratio between charged pions π−/π+, and the elliptic flow ratio or difference between free neutrons and protons v2n/v2p (v2n-v2p), are studied within the ultrarelativistic quantum molecular dynamics (UrQMD) model. In practice, Au + Au collisions with impact parameter b = 5 fm and beam energy Elab = 400 MeV/nucleon are calculated. It is found that the effect of the initialization on the yields of free protons and neutrons is small, while for the yield of pions, the directed and elliptic flows are found to be apparently influenced by the choice of initialization because of the strong memory effects. Regarding the isospin-sensitive observables, the effect of the initialization on Nn/Np and 3H/3He is negligible, while π−/π+ and v2n/v2p (v2n-v2p) display a distinct difference among different initializations. The fingerprints of symmetry energy on π−/π+ and v2n/v2p can be either enhanced or reduced when different initializations are utilized.

A universal framework for featurization of atomistic systems

Molecular dynamics simulations are an invaluable tool in numerous scientific fields. However, the ubiquitous classical force fields cannot describe reactive systems, and quantum molecular dynamics are too computationally demanding to treat large systems or long timescales. Reactive force fields based on physics or machine learning can be used to bridge the gap in time and length scales, but these force fields require substantial effort to construct and are highly specific to a given chemical composition and application. A significant limitation of machine learning models is the use of element-specific features, leading to models that scale poorly with the number of elements. This work introduces the Gaussian multipole (GMP) featurization scheme that utilizes physically-relevant multipole expansions of the electron density around atoms to yield feature vectors that interpolate between element types and have a fixed dimension regardless of the number of elements present. We combine GMP with neural networks to directly compare it to the widely used Behler-Parinello symmetry functions for the MD17 dataset, revealing that it exhibits improved accuracy and computational efficiency. Further, we demonstrate that GMP-based models can achieve chemical accuracy for the QM9 dataset, and their accuracy remains reasonable even when extrapolating to new elements. Finally, we test GMP-based models for the Open Catalysis Project (OCP) dataset, revealing comparable performance to graph convolutional deep learning models. The results indicate that this featurization scheme fills a critical gap in the construction of efficient and transferable machine-learned force fields.

Ultrafast dynamics with the exact factorization

The exact factorization of the time-dependent electron–nuclear wavefunction has been employed successfully in the field of quantum molecular dynamics simulations for interpreting and simulating light-induced ultrafast processes. In this work, we summarize the major developments leading to the formulation of a trajectory-based approach, derived from the exact factorization equations, capable of dealing with nonadiabatic electronic processes, and including spin-orbit coupling and the non-perturbative effect of an external time-dependent field. This trajectory-based quantum-classical approach has been dubbed coupled-trajectory mixed quantum-classical (CT-MQC) algorithm, whose performance is tested here to study the photo-dissociation dynamics of IBr. Graphic abstract

Effect of the Width of Gaussian Wave Packets on the Stability of the Nuclei

The role of the range of interaction on the stability of the nuclei propagating with and without momentum dependent interactions is analyzed within the framework of Quantum Molecular Dynamics (QMD) model. A detailed study is carried out by taking different equations of state (i.e., static soft and hard and the momentum dependent soft and hard) for the selected nuclei from 12C to 197Au. Comparison is done by using the standard and the double width of the Gaussian wave packets. We find that the effect of the double width of the Gaussian wave packets on the stability of the initial stage nuclei cannot be neglected. The nuclei having double width do not emit free nucleons for a long period of time. Also, the ground state properties of all the nuclei are described well. In the low mass region, the obtained nuclei are less bound but stable. Heavy mass nuclei have proper binding energy and are stable.

Particle ratios within EPOS, UrQMD and thermal models at AGS, SPS and RHIC energies

The particle ratios [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] measured at AGS, SPS and RHIC energies are compared with large statistical ensembles of 100,000 events deduced from the CRMC EPOS [Formula: see text] and the Ultra-relativistic Quantum Molecular Dynamics (UrQMD) hybrid model. In the UrQMD hybrid model two types of phase transitions are taken into account. All these data are then confronted with the ideal Hadron Resonance Gas Model. The two types of phase transitions are apparently indistinguishable. Apart from [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text], the UrQMD hybrid model agrees well with the CRMC EPOS [Formula: see text]. We also conclude that the CRMC EPOS [Formula: see text] seems to largely underestimate [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text].