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Recent advances in machine learning have facilitated numerically accurate solution of the electronic Schr\"{o}dinger equation (SE) by integrating various neural network (NN)-based wavefunction ansatzes with variational Monte Carlo methods. Nevertheless, such NN-based methods are all based on the Born-Oppenheimer approximation (BOA) and require computationally expensive training for each nuclear configuration. In this work, we propose a novel NN architecture, Schr\"{o}dingerNet, to solve the full electronic-nuclear SE by defining a loss function designed to equalize local energies across the system. This approach is based on a translationally, rotationally and permutationally symmetry-adapted total wavefunction ansatz that includes both nuclear and electronic coordinates. This strategy not only allows for an efficient and accurate generation of a continuous potential energy surface at any geometry within the well-sampled nuclear configuration space, but also incorporates non-BOA corrections, through a single training process. Comparison with benchmarks of atomic and small molecular systems demonstrates its accuracy and efficiency., Comment: 5 figure

To understand the recently observed mysterious non-adiabatic energy transfer for hyperthermal H atom scattering from a semiconductor surface, Ge(111)c(2*8), we present a mixed quantum-classical non-adiabatic molecular dynamics model based on time-dependent evolution of Kohn-Sham orbitals and a classical path approximation. Our results suggest that facile non-adiabatic transitions occur selectively at the rest atom site, featuring excitation of valance band electrons to the conduction band, but not at the adatom site. This drastic site specificity can be attributed to the changes of the local band structure upon energetic H collisions at different surface sites, leading to transient near-degeneracies and significant couplings between occupied and unoccupied orbitals at the rest atom, but not at the adatom. These insights shed valuable light on the collisional induced non-adiabatic dynamics at semiconductor surfaces.

The calcium monofluoride (CaF) molecule has emerged as a promising candidate for precision measurements, quantum simulation, and ultracold chemistry experiments. Inelastic and reactive collisions of laser cooled CaF molecules in optical tweezers have recently been reported and collisions of cold Li atoms with CaF are of current experimental interest. In this paper, we report ab initio electronic structure and full-dimensional quantum dynamical calculations of the Li + CaF $\to$ LiF + Ca chemical reaction. The electronic structure calculations are performed using the internally contracted multi-reference configuration-interaction method with Davidson correction (MRCI+Q). An analytic fit of the interaction energies is obtained using a many-body expansion method. A coupled-channel quantum reactive scattering approach implemented in hyperspherical coordinates is adopted for the scattering calculations under cold conditions. Results show that the Li + CaF reaction populates several low-lying vibrational levels and many rotational levels of the product LiF molecule and that the reaction is inefficient in the 1-100 mK regime allowing sympathetic cooling of CaF by collisions with cold Li atoms.

The H$_2$+H$_2$ system has long been considered as a benchmark system for ro-vibrational energy transfer in bimolecular collisions. However, most studies thus far have focused on collisions involving H$_2$ molecules in the ground vibrational level or in the first excited vibrational state. While H$_2$+H$_2$/HD collisions have received wide attention due to the important role they play in astrophysics, D$_2$+D$_2$ collisions have received much less attention. Recently, Zhou et al. [Nat. Chem. 4 658 (2022)] examined stereodynamic aspects of rotational energy transfer in collisions of two aligned D$_2$ molecules prepared in the $v=2$ vibrational level and $j=2$ rotational level. Here, we report quantum calculations of rotational and vibrational energy transfer in collisions of two D$_2$ molecules prepared in vibrational levels up to $v=2$ and identify key resonance features that contribute to the angular distribution in the experimental results of Zhou et al. The quantum scattering calculations were performed in full dimensionality and using the rigid-rotor approximation using a recently-developed highly-accurate six-dimensional potential energy surface for the H$_4$ system that allows descriptions of collisions involving highly vibrationally excited H$_2$ and its isotopologues., Comment: 9 pages, 12 figures

Optical pumping of molecules provides unique opportunities for control of chemical reactions at a wide range of rotational energies. This work reports a chemical reaction with extreme rotational excitation of a reactant and its kinetic characterization. We investigate the chemical reactivity for the hydrogen abstraction reaction SiO$^+$ + H$_2$ $\rightarrow$ SiOH$^+$ + H in an ion trap. The SiO$^+$ cations are prepared in a narrow rotational state distribution, including super-rotor states with rotational quantum number $\it{(j)}$ as high as 170, using a broad-band optical pumping method. We show that the super-rotor states of SiO$^+$ substantially enhance the reaction rate, a trend reproduced by complementary theoretical studies. We reveal the mechanism for the rotational enhancement of the reactivity to be a strong coupling of the SiO$^+$ rotational mode with the reaction coordinate at the transition state on the dominant dynamical pathway.

Resonant scattering of optically state-prepared and aligned molecules in the cold regime allows the most detailed interrogation and control of bimolecular collisions. This technique has recently been applied to collisions of two aligned ortho-D2 molecules prepared in the j=2 rotational level of the v=2 vibrational manifold using the Stark-induced adiabatic Raman passage technique. Here, we develop the theoretical formalism for collisions of two aligned molecules and apply our approach to state-prepared D2(v=2,j=2) + D2(v=2,j=2) --> D2(v=2,j=2) + D2(v=2,j=0) collisions. Quantum scattering calculations were performed in full-dimensionality on an accurate H$_2$-H$_2$ interaction potential. Key features of the experimental angular distributions are reproduced and attributed primarily to a partial wave resonance with orbital angular momentum L=4

Trapped Be+ ions are a leading platform for quantum information science [1], but reactions with background gas species, such as H2 and H2O, result in qubit loss. Our experiment reveals that the BeOH+ ion is the final trapped ion species when both H2 and H2O exist in a vacuum system with cold, trapped Be+. To understand the loss mechanism, low-temperature reactions between sympathetically cooled BeD+ ions and H2O molecules have been investigated using an integrated, laser-cooled Be+ ion trap and high-resolution Time-of-Flight (TOF) mass spectrometer (MS) [2]. Among all the possible products,BeH2O+, H2DO+, BeOD+, and BeOH+, only the BeOH+ molecular ion was observed experimentally, with the assumed co-product of HD. Theoretical analyses based on explicitly correlated restricted coupled cluster singles, doubles, and perturbative triples (RCCSD(T)-F12) method with the augmented correlation-consistent polarized triple zeta (AVTZ) basis set reveal that two intuitive direct abstraction product channels, Be + H2DO+ and D + BeH2O+, are not energetically accessible at the present reaction temperature (~150 K). Instead, a double displacement BeOH+ + HD product channel is accessible due to a large exothermicity of 1.885 eV through a submerged barrier in the reaction pathway. While the BeOD+ + H2 product channel has a similar exothermicity, the reaction pathway is dynamically unfavourable, as suggested by a Sudden Vector Projection analysis. This work sheds light on the origin of the loss and contaminations of the laser-cooled Be+ ions in quantum-information experiments.

We examine rotational transitions of HCl in collisions with H$_2$ by carrying out quantum mechanical close-coupling and quasi-classical trajectory calculations on a recently developed globally accurate full-dimensional ab initio potential energy surface for the H$_3$Cl system. Signatures of rainbow scattering in rotationally inelastic collisions are found in the state resolved integral and differential cross sections as functions of the impact parameter (initial orbital angular momentum) and final rotational quantum number. We show the coexistence of distinct dynamical regimes for the HCl rotational transition driven by the short-range repulsive and long-range attractive forces whose relative importance depends on the collision energy and final rotational state suggesting that classification of rainbow scattering into rotational and $l$-type rainbows is effective for H$_2$+HCl collisions. While the quasi-classical trajectory method satisfactorily predicts the overall behavior of the rotationally inelastic cross sections, its capability to accurately describe signatures of rainbow scattering appears to be limited for the present system., Comment: 9 pages, 6 figures (Supplementary Material: 3 pages, 5 figures)

Chemical reactions represent a class of quantum problems that challenge both the current theoretical understanding and computational capabilities. Reactions that occur at ultralow temperatures provide an ideal testing ground for quantum chemistry and scattering theories, as they can be experimentally studied with unprecedented control, yet display dynamics that are highly complex. Here, we report the full product state distribution for the reaction 2KRb $\rightarrow$ K$_2$ + Rb$_2$. Ultracold preparation of the reactants grants complete control over their initial quantum degrees of freedom, while state-resolved, coincident detection of both products enables the measurement of scattering probabilities into all 57 allowed rotational state-pairs. Our results show an overall agreement with a state-counting model based on statistical theory, but also reveal several deviating state-pairs. In particular, we observe a strong suppression of population in the state-pair closest to the exoergicity limit, which we precisely determine to be $9.7711^{+0.0007}_{-0.0005}$ cm$^{-1}$, as a result of the long-range potential inhibiting the escape of products. The completeness of our measurements provides a valuable benchmark for quantum dynamics calculations beyond the current state-of-the-art., Comment: 31 pages, 6 figures

Several full-dimensional potential energy surfaces (PESs) are reported for vibrating CO adsorbates at two coverages on a rigid NaCl(100) surface based on first principles calculations. These PESs reveal a rather flat energy landscape for physisorption of vibrationless CO on NaCl(100), evidenced by various C-down adsorption patterns within a small energy range. Agreement with available experimental results is satisfactory, although quantitative differences exist. These PESs are used to explore isomerization pathways between the C-down and higher energy O-down configurations, which reveal a significant isomerization barrier. As CO vibration is excited, however, the energy order of the two isomer changes, which helps to explain the experimental observed flipping of vibrationally excited CO adsorbates.

Stereodynamic control of resonant molecular collisions has emerged as a new frontier in cold molecule research. Recent experimental studies have focused on weakly interacting molecular systems such as HD collisions with H$_2$, D$_2$ and He. We report here the possibility of such control in strongly interacting systems taking rotational relaxation in cold collisions of HCl and H$_2$. Using explicit quantum scattering calculations in full six dimensions it is shown that robust control of the collision dynamics is possible even when multiple (overlapping) shape-resonances coexist in a narrow energy range, indicating that cold stereochemistry offers great promise for many molecules beyond simple systems. We demonstrate a striking case where two prominent peaks in overlapping resonances are switched-off simultaneously by suitable alignment of the HCl molecule., Comment: 5 pages, 4 figures, 31 references and Supplemental Material (5 pages, 5 figures)

Controlling the pathways and outcomes of reactions is a broadly pursued goal in chemistry. In gas phase reactions, this is typically achieved by manipulating the properties of the reactants, including their translational energy, orientation, and internal quantum state. In contrast, here we influence the pathway of a reaction via its intermediate complex, which is generally too short-lived to be affected by external processes. In particular, the ultracold preparation of potassium-rubidium (KRb) reactants leads to a long-lived intermediate complex (K$_2$Rb$_2^*$), which allows us to steer the reaction away from its nominal ground-state pathway onto a newly identified excited-state pathway using a laser source at 1064 nm, a wavelength commonly used to confine ultracold molecules. Furthermore, by monitoring the change in the complex population after the sudden removal of the excitation light, we directly measure the lifetime of the complex to be $360 \pm 30$ ns, in agreement with our calculations based on the Rice-Ramsperger-Kassel-Marcus (RRKM) statistical theory. Our results shed light on the origin of the two-body loss widely observed in ultracold molecule experiments. Additionally, the long complex lifetime, coupled with the observed photo-excitation pathway, opens up the possibility to spectroscopically probe the structure of the complex with high resolution, thus elucidating the reaction dynamics., Comment: 18 pages, 5 figures

A high-dimensional potential energy surface (PES) for CO interaction with the Au(111) surface is developed using a machine-learning algorithm. Including both molecular and surface coordinates, this PES enables the simulation of the recent experiment on scattering of vibrationally excited CO from Au(111). Trapping in a physisorption well is observed to increase with decreasing incidence energy. While energy dissipation of physisorbed CO is slow, due to weak coupling with both the phonons and electron-hole pairs, its access to the chemisorption well facilitates fast vibrational relaxation of CO through nonadiabatic coupling with surface electron-hole pairs.

Measuring inelastic rates with partial wave resolution requires temperatures close to a Kelvin or below, even for the lightest molecule. In a recent experiment Perreault et al. [1] studied collisional relaxation of excited HD molecules in the v = 1, j = 2 state by para- and ortho-H2 at a temperature of about 1 K, extracting the angular distribution of scattered HD in the v = 1,j = 0 state. By state-preparation of the HD molecules, control of the angular distribution of scattered HD was demonstrated. Here, we report a first-principles simulation of that experiment which enables us to attribute the main features of the observed angular distribution to a single L = 2 partial-wave shape resonance. Our results demonstrate important stereodynamical insights that can be gained when numerically-exact quantum scattering calculations are combined with experimental results in the few-partial-wave regime., Comment: 5 pages, 4 figures

The mode specific dissociative chemisorption dynamics of ammonia on the Ru(0001) surface is investigated using a quasi-classical trajectory (QCT) method on a new global potential energy surface (PES) with twelve dimensions. The PES is constructed by fitting 92524 density functional theory points using the permutation invariant polynomial-neural network method, which rigorously enforces the permutation symmetry of the three hydrogen atoms as well as the surface periodicity. The PES enables highly efficient QCT simulations as well as future quantum dynamical studies of the scattering/dissociation dynamics. The QCT calculations yield satisfactory agreement with experiment and suggest strong mode specificity, in general agreement with the predictions of the Sudden Vector Projection model.

The fragmentation dynamics of predissociative SO2(C1B2) is investigated on an accurate adiabatic potential energy surface (PES) determined from high level ab initio data. This singlet PES features non-C2v equilibrium geometries for SO2, which are separated from the SO + O dissociation limit by a barrier resulting from a conical intersection with a repulsive singlet state. The ro-vibrational state distribution of the SO fragment is determined quantum mechanically for many predissociative states of several sulfur isotopomers of SO2. Significant rotational and vibrational excitations are found in the SO fragment. It is shown that these fragment internal state distributions are strongly dependent on the predissociative vibronic states, and the excitation typically increases with the photon energy.

This Feature Article presents an overview of the current status of Ring Polymer Molecular Dynamics (RPMD) rate theory. We first analyze the RPMD approach and its connection to quantum transition-state theory. We then focus on its practical applications to prototypical chemical reactions in the gas phase, which demonstrate how accurate and reliable RPMD is for calculating thermal chemical reaction rate coefficients in multifarious cases. This review serves as an important checkpoint in RPMD rate theory development, which shows that RPMD is shifting from being just one of recent novel ideas to a well-established and validated alternative to conventional techniques for calculating thermal chemical rate coefficients. We also hope it will motivate further applications of RPMD to various chemical reactions.

Rate constants for the N + C2 reaction have been measured in a continuous supersonic flow reactor over the range 57 K to 296 K by the relative rate technique employing the N + OH - H + NO reaction as a reference. Excess concentrations of atomic nitrogen were produced by the microwave discharge method and C2 and OH radicals were created by the in-situ pulsed laser photolysis of precursor molecules C2Br4 and H2O2 respectively. In parallel, quantum dynamics calculations were performed based on an accurate global potential energy surfaces for the three lowest lying quartet states of the C2N molecule. The 14A" potential energy surface is barrierless, having two deep potential wells corresponding to the NCC and CNC intermediates. Both the experimental and theoretical work show that the rate constant decreases to low temperature, although the experimentally measured values fall more rapidly than the theoretical ones except at the lowest temperatures. Astrochemical simulations indicate that this reaction could be the dominant source of CN in dense interstellar clouds., Comment: Accepted to Physical Chemistry Chemical Physics

Chirped-Pulse millimetre-Wave (CPmmW) rotational spectroscopy provides a new class of information about photolysis transition state(s). Measured intensities in rotational spectra determine species-isomer-vibrational populations, provided that rotational populations can be thermalized. The formation and detection of S0 vinylidene is discussed in the limits of low and high initial rotational excitation. CPmmW spectra of 193 nm photolysis of Vinyl Cyanide (Acrylonitrile) contain J=0-1 transitions in more than 20 vibrational levels of HCN, HNC, but no transitions in vinylidene or highly excited local-bender vibrational levels of acetylene. Reasons for the non-observation of the vinylidene co-product of HCN are discussed., Comment: Accepted by Faraday Discussions