Breakdown of energy transfer gap laws revealed by full-dimensional quantum scattering between HF molecules

The evolution of machine learning potentials for molecules, reactions and materials

Recent years have witnessed the fast development of machine learning potentials (MLPs) and their widespread applications in chemistry, physics, and material science. By fitting discrete ab initio data faithfully to continuous and symmetry-preserving mathematical forms, MLPs have enabled accurate and efficient atomistic simulations in a large scale from first principles. In this review, we provide an overview of the evolution of MLPs in the past two decades and focus on the state-of-the-art MLPs proposed in the last a few years for molecules, reactions, and materials. We discuss some representative applications of MLPs and the trend of developing universal potentials across a variety of systems. Finally, we outline a list of open challenges and opportunities in the development and applications of MLPs.

Rotational energy transfer in the collision of N2O with He atom

The quantum state-to-state rotationally inelastic quenching of N2O by colliding with a He atom is studied on an ab initio potential energy surface with N2O lying on its vibrational ground state. The cross sections for collision energies from 10-6-100 cm-1 and rate constants from 10-5-10 K are calculated employing the fully converged quantum close-coupling method for the quenching of the j = 1-6 rotational states of N2O. Numerous van der Waals shapes or Feshbach resonances are observed; the cross sections of different channels are found to follow the Wigner scaling law in the cold threshold regime and may intersect with each other. In order to interpret the mechanism and estimate the cross sections of the rotational energy transfer, we propose a minimal classical model of collision between an asymmetric double-shell ellipsoid and a point particle. The classical model reproduces the quantum scattering results and points out the attractive interactions and the potential asymmetry can affect the collision process. The resulting insights are expected to expand our interpretations of inelastic scattering and energy transfer in molecular collisions.

An effective approximation of Coriolis coupling in reactive scattering: application to the time-dependent wave packet calculations

Coriolis coupling plays a crucial role in reactive scattering, but dynamics calculations including the complete Coriolis coupling significantly increase the difficulty of numerical evolution due to the corresponding expensive matrix processing. The coupled state approximation that completely ignores the off-diagonal Coriolis coupling saves computational cost significantly but its error is usually unacceptable. In this paper, an improved coupled state approximation inspired by recently published results [D. Yang, X. Hu, D. H. Zhang and D. Xie, J. Chem. Phys., 2018, 148, 084101.] of the inelastic scattering problem is extended to deal with the reactive scattering. The calculations using the time-dependent wave packet method reveal that the new method can accurately reproduce the rigorous results of the H + HD (j0 < 3) → D + H2 reaction and immensely improve the computational efficiency. Additionally, we extend the new method to the non-adiabatic Li(2p) + H2 (v0 = 0, j0 = 0, 1) → H + LiH reaction, showcasing its advantages of low computational cost and high accuracy.

Recent advances in quantum theory on ro-vibrationally inelastic scattering

Molecular collisions are of fundamental importance in understanding intermolecular interaction and dynamics. Its importance is accentuated in cold and ultra-cold collisions because of the dominant quantum mechanical nature of the scattering. We review recent advances in the time-independent approach to quantum mechanical characterization of non-reactive scattering in tetratomic systems, which is ideally suited for large collisional de Broglie wavelengths characteristic in cold and ultracold conditions. We discuss quantum scattering algorithms between two diatoms and between a triatom and an atom and their implementation, as well as various approximate schemes. They not only enable the characterization of collision dynamics in realistic systems but also serve as benchmarks for developing more approximate methods.

Full-dimensional quantum studies of vibrational energy transfer dynamics between H2O and Ar: theory assessing experiment

We report the first full-dimensional quantum mechanical calculations of the ro-vibrational inelastic scattering dynamics between water molecules and argon atoms on an accurate potential energy surface, using a recently developed time-independent quantum method based on the close-coupling approach. The state-to-state integral cross-sections and rate coefficients show strong observance of gap laws. The calculated thermal rate coefficients for the relaxation of the stretching fundamental states of H₂O are in good agreement with experimental values, while those for the bending overtone state are approximately five times smaller than the values extracted through a previous kinetic modeling of fluorescence decay data. Our state-specific quantum scattering results suggest the need to reassess the kinetic modeling of the experimental data. This work advanced our understanding of the quantum dynamics of vibrationally inelastic energy transfer processes involving polyatomic molecules.

Vibrational energy pooling via collisions between asymmetric stretching excited CO2: a quasi-classical trajectory study on an accurate full-dimensional potential energy surface

In low temperature plasmas, energy transfer between asymmetric stretching excited CO₂ molecules can be highly efficient, which leads to further excitation (and de-excitation) of the CO₂ molecules: CO₂(v_as) + CO₂(v_as) → CO₂(v_as + 1) + CO₂(v_as - 1). Through such a vibrational ladder climbing mechanism, CO₂ can be activated and eventually dissociates. To gain mechanistic insight of such processes, a full-dimensional accurate potential energy surface (PES) for the CO₂ + CO₂ system is developed using the permutational invariant polynomial-neural network method based on CCSD(T)-F12a/AVTZ energies at about 39 000 geometries. This PES is used in quasi-classical trajectory (QCT) studies of the vibrational energy transfer between CO₂ molecules excited in the asymmetric stretching mode. A machine learning algorithm is used to determine state-specific rate coefficients for the vibrational transfer processes from a limited data set. In addition to the CO₂(v_as + 1) + CO₂(v_as - 1) channel, the QCT simulations revealed significant contributions from the CO₂(v_as + 2,3) + CO₂(v_as - 2,3) channels, particularly at low collision energies/temperatures. These multi-vibrational-quantum processes are attributed to enhanced energy flow in the collisional complex formed by enhanced dipole-dipole interaction between asymmetric stretching excited CO₂ molecules.

A Time-Independent Quantum Approach to Ro-vibrationally Inelastic Scattering between Atoms and Triatomic Molecules

A full-dimensional time-independent quantum mechanical theory for ro-vibrationally inelastic scattering of triatomic molecules with atoms is formulated. The Jacobi-Radau coordinate system used in the calculation allows not only a near perfect description of the vibrational problem but also the adaptation of the exchange symmetry for A₂B type triatoms. The S-matrix elements are obtained by solving the close-coupling equations with contracted basis using the log-derivative method. This method is applied to the inelastic scattering of the water molecule by a chlorine atom, which sheds light on the energy gap law in energy transfer in atom-triatom collisions.

Quantum dynamics of the energy transfer for vibrationally excited HF (v = 7) colliding with D2 (v = 0): Theory assessing experiment

It is still challenging to accurately qualify the rate coefficients for vibrationally excited molecules in experiment. In particular, for the energy transfer between HF (v = 7) and D₂ (v = 0), which is a prototype for near resonant collisional transfer of vibrational excitation from one molecule to the other, the two available experimental results of rate coefficients contradict each other by a factor of nearly 20. In order to benchmark these data, in this work, the rate coefficients of vibration-vibration energy transfer processes of this system at temperatures ranging from 100 to 1500 K were calculated by employing the coupled-states approximation based on our recently developed full-dimensional ab initio intermolecular potential energy surface. The state-to-state rate coefficients were found to follow the general energy gap law. The calculated total vibration-vibration energy transfer rate coefficients decrease with the increase in the angular momentum of HF at most temperatures. The vibrational relaxation rate coefficient decreases monotonously with the temperature, and the calculated result of 8.1 × 10^-11 cm³ mol^-1 s^-1 at room temperature is in very good agreement with the experimental value reported by Dzelzkalns and Kaufman [J. Chem. Phys. 77, 3508 (1982)].

Quantum Dynamics of Rotational Energy Transfer Processes for N2-HF and N2-DF Systems

The rate coefficients of rotationally inelastic collision processes for N₂-HF as well as N₂-DF systems were calculated by applying the recently developed coupled-states approximation including the nearest neighbor Coriolis couplings approach, based on the full-dimensional ab initio intermolecular potential energy surface. It was found that the energy gap law governs these energy transfer processes. For rotational quenching of N₂ (j₁ = 2-10) by the ground rotational state of HF, j₁ = 6 and 5 have the maximum quenching rate for ortho-N₂ and para-N₂, respectively. Quenching rate coefficients for initially excited HF and DF (j₂ = 1) in collisions with N₂ were also reported, where N₂-DF has a larger quenching rate than N₂-HF due to larger density of states of the N₂-DF system.

Evaluating the Transition Towards Post-Carbon Cities: A Literature Review

To achieve the new European targets concerning CO2 emission reduction, the concept of a post-carbon city has been promoted, which is focused on low-energy and low-emission buildings provided with intelligent heating and cooling systems, electric and hybrid cars, and better public transport. This paradigm entails the inclusion of aspects not strictly related to energy exploitation but referring to environmental, social, and economic domains, such as improvement in local energy security, people’s opinion on different energy solutions, economic co-benefits for private users, environmental externalities, and so on. In this domain, it is of particular importance to provide the decision makers with evaluation tools able to consider the complexity of the impacts, thus leading to the choice of the most sustainable solutions. The paper aims to investigate the scientific literature in the context of evaluation frameworks for supporting decision problems related to the energy transition. The review is carried out through the scientific database SCOPUS. The analysis allows for systematizing the contributions according to the main families of evaluation methodologies, discussing to what extent they can be useful in real-world applications. The paper also proposes emerging trends and innovative research lines in the domain of energy planning and urban management. While the energy transition is an important trend, the analysis showed that few studies were conducted on the evaluation of projects, plans, and policies that aim to reach post-carbon targets. The scales of application refer mainly to global or national levels, while few studies have been developed at the district level. Life cycle thinking techniques, such as life cycle assessment and cost-benefit analysis, were widely used in this research field.