New Algorithms to Generate Permutationally Invariant Polynomials and Fundamental Invariants for Potential Energy Surface Fitting

Symmetric functions, such as Permutationally Invariant Polynomials (PIPs) and Fundamental Invariants (FIs), are effective and concise descriptors for incorporating permutation symmetry into neural network (NN) potential energy surface (PES) fitting. The traditional algorithm for generating such symmetric polynomials has a factorial time complexity of N!, where N is the number of identical atoms, posing a significant challenge to applying symmetric polynomials as descriptors of NN PESs for larger systems, particularly with more than 10 atoms. Herein, we report a new algorithm which has only linear time complexity for identical atoms. It can tremendously accelerate generation process of symmetric polynomials for molecular systems. The proposed algorithm is based on graph connectivity analysis following the action of the generation set of molecular permutational group. For instance, in the case of calculating the invariant polynomials for a 15-atom molecule, such as tropolone, our algorithm is approximately 2 million times faster than the previous method. The efficiency of the new algorithm can be further enhanced with increasing molecular size and number of identical atoms, making the FI-NN approach feasible for systems with over 10 atoms and high symmetry demands.

Zero-Point-Energy Driven Isotopic Exchange of the [H3O]- anion Probed by Mid-Infrared Action Spectroscopy

We present the first observation of vibrational transitions in the [H3O]- anion, an intermediate in the anion-molecule reaction of water, H2O, and hydride, H-, using a laser-induced isotopic H/D exchange reaction action spectroscopy scheme applied to anions. The observed bands are assigned as the fundamental and first overtone of the H2O-H- vibrational stretching mode, based on anharmonic calculations within the vibrational perturbation theory and vibrational configuration interaction. Although the D2O·D- species has the lowest energy, our experiments confirm the D2O·H- isotope to be a sink of the H/D exchange reaction. Ab initio calculations corroborate that the formation of D2O·H- is favored, as the zero-point-energy difference is larger between D2 and H2 than between D2O·H- and D2O·D-.

Accurate fundamental invariant-neural network representation of ab initio potential energy surfaces

Highly accurate potential energy surfaces are critically important for chemical reaction dynamics. The large number of degrees of freedom and the intricate symmetry adaption pose a big challenge to accurately representing potential energy surfaces (PESs) for polyatomic reactions. Recently, our group has made substantial progress in this direction by developing the fundamental invariant-neural network (FI-NN) approach. Here, we review these advances, demonstrating that the FI-NN approach can represent highly accurate, global, full-dimensional PESs for reactive systems with even more than 10 atoms. These multi-channel reactions typically involve many intermediates, transition states, and products. The complexity and ruggedness of this potential energy landscape present even greater challenges for full-dimensional PES representation. These PESs exhibit a high level of complexity, molecular size, and accuracy of fit. Dynamics simulations based on these PESs have unveiled intriguing and novel reaction mechanisms, providing deep insights into the intricate dynamics involved in combustion, atmospheric, and organic chemistry.

Validating experiments for the reaction H2 + NH2- by dynamical calculations on an accurate full-dimensional potential energy surface

Ion-molecule reactions play key roles in the field of ion related chemistry. As a prototypical multi-channel ion-molecule reaction, the reaction H₂ + NH₂^- → NH₃ + H^- has been studied for decades. In this work, we develop a new globally accurate potential energy surface (PES) for the title system based on hundreds of thousands of sampled points over a wide dynamically relevant region that covers long-range interacting configuration space. The permutational invariant polynomial-neural network (PIP-NN) method is used for fitting and the resulting total root mean squared error (RMSE) is extremely small, 0.026 kcal mol^-1. Extensive dynamical and kinetic calculations are carried out on this PIP-NN PES. Impressively, a unique phenomenon of significant reactivity suppression by exciting the rotational mode of H₂ is reported, supported by both the quasi-classical trajectory (QCT) and quantum dynamics (QD) calculations. Further analysis uncovers that exciting the H₂ rotational mode would prevent the formation of the reactant complex and thus suppress the reactivity. The calculated rate coefficients for H₂/D₂ + NH₂^- agree well with the experimental results, which show an inverse temperature dependence from 50 to 300 K, consistent with the capture nature of this barrierless reaction. The significant kinetic isotope effect observed by experiments is well reproduced by the QCT computations as well.

Influence of local microenvironment on the double hydrogen transfer in porphycene

We performed time-resolved transient absorption and fluorescence anisotropy measurements in order to study tautomerization of porphycene in rigid polymer matrices at cryogenic temperatures. Studies were carried out in poly(methyl methacrylate) (PMMA), poly(vinyl butyral) (PVB), and poly(vinyl alcohol) (PVA). The results prove that in all studied media hydrogen tunnelling plays a significant role in the double hydrogen transfer which becomes very sensitive to properties of the environment below approx. 150 K. We also demonstrate that there exist two populations of porphycene molecules in rigid media: "hydrogen-transferring" molecules, in which tautomerization occurs on time scales below 1 ns and "frozen" molecules in which double hydrogen transfer is too slow to be monitored with nanosecond techniques. The number of "frozen" molecules increases when the sample is cooled. We explain this effect by interactions of guest molecules with a rigid host matrix which disturbs symmetry of porphycene and hinders tunnelling. Temperature dependence of the number of hydrogen-transferring molecules suggests that the factor which restores the symmetry of the double-minimum potential well in porphycene are intermolecular vibrations localized in separated regions of the amorphous polymer.

Dynamics and kinetics of the OH + HO2 → H2O + O2 (1Δg) reaction on a global full-dimensional singlet-state potential energy surface

The reaction dynamics and kinetics of OH + HO₂ → H₂O + O₂ on the singlet state were revealed by theory, based on an accurate full-dimensional PES.