Interpolation of multi-sheeted multi-dimensional potential-energy surfaces via a linear optimization procedure

Fitting of Coupled Potential Energy Surfaces via Discovery of Companion Matrices by Machine Intelligence

Fitting coupled potential energy surfaces is a critical step in simulating electronically nonadiabatic chemical reactions and energy transfer processes. Analytic representation of coupled potential energy surfaces enables one to perform detailed dynamics calculations. Traditionally, fitting is performed in a diabatic representation to avoid fitting the cuspidal ridges of coupled adiabatic potential energy surfaces at conical intersection seams. In this work, we provide an alternative approach by carrying out fitting in the adiabatic representation using a modified version of the Frobenius companion matrices, whose usage was first proposed by Opalka and Domcke. Their work involved minimizing the errors in fits of the characteristic polynomial coefficients (CPCs) and diagonalizing the resulting companion matrix, whose eigenvalues are adiabatic potential energies. We show, however, that this may lead to complex eigenvalues and spurious discontinuities. To alleviate this problem, we provide a new procedure for the automatic discovery of CPCs and the diagonalization of a companion matrix by using a special neural network architecture. The method effectively allows analytic representation of global coupled adiabatic potential energy surfaces and their gradients with only adiabatic energy input and without experience-based selection of a diabatization scheme. We demonstrate that the new procedure, called the companion matrix neural network (CMNN), is successful by showing applications to LiH, H3, phenol, and thiophenol.

A diabatization method based upon integrating the diabatic potential gradient difference

In this work we develop a new scheme to construct a diabatic potential energy matrix (DPEM). We propose a diabatization method which is based on integrating the diabatic potential gradient difference to diabatize adiabatic ab initio energies. This method is capable of performing high-precision adiabatic-to-diabatic transformations, with a unique advantage in effectively handling the significant fluctuations in derivative-couplings caused by conical intersection (CI) seams. The above scheme is applied to the DPEM construction of the Na(3p) + H2 → NaH + H reaction. The fitting data including adiabatic energies, energy gradients and derivative-couplings obtained from a previous benchmark DPEM are diabatized and fitted using a general neural network fitting procedure to generate the DPEM. The produced DPEM can effectively describe nonadiabatic processes involving different electronic states. We further perform quantum dynamical calculations on the new DPEM and the previous benchmark DPEM, and the obtained results demonstrate the effectiveness of our scheme.

Quantum simulation of conical intersections

We explore the simulation of conical intersections (CIs) on quantum devices, setting the groundwork for potential applications in nonadiabatic quantum dynamics within molecular systems. The intersecting potential energy surfaces of H3+ are computed from a variance-based contracted quantum eigensolver. We show how the CIs can be correctly described on quantum devices using wavefunctions generated by the anti-Hermitian contracted Schrödinger equation ansatz, which is a unitary transformation of wavefunctions that preserves the topography of CIs. A hybrid quantum-classical procedure is used to locate the seam of CIs. Additionally, we discuss the quantum implementation of the adiabatic to diabatic transformation and its relation to the geometric phase effect. Results on noisy intermediate-scale quantum devices showcase the potential of quantum computers in dealing with problems in nonadiabatic chemistry.

Machine Learning Seams of Conical Intersection: A Characteristic Polynomial Approach

The machine learning of potential energy surfaces (PESs) has undergone rapid progress in recent years. The vast majority of this work, however, has been focused on the learning of ground state PESs. To reliably extend machine learning protocols to excited state PESs, the occurrence of seams of conical intersections between adiabatic electronic states must be correctly accounted for. This introduces a serious problem, for at such points, the adiabatic potentials are not differentiable to any order, complicating the application of standard machine learning methods. We show that this issue may be overcome by instead learning the coordinate-dependent coefficients of the characteristic polynomial of a simple decomposition of the potential matrix. We demonstrate that, through this approach, quantitatively accurate machine learning models of seams of conical intersection may be constructed.

High-fidelity first principles nonadiabaticity: diabatization, analytic representation of global diabatic potential energy matrices, and quantum dynamics

Nonadiabatic dynamics, which goes beyond the Born-Oppenheimer approximation, has increasingly been shown to play an important role in chemical processes, particularly those involving electronically excited states. Understanding multistate dynamics requires rigorous quantum characterization of both electronic and nuclear motion. However, such first principles treatments of multi-dimensional systems have so far been rather limited due to the lack of accurate coupled potential energy surfaces and difficulties associated with quantum dynamics. In this Perspective, we review recent advances in developing high-fidelity analytical diabatic potential energy matrices for quantum dynamical investigations of polyatomic uni- and bi-molecular nonadiabatic processes, by machine learning of high-level ab initio data. Special attention is paid to methods of diabatization, high fidelity construction of multi-state coupled potential energy surfaces and property surfaces, as well as quantum mechanical characterization of nonadiabatic nuclear dynamics. To illustrate the tremendous progress made by these new developments, several examples are discussed, in which direct comparison with quantum state resolved measurements led to either confirmation of the observation or sometimes reinterpretation of the experimental data. The insights gained in these prototypical systems greatly advance our understanding of nonadiabatic dynamics in chemical systems.

A Full-Dimensional Potential Energy Surface and Dynamics of the Multichannel Reaction between H and HO2

In addition to its vital significance in combustion and atmospheric chemistry, the reaction between H' and HO₂ on the ground triplet state represents a prototype with multiple product channels, including H₂ + O₂, OH + OH, O + H₂O, and H + H'O₂. In this work, a full-dimensional accurate potential energy surface (PES) for the title reaction was developed to provide reliable descriptions for all dynamically relevant regions. Using this PES, we adopted the quasi-classical trajectory approach to study the corresponding reaction dynamics, including the reactivity of each product channel and the associated product branching ratio, the product energy distributions, product angular distributions, and associated microscopic mechanisms. For representing distributions of the product energies, such as product translational energy as well as product rotational and vibrational energies, both the traditional histogram and the kernel density estimation (KDE) methods were used and compared. It seems that the features of the resulting distributions in this work are very similar to each other among different methods. The KDE method is suggested for statistics, particularly for those populations with small oscillations in the histogram plot.

High-Fidelity Potential Energy Surfaces for Gas-Phase and Gas-Surface Scattering Processes from Machine Learning

In this Perspective, we review recent advances in constructing high-fidelity potential energy surfaces (PESs) from discrete ab initio points, using machine learning tools. Such PESs, albeit with substantial initial investments, provide significantly higher efficiency than direct dynamics methods and/or high accuracy at a level that is not affordable by on-the-fly approaches. These PESs not only are a necessity for quantum dynamical studies because of delocalization of wave packets but also enable the study of low-probability and long-time events in (quasi-)classical treatments. Our focus here is on inelastic and reactive scattering processes, which are more challenging than bound systems because of the involvement of continua. Relevant applications and developments for dynamical processes in both the gas phase and at gas-surface interfaces are discussed.

A critical comparison of neural network potentials for molecular reaction dynamics with exact permutation symmetry

Several symmetry strategies have been compared in fitting full dimensional accurate potentials for reactive systems based on a neural network approach.

On the higher-order T2 ⊗ (e + t2) Jahn–Teller coupling effects in the photodetachment spectrum of the alanate anion (AlH4−)

The higher-order JT coupling terms (beyond the standard second-order JT theory) are important to understand the first photoelectron band of AlH₄.

Dissociative chemisorption of methane on Ni(111) using a chemically accurate fifteen dimensional potential energy surface

A new chemically accurate potential energy surface for the dissociative chemisorption of methane on the rigid Ni(111) surface.

Origin of distinct structural symmetry of the neopentane cation in the ground electronic state compared to the methane cation

An ab initio quantum dynamics study has been performed to explore the distinct structural symmetry of C(CH3)4(+) in the ground electronic state compared to CH4(+). Additionally, the underlying details of the highly diffuse and complex vibronic structure of the first photoelectron band of C(CH3)4 have been investigated. Associated potential energy surfaces over the two-dimensional space of nuclear coordinates, subject to the T2⊗ (e + t2) Jahn-Teller effect, are established from extensive electronic structure calculations and (then) the nuclear dynamics calculations are done on them via wave packet propagation including the nonadiabatic coupling of the three electronic sheets. The theoretical results are in good agreement with experimental observations. The JT stabilization energies due to T2⊗e, T2⊗t2 and T2⊗ (e + t2) distortions in the X[combining tilde](2)T2 electronic manifold of C(CH3)4(+) illustrate that the highest stabilization occurs through the T2⊗t2-JT distortion (in the ground state of C(CH3)4(+)). However, CH4(+) gains such maximum stabilization due to T2⊗ (e + t2)-JT distortion. From this novel result and applying the epikernel principle, we propose that the structural evolution of C(CH3)4(+) from Td to C3v minimum energy configuration occurs via JT active vibrations of t2 symmetry, whereas CH4(+) rearranges to the C2v structure through a combination of JT active e and t2 bending vibrations.