Enabling complete multichannel nonadiabatic dynamics: A global representation of the two-channel coupled, 1,21A and 13A states of NH3 using neural networks

Revisiting the intricate photodissociation mechanism of ammonia along the minor NH + H2 pathway

In this manuscript we revisit and extend the analysis of the internal conversion and intersystem crossing dynamics of ammonia originating from excitation to its first excited singlet state S1 and leading to the major NH2 + H and minor NH + H2 pathways as investigated by Wang et al. (Phys. Chem. Chem. Phys. 2022, 24, 15060). To perform extensive simulations, we use the machine-learned interatomic potentials, developed by the same authors (Y. Wang et al., J. Chem. Phys. 2021, 154, 094121) interfaced with the SHARC program package. Based on the analysis of 50 000 coupled trajectories, we fit a kinetic model for the major and minor reaction channels that also provides the minimal amount of time required for the dissociation to occur. The model predicts that the time constant associated with the rare pathway is two orders of magnitude larger than that of the frequent reaction, leading to an extrapolated quantum yield of 0.64% for the NH + H2 photoproduct. This quantum yield is in agreement with available experimental measurements carried out with an excitation pulse of 193 nm, around which we excite ammonia. A comprehensive analysis of the electronic states and structures involved in the minor channel reveals that dissociation occurs in a concerted manner via three main mechanisms. The majority of the trajectories (98%) undergo nonradiative relaxation to the electronic ground state, from where 29% directly dissociate. Additionally, we observe reverse internal conversion (58%) as well as intersystem crossing (10%), as operative pathways responsible of the rare photodissociation reaction. These findings provide valuable insights into the dynamics of ammonia photodissociation, particularly its less-studied fragmentation pathway.

Spin-Orbit Coupling and Admixture Coefficients in SA-CASSCF and MS-CASPT2, and Triplet Excitation Yield Simulated via Trajectory Surface Hopping and Calibrated SA-CASSCF in 1,2-Dioxetane Derivatives

The energy gaps, spin-orbit coupling (SOC), and admixture coefficients over a series of the configurations are evaluated by the SA-CASSCF/6-31G, SA-CASSCF/6-31G*, SA-CASSCF/ANO-RCC-VDZP, and MS-CASPT2/ANO-RCC-VDZP to reveal the extent of the inaccuracy of the SA-CASSCF. By comparing the mean absolute errors for the energy gaps and the admixture coefficient magnitudes (ACMs) measured between the SA-CASSCF/6-31G, SA-CASSCF/6-31G*, or SA-CASSCF/ANO-RCC-VDZP and the MS-CASPT2/ANO-RCC-VDZP, the SA-CASSCF/6-31G is selected as the electronic structure method in the nonadiabatic molecular dynamics simulation. The major components of the ACMs of the SA-CASSCF/6-31G and MS-CASPT2/ANO-RCC-VDZP are identified and compared; we find that the ACMs are underestimated by the SA-CASSCF/6-31G, which is verified by the reasonable triplet quantum yield simulated by the trajectory surface hopping and the calibrated SA-CASSCF/6-31G. The magnitude of the singlet-triplet mixing positively correlates to the hopping probability between the mixed singlet and triplet states, which is confirmed by the computed S-T transition probability.

Uncertainty Quantification and Flagging of Unreliable Predictions in Predicting Mass Spectrometry-Related Properties of Small Molecules Using Machine Learning

Mass spectral identification (in particular, in metabolomics) can be refined by comparing the observed and predicted properties of molecules, such as chromatographic retention. Significant advancements have been made in predicting these values using machine learning and deep learning. Usually, model predictions do not contain any indication of the possible error (uncertainty) or only one criterion is used for this purpose. The spread of predictions of several models included in the ensemble, and the molecular similarity of the considered molecule and the most "similar" molecule from the training set, are values that allow us to estimate the uncertainty. The Euclidean distance between vectors, calculated based on real-valued molecular descriptors, can be used for the assessment of molecular similarity. Another factor indicating uncertainty is the molecule's belonging to one of the clusters (data set clustering). Together, all three factors can be used as features for the uncertainty assessment model. Classification models that predict whether a prediction belongs to the worst 15% were obtained. The area under the receiver operating curve value is in the range of 0.73-0.82 for the considered tasks: the prediction of retention indices in gas chromatography, retention times in liquid chromatography, and collision cross-sections in ion mobility spectroscopy.

Floquet-Engineered Photodissociation Simulated Using Coupled Potential Energy and Dipole Matrices

We simulate the nonadiabatic molecular dynamics of ammonia photodissociation in the presence of an external laser field by using an approximate Floquet Hamiltonian. The dipole-field interaction gives rise to seams of light-induced conical intersection (LICI), which can significantly change the topography of the coupled potential energy surfaces. We perform quasiclassical trajectories based on recently reported diabatic potential energy matrices (DPEM) and dipole matrices. It is shown that the branching ratio of ground and excited state NH2 is drastically altered by laser-dipole interaction, which is a signature of nonadiabatic effects induced by light.

Dissociation Time, Quantum Yield, and Dynamic Reaction Pathways in the Thermolysis of trans-3,4-Dimethyl-1,2-dioxetane

The thermolysis of trans-3,4-dimethyl-1,2-dioxetane is studied by trajectory surface hopping. The significant difference between long and short dissociation times is rationalized by frustrated dissociations and the time spent in triplet states. If the C-C bond breaks through an excited state channel, then the trajectory passes over a ridge of the potential energy surface of that state. The calculated triplet quantum yields match the experimental results. The dissociation half-times and quantum yields follow the same ascending order as per the product states, justifying the conjecture that the longer dissociation time leads to a higher quantum yield, proposed in the context of the methylation effect. The populations of the molecular Coulomb Hamiltonian and diagonal states reach equilibrium, but the triplet populations with different Sz components fluctuate indefinitely. Certain initial velocities, leading the trajectories to given product states, can be identified as the most characteristic features for sorting trajectories according to their product states.

Quantum Dynamics of Photodissociation: Recent Advances and Challenges

Recent advances in constructing accurate potential energy surfaces and nonadiabatic couplings from high-level ab initio data have revealed detailed potential landscapes in not only the ground electronic state but also excited ones. They enabled quantitatively accurate characterization of photoexcited reactive systems using quantum mechanical methods. In this Perspective, we survey the recent progress in quantum mechanical studies of adiabatic and nonadiabatic photodissociation dynamics, focusing on initial state control and product energy disposal. These new insights helped to understand quantum effects in small prototypical systems, and the results serve as benchmarks for developing more approximate theoretical methods.

Toward a Unified Analytical Description of Internal Conversion and Intersystem Crossing in the Photodissociation of Thioformaldehyde. I. Diabatic Singlet States

The photodissociation of thioformaldehyde is an archetypal system for the study of competition between internal conversion and intersystem crossing, which involves its two singlet states (S0 and S1) and two triplet states (T1 and T2). In order to perform accurate dynamic simulations, either quantum or quasi-classical, it is essential to construct an analytical representation for all necessary electronic structure data. In this work, a diabatic potential energy matrix (DPEM), Hd, for the two singlet states (S0 and S1) is reported. The analytical form of DPEM is symmetrized and constructed to reproduce adiabatic energies, energy gradients, and derivative couplings obtained from high-level multireference configuration interaction wave functions. The Hd is fully saturated in the molecular configuration space with a trajectory-guided point sampling approach. This Hd can provide the accurate description of the photodissociation of thioformaldehyde on its singlet states and is also a necessary part for incorporating the spin-orbit couplings into a unified diabatic framework. Preliminary quasi-classical trajectory simulations show that a roaming mechanism also exists in the molecular dissociation channel of thioformaldehyde.

Constructing Diabatic Potential Energy Matrices with Neural Networks Based on Adiabatic Energies and Physical Considerations: Toward Quantum Dynamic Accuracy

A permutation invariant polynomial-neural network (PIP-NN) approach for constructing the global diabatic potential energy matrices (PEMs) of the coupled states of molecules is proposed. Specifically, the diabatization scheme is based merely on the adiabatic energy data of the system, which is ideally a most convenient way due to not requiring additional ab initio calculations for the data of the derivative coupling or any other physical properties of the molecule. Considering the permutation and coupling characteristics of the system, particularly in the presence of conical intersections, some vital treatments for the off-diagonal terms in diabatic PEM are essentially needed. Taking the photodissociation of H₂O(X~/B~)/NH₃(X~/A~) and nonadiabatic reaction Na(3p) + H₂ → NaH(Σ⁺) + H for example, this PIP-NN method is shown to build up the global diabatic PEMs effectively and accurately. The root-mean-square errors of the adiabatic potential energies in the fitting for three different systems are all small (<10 meV). Further quantum dynamic calculations show that the absorption spectra and product branching ratios in both H₂O(X~/B~) and NH₃(X~/A~) nonadiabatic photodissociation are well reproduced on the new diabatic PEMs, and the nonadiabatic reaction probability of Na(3p) + H₂ → NaH(Σ⁺) + H obtained on the new diabatic PEMs of the 1²A₁ and 1²B₂ states is in reasonably good agreement with previous theoretical result as well, validating this new PIP-NN method.

Accurate Full-Dimensional Global Diabatic Potential Energy Matrix for the Two Lowest-Lying Electronic States of the H + O2 ↔ HO + O Reaction

A new and more accurate diabatic potential energy matrix (DPEM) is developed for the two lowest-lying electronic states of HO₂, covering both the strong interaction region and reaction asymptotes. The ab initio calculations were performed at the Davidson corrected multireference configuration interaction level with the augmented correlation-consistent polarized valence quintuple-zeta basis set (MRCI+Q/AV5Z). The accuracy of the electronic structure calculations is validated by excellent agreement with the experimental HO₂ equilibrium geometry, fundamental vibrational frequencies, and H + O₂ ↔ OH + O reaction energy. Through the combination of an electronic angular momentum-method and a configuration interaction vector-based method, the mixing angle between the first two ²A″ states of HO₂ was successfully determined. Elements of the 2×2 DPEM were fit to neural networks with a proper account of the complete nuclear permutation inversion symmetry of HO₂. The DPEM correctly predicted the properties of conical intersection seams at linear and T-shape geometries, thus providing a reliable platform for studying both the spectroscopy of HO₂ and the nonadiabatic dynamics for the H + O₂ ↔ OH + O reaction.

Accurate and Interpretable Dipole Interaction Model-Based Machine Learning for Molecular Polarizability

Polarizabilities play significant roles in describing dispersive and inductive interactions of the atom and molecular systems. However, an accurate prediction of molecular polarizabilities from first principles is computationally prohibitive. Although physical models or statistical machine learning models have been proposed, either a lack of accurate description of local chemical environments or demanding a large number of samples for training has limited their practical applications. In this study, we combine a physically inspired dipole interaction model and an accurate neural network method for predicting the polarizability tensors of molecules. With the local chemical environment precisely described and the requirement of rotational covariance naturally fulfilled, this hybrid model is proven to give an accurate molecular polarizability prediction, essentially reducing the number of training samples. The atomic polarizabilities are physically interpretable and transferable to larger molecules unseen in the training set. This promising method may find its wide range of applications, such as spectroscopic simulations and the construction of polarizable force fields.

Data-Driven Many-Body Potential Energy Functions for Generic Molecules: Linear Alkanes as a Proof-of-Concept Application

We present a generalization of the many-body energy (MB-nrg) theoretical/computational framework that enables the development of data-driven potential energy functions (PEFs) for generic covalently bonded molecules, with arbitrary quantum mechanical accuracy. The "nearsightedness of electronic matter" is exploited to define monomers as "natural building blocks" on the basis of their distinct chemical identity. The energy of generic molecules is then expressed as a sum of individual many-body energies of incrementally larger subsystems. The MB-nrg PEFs represent the low-order n-body energies, with n = 1-4, using permutationally invariant polynomials derived from electronic structure data carried out at an arbitrary quantum mechanical level of theory, while all higher-order n-body terms (n > 4) are represented by a classical many-body polarization term. As a proof-of-concept application of the general MB-nrg framework, we present MB-nrg PEFs for linear alkanes. The MB-nrg PEFs are shown to accurately reproduce reference energies, harmonic frequencies, and potential energy scans of alkanes, independently of their length. Since, by construction, the MB-nrg framework introduced here can be applied to generic covalently bonded molecules, we envision future computer simulations of complex molecular systems using data-driven MB-nrg PEFs, with arbitrary quantum mechanical accuracy.

Internal conversion and intersystem crossing dynamics based on coupled potential energy surfaces with full geometry-dependent spin-orbit and derivative couplings. Nonadiabatic photodissociation dynamics of NH3(A) leading to the NH(X3Σ-, a1Δ) + H2 channel

We simulate the photodissociation of NH₃ originating from its first excited singlet state S₁ into the NH₂ + H (radical) and NH + H₂ (molecular) channels. The states considered are the ground singlet state S₀, the first excited singlet state S₁ and the lowest-lying triplet state T₁, which permit for the first time a uniform treatment of the internal conversion and intersystem crossing. The simulations are based on a diabatic potential energy matrix (DPEM) of S₀, S₁ coupled by a conical intersection seam, as well as a potential energy surface (PES) for T₁ coupled by spin-orbit coupling (SOC) to the two singlet states. The DPEM and PES are fitted to ab initio electronic structure data (ESD) including energies, energy gradients, and derivative couplings. The DPEM also defines an adiabatic to diabatic state (AtD) transformation, which is used to transform the singular adiabatic SOC into a smooth function of the nuclear coordinates in the diabatic representation, allowing the diabatic SOC to be fit to an analytical functional form. ESD and SOC data obtained from these surfaces can serve as input for either quantum or semi-classical characterization of the nonadiabatic dynamics. Using the SHARC suite of programs, nonadiabatic simulations based on over 40 000 semi-classical trajectories assess the convergence of our results. The production of NH + H₂ is not direct, but is only achieved through a quasi-statistical dissociation mechanism after internal conversion to the ground electronic state. This leads to a much lower yield comparing with the main NH₂ + H channel. The NH(X³Σ^_) radical produced through the intersystem crossing from S₀ to T₁ is rare (∼0.2%) compared to NH(a¹Δ) due to the process being spin forbidden.

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.

Conical intersection seams in spin-orbit coupled systems with an even number of electrons: A numerical study based on neural network fit surfaces

In this work, we consider the existence and topography of seams of conical intersections (CIs) for two key singlet-triplet systems, including a uniformly scaled spin-orbit interaction. The basic one triplet and one singlet state system denoted as (S₀,T₁) and the two singlets and one triplet system denoted as (S₀,S₁,T₁) are treated. Essential to this analysis are realistic electronic structure data taken from a recently reported neural network fit for the 1,2¹A and 1³A states of NH₃, including H_sf (spin-free) and H_so (spin-orbit) surfaces derived from high quality ab initio wavefunctions. Three types of seams for the (S₀,S₁,T₁) system are reported, which depend on the choice of the electronic Hamiltonian, H^e. The nonrelativistic CI seam [H^e = H_sf, (S₀,S₁)], the energy minimized nonrelativistic singlet-triplet intersection seam [H^e = H_sf, (S₀,T₁)], and the fully relativistic seam in the spin-diabatic representation (H^e = H_tot = H_sf + H_so) are reported as functions of R(N-H). The derivative couplings are computed using H^e = H_tot and H_sf from the fit data. The line integral of the derivative coupling is employed to juxtapose the geometric phase in the relativistic, H^e = H_tot, and nonrelativistic, H^e = H_sf, cases. It is found for the (S₀,T₁) system that there is no CI in the spin-adiabatic representation, while for the (S₀,S₁,T₁) system, CI can only be formed for two pairs of spin-adiabatic electronic states. The geometric phase effect thus needs to be handled with care when it comes to spin-nonconserving dynamics simulations.

General Many-Body Framework for Data-Driven Potentials with Arbitrary Quantum Mechanical Accuracy: Water as a Case Study

We present a general framework for the development of data-driven many-body (MB) potential energy functions (MB-QM PEFs) that represent the interactions between small molecules at an arbitrary quantum-mechanical (QM) level of theory. As a demonstration, a family of MB-QM PEFs for water is rigorously derived from density functionals belonging to different rungs across Jacob's ladder of approximations within density functional theory (MB-DFT) and from Møller-Plesset perturbation theory (MB-MP2). Through a systematic analysis of individual MB contributions to the interaction energies of water clusters, we demonstrate that all MB-QM PEFs preserve the same accuracy as the corresponding ab initio calculations, with the exception of those derived from density functionals within the generalized gradient approximation (GGA). The differences between the DFT and MB-DFT results are traced back to density-driven errors that prevent GGA functionals from accurately representing the underlying molecular interactions for different cluster sizes and hydrogen-bonding arrangements. We show that this shortcoming may be overcome, within the MB formalism, by using density-corrected functionals (DC-DFT) that provide a more consistent representation of each individual MB contribution. This is demonstrated through the development of a MB-DFT PEF derived from DC-PBE-D3 data, which more accurately reproduce the corresponding ab initio results.

Enabling a Unified Description of Both Internal Conversion and Intersystem Crossing in Formaldehyde: A Global Coupled Quasi-Diabatic Hamiltonian for Its S0, S1, and T1 States

In our recent work, a diabatic Hamiltonian that couples the S₀ and S₁ states of formaldehyde was constructed using a robust fitting-and-diabatizing procedure with artificial neural networks, which is capable of representing adiabatic energies, energy gradients, and derivative couplings over a wide range of geometries including seams of conical intersection. In this work, based on the diabatization of S₀ and S₁, the spin-orbit couplings between singlet states (S₀, S₁) and triplet state T₁ are also determined in the same diabatic representation. The diabatized spin-orbit couplings are then fit with a symmetrized neural-network functional form. The ab initio spin-orbit couplings are well reproduced in large configuration space. Together with the neural-network-based potential energy surface for T₁, the full quasi-diabatic Hamiltonian for the S₀, S₁, and T₁ states is completed, enabling a unified description of both internal conversion and intersystem crossing in formaldehyde. The vibrational levels on the three adiabatic states are found to be in good agreement with known experimental band origins.