Machine learning accelerated non-adiabatic molecular dynamics for exciton polaritons
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New Methods for Predicting Non-Born-Oppenheimer Chemistry
Current methods for modeling non-adiabatic molecular dynamics face fundamental limitations when treating geometric phase effects: quantum mechanical phenomena where nuclear wavepackets acquire phase shifts when encircling conical intersections. Existing approaches either neglect these effects entirely or rely on potential energy surfaces arising from the Born-Oppenheimer approximation, which introduce artificial singularities and can overestimate geometric phase contributions. This project developed a new theoretical framework based on exact factorization (XF) methods to overcome these limitations. We derived mathematical formulations for hybrid quantum-classical XF dynamics that selectively treat critical nuclear degrees of freedom quantum mechanically while propagating others classically. This approach addresses the computational intractability that has previously limited exact methods to toy systems. Key innovations include a new approach to systematically identifying nuclear coordinates requiring quantum treatment, as well as novel implementation strategies that interface with existing quantum chemistry codes. The project also developed a proof-of-concept code for treating Jahn-Teller systems and creation of educational materials on non-adiabatic dynamics geared at the graduate level. The theoretical framework developed will enable future systematically improvable calculations of nuclear quantum effects in realistic molecular systems, filling a critical gap in non-adiabatic dynamics methods. This foundation supports future development of predictive tools for designing energy-relevant photochemical processes where quantum coherence effects may be exploited to control reaction outcomes.
38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗
Ultrafast electronic relaxation pathways of the molecular photoswitch quadricyclane
Abstract The light-induced ultrafast switching between molecular isomers norbornadiene and quadricyclane can reversibly store and release a substantial amount of chemical energy. Prior work observed signatures of ultrafast molecular dynamics in both isomers upon ultraviolet excitation but could not follow the electronic relaxation all the way back to the ground state experimentally. Here we study the electronic relaxation of quadricyclane after exciting in the ultraviolet (201 nanometres) using time-resolved gas-phase extreme ultraviolet photoelectron spectroscopy combined with non-adiabatic molecular dynamics simulations. We identify two competing pathways by which electronically excited quadricyclane molecules relax to the electronic ground state. The fast pathway (<100 femtoseconds) is distinguished by effective coupling to valence electronic states, while the slow pathway involves initial motions across Rydberg states and takes several hundred femtoseconds. Both pathways facilitate interconversion between the two isomers, albeit on different timescales, and we predict that the branching ratio of norbornadiene/quadricyclane products immediately after returning to the electronic ground state is approximately 3:2.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
High-throughput and data-driven search for stable optoelectronic AMSe 3 materials
The rapid advancement in emerging optoelectronic technologies demands highly efficient, affordable, and ecofriendly materials. In this context, ternary chalcogenides, especially ternary selenides, show early promise as a material class due to their stability and remarkable electronic, optical, and transport properties. In this work, we integrate first-principles-based high-throughput computations with machine learning (ML) techniques to predict the thermodynamic stability and optoelectronic properties of 920 valency-satisfied selenide compounds. Through investigating polymorphism, our study reveals the edge-sharing orthorhombic Pnma phase (NH 4 CdCl 3 -type) as the most stable structure for most ternary selenides. High-fidelity supervised ML models are trained and tested to accelerate stability and band gap predictions. These data-driven models pin down the most influential features that dominantly control key material characteristics. The multistep high-throughput computations identify the ternary selenides with optimal direct band gaps, light carrier masses, and strong optical absorption edges. The extensive materials screening considering phase stability, toxicity, and defect tolerance, finally identifies the seven most suitable candidates for photovoltaic applications. Two of these final compounds, SrZrSe 3 and SrHfSe 3 , have already been synthesized in a single-phase form, with the latter showing an optically suitable band gap, aligning well with our findings. The non-adiabatic molecular dynamics reveal sufficiently long photoexcited charge carrier lifetimes (on the order of nanoseconds) in some of these selected selenide materials, indicating their exciting characteristics. Overall, our study suggests a robust in silico framework that can be extended to screen large datasets of various material classes for identifying promising photoactive candidates.
36 MATERIALS SCIENCE↗
Quantum dynamics simulations of the 2D spectroscopy for exciton polaritons
We develop an accurate and numerically efficient non-adiabatic path-integral approach to simulate the non-linear spectroscopy of exciton–polariton systems. This approach is based on the partial linearized density matrix approach to model the exciton dynamics with explicit propagation of the phonon bath environment, combined with a stochastic Lindblad dynamics approach to model the cavity loss dynamics. Through simulating both linear and polariton two-dimensional electronic spectra, we systematically investigate how light–matter coupling strength and cavity loss rate influence the optical response signal. Our results confirm the polaron decoupling effect, which is the reduced exciton–phonon coupling among polariton states due to the strong light–matter interactions. We further demonstrate that the polariton coherence time can be significantly prolonged compared to the electronic coherence outside the cavity.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Nonadiabatic dynamics with classical trajectories: The problem of an initial coherent superposition of electronic states
Advances in coherent light sources and development of pump–probe techniques in recent decades have opened the way to study electronic motion in its natural time scale. When an ultrashort laser pulse interacts with a molecular target, a coherent superposition of electronic states is created and the triggered electron dynamics is coupled to the nuclear motion. A natural and computationally efficient choice to simulate this correlated dynamics is a trajectory-based method where the quantum-mechanical electronic evolution is coupled to a classical-like nuclear dynamics. These methods must approximate the initial correlated electron–nuclear state by associating an initial electronic wavefunction to each classical trajectory in the ensemble. Different possibilities exist that reproduce the initial populations of the exact molecular wavefunction when represented in a basis. We show that different choices yield different dynamics and explore the effect of this choice in Ehrenfest, surface hopping, and exact-factorization-based coupled-trajectory schemes in a one-dimensional two-electronic-state model system that can be solved numerically exactly. Furthermore, this work aims to clarify the problems that standard trajectory-based techniques might have when a coherent superposition of electronic states is created to initialize the dynamics, to discuss what properties and observables are affected by different choices of electronic initial conditions and to point out the importance of quantum-momentum-induced electronic transitions in coupled-trajectory schemes.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Ligand Controls Excited Charge Carrier Dynamics in Metal-Rich CdSe Quantum Dots: Computational Insights
Small metal-rich semiconducting quantum dots (QDs) are promising for solid-state lighting and single-photon emission due to their highly tunable yet narrow emission line widths. Nonetheless, the anionic ligands commonly employed to passivate these QDs exert a substantial influence on the optoelectronic characteristics, primarily owing to strong electron–phonon interactions. In this work, we combine time-domain density functional theory and nonadiabatic molecular dynamics to investigate the excited charge carrier dynamics of Cd 28 Se 17 X 22 QDs (X = HCOO – , OH – , Cl – , and SH – ) at ambient conditions. These chemically distinct but regularly used molecular groups influence the dynamic surface-ligand interfacial interactions in Cd-rich QDs, drastically modifying their vibrational characteristics. The strong electron–phonon coupling leads to substantial transient variations at the band edge states. The strength of these interactions closely depends on the physicochemical characteristics of passivating ligands. Consequently, the ligands largely control the nonradiative recombination rates and emission characteristics in these QDs. Our simulations indicate that Cd 28 Se 17 (OH) 22 has the fastest nonradiative recombination rate due to the strongest electron–phonon interactions. Conversely, QDs passivated with thiolate or chloride exhibit considerably longer carrier lifetimes and suppressed nonradiative processes. The ligand-controlled electron–phonon interactions further give rise to the broadest and narrowest intrinsic optical line widths for OH and Cl-passivated single QDs, respectively. Finally, obtained computational insights lay the groundwork for designing appropriate passivating ligands on metal-rich QDs, making them suitable for a wide range of applications, from blue LEDs to quantum emitters.
36 MATERIALS SCIENCE↗
Exciting DeePMD: Learning excited-state energies, forces, and non-adiabatic couplings
We extend the DeePMD neural network architecture to predict electronic structure properties necessary to perform non-adiabatic dynamics simulations. While learning the excited state energies and forces follows a straightforward extension of the DeePMD approach for ground-state energies and forces, how to learn the map between the non-adiabatic coupling vectors (NACV) and the local chemical environment descriptors of DeePMD is less trivial. Most implementations of machine-learning-based non-adiabatic dynamics inherently approximate the NACVs, with an underlying assumption that the energy-difference-scaled NACVs are conservative fields. We overcome this approximation, implementing the method recently introduced by Richardson [J. Chem. Phys. 158, 011102 (2023)], which learns the symmetric dyad of the energy-difference-scaled NACV. Furthermore, the efficiency and accuracy of our neural network architecture are demonstrated through the example of the methaniminium cation CH 2 NH 2 + .
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Imaging transient molecular configurations in UV-excited diiodomethane
Femtosecond structural dynamics of diiodomethane (CH 2 I 2 ) triggered by ultraviolet (UV) photoabsorption at 290 and 330 nm are studied using time-resolved coincident Coulomb explosion imaging driven by a near-infrared probe pulse. Here, we map the dominant single-photon process, the cleavage of the carbon–iodine bond producing rotationally excited CH 2 I radical, identify the contributions of the three-body (CH 2 + I + I) dissociation and molecular iodine formation channels, which are primarily driven by the absorption of more than one UV photon, and demonstrate the existence of a weak reaction pathway involving the formation of short-lived transient species resembling iso-CH 2 I 2 -like geometries with a slightly shorter I–I separation compared to the ground-state CH 2 I 2 . These transient molecular configurations, which can be separated from the other channels by applying a set of conditions on the correlated momenta of three ionic fragments, are formed within ∼100 fs after the initial photoexcitation and decay within the next 100 fs.
Atomic and molecular processes↗
Polariton spectra under the collective coupling regime. II. 2D non-linear spectra
In our previous work [Mondal et al., J. Chem. Phys. 162, 014114 (2025)], we developed several efficient computational approaches to simulate exciton–polariton dynamics described by the Holstein–Tavis–Cummings (HTC) Hamiltonian under the collective coupling regime. Here, we incorporated these strategies into the previously developed Lindblad-partially linearized density matrix ($\mathscr{L}$-PLDM) approach for simulating 2D electronic spectroscopy (2DES) of exciton–polariton under the collective coupling regime. In particular, we apply the efficient quantum dynamics propagation scheme developed in Paper I to both the forward and the backward propagations in the PLDM and develop an efficient importance sampling scheme and graphics processing unit vectorization scheme that allow us to reduce the computational costs from $\mathscr{O}$($\mathscr{K}$ 2 )$\mathscr{O}$(T 3 ) to $\mathscr{O}$($\mathscr{K}$)$\mathscr{O}$(T 0 ) for the 2DES simulation, where $\mathscr{K}$ is the number of states and T is the number of time steps of propagation. As a result, we further simulated the 2DES for an HTC Hamiltonian under the collective coupling regime and analyzed the signal from both rephasing and non-rephasing contributions of the ground state bleaching, excited state emission, and stimulated emission pathways.
2D non-linear spectra↗
Non-adiabatic quantum interference and complex formation in ultracold collisions of Rb with KRb
Ultracold elastic collisions of 87 Rb with 40 K 87 Rb in its ground vibrational and rotational state are investigated using a first principles based theoretical methodology. Full-dimensional ab initio computed potential energy surfaces are reported that include the two lowest-lying electronic states, their conical intersection, non-adiabatic couplings and an accurate long-range behavior. A numerically exact time-independent quantum dynamics method in hyperspherical coordinates is used to compute the elastic scattering cross sections, rate coefficients and collision lifetime spectrum. The quantum scattering calculations include all degrees of freedom and treat both electronic states and their non-adiabatic couplings using a two-state diabatic representation. The theoretically computed elastic rate coefficient is in good agreement with the recently reported experimental value. Significant non-adiabatic quantum interference effects are shown to originate from the unique properties of ultracold collisions and the geometric phase associated with the conical intersection. A high-resolution collision energy grid is used to investigate the origin of the experimentally reported long-lived 3-body collision complexes.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Surface hopping molecular dynamics simulation of ultrafast methyl iodide photodissociation mapped by Coulomb explosion imaging
Our simulation demonstrates the robustness of the Coulomb explosion imaging technique in studying methyl iodide photodissociation, and shows that it can be effectively used for imaging non-adiabatic transitions in coordinate space.
Ding, Yijue↗
Excitons in Hematite Fe 2 O 3 : Short-Time Dynamics from TD-DFT and Non-Adiabatic Dynamics Theories
We present a first-principles study of the short-time dynamics of excitons in hematite Fe 2 O 3 . We used time-dependent density functional theory (TD-DFT) with an underlying DFT+U treatment of electron interactions to characterize the electronic structure of excitons and nonadiabatic molecular dynamics theory (NA-MD) to determine their recombination (electronic ground-state recovery) and relaxation dynamics. Decoherence-corrected trajectory surface hopping approaches in NA-MD simulations yielded recovery times of ~1.1 to 1.8 ns and “higher-lying” exciton relaxation times of ~60 to 70 fs, in accord with experimentally derived lifetimes. With hematite phonons in the range of ~100 to 700 cm –1 , higher-lying excitons relax within one or two oscillations of the phonons before getting trapped into an electron–hole pair Exc-3 structure on the first excited state potential energy surface. This structure resembles already a pair of polarons (electron polaron plus hole polaron) with associated lattice distortions three (3) basal planes away. On longer time scales, the electron–hole bipolaronic pair hops to structures Exc-5, then Exc-7, then Exc-9, ... with the electron polaron and hole polaron separated by 5, 7, 9, ... basal planes in a process of charge separation. The largest frequency phonon ~672 cm –1 for the Exc-3 exciton structure is associated with the electron polaron moiety of the exciton. This phonon is a good candidate for giving rise to the recently observed and reported postexcitation transient IR absorption peak.
36 MATERIALS SCIENCE↗
ELECTRONIC STRUCTURE METHODS AND PROTOCOLS WITH APPLICATION TO DYNAMICS, KINETICS AND THERMOCHEMISTRY
Hydrocarbon combustion involves the reaction dynamics of a tremendous number of species beginning with many-component fuel mixtures and proceeding via a complex system of intermediates to form primary and secondary products. Combustion conditions corresponding to new advanced engines and/or alternative fuels rely increasingly on autoignition and low-temperature-combustion chemistry. In these regimes various transient radical species such as HO2, ROO·, ·QOOH, HCO, NO2, HOCO, and Criegee intermediates play important roles in determining the detailed as well as more general dynamics. A clear understanding and accurate representation of these processes is needed for effective modeling. Given the difficulties associated with making reliable experimental measurements of these systems, computation can play an important role in developing these energy technologies. Accurate calculations have their own challenges since even within the simplest dynamical approximations such as transition state theory, the rates depend exponentially on critical barrier heights and these may be sensitive to the level of quantum chemistry. Moreover, it is well-known that in many cases it is necessary to go beyond statistical theories and consider the dynamics. Quantum tunneling, resonances, radiative transitions, and non-adiabatic effects governed by spin-orbit or derivative coupling can be determining factors in those dynamics. Building upon progress made during a period of prior support through the DOE Early Career Program, this project combines developments in the areas of potential energy surface (PES) fitting and multistate multireference quantum chemistry to allow spectroscopically and dynamically/kinetically accurate investigations of key molecular systems (such as those mentioned above), many of which are radicals with strong multireference character and have the possibility of multiple electronic states contributing to the observed dynamics. An ongoing area of investigation is to develop general strategies for robustly convergent electronic structure theory for global multichannel reactive surfaces including diabatization of energy and other relevant surfaces such as dipole transition. Combining advances in ab initio methods with automated interpolative PES fitting allows the construction of high-quality PESs (incorporating thousands of high-level data) to be done rapidly through parallel processing on high-performance computing (HPC) clusters. In addition, new methods and approaches to electronic structure theory will be developed and tested through applications. This project will explore limitations in traditional multireference calculations (e.g., MRCI) such as those imposed by internal contraction, lack of high-order correlation treatment and poor scaling. Methods such as DMRG-based extended active-space CASSCF and various Quantum Monte Carlo (QMC) methods will be applied (including VMC/DMC and FCIQMC). Insight into the relative significance of different orbital spaces and the robustness of application of these approaches on leadership class computing architectures will be gained. Synergy with other components of this research program such as automated PES fitting and multireference quantum chemistry will be used to address challenges encountered by the standard approaches to computational thermochemistry (those being single-reference quantum chemistry and perturbative treatments of the anharmonic vibrational energy, which break down for some cases of electronic structure or floppy strongly coupled vibrational modes).
74 ATOMIC AND MOLECULAR PHYSICS↗
X-ray induced Coulomb explosion imaging of transient excited-state structural rearrangements in CS2
Abstract Structural imaging of transient excited-state species is a key goal of molecular physics, promising to unveil rich information about the dynamics underpinning photochemical transformations. However, separating the electronic and nuclear contributions to the spectroscopic observables is challenging, and typically requires the application of high-level theory. Here, we employ site-selective ionisation via ultrashort soft X-ray pulses and time-resolved Coulomb explosion imaging to interrogate structural dynamics of the ultraviolet photochemistry of carbon disulfide. This prototypical system exhibits the complex motifs of polyatomic photochemistry, including strong non-adiabatic couplings, vibrational mode couplings, and intersystem crossing. Immediately following photoexcitation, we observe Coulomb explosion signatures of highly bent and stretched excited-state geometries involved in the photodissociation. Aided by a model to interpret such changes, we build a comprehensive picture of the photoinduced nuclear dynamics that follows initial bending and stretching motions, as the reaction proceeds towards photodissociation.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Excited state dynamics of azanaphthalenes reveal opportunities for the rational design of photoactive molecules
Abstract Various photoactive molecules contain motifs built on aza-aromatic heterocycles, although a detailed understanding of the excited state photophysics and photochemistry in such systems is not fully developed. To help address this issue, the non-adiabatic dynamics operating in azanaphthalenes under hexane solvation was studied following 267 nm excitation using ultrafast transient absorption spectroscopy. Specifically, the species quinoline, isoquinoline, quinazoline, quinoxaline, 1,6-naphthyridine, and 1,8-naphthyridine were investigated, providing a systematic variation in the relative positioning of nitrogen heteroatom centres within a bicyclic aromatic structure. Our results indicate considerable differences in excited state lifetimes, and in the propensity for intersystem crossingvsinternal conversion across the molecular series. The overall pattern of behaviour can be explained in terms of potential energy barriers and spin-orbit coupling effects, as demonstrated by extensive quantum chemistry calculations undertaken at the SCS-ADC(2) level of theory. The fact that quantum chemistry calculations can achieve such detailed and nuanced agreement with experimental data across a full set of six molecules exhibiting subtle variations in their composition provides an excellent example of the current state-of-the-art and is indicative of future opportunities for rational design of photoactive molecules.
Chemistry↗
Spin-Controllable Dynamics in Defect-Engineered Carbon Nanotubes as Single Photon Emitters: Data-Driven Modeling and Computations
Quantum technologies, such as quantum computing and sensing, require efficient single-photon emission (SPE) sources that operate at room temperature in telecom wavelengths. While several materials can serve as SPE sources, no single platform meets all the criteria for efficiency, ambient operation, and scalability. Single-walled carbon nanotubes (SWCNTs) with covalently attached molecules offer a promising solution. Their SPE can be easily tuned via modifications of the SWCNT's diameter, chirality, and bonded molecules, enabling emission across near-IR to telecom wavelengths at ambient conditions. However, to fully realize the potential of SWCNTs and unlock their quantum capabilities, a deeper understanding of how structural defects from molecular adducts affect their emission and competing photoexcited processes is essential. To address this gap in our knowledge, this project combined quantum chemistry calculations with data-driven methods of cheminformatics (QSAR) and machine learning (ML). The developed computational approaches have provided several design strategies for covalent functionalization of SWCNTs to improve their optical response. The collaboration with Los Alamos National Lab (LANL) enabled direct comparison of computational and experimental data, facilitating method validation. This partnership was enhanced through access to LANL's Center for Integrated Nanotechnologies (CINT) utilizing User Facility Program and summer internships, which provided three NDSU graduate students with hands-on experience at LANL. The outcomes of this project included (1) Advancing the current stage of computational methods in accurate modeling of non-adiabatic spin-dependent photoexcited dynamics and its applicability to nanosystems consisting of thousands of atoms, realized as open-access codes linked to existing DFT-based software; (2) Establishing the relationship between the structure of adducts and SWCNTs and intrinsic excitonic and spin properties of defect states for guiding novel synthetic strategies and experimental probes of chemically functionalized SWCNTs as near-IR emitting materials; (3) Generating virtual libraries of hypothetical functionalized SWCNTs for virtual screening of their chemical structures and optical properties, leveraging new functionalities of SWCNTs; (4) Offering a unique experience for NDSU graduate students that prepared them for future scientific careers related to materials modeling and big data processing. These results were summarized in 12 published journal papers and 3 recently submitted papers. One of a key finding is that the position of defect sites on the SWCNT surface primarily drives the emission redshift (up to 100 meV), while the polarity of the defect-inducing molecules has a much smaller effect (~10 meV). However, the electron-donating or withdrawing properties of a molecule influence selecting reactivity of defect sites. These insights important for optimizing synthetic protocols for desired emissions in SWCNTs. We also revealed that the interaction between two defects at various positions on the SWCNT enhances the redshift and optical activity of states, favoring strong near-IR emission. This suggests that manipulations in defect concentrations is a promising strategy for controlling efficient emission. Mostly important, the defect position was found controllable by the spin states of photoexcited intermediates: Excited aromatic molecules form ortho defects with SWCNTs at their singlet states in the presence of oxygen, while oxygen-free conditions favor para defects via the triplet-state mechanism. Additionally, a heat-activated [2+2] cycloaddition reaction facilitates divalent defect formation with fewer bonding positions that narrows emission bands. These groundbreaking findings have been experimentally validated and significantly advance our understanding of defect chemistry in SWCNTs. Using a novel encoding technique and 3D-MoRSE descriptors, we developed highly accurate ML/QSAR models to predict both the 3D structure and optical properties of SWCNTs with chemical defects. This model enabled the creation of a virtual library of 125,556 structures, providing new insights into the relationship between SWCNT-defect structure and emission.
77 NANOSCIENCE AND NANOTECHNOLOGY↗
Tracking ultrafast non-adiabatic dissociation dynamics of the deuterated water dication molecule
Here, we applied reaction microscopy to elucidate fast non-adiabatic dissociation dynamics of deuterated water molecules after direct photo-double ionization at 61 eV with synchrotron radiation. For the very rare D + + O + + D breakup channel, the particle momenta, angular, and energy distributions of electrons and ions, measured in coincidence, reveal distinct electronic dication states and their dissociation pathways via spin–orbit coupling and charge transfer at crossings and seams on the potential energy surfaces. Notably, we could distinguish between direct and fast sequential dissociation scenarios. For the latter case, our measurements reveal the geometry and orientation of the deuterated water molecule with respect to the polarization vector that leads to this rare 3-body molecular breakup channel. Aided by multi-reference configuration-interaction calculations, the dissociation dynamics could be traced on the relevant potential energy surfaces and particularly their crossings and seams. This approach also unraveled the ultrafast time scales governing these processes.
74 ATOMIC AND MOLECULAR PHYSICS↗