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Methodologies for training machine learning potentials (MLPs) with quantum-mechanical simulation data have recently seen tremendous progress. Experimental data have a very different character than simulated data, and most MLP training procedures cannot be easily adapted to incorporate both types of data into the training process. We investigate a training procedure based on iterative Boltzmann inversion that produces a pair potential correction to an existing MLP using equilibrium radial distribution function data. By applying these corrections to an MLP for pure aluminum based on density functional theory, we observe that the resulting model largely addresses previous overstructuring in the melt phase. Interestingly, the corrected MLP also exhibits improved performance in predicting experimental diffusion constants, which are not included in the training procedure. The presented method does not require autodifferentiating through a molecular dynamics solver and does not make assumptions about the MLP architecture. Our results suggest a practical framework for incorporating experimental data into machine learning models to improve the accuracy of molecular dynamics simulations.

Catalyzed by enormous success in the industrial sector, many research programs have been exploring data-driven, machine learning approaches. Performance can be poor when the model is extrapolated to new regions of chemical space, e.g., new bonding types, new many-body interactions. Another important limitation is the spatial locality assumption in model architecture, and this limitation cannot be overcome with larger or more diverse datasets. The outlined challenges are primarily associated with the lack of electronic structure information in surrogate models such as interatomic potentials. Given the fast development of machine learning and computational chemistry methods, we expect some limitations of surrogate models to be addressed in the near future; nevertheless spatial locality assumption will likely remain a limiting factor for their transferability. Here, we suggest focusing on an equally important effort-design of physics-informed models that leverage the domain knowledge and employ machine learning only as a corrective tool. In the context of material science, we will focus on semi-empirical quantum mechanics, using machine learning to predict corrections to the reduced-order Hamiltonian model parameters. The resulting models are broadly applicable, retain the speed of semiempirical chemistry, and frequently achieve accuracy on par with much more expensive ab initio calculations. These early results indicate that future work, in which machine learning and quantum chemistry methods are developed jointly, may provide the best of all worlds for chemistry applications that demand both high accuracy and high numerical efficiency., (© 2023 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).)

The global energy optimization problem is an acute and important problem in chemistry. It is crucial to know the geometry of the lowest energy isomer (global minimum, GM) of a given compound for the evaluation of its chemical and physical properties. This problem is especially relevant for atomic clusters. Due to the exponential growth of the number of local minima geometries with the increase of the number of atoms in the cluster, it is important to find a computationally efficient and reliable method to navigate the energy landscape and locate a true global minima structure. Newly developed neural network (NN) atomistic potentials offer a numerically efficient and relatively accurate approach for molecular structure optimization. An important question that needs to be answered is "Can NN potentials, trained on a given set, represent the potential energy surface (PES) of a neighboring domain?". In this work, we tested the applicability of ANI-1ccx and ANI-nr NN atomistic potentials for the global minima optimization of carbon clusters C n ( n = 3-10). We showed that with the introduction of the cluster connectivity restriction and consequent DFT or ab initio calculations, ANI-1ccx and ANI-nr can be considered as robust PES pre-samplers that can capture the GM structure even for large clusters such as C 20 .

Extended Lagrangian Born-Oppenheimer molecular dynamics (XL-BOMD) in its most recent shadow potential energy version has been implemented in the semiempirical PyTorch-based software PySeQM. The implementation includes finite electronic temperatures, canonical density matrix perturbation theory, and an adaptive Krylov subspace approximation for the integration of the electronic equations of motion within the XL-BOMB approach (KSA-XL-BOMD). The PyTorch implementation leverages the use of GPU and machine learning hardware accelerators for the simulations. The new XL-BOMD formulation allows studying more challenging chemical systems with charge instabilities and low electronic energy gaps. The current public release of PySeQM continues our development of modular architecture for large-scale simulations employing semi-empirical quantum-mechanical treatment. Applied to molecular dynamics, simulation of 840 carbon atoms, one integration time step executes in 4 s on a single Nvidia RTX A6000 GPU.

Atomistic machine learning focuses on the creation of models that obey fundamental symmetries of atomistic configurations, such as permutation, translation, and rotation invariances. In many of these schemes, translation and rotation invariance are achieved by building on scalar invariants, e.g., distances between atom pairs. There is growing interest in molecular representations that work internally with higher rank rotational tensors, e.g., vector displacements between atoms, and tensor products thereof. Here, we present a framework for extending the Hierarchically Interacting Particle Neural Network (HIP-NN) with Tensor Sensitivity information (HIP-NN-TS) from each local atomic environment. Crucially, the method employs a weight tying strategy that allows direct incorporation of many-body information while adding very few model parameters. We show that HIP-NN-TS is more accurate than HIP-NN, with negligible increase in parameter count, for several datasets and network sizes. As the dataset becomes more complex, tensor sensitivities provide greater improvements to model accuracy. In particular, HIP-NN-TS achieves a record mean absolute error of 0.927 kcalmol for conformational energy variation on the challenging COMP6 benchmark, which includes a broad set of organic molecules. We also compare the computational performance of HIP-NN-TS to HIP-NN and other models in the literature., (© 2023 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).)

Highly energetic electron-hole pairs (hot carriers) formed from plasmon decay in metallic nanostructures promise sustainable pathways for energy-harvesting devices. However, efficient collection before thermalization remains an obstacle for realization of their full energy generating potential. Addressing this challenge requires detailed understanding of physical processes from plasmon excitation in the metal to their collection in a molecule or a semiconductor, where atomistic theoretical investigation may be particularly beneficial. Unfortunately, first-principles theoretical modeling of these processes is extremely costly, preventing a detailed analysis over a large number of potential nanostructures and limiting the analysis to systems with a few 100s of atoms. Recent advances in machine learned interatomic potentials suggest that dynamics can be accelerated with surrogate models which replace the full solution of the Schrödinger Equation. Here, we modify an existing neural network, Hierarchically Interacting Particle Neural Network (HIP-NN), to predict plasmon dynamics in Ag nanoparticles. The model takes as a minimum as three time steps of the reference real-time time-dependent density functional theory (rt-TDDFT) calculated charges as history and predicts trajectories for 5 fs in great agreement with the reference simulation. Further, we show that a multistep training approach in which the loss function includes errors from future time-step predictions can stabilize the model predictions for the entire simulated trajectory (∼25 fs). This extends the model's capability to accurately predict plasmon dynamics in large nanoparticles of up to 561 atoms, not present in the training data set. More importantly, with machine learning models on GPUs, we gain a speed-up factor of ∼10 3 as compared with the rt-TDDFT calculations when predicting important physical quantities such as dynamic dipole moments in Ag 55 and a factor of ∼10 4 for extended nanoparticles that are 10 times larger. This underscores the promise of future machine learning accelerated electron/nuclear dynamics simulations for understanding fundamental properties of plasmon-driven hot carrier devices.

Machine learning (ML) models, if trained to data sets of high-fidelity quantum simulations, produce accurate and efficient interatomic potentials. Active learning (AL) is a powerful tool to iteratively generate diverse data sets. In this approach, the ML model provides an uncertainty estimate along with its prediction for each new atomic configuration. If the uncertainty estimate passes a certain threshold, then the configuration is included in the data set. Here we develop a strategy to more rapidly discover configurations that meaningfully augment the training data set. The approach, uncertainty-driven dynamics for active learning (UDD-AL), modifies the potential energy surface used in molecular dynamics simulations to favor regions of configuration space for which there is large model uncertainty. The performance of UDD-AL is demonstrated for two AL tasks: sampling the conformational space of glycine and sampling the promotion of proton transfer in acetylacetone. The method is shown to efficiently explore the chemically relevant configuration space, which may be inaccessible using regular dynamical sampling at target temperature conditions., (© 2023. The Author(s).)

High-harmonic generation (HHG) in solids has been touted as a way to probe ultrafast dynamics and crystal symmetries in condensed matter systems. Here, we investigate the polarization properties of high-order harmonics generated in monolayer MoS_{2}, as a function of crystal orientation relative to the mid-infrared laser field polarization. At several different laser wavelengths we experimentally observe a prominent angular shift of the parallel-polarized odd harmonics for energies above approximately 3.5 eV, and our calculations indicate that this shift originates in subtle differences in the recombination dipole strengths involving multiple conduction bands. This observation is material specific and is in addition to the angular dependence imposed by the dynamical symmetry properties of the crystal interacting with the laser field, and may pave the way for probing the vectorial character of multiband recombination dipoles.

Machine learning (ML) is becoming a method of choice for modelling complex chemical processes and materials. ML provides a surrogate model trained on a reference dataset that can be used to establish a relationship between a molecular structure and its chemical properties. This Review highlights developments in the use of ML to evaluate chemical properties such as partial atomic charges, dipole moments, spin and electron densities, and chemical bonding, as well as to obtain a reduced quantum-mechanical description. We overview several modern neural network architectures, their predictive capabilities, generality and transferability, and illustrate their applicability to various chemical properties. We emphasize that learned molecular representations resemble quantum-mechanical analogues, demonstrating the ability of the models to capture the underlying physics. We also discuss how ML models can describe non-local quantum effects. Finally, we conclude by compiling a list of available ML toolboxes, summarizing the unresolved challenges and presenting an outlook for future development. The observed trends demonstrate that this field is evolving towards physics-based models augmented by ML, which is accompanied by the development of new methods and the rapid growth of user-friendly ML frameworks for chemistry., (© 2022. Springer Nature Limited.)

Conventional machine-learning (ML) models in computational chemistry learn to directly predict molecular properties using quantum chemistry only for reference data. While these heuristic ML methods show quantum-level accuracy with speeds several orders of magnitude faster than traditional quantum chemistry methods, they suffer from poor extensibility and transferability; i.e., their accuracy degrades on large or new chemical systems. Incorporating quantum chemistry frameworks into the ML models directly solves this problem. Here we take the structure of semiempirical quantum mechanics (SEQM) methods to construct dynamically responsive Hamiltonians. SEQM methods use empirical parameters fitted to experimental properties to construct reduced-order Hamiltonians, facilitating much faster calculations than ab initio methods but with compromised accuracy. By replacing these static parameters with machine-learned dynamic values inferred from the local environment, we greatly improve the accuracy of the SEQM methods. Trained on molecular energies and atomic forces, these dynamically generated Hamiltonian parameters show a strong correlation with atomic hybridization and bonding. Trained with only about 60,000 small organic molecular conformers, the resulting model retains interpretability, extensibility, and transferability when testing on much larger chemical systems and predicting various molecular properties. Overall, this work demonstrates the virtues of incorporating physics-based descriptions with ML to develop models that are simultaneously accurate, transferable, and interpretable.

Machine learning (ML) is quickly becoming a premier tool for modeling chemical processes and materials. ML-based force fields, trained on large data sets of high-quality electron structure calculations, are particularly attractive due their unique combination of computational efficiency and physical accuracy. This Perspective summarizes some recent advances in the development of neural network-based interatomic potentials. Designing high-quality training data sets is crucial to overall model accuracy. One strategy is active learning, in which new data are automatically collected for atomic configurations that produce large ML uncertainties. Another strategy is to use the highest levels of quantum theory possible. Transfer learning allows training to a data set of mixed fidelity. A model initially trained to a large data set of density functional theory calculations can be significantly improved by retraining to a relatively small data set of expensive coupled cluster theory calculations. These advances are exemplified by applications to molecules and materials.

Phosphorescence is commonly utilized for applications including light-emitting diodes and photovoltaics. Machine learning (ML) approaches trained on ab initio datasets of singlet-triplet energy gaps may expedite the discovery of phosphorescent compounds with the desired emission energies. However, we show that standard ML approaches for modeling potential energy surfaces inaccurately predict singlet-triplet energy gaps due to the failure to account for spatial localities of spin transitions. To solve this, we introduce localization layers in a neural network model that weight atomic contributions to the energy gap, thereby allowing the model to isolate the most determinative chemical environments. Trained on the singlet-triplet energy gaps of organic molecules, we apply our method to an out-of-sample test set of large phosphorescent compounds and demonstrate the substantial improvement that localization layers have on predicting their phosphorescence energies. Remarkably, the inferred localization weights have a strong relationship with the ab initio spin density of the singlet-triplet transition, and thus infer localities of the molecule that determine the spin transition, despite the fact that no direct electronic information was provided during training. The use of localization layers is expected to improve the modeling of many localized, non-extensive phenomena and could be implemented in any atom-centered neural network model., Competing Interests: There are no conflicts to declare., (This journal is © The Royal Society of Chemistry.)

The Hückel Hamiltonian is an incredibly simple tight-binding model known for its ability to capture qualitative physics phenomena arising from electron interactions in molecules and materials. Part of its simplicity arises from using only two types of empirically fit physics-motivated parameters: the first describes the orbital energies on each atom and the second describes electronic interactions and bonding between atoms. By replacing these empirical parameters with machine-learned dynamic values, we vastly increase the accuracy of the extended Hückel model. The dynamic values are generated with a deep neural network, which is trained to reproduce orbital energies and densities derived from density functional theory. The resulting model retains interpretability, while the deep neural network parameterization is smooth and accurate and reproduces insightful features of the original empirical parameterization. Overall, this work shows the promise of utilizing machine learning to formulate simple, accurate, and dynamically parameterized physics models.

Machine learning, trained on quantum mechanics (QM) calculations, is a powerful tool for modeling potential energy surfaces. A critical factor is the quality and diversity of the training dataset. Here we present a highly automated approach to dataset construction and demonstrate the method by building a potential for elemental aluminum (ANI-Al). In our active learning scheme, the ML potential under development is used to drive non-equilibrium molecular dynamics simulations with time-varying applied temperatures. Whenever a configuration is reached for which the ML uncertainty is large, new QM data is collected. The ML model is periodically retrained on all available QM data. The final ANI-Al potential makes very accurate predictions of radial distribution function in melt, liquid-solid coexistence curve, and crystal properties such as defect energies and barriers. We perform a 1.3M atom shock simulation and show that ANI-Al force predictions shine in their agreement with new reference DFT calculations.

We present a versatile new code released for open community use, the nonadiabatic excited state molecular dynamics (NEXMD) package. This software aims to simulate nonadiabatic excited state molecular dynamics using several semiempirical Hamiltonian models. To model such dynamics of a molecular system, the NEXMD uses the fewest-switches surface hopping algorithm, where the probability of transition from one state to another depends on the strength of the derivative nonadiabatic coupling. In addition, there are a number of algorithmic improvements such as empirical decoherence corrections and tracking trivial crossings of electronic states. While the primary intent behind the NEXMD was to simulate nonadiabatic molecular dynamics, the code can also perform geometry optimizations, adiabatic excited state dynamics, and single-point calculations all in vacuum or in a simulated solvent. In this report, first, we lay out the basic theoretical framework underlying the code. Then we present the code's structure and workflow. To demonstrate the functionality of NEXMD in detail, we analyze the photoexcited dynamics of a polyphenylene ethynylene dendrimer (PPE, C 30 H 18 ) in vacuum and in a continuum solvent. Furthermore, the PPE molecule example serves to highlight the utility of the getexcited.py helper script to form a streamlined workflow. This script, provided with the package, can both set up NEXMD calculations and analyze the results, including, but not limited to, collecting populations, generating an average optical spectrum, and restarting unfinished calculations.

A new open-source high-performance implementation of Born Oppenheimer molecular dynamics based on semiempirical quantum mechanics models using PyTorch called PYSEQM is presented. PYSEQM was designed to provide researchers in computational chemistry with an open-source, efficient, scalable, and stable quantum-based molecular dynamics engine. In particular, PYSEQM enables computation on modern graphics processing unit hardware and, through the use of automatic differentiation, supplies interfaces for model parameterization with machine learning techniques to perform multiobjective training and prediction. The implemented semiempirical quantum mechanical methods (MNDO, AM1, and PM3) are described. Additional algorithms include a recursive Fermi-operator expansion scheme (SP2) and extended Lagrangian Born Oppenheimer molecular dynamics allowing for rapid simulations. Finally, benchmark testing on the nanostar dendrimer and a series of polyethylene molecules provides a baseline of code efficiency, time cost, and scaling and stability of energy conservation, verifying that PYSEQM provides fast and accurate computations.

Maximum diversification of data is a central theme in building generalized and accurate machine learning (ML) models. In chemistry, ML has been used to develop models for predicting molecular properties, for example quantum mechanics (QM) calculated potential energy surfaces and atomic charge models. The ANI-1x and ANI-1ccx ML-based general-purpose potentials for organic molecules were developed through active learning; an automated data diversification process. Here, we describe the ANI-1x and ANI-1ccx data sets. To demonstrate data diversity, we visualize it with a dimensionality reduction scheme, and contrast against existing data sets. The ANI-1x data set contains multiple QM properties from 5 M density functional theory calculations, while the ANI-1ccx data set contains 500 k data points obtained with an accurate CCSD(T)/CBS extrapolation. Approximately 14 million CPU core-hours were expended to generate this data. Multiple QM calculated properties for the chemical elements C, H, N, and O are provided: energies, atomic forces, multipole moments, atomic charges, etc. We provide this data to the community to aid research and development of ML models for chemistry.

Optically active molecular materials, such as organic conjugated polymers and biological systems, are characterized by strong coupling between electronic and vibrational degrees of freedom. Typically, simulations must go beyond the Born-Oppenheimer approximation to account for non-adiabatic coupling between excited states. Indeed, non-adiabatic dynamics is commonly associated with exciton dynamics and photophysics involving charge and energy transfer, as well as exciton dissociation and charge recombination. Understanding the photoinduced dynamics in such materials is vital to providing an accurate description of exciton formation, evolution, and decay. This interdisciplinary field has matured significantly over the past decades. Formulation of new theoretical frameworks, development of more efficient and accurate computational algorithms, and evolution of high-performance computer hardware has extended these simulations to very large molecular systems with hundreds of atoms, including numerous studies of organic semiconductors and biomolecules. In this Review, we will describe recent theoretical advances including treatment of electronic decoherence in surface-hopping methods, the role of solvent effects, trivial unavoided crossings, analysis of data based on transition densities, and efficient computational implementations of these numerical methods. We also emphasize newly developed semiclassical approaches, based on the Gaussian approximation, which retain phase and width information to account for significant decoherence and interference effects while maintaining the high efficiency of surface-hopping approaches. The above developments have been employed to successfully describe photophysics in a variety of molecular materials.

Laser-induced fluorescence excitation and dispersed fluorescence spectra of a model flexible bichromophore, 1,1-diphenylethane (DPE), have been recorded under jet-cooled conditions in the gas phase in the region near the first pair of near-degenerate excited states (S 1 and S 2 ). The S 1 and S 2 origin transitions have been identified at 37 397 and 37 510 cm -1 , a splitting of 113 cm -1 . This splitting is four times smaller than the excitonic splitting calculated by ab initio methods at the EOM-CCSD/cc-pVDZ level of theory (410 cm -1 ), which necessarily relies on the Born-Oppenheimer approximation. Dispersed fluorescence spectra provide a state-to-state picture of the vibronic coupling. These results are compared with the results of a multimode vibronic coupling model capable of treating chromophores in asymmetric environments. This model was used to predict the splitting between S 1 and S 2 origins close to the experiment, reduced from its pure excitonic value by Franck-Condon quenching. Quantitative accuracy is achieved by the model, lending insight into the state-to-state mixing that occurs between individual S 1 and S 2 vibronic levels. The S 2 origin is determined to be mixed with S 1 (v) levels by two mechanisms common to internal conversion in almost any setting; namely, (i) mixing involving near-degenerate levels with large vibrational quantum number changes that are not governed by Δv = 1 Herzberg-Teller (HT) selection rules, and (ii) mixing with levels with larger energy gaps that do follow these selection rules. In DPE, the asymmetric ring flapping vibrational mode R¯ dominates the HT coupling.

The ability to accurately and efficiently compute quantum-mechanical partial atomistic charges has many practical applications, such as calculations of IR spectra, analysis of chemical bonding, and classical force field parametrization. Machine learning (ML) techniques provide a possible avenue for the efficient prediction of atomic partial charges. Modern ML advances in the prediction of molecular energies [i.e., the hierarchical interacting particle neural network (HIP-NN)] has provided the necessary model framework and architecture to predict transferable, extensible, and conformationally dynamic atomic partial charges based on reference density functional theory (DFT) simulations. Utilizing HIP-NN, we show that ML charge prediction can be highly accurate over a wide range of molecules (both small and large) across a variety of charge partitioning schemes such as the Hirshfeld, CM5, MSK, and NBO methods. To demonstrate transferability and size extensibility, we compare ML results with reference DFT calculations on the COMP6 benchmark, achieving errors of 0.004e - (elementary charge). This is remarkable since this benchmark contains two proteins that are multiple times larger than the largest molecules in the training set. An application of our atomic charge predictions on nonequilibrium geometries is the generation of IR spectra for organic molecules from dynamical trajectories on a variety of organic molecules, which show good agreement with calculated IR spectra with reference method. Critically, HIP-NN charge predictions are many orders of magnitude faster than direct DFT calculations. These combined results provide further evidence that ML (specifically HIP-NN) provides a pathway to greatly increase the range of feasible simulations while retaining quantum-level accuracy.

The development of accurate and transferable machine learning (ML) potentials for predicting molecular energetics is a challenging task. The process of data generation to train such ML potentials is a task neither well understood nor researched in detail. In this work, we present a fully automated approach for the generation of datasets with the intent of training universal ML potentials. It is based on the concept of active learning (AL) via Query by Committee (QBC), which uses the disagreement between an ensemble of ML potentials to infer the reliability of the ensemble's prediction. QBC allows the presented AL algorithm to automatically sample regions of chemical space where the ML potential fails to accurately predict the potential energy. AL improves the overall fitness of ANAKIN-ME (ANI) deep learning potentials in rigorous test cases by mitigating human biases in deciding what new training data to use. AL also reduces the training set size to a fraction of the data required when using naive random sampling techniques. To provide validation of our AL approach, we develop the COmprehensive Machine-learning Potential (COMP6) benchmark (publicly available on GitHub) which contains a diverse set of organic molecules. Active learning-based ANI potentials outperform the original random sampled ANI-1 potential with only 10% of the data, while the final active learning-based model vastly outperforms ANI-1 on the COMP6 benchmark after training to only 25% of the data. Finally, we show that our proposed AL technique develops a universal ANI potential (ANI-1x) that provides accurate energy and force predictions on the entire COMP6 benchmark. This universal ML potential achieves a level of accuracy on par with the best ML potentials for single molecules or materials, while remaining applicable to the general class of organic molecules composed of the elements CHNO.

A method for efficiently simulating nonadiabatic molecular dynamics (NAMD) of nanoscale and condensed phase systems is developed and tested. The electronic structure, including force and nonadiabatic coupling, are obtained with the fragment molecular orbital (FMO) approximation, which provides significant computational savings by splitting the system into fragments and computing electronic properties of each fragment subject to the external field due to other all other fragments. The efficiency of the developed technique is demonstrated by studying the effect of explicit solvent molecules on excited state relaxation in the Fe(CO)4 complex. The relaxation in the gas phase occurs on a 50 fs time scale, which is in excellent agreement with previously recorded femtosecond pump-probe spectroscopy. Adding a solvation shell of ethanol molecules to the simulation results in an increase in the excited state lifetime to 100 fs, in agreement with recent femtosecond X-ray spectroscopy measurements.

A theoretical model based on Fulton and Gouterman dimer Hamiltonian [J. Chem. Phys. 35, 1059 (1961)] is used to understand the jet cooled spectra of partly deuterated diphenylmethane (DPM-d5), reported in adjoining paper by Zwier and co-workers ["Vibronic coupling in asymmetric bichromophores: Experimental investigation of diphenylmethane-d5," J. Chem. Phys. 141, 064316 (2014)]. The model is extended to include multiple vibrational modes, vibrational asymmetries between the monomers, and inter-monomer modes. Time dependent density functional theory and equation of motion coupled cluster electronic structure calculations are used to obtain parameters for the model Hamiltonian. The monomer units for DPM-d5 are toluene and partially deuterated toluene-d5. The comparisons of modeled and experimental spectra show that the model captures the vibronic effects on a multitude of observables, including anomalously intense vibrational states, transition dipole moment directions, and localization/delocalization phenomena of both the vibronic and electronic wavefunctions. Following the success of the model, a qualitative picture of vibronic coupling in DPM-d5 is built using only three active vibrations. This illustrates the ability of the model to not just qualitatively predict but also phenomenologically explain the vibronic effects observed in spectra of complex bichromophores.

Vibrationally and rotationally resolved electronic spectra of diphenylmethane-d5 (DPM-d5) are reported in the isolated-molecule environment of a supersonic expansion. While small, the asymmetry induced by deuteration of one of the aromatic rings is sufficient to cause several important effects that change the principle mechanism of vibronic coupling between the close-lying S1 and S2 states, and spectroscopic signatures such coupling produces. The splitting between S1 and S2 origins is 186 cm(-1), about 50% greater than its value in DPM-d0 (123 cm(-1)), and an amount sufficient to bring the S2 zero-point level into near-resonance with the v = 1 level in the S1 state of a low-frequency phenyl flapping mode, ν(R) = 191 cm(-1). Dispersed fluorescence spectra bear clear evidence that Δv(R) = 1 Herzberg-Teller coupling dominates the near-resonant internal mixing between the S1 and S2 manifolds. The fluorescence into each pair of Franck-Condon active ring modes shows an asymmetry that suggests incorrectly that the S1 and S2 states may be electronically localized. From rotationally resolved studies, the S0 and S1 states have been well-fit to asymmetric rotor Hamiltonians while the S2 state is perturbed and not fit. The transition dipole moment (TDM) orientation of the S1 state is nearly perpendicular to the C2 symmetry axes with 66(2)%:3(1)%:34(2)% a:b:c hybrid-type character while that of the S2 origin contains 50(10)% a:c-type (S1) and 50(10)% b-type (S2) character. A model is put forward that explains qualitatively the TDM compositions and dispersed emission patterns without the need to invoke electronic localization. The experimental data discussed here serve as a foundation for a multi-mode vibronic coupling model capable of being applied to asymmetric bichromophores, as presented in the work of B. Nebgen and L. V. Slipchenko ["Vibronic coupling in asymmetric bichromophores: Theory and application to diphenylmethane-d5," J. Chem. Phys. (submitted)].

The state-dependent spectroscopy of α-methylbenzyl radical (α-MeBz) has been studied under jet-cooled conditions. Two-color resonant two-photon ionization (2C-R2PI), laser-induced fluorescence, and dispersed fluorescence spectra were obtained for the D0-D1 electronic transition of this prototypical resonance-stabilized radical in which the methyl group is immediately adjacent to the primary radical site. Extensive Franck-Condon activity in hindered rotor levels was observed in the excitation spectrum, reflecting a reorientation of the methyl group upon electronic excitation. Dispersed fluorescence spectra from the set of internal rotor levels are combined with the excitation spectrum to obtain a global fit of the barrier heights and angular change of the methyl group in both D0 and D1 states. The best-fit methyl rotor potential in the ground electronic state (D0) is a flat-topped 3-fold potential (V3" = 151 cm(-1), V6" = 34 cm(-1)) while the D1 state has a lower barrier (V3' = 72 cm(-1), V6' = 15 cm(-1)) with Δφ = ± π/3, π, consistent with a reorientation of the methyl group upon electronic excitation. The ground state results are compared with calculations carried out at the DFT B3LYP level of theory using the 6-311+G(d,p) basis set, and a variety of excited state calculations are carried out to compare against experiment. The preferred geometry of the methyl rotor in the ground state is anti, which switches to syn in the D1 state and in the cation. The calculations uncover a subtle combination of effects that contribute to the shift in orientation and change in barrier in the excited state relative to ground state. Steric interaction favors the anti conformation, while hyperconjugation is greater in the syn orientation. The presence of a second excited state close by D1 is postulated to influence the methyl rotor properties. A resonant ion-dip infrared (RIDIR) spectrum in the alkyl and aromatic CH stretch regions was also recorded, probing in a complementary way the state-dependent conformation of α-MeBz. Using a scheme in which infrared depletion occurs between excitation and ionization steps of the 2C-R2PI process, analogous infrared spectra in D1 were also obtained, probing the response of the CH stretch fundamentals to electronic excitation. A reduced-dimension Wilson G-matrix model was implemented to simulate and interpret the observed infrared results. Finally, photoionization efficiency scans were carried out to determine the adiabatic ionization threshold of α-MeBz (IP = 6.835 ± 0.002 eV) and provide thresholds for ionization out of specific internal rotor levels, which report on the methyl rotor barrier in the cation state.

The theory for modeling vibronic interactions in bichromophores was introduced in sixties by Witkowski and Moffitt [J. Chem. Phys. 33, 872 (1960)] and extended by Fulton and Gouterman [J. Chem. Phys. 35, 1059 (1961)]. The present work describes extension of this vibronic model to describe bichromophores with broken vibrational symmetry such as partly deuterated molecules. Additionally, the model is extended to include inter-chromophore vibrational modes. The model can treat multiple vibrational modes by employing Lanczos diagonalization procedure of sparse matrices. The developed vibronic model is applied to simulation of vibronic spectra of flexible bichromophore diphenylmethane and compared to high-resolution experimental spectra [J. A. Stearns, N. R. Pillsbury, K. O. Douglass, C. W. Müller, T. S. Zwier, and D. F. Plusquellic, J. Chem. Phys. 129, 224305 (2008)].

The structures of eight related known intermetallic structure types are the impetus to this paper: Li21Si5, Mg44Rh7, Zn13(Fe,Ni)2, Mg6Pd, Na6Tl, Zn91Ir11, Li13Na29Ba19, and Al69Ta39. All belong to the F43m space group, have roughly 400 atoms in their cubic unit cells, are built up at least partially from the gamma-brass structure, and exhibit pseudo-tenfold symmetric diffraction patterns. These pseudo-tenfold axes lie in the {110} directions, and thus present a paradox. The {110} set is comprised of three pairs of perpendicular directions. Yet no 3D point group contains a single pair of perpendicular fivefold axes (by Friedel's Law, a fivefold axis leads to a tenfold diffraction pattern). The current work seeks to resolve this paradox. Its resolution is based on the largest of all 4D Platonic solids, the 600-cell. We first review the 600-cell, building an intuition discussing 4D polyhedroids (4D polytopes). We then show that the positions of common atoms in the F43m structures lie close to the positions of vertices in a 3D projection of the 600-cell. For this purpose, we develop a projection method that we call intermediate projection. The introduction of the 600-cell resolves the above paradox. This 4D Platonic solid contains numerous orthogonal fivefold rotations. The six fivefold directions that are best preserved after projection prove to lie along the {110} directions of the F43m structures. Finally, this paper shows that at certain ideal projected cluster sizes related to one another by the golden mean (tau=(1+ radical 5)/2), constructive interference leading to tenfold diffraction patterns is optimized. It is these optimal values that predominate in actual F43m structures. Explicit comparison of experimental cluster sizes and theoretically derived cluster sizes shows a clear correspondence, both for isolated and crystalline pairs of projected 600-cells.

Of the most common cubic intermetallic structure types, several (MgCu(2), Cu(5)Zn(8), Ti(2)Ni, and alpha-Mn) have superstructures with unusual symmetry properties. These superstructures (Be(5)Au, Li(21)Si(5), Sm(11)Cd(45), and Mg(44)Ir(7)) have the unusual property of pairs of perpendicular pseudo fivefold axes, most apparent in their X-ray diffraction patterns. The current work shows that an 8D to 3D projection method cleanly describes most (and in one case, all) of the atomic positions in the four superstructures mentioned above. This type of projection, which maps the E(8) lattice (a mathematically simple 8D crystal) into 3D space, combines the desired higher dimensional point group's perpendicular fivefold rotations with 3D translational symmetry-exactly what we see in the experimental crystal structures. The projection method successfully accounts for all heavy atom positions in the four superstructures, and at least 60-70 % of the light atom positions. The results suggest that all of these structures, previously known to be connected only by qualitative similarities in their atomic "clusters", are approximants of a single, as-yet unknown, class of quasicrystal.