Less is more: Sampling chemical space with active learning.

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.

Fragment Molecular Orbital Nonadiabatic Molecular Dynamics for Condensed Phase Systems.

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.

Jet-cooled spectroscopy of the α-methylbenzyl radical: probing the state-dependent effects of methyl rocking against a radical site.

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.

Vibronic coupling in asymmetric bichromophores: theory and application to diphenylmethane.

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)].

Graphics Processing Unit-Accelerated Semiempirical Born Oppenheimer Molecular Dynamics Using PyTorch.

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.

The mystery of perpendicular fivefold axes and the fourth dimension in intermetallic structures.

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.

Laves phases, gamma-brass, and 2x2x2 superstructures: a new class of quasicrystal approximants and the suggestion of a new quasicrystal.

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.