Calculation of matrix elements for one- dimensional quantum-mechanical problems.
Matrix elements calculation for one dimensional quantum-mechanical problems using transformation theory
Certain, P. R.↗
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A quantum-mechanical method for calculating level widths and shifts, applicable to type I unimolecular predissociation
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Zimmerman, I. H.↗
Mechanism of Catalysis by L -Asparaginase
Two bacterial type II L -asparaginases, from Escherichia coli and Dickeya chrysanthemi, have played a critical role for more than 40 years as therapeutic agents against juvenile leukemias and lymphomas. Despite a long history of successful pharmacological applications and the apparent simplicity of the catalytic reaction, controversies still exist regarding major steps of the mechanism. In this report, we provide a detailed description of the reaction catalyzed by E. coli type II L -asparaginase (EcAII). Our model was developed on the basis of new structural and biochemical experiments combined with previously published data. The proposed mechanism is supported by quantum chemistry calculations based on density functional theory. In this work, we provide strong evidence that EcAII catalyzes the reaction according to the double-displacement (ping-pong) mechanism, with formation of a covalent intermediate. Several steps of catalysis by EcAII are unique when compared to reactions catalyzed by other known hydrolytic enzymes. Here, the reaction is initiated by a weak nucleophile, threonine, without direct assistance of a general base, although a distant general base is identified. Furthermore, tetrahedral intermediates formed during the catalytic process are stabilized by a never previously described motif. Although the scheme of the catalytic mechanism was developed only on the basis of data obtained from EcAII and its variants, this novel mechanism of enzymatic hydrolysis could potentially apply to most (and possibly all) L -asparaginases.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Reactive Molecular Dynamics Simulations and Quantum Chemistry Calculations To Investigate Soot-Relevant Reaction Pathways for Hexylamine Isomers
Sooting tendencies of a series of nitrogen-containing hydrocarbons (NHCs) have been recently characterized experimentally using the yield sooting index (YSI) methodology. This work aims to identify soot-relevant reaction pathways for three selected C6H15N amines, namely, dipropylamine (DPA), diisopropylamine (DIPA), and 3,3-dimethylbutylamine (DMBA) using ReaxFF molecular dynamics (MD) simulations and quantum mechanical (QM) calculations and to interpret the experimentally observed trends. ReaxFF MD simulations are performed to determine the important intermediate species and radicals involved in the fuel decomposition and soot formation processes. QM calculations are employed to extensively search for chemical reactions involving these species and radicals based on the ReaxFF MD results and also to quantitatively characterize the potential energy surfaces. Specifically, ReaxFF simulations are carried out in the NVT ensemble at 1400, 1600, and 1800 K, where soot has been identified to form in the YSI experiment. These simulations account for the interactions among test fuel molecules and pre-existing radicals and intermediate species generated from rich methane combustion, using a recently proposed simulation framework. ReaxFF simulations predict that the reactivity of the amines decrease in the order DIPA > DPA > DMBA, independent of temperature. Both QM calculations and ReaxFF simulations predict that C2H4, C3H6, and C4H8 are the main nonaromatic soot precursors formed during the decomposition of DPA, DIPA, and DMBA, respectively, and the associated reaction pathways are identified for each amine. Both theoretical methods predict that sooting tendency increases in the order DPA, DIPA, and DMBA, consistent with the experimentally measured trend in YSI. This work demonstrates that sooting tendencies and soot-relevant reaction pathways of fuels with unknown chemical kinetics can be identified efficiently through combined ReaxFF and QM simulations. Overall, predictions from ReaxFF simulations and QM calculations are consistent, in terms of fuel reactivity, major intermediates, and major nonaromatic soot precursors.
fuel decomposition↗
Improved techniques for outgoing wave variational principle calculations of converged state-to-state transition probabilities for chemical reactions
Improved techniques and well-optimized basis sets are presented for application of the outgoing wave variational principle to calculate converged quantum mechanical reaction probabilities. They are illustrated with calculations for the reactions D + H2 yields HD + H with total angular momentum J = 3 and F + H2 yields HF + H with J = 0 and 3. The optimization involves the choice of distortion potential, the grid for calculating half-integrated Green's functions, the placement, width, and number of primitive distributed Gaussians, and the computationally most efficient partition between dynamically adapted and primitive basis functions. Benchmark calculations with 224-1064 channels are presented.
Mielke, Steven L.↗
Adequacy of classical inverse bremsstrahlung theory for low-temperature plasmas
The authors examine those plasma heating conditions under which a theory more accurate than the classical inverse bremsstrahlung theory should be used to predict absorption coefficients when laser energy is injected into the plasma. A correlation plot for measured absorption coefficients at three laser wavelengths versus those calculated by quantum mechanical theory yields a correlation coefficient for the least-squares fit of 0.994. A plot of the ratio of the quantum-mechanically corrected electron ion inverse bremsstrahlung absorption coefficient to that calculated by classical methods versus plasma temperature shows that at around 20 eV and above the differences between classical and quantum predictions are negligible, but significant errors could arise from application of classical theories to lower-temperature plasmas. Some recent experiments in the literature are shown to be worthy of reinterpretation in this light.
Billman, K. W.↗
Tunneling calculations for GaAs-Al(x)Ga(1-x) as graded band-gap sawtooth superlattices
Quantum mechanical tunneling calculations for sawtooth (linearly graded band-gap) and step-barrier AlGaAs superlattices were performed by means of a transfer matrix method, within the effective mass approximation. The transmission coefficient and tunneling current versus applied voltage were computed for several representative structures. Particular consideration was given to effective mass variations. The tunneling properties of step and sawtooth superlattices show some qualitative similarities. Both structures exhibit resonant tunneling, however, because they deform differently under applied fields, the J-V curves differ.
Forrest, Kathrine A.↗
Applications of time-dependent perturbation theory.
Atomic and molecular time-dependent quantum- mechanical perturbation theory with differential equation formulation within Hartree-Fock approximation
TIME DEPENDENCY↗
An effective field theory of quantum mechanical black hole horizons
We develop an effective theory which describes black holes with quantum mechanical horizons that is valid at scales long compared to the Schwarzschild radius but short compared to the lifetime of the black hole. Our formalism allows one to calculate the quantum mechanical effects in scattering processes involving black hole asymptotic states. We point out that the EFT Wightman functions which describe Hawking radiation in the Unruh vacuum are not Planck suppressed and are actually enhanced relative to those in the Boulware vacuum, for which such radiation is absent. We elaborate on this point showing how the non-Planck suppressed effects of Hawking radiation cancel in classical observables.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
AQuaRef: machine learning accelerated quantum refinement of protein structures
Cryo-EM and X-ray crystallography provide crucial experimental data for obtaining atomic-detail models of biomacromolecules. Refining these models relies on library-based stereochemical data, which, in addition to being limited to known chemical entities, do not include meaningful noncovalent interactions. Quantum mechanical (QM) calculations could alleviate these issues but are too expensive for large molecules. Here we present a novel AI-enabled Quantum Refinement (AQuaRef) based on AIMNet2 machine learned interatomic potential (MLIP) mimicking QM at substantially lower computational costs. By refining 41 cryo-EM and 30 X-ray structures, we show that this approach yields atomic models with superior geometric quality compared to standard techniques, while maintaining an equal or better fit to experimental data. Notably, AQuaRef aids in determining proton positions, as illustrated in the challenging case of short hydrogen bonds in the parkinsonism-associated human protein DJ-1 and its bacterial homolog YajL.
Zubatyuk, Roman [Carnegie Mellon University, Pitts↗
Direct calculation of the reactive transition matrix by L-squared quantum mechanical variational methods with complex boundary conditions
A new formalism of the generalized Newton variational principle for the calculation of quantum mechanical state-to-state reaction probabilities is presented. The reformulation involves solving directly for the transition matrix rather than the reactance mtrix so that calculations may be carried out for individual columns of the transition matrix without obtaining solutions for all possible initial channels. The convergence of calculations with real and complex boundary conditions are compared for H + H2 - H2 + H, O + H2 - OH + H, and O + HD - OH + D and OD + H.
Sun, Yan↗
Comparison of cross sections from the quasi-classical trajectory method and the j(z)-conserving centrifugal sudden approximation with accurate quantum results for an atom-rigid nonlinear polyatomic collision
We report the results of a series of calculations of state-to-state integral cross sections for collisions between O and nonvibrating H2O in the gas phase on a model nonreactive potential energy surface. The dynamical methods used include converged quantum mechanical scattering calculations, the j(z) conserving centrifugal sudden (j(z)-CCS) approximation, and quasi-classical trajectory (QCT) calculations. We consider three total energies 0.001, 0.002, and 0.005 E(h) and the nine initial states with rotational angular momentum less than or equal to 2 (h/2 pi). The j(z)-CCS approximation gives good results, while the QCT method can be quite unreliable for transitions to specific rotational sublevels. However, the QCT cross sections summed over final sublevels and averaged over initial sublevels are in better agreement with the quantum results.
Schwenke, David W.↗
Protein–Ligand Binding Free-Energy Calculations with ARROW–A Purely First-Principles Parameterized Polarizable Force Field
Protein–ligand binding free-energy calculations using molecular dynamics (MD) simulations have emerged as a powerful tool for in silico drug design. Here, we present results obtained with the ARROW force field (FF)–a multipolar polarizable and physics-based model with all parameters fitted entirely to high-level ab initio quantum mechanical (QM) calculations. ARROW has already proven its ability to determine solvation free energy of arbitrary neutral compounds with unprecedented accuracy. The ARROW FF parameterization is now extended to include coverage of all amino acids including charged groups, allowing molecular simulations of a series of protein–ligand systems and prediction of their relative binding free energies. We ensure adequate sampling by applying a novel technique that is based on coupling the Hamiltonian Replica exchange (HREX) with a conformation reservoir generated via potential softening and nonequilibrium MD. ARROW provides predictions with near chemical accuracy (mean absolute error of ~0.5 kcal/mol) for two of the three protein systems studied here (MCL1 and Thrombin). The third protein system (CDK2) reveals the difficulty in accurately describing dimer interaction energies involving polar and charged species. Overall, for all of the three protein systems studied here, ARROW FF predicts relative binding free energies of ligands with a similar accuracy level as leading nonpolarizable force fields.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Is Deprotonation of the Oxygen-Evolving Complex of Photosystem II during the S 1 → S 2 Transition Suppressed by Proton Quantum Delocalization?
We address the protonation state of the water-derived ligands in the oxygen-evolving complex (OEC) of photosystem II (PSII), prepared in the S 2 state of the Kok cycle. We perform quantum mechanics/molecular mechanics calculations of isotropic proton hyperfine coupling constants, with direct comparisons to experimental data from two-dimensional hyperfine sublevel correlation (HYSCORE) spectroscopy and extended X-ray absorption fine structure (EXAFS). We find a low-barrier hydrogen bond with significant delocalization of the proton shared by the water-derived ligand, W1, and the aspartic acid residue D1–D61 of the D1 polypeptide. The lowering of the zero-point energy of a shared proton due to quantum delocalization precludes its release to the lumen during the S 1 → S 2 transition. Retention of the proton facilitates the shuttling of a proton during the isomerization of the tetranuclear manganese–calcium–oxo (Mn 4 Ca–oxo) cluster, from the “open” to “closed” conformation, a step suggested to be necessary for oxygen evolution from previous studies. Our findings suggest that quantum-delocalized protons, stabilized by low-barrier hydrogen bonds in model catalytic systems, can facilitate the accumulation of multiple oxidizing equivalents at low overpotentials.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Quantum mechanical model of three-body rearrangement scattering. II - Calculations for a resonance energy
Resonance energy calculation and transmission coefficient estimate for quantum mechanical model of reactive scattering of three atoms in line
Dion, D. R.↗
Phase shifts and the quantum mechanical hamilton-jacobi equation
Accurate values of phase shifts calculated by integration of quantum mechanical Hamilton- Jacobi equation
HAMILTON-JACOBI EQUATION↗
Phase Stability in U-6Nb Alloy Doped with Ti from the First Principles Theory
First-principles calculations within the density-functional-theory (DFT) approach are conducted in order to explore and explain the effect of small amounts of titanium on phase stability in the U-6Nb alloy. During rapid quenching from high to room temperature, metastable phases α' (orthorhombic), α" (monoclinic), and γ 0 (tetragonal) can form, depending on Nb concentration. Important mechanical properties depend on the crystal structure and, therefore, an understanding of the effect of impurities on phase stability is essential. Insights on this issue are obtained from quantum-mechanical DFT calculations. The DFT framework does not rely on any material-specific assumptions and is therefore ideal for an unbiased investigation of the U-Nb system.
36 MATERIALS SCIENCE↗
Learning together: Towards foundation models for machine learning interatomic potentials with meta-learning
Abstract The development of machine learning models has led to an abundance of datasets containing quantum mechanical (QM) calculations for molecular and material systems. However, traditional training methods for machine learning models are unable to leverage the plethora of data available as they require that each dataset be generated using the same QM method. Taking machine learning interatomic potentials (MLIPs) as an example, we show that meta-learning techniques, a recent advancement from the machine learning community, can be used to fit multiple levels of QM theory in the same training process. Meta-learning changes the training procedure to learn a representation that can be easily re-trained to new tasks with small amounts of data. We then demonstrate that meta-learning enables simultaneously training to multiple large organic molecule datasets. As a proof of concept, we examine the performance of a MLIP refit to a small drug-like molecule and show that pre-training potentials to multiple levels of theory with meta-learning improves performance. This difference in performance can be seen both in the reduced error and in the improved smoothness of the potential energy surface produced. We therefore show that meta-learning can utilize existing datasets with inconsistent QM levels of theory to produce models that are better at specializing to new datasets. This opens new routes for creating pre-trained, foundation models for interatomic potentials.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗