SCN as a local probe of protein structural dynamics.

The dynamics of lysozyme is probed by attaching -SCN to all alanine residues. The one-dimensional infrared spectra exhibit frequency shifts in the position of the maximum absorption of 4 cm-1, which is consistent with experiments in different solvents and indicates moderately strong interactions of the vibrational probe with its environment. Isotopic substitution 12C → 13C leads to a redshift by -47 cm-1, which agrees quantitatively with experiments for CN-substituted copper complexes in solution. The low-frequency, far-infrared part of the protein spectra contains label-specific information in the difference spectra when compared with the wild type protein. Depending on the position of the labels, local structural changes are observed. For example, introducing the -SCN label at Ala129 leads to breaking of the α-helical structure with concomitant change in the far-infrared spectrum. Finally, changes in the local hydration of SCN-labeled alanine residues as a function of time can be related to the reorientation of the label. It is concluded that -SCN is potentially useful for probing protein dynamics, both in the high-frequency part (CN-stretch) and in the far-infrared part of the spectrum.

High-Energy Reaction Dynamics of N3.

The atom-exchange and atomization dissociation dynamics for the N(4S) + N2(1Σg+) reaction are studied using a reproducing kernel Hilbert space (RKHS)-based, global potential energy surface (PES) at the MRCI-F12/aug-cc-pVTZ-F12 level of theory (MRCI, multireference configuration interaction). For the atom exchange reaction (NANB + NC → NANC + NB), computed thermal rates and their temperature dependence from quasi-classical trajectory (QCT) simulations agree to within error bars with the available experiments. Companion QCT simulations using a recently published CASPT2-based PES confirm these findings. For the atomization reaction, leading to three N(4S) atoms, the computed rates from the RKHS-PES overestimate the experimentally reported rates by 1 order of magnitude, whereas those from the permutationally invariant polynomial (PIP)-PES agree favorably, and the T dependence of both computations is consistent with the experiment. These differences can be traced back to the different methods and basis sets used. The lifetime of the metastable N3 molecule is estimated to be ∼200 fs depending on the initial state of the reactants. Finally, neural-network-based exhaustive state-to-distribution models are presented using both PESs for the atom exchange reaction. These models will be instrumental for a broader exploration of the reaction dynamics of air.

Systematic improvement of empirical energy functions in the era of machine learning.

The impact of targeted replacement of individual terms in empirical force fields is quantitatively assessed for pure water, dichloromethane (CH 2 Cl 2 ), and solvated K + and Cl - ions. For the electrostatic interactions, point charges (PCs) and machine learning (ML)-based minimally distributed charges (MDCM) fitted to the molecular electrostatic potential are evaluated together with electrostatics based on the Coulomb integral. The impact of explicitly including second-order terms is investigated by adding a fragment molecular orbital (FMO)-derived polarization energy to an existing force field, in this case CHARMM. It is demonstrated that anisotropic electrostatics reduce the RMSE for water (by 1.4 kcal/mol), CH 2 Cl 2 (by 0.8 kcal/mol) and for solvated Cl - clusters (by 0.4 kcal/mol). An additional polarization term can be neglected for CH 2 Cl 2 but further improves the models for pure water (by ∼ 1.0 kcal/mol) and hydrated Cl - (by 0.4 kcal/mol), and is key for solvated K + , reducing the RMSE by 2.3 kcal/mol. A 12-6 Lennard-Jones functional form performs satisfactorily with PC and MDCM electrostatics, but is not appropriate for descriptions that account for the electrostatic penetration energy. The importance of many-body contributions is assessed by comparing a strictly 2-body approach with self-consistent reference data. Two-body interactions suffice for CH 2 Cl 2 whereas water and solvated K + and Cl - ions require explicit many-body corrections. Finally, a many-body-corrected dimer potential energy surface exceeds the accuracy attained using a conventional empirical force field, potentially reaching that of an FMO calculation. The present work systematically quantifies which terms improve the performance of an existing force field and what reference data to use for parametrizing these terms in a tractable fashion for ML fitting of pure and heterogeneous systems.

OH-Formation following vibrationally induced reaction dynamics of H2COO.

The reaction dynamics of H2COO to form HCOOH and dioxirane as first steps for OH-elimination is quantitatively investigated. Using a machine learned potential energy surface (PES) at the CASPT2/aug-cc-pVTZ level of theory vibrational excitation along the CH-normal mode νCH with energies up to 40.0 kcal mol-1 (∼5νCH) leads almost exclusively to HCOOH which further decomposes into OH + HCO. Although the barrier to form dioxirane is only 21.4 kcal mol-1 the reaction probability to form dioxirane is two orders of magnitude lower if the CH-stretch mode is excited. Following the dioxirane-formation pathway is facile, however, if the COO-bend vibration is excited together with energies equivalent to ∼2νCH or ∼3νCOO. For OH-formation in the atmosphere the pathway through HCOOH is probably most relevant because the alternative pathways (through dioxirane or formic acid) involve several intermediates that can de-excite through collisions, relax via internal vibrational relaxation (IVR), or pass through loose and vulnerable transition states (formic acid). This work demonstrates how, by selectively exciting particular vibrational modes, it is possible to dial into desired reaction channels with a high degree of specificity.

Numerical Accuracy Matters: Applications of Machine Learned Potential Energy Surfaces.

The role of numerical accuracy in training and evaluating neural network-based potential energy surfaces is examined for different experimental observables. For observables that require third- and fourth-order derivatives of the potential energy with respect to Cartesian coordinates single-precision arithmetics as is typically used in ML-based approaches is insufficient and leads to roughness of the underlying PES as is explicitly demonstrated. Increasing the numerical accuracy to double-precision gives a smooth PES with higher-order derivatives that are numerically stable and yield meaningful anharmonic frequencies and tunneling splitting as is demonstrated for H2CO and malonaldehyde. For molecular dynamics simulations, which only require first-order derivatives, single-precision arithmetics appears to be sufficient, though.

Improving potential energy surfaces using measured Feshbach resonance states.

The structure and dynamics of a molecular system is governed by its potential energy surface (PES), representing the total energy as a function of the nuclear coordinates. Obtaining accurate potential energy surfaces is limited by the exponential scaling of Hilbert space, restricting quantitative predictions of experimental observables from first principles to small molecules with just a few electrons. Here, we present an explicitly physics-informed approach for improving and assessing the quality of families of PESs by modifying them through linear coordinate transformations based on experimental data. We demonstrate this "morphing" of the PES for the He - H2+ complex using recent comprehensive Feshbach resonance (FR) measurements for reference PESs at three different levels of quantum chemistry. In all cases, the positions and intensities of peaks in the energy distributions are improved. We find these observables to be mainly sensitive to the long-range part of the PES.

Molecular Simulation for Atmospheric Reactions: Non-Equilibrium Dynamics, Roaming, and Glycolaldehyde Formation following Photoinduced Decomposition of syn-Acetaldehyde Oxide.

The decomposition dynamics of vibrationally excited syn-CH3CHOO to form vinoxy + hydroxyl (CH2CHO + OH) radicals or to recombine to form glycolaldehyde (CH2OHCHO) are characterized using statistically significant numbers of molecular dynamics simulations using a full-dimensional neural-network-based potential energy surface at the CASPT2 level of theory. The computed final OH-translational and rotational state distributions agree well with experiments and probe the still unknown O-O bond strength DeOO for which best values from 22 to 25 kcal/mol are found. OH-elimination rates are consistent with experiments and do not vary appreciably with DeOO due to the non-equilibrium nature of the process. In addition to the OH-elimination pathway, OH roaming is observed following O-O scission, which leads to glycolaldehyde formation on the picosecond time scale. Together with recent work involving the methyl-ethyl-substituted Criegee intermediate, we conclude that OH roaming is a general pathway to be included in molecular-level modeling of atmospheric processes. This work demonstrates that atomistic simulations with machine-learned energy functions provide a viable route for exploring the chemistry and reaction dynamics of atmospheric reactions.

Experimental and Theoretical Studies of Hyperthermal N + O2 Collisions.

The dynamics of hyperthermal N(4S) + O2 collisions were investigated both experimentally and theoretically. Crossed molecular beams experiments were performed at an average center-of-mass (c.m.) collision energy of ⟨Ecoll⟩ = 77.5 kcal mol-1, with velocity- and angle-resolved product detection by a rotatable mass spectrometer detector. Nonreactive (N + O2) and reactive (NO + O) product channels were identified. In the c.m. reference frame, the nonreactively scattered N atoms and reactively scattered NO molecules were both directed into the forward direction with respect to the initial direction of the reagent N atoms. On average, more than 90% of the available energy (⟨Eavl⟩ = 77.5 kcal mol-1) was retained in translation of the nonreactive products (N + O2), whereas a much smaller fraction of the available energy for the reactive pathway (⟨Eavl⟩ = 109.5 kcal mol-1) went into translation of the NO + O products, and the distribution of translational energies for this channel was broad, indicating extensive internal excitation in the nascent NO molecules. The experimentally derived c.m. translational energy and angular distributions of the reactive products suggested at least two dynamical pathways to the formation of NO + O. Quasiclassical trajectory (QCT) calculations were performed with a collision energy of Ecoll = 77 kcal mol-1 using two sets of potential energy surfaces, denoted as PES-I and PES-II, and these theoretical results were compared to each other and to the experimental results. PES-I is a reproducing kernel Hilbert space (RKHS) representation of multireference configurational interaction (MRCI) energies, while PES-II is a many-body permutation invariant polynomial (MB-PIP) fit of complete active space second order perturbation (CASPT2) points. The theoretical investigations were both consistent with the experimental suggestion of two dynamical pathways to produce NO + O, where reactive collisions may proceed on the doublet (12A') and quartet (14A') surfaces. When analyzed with this theoretical insight, the experimental c.m. translational energy and angular distributions were in reasonably good agreement with those predicted by the QCT calculations, although minor differences were observed which are discussed. Theoretical translational energy and angular distributions for the nonreactive N + O2 products matched the experimental translational energy and angular distributions almost quantitatively. Finally, relative yields for the nonreactive and reactive scattering channels were determined from the experiment and from both theoretical methods, and all results are in reasonable agreement.

The first HyDRA challenge for computational vibrational spectroscopy.

Vibrational spectroscopy in supersonic jet expansions is a powerful tool to assess molecular aggregates in close to ideal conditions for the benchmarking of quantum chemical approaches. The low temperatures achieved as well as the absence of environment effects allow for a direct comparison between computed and experimental spectra. This provides potential benchmarking data which can be revisited to hone different computational techniques, and it allows for the critical analysis of procedures under the setting of a blind challenge. In the latter case, the final result is unknown to modellers, providing an unbiased testing opportunity for quantum chemical models. In this work, we present the spectroscopic and computational results for the first HyDRA blind challenge. The latter deals with the prediction of water donor stretching vibrations in monohydrates of organic molecules. This edition features a test set of 10 systems. Experimental water donor OH vibrational wavenumbers for the vacuum-isolated monohydrates of formaldehyde, tetrahydrofuran, pyridine, tetrahydrothiophene, trifluoroethanol, methyl lactate, dimethylimidazolidinone, cyclooctanone, trifluoroacetophenone and 1-phenylcyclohexane-cis-1,2-diol are provided. The results of the challenge show promising predictive properties in both purely quantum mechanical approaches as well as regression and other machine learning strategies.

PhysNet meets CHARMM: A framework for routine machine learning/molecular mechanics simulations.

Full-dimensional potential energy surfaces (PESs) based on machine learning (ML) techniques provide a means for accurate and efficient molecular simulations in the gas and condensed phase for various experimental observables ranging from spectroscopy to reaction dynamics. Here, the MLpot extension with PhysNet as the ML-based model for a PES is introduced into the newly developed pyCHARMM application programming interface. To illustrate the conception, validation, refining, and use of a typical workflow, para-chloro-phenol is considered as an example. The main focus is on how to approach a concrete problem from a practical perspective and applications to spectroscopic observables and the free energy for the -OH torsion in solution are discussed in detail. For the computed IR spectra in the fingerprint region, the computations for para-chloro-phenol in water are in good qualitative agreement with experiment carried out in CCl4. Moreover, relative intensities are largely consistent with experimental findings. The barrier for rotation of the -OH group increases from ∼3.5 kcal/mol in the gas phase to ∼4.1 kcal/mol from simulations in water due to favorable H-bonding interactions of the -OH group with surrounding water molecules.

Transfer-learned potential energy surfaces: Toward microsecond-scale molecular dynamics simulations in the gas phase at CCSD(T) quality.

The rise of machine learning has greatly influenced the field of computational chemistry and atomistic molecular dynamics simulations in particular. One of its most exciting prospects is the development of accurate, full-dimensional potential energy surfaces (PESs) for molecules and clusters, which, however, often require thousands to tens of thousands of ab initio data points restricting the community to medium sized molecules and/or lower levels of theory (e.g., density functional theory). Transfer learning, which improves a global PES from a lower to a higher level of theory, offers a data efficient alternative requiring only a fraction of the high-level data (on the order of 100 are found to be sufficient for malonaldehyde). This work demonstrates that even with Hartree-Fock theory and a double-zeta basis set as the lower level model, transfer learning yields coupled-cluster single double triple [CCSD(T)]-level quality for H-transfer barrier energies, harmonic frequencies, and H-transfer tunneling splittings. Most importantly, finite-temperature molecular dynamics simulations on the sub-µs time scale in the gas phase are possible and the infrared spectra determined from the transfer-learned PESs are in good agreement with the experiment. It is concluded that routine, long-time atomistic simulations on PESs fulfilling CCSD(T)-standards become possible.

Low-temperature kinetics for the N + NO reaction: experiment guides the way.

The reaction N(4S) + NO(X2Π) → O(3P) + N2(X1Σ+g) plays a pivotal role in the conversion of atomic to molecular nitrogen in dense interstellar clouds and in the atmosphere. Here we report a joint experimental and computational investigation of the N + NO reaction with the aim of providing improved constraints on its low temperature reactivity. Thermal rates were measured over the 50 to 296 K range in a continuous supersonic flow reactor coupled with pulsed laser photolysis and laser induced fluorescence for the production and detection of N(4S) atoms, respectively. With decreasing temperature, the experimentally measured reaction rate was found to monotonously increase up to a value of (6.6 ± 1.3) × 10-11 cm3 s-1 at 50 K. To confirm this finding, quasi-classical trajectory simulations were carried out on a previously validated, full-dimensional potential energy surface (PES). However, around 50 K the computed rates decreased which required re-evaluation of the reactive PES in the long-range part due to a small spurious barrier with a height of ∼40 K in the entrance channel. By exploring different correction schemes the measured thermal rates can be adequately reproduced, displaying a clear negative temperature dependence over the entire temperature range. The possible astrochemical implications of an increased reaction rate at low temperature are also discussed.

Conformational and state-specific effects in reactions of 2,3-dibromobutadiene with Coulomb-crystallized calcium ions.

Recent advances in experimental methodology enabled studies of the quantum-state- and conformational dependence of chemical reactions under precisely controlled conditions in the gas phase. Here, we generated samples of selected gauche and s-trans 2,3-dibromobutadiene (DBB) by electrostatic deflection in a molecular beam and studied their reaction with Coulomb crystals of laser-cooled Ca+ ions in an ion trap. The rate coefficients for the total reaction were found to strongly depend on both the conformation of DBB and the electronic state of Ca+. In the (4p)2P1/2 and (3d)2D3/2 excited states of Ca+, the reaction is capture-limited and faster for the gauche conformer due to long-range ion-dipole interactions. In the (4s)2S1/2 ground state of Ca+, the reaction rate for s-trans DBB still conforms with the capture limit, while that for gauche DBB is strongly suppressed. The experimental observations were analysed with the help of adiabatic capture theory, ab initio calculations and reactive molecular dynamics simulations on a machine-learned full-dimensional potential energy surface of the system. The theory yields near-quantitative agreement for s-trans-DBB, but overestimates the reactivity of the gauche-conformer compared to the experiment. The present study points to the important role of molecular geometry even in strongly reactive exothermic systems and illustrates striking differences in the reactivity of individual conformers in gas-phase ion-molecule reactions.

Interaction at a distance: Xenon migration in Mb.

The transport of ligands, such as NO or O2, through internal cavities is essential for the function of globular proteins, including hemoglobin, myoglobin (Mb), neuroglobin, truncated hemoglobins, or cytoglobin. For Mb, several internal cavities (Xe1 through Xe4) were observed experimentally and they were linked to ligand storage. The present work determines barriers for xenon diffusion and relative stabilization energies for the ligand in the initial and final pocket, linking a transition depending on the occupancy state of the remaining pockets from both biased and unbiased molecular dynamics simulations. It is found that the energetics of a particular ligand migration pathway may depend on the direction in which the transition is followed and the occupancy state of the other cavities. Furthermore, the barrier height for a particular transition can depend in a non-additive fashion on the occupancy of either cavity A or B or simultaneous population of both cavities, A and B. Multiple repeats for the Xe1 → Xe2 transition reveal that the activation barrier is a distribution of barrier heights rather than one single value, which is confirmed by a distribution of transition times for the same transition from unbiased simulations. Dynamic cross correlation maps demonstrate that correlated motions occur between adjacent residues or through space, residue Phe138 is found to be a gate for the Xe1 → Xe2 transition, and the volumes of the internal cavities vary along the diffusion pathway, indicating that there is dynamic communication between the ligand and the protein. These findings suggest that Mb is an allosteric protein.

Tomography of Feshbach resonance states.

Feshbach resonances are fundamental to interparticle interactions and become particularly important in cold collisions with atoms, ions, and molecules. In this work, we present the detection of Feshbach resonances in a benchmark system for strongly interacting and highly anisotropic collisions: molecular hydrogen ions colliding with noble gas atoms. The collisions are launched by cold Penning ionization, which exclusively populates Feshbach resonances that span both short- and long-range parts of the interaction potential. We resolved all final molecular channels in a tomographic manner using ion-electron coincidence detection. We demonstrate the nonstatistical nature of the final-state distribution. By performing quantum scattering calculations on ab initio potential energy surfaces, we show that the isolation of the Feshbach resonance pathways reveals their distinctive fingerprints in the collision outcome.

Molecular-level understanding of the rovibrational spectra of N2O in gaseous, supercritical, and liquid SF6 and Xe.

The transition between the gas-, supercritical-, and liquid-phase behavior is a fascinating topic, which still lacks molecular-level understanding. Recent ultrafast two-dimensional infrared spectroscopy experiments suggested that the vibrational spectroscopy of N2O embedded in xenon and SF6 as solvents provides an avenue to characterize the transitions between different phases as the concentration (or density) of the solvent increases. The present work demonstrates that classical molecular dynamics (MD) simulations together with accurate interaction potentials allows us to (semi-)quantitatively describe the transition in rotational vibrational infrared spectra from the P-/R-branch line shape for the stretch vibrations of N2O at low solvent densities to the Q-branch-like line shapes at high densities. The results are interpreted within the classical theory of rigid-body rotation in more/less constraining environments at high/low solvent densities or based on phenomenological models for the orientational relaxation of rotational motion. It is concluded that classical MD simulations provide a powerful approach to characterize and interpret the ultrafast motion of solutes in low to high density solvents at a molecular level.

Local Hydration Control and Functional Implications Through S-Nitrosylation of Proteins: Kirsten Rat Sarcoma Virus (K-RAS) and Hemoglobin (Hb).

S-nitrosylation, the covalent addition of NO to the thiol side chain of cysteine, is an important post-transitional modification (PTM) that can affect the function of proteins. As such, PTMs extend and diversify protein function and thus characterizing consequences of PTM at a molecular level is of great interest. Although PTMs can be detected through various direct/indirect methods, they lack the capability to investigate the modifications with molecular detail. In the present work local and global structural dynamics, their correlation, the hydration structure, and the infrared spectroscopy for WT and S-nitrosylated Kirsten rat sarcoma virus (K-RAS) and hemoglobin (Hb) are characterized from molecular dynamics simulations. It is found that attaching NO to Cys118 in K-RAS rigidifies the protein in the Switch-I region which has functional implications, whereas for Hb, nitrosylation at Cys93 at the ß1 chain increases the flexibility of secondary structural motives for Hb in its T0 and R4 conformational substates. Solvent water access decreased by 40% after nitrosylation in K-RAS, similar to Hb for which, however, local hydration of the R4SNO state is yet lower than for T0SNO. Finally, S-nitrosylation leads to detectable peaks for the NO stretch frequency, but the congested IR spectral region will make experimental detection of these bands difficult. Overall, S-nitrosylation in these two proteins is found to influence hydration, protein flexibility, and conformational dynamics which are all eventually involved in protein regulation and function at a molecular level.

Neural network potentials for chemistry: concepts, applications and prospects.

Artificial Neural Networks (NN) are already heavily involved in methods and applications for frequent tasks in the field of computational chemistry such as representation of potential energy surfaces (PES) and spectroscopic predictions. This perspective provides an overview of the foundations of neural network-based full-dimensional potential energy surfaces, their architectures, underlying concepts, their representation and applications to chemical systems. Methods for data generation and training procedures for PES construction are discussed and means for error assessment and refinement through transfer learning are presented. A selection of recent results illustrates the latest improvements regarding accuracy of PES representations and system size limitations in dynamics simulations, but also NN application enabling direct prediction of physical results without dynamics simulations. The aim is to provide an overview for the current state-of-the-art NN approaches in computational chemistry and also to point out the current challenges in enhancing reliability and applicability of NN methods on a larger scale.

Water dynamics around T0 vs R4 of hemoglobin from local hydrophobicity analysis.

The local hydration around tetrameric hemoglobin (Hb) in its T0 and R4 conformational substates is analyzed based on molecular dynamics simulations. Analysis of the local hydrophobicity (LH) for all residues at the α1ß2 and α2ß1 interfaces, responsible for the quaternary T → R transition, which is encoded in the Monod-Wyman-Changeux model, as well as comparison with earlier computations of the solvent accessible surface area, makes clear that the two quantities measure different aspects of hydration. Local hydrophobicity quantifies the presence and structure of water molecules at the interface, whereas "buried surface" reports on the available space for solvent. For simulations with Hb frozen in its T0 and R4 states, the correlation coefficient between LH and buried surface is 0.36 and 0.44, respectively, but it increases considerably if the 95% confidence interval is used. The LH with Hb frozen and flexible changes little for most residues at the interfaces but is significantly altered for a few select ones: Thr41α, Tyr42α, Tyr140α, Trp37ß, Glu101ß (for T0) and Thr38α, Tyr42α, Tyr140α (for R4). The number of water molecules at the interface is found to increase by ∼25% for T0 → R4, which is consistent with earlier measurements. Since hydration is found to be essential to protein function, it is clear that hydration also plays an essential role in allostery.

Molecular Dynamics with Conformationally Dependent, Distributed Charges.

Accounting for geometry-induced changes in the electronic distribution in molecular simulation is important for capturing effects such as charge flow, charge anisotropy, and polarization. Multipolar force fields have demonstrated their ability to correctly represent chemically significant features such as anisotropy and sigma holes. It has also been shown that off-center point charges offer a compact alternative with similar accuracy. Here, it is demonstrated that allowing relocation of charges within a minimally distributed charge model (MDCM) with respect to their reference atoms is a viable route to capture changes in the molecular charge distribution depending on geometry, i.e., intramolecular polarization. The approach, referred to as "flexible MDCM" (fMDCM), is validated on a number of small molecules and provides accuracies in the electrostatic potential (ESP) of 0.5 kcal/mol on average compared with reference data from electronic structure calculations, whereas MDCM and point charges have root mean squared errors of a factor of 2 to 5 higher. In addition, MD simulations in the NVE ensemble using fMDCM for a box of flexible water molecules with periodic boundary conditions show a width of 0.1 kcal/mol for the fluctuation around the mean at 300 K on the 10 ns time scale. For water, the equilibrium valence angle in the gas phase is found to increase by 2° for simulations in the condensed phase which is consistent with experiment. The accuracy in capturing the geometry dependence of the ESP together with the long-time stability in energy conserving simulations makes fMDCM a promising tool to introduce advanced electrostatics into atomistic simulations.