Non-conventional force fields for applications in spectroscopy and chemical reaction dynamics

Force Fields for Deep Eutectic Mixtures: Application to Structure, Thermodynamics and 2D-Infrared Spectroscopy

Parametrizing energy functions for ionic systems can be challenging. Here, the total energy function for an eutectic system consisting of water, SCN-, K+ and acetamide is improved vis-a-vis experimentally measured properties. Given the importance of electrostatic interactions, two different types of models are considered: the first (model M0) uses atom-centered multipole whereas the other two (models M1 and M2) are based on fluctuating minimal distributed charges (fMDCM) that respond to geometrical changes of SCN-. The Lennard-Jones parameters of the anion are adjusted to best reproduce experimentally known hydration free energies and densities, which are matched to within a few percent for the final models irrespective of the electrostatic model. Molecular dynamics simulations of the eutectic mixtures with varying water content (between 0 and 100%) yield radial distribution functions and frequency correlation functions for the CN-stretch vibration. Comparison with experiments indicates that models based on fMDCM are considerably more consistent than those using multipoles. Computed viscosities from models M1 and M2 are within 30% of measured values and their change with increasing water content is consistent with experiments. This is not the case for model M0.

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.

Vibrational Circular Dichroism Spectroscopy with a Classical Polarizable Force Field: Alanine in the Gas and Condensed Phases

Polarizable force fields are an essential component for the chemically accurate modeling of complex molecular systems with a significant degree of fluxionality, beyond harmonic or perturbative approximations. In this contribution we examine the performance of such an approach for the vibrational spectroscopy of the alanine amino acid, in the gas and condensed phases, from the Fourier transform of appropriate time correlation functions generated along molecular dynamics (MD) trajectories. While the infrared (IR) spectrum only requires the electric dipole moment, the vibrational circular dichroism (VCD) spectrum further requires knowledge of the magnetic dipole moment, for which we provide relevant expressions to be used with polarizable force fields. The AMOEBA force field was employed here to model alanine in the neutral and zwitterionic isolated forms, solvated by water or nitrogen, and as a crystal. Within this framework, comparison of the electric and magnetic dipole moments to those obtained with nuclear velocity perturbation theory based on density-functional theory for the same MD trajectories are found to agree well with one another. The statistical convergence of the IR and VCD spectra is examined and found to be more demanding in the latter case. Comparisons with experimental frequencies are also provided for the condensed phases.

A Machine Learning Force Field for Bio-Macromolecular Modeling Based on Quantum Chemistry-Calculated Interaction Energy Datasets

Accurate energy data from noncovalent interactions are essential for constructing force fields for molecular dynamics simulations of bio-macromolecular systems. There are two important practical issues in the construction of a reliable force field with the hope of balancing the desired chemical accuracy and working efficiency. One is to determine a suitable quantum chemistry level of theory for calculating interaction energies. The other is to use a suitable continuous energy function to model the quantum chemical energy data. For the first issue, we have recently calculated the intermolecular interaction energies using the SAPT0 level of theory, and we have systematically organized these energies into the ab initio SOFG-31 (homodimer) and SOFG-31-heterodimer datasets. In this work, we re-calculate these interaction energies by using the more advanced SAPT2 level of theory with a wider series of basis sets. Our purpose is to determine the SAPT level of theory proper for interaction energies with respect to the CCSD(T)/CBS benchmark chemical accuracy. Next, to utilize these energy datasets, we employ one of the well-developed machine learning techniques, called the CLIFF scheme, to construct a general-purpose force field for biomolecular dynamics simulations. Here we use the SOFG-31 dataset and the SOFG-31-heterodimer dataset as the training and test sets, respectively. Our results demonstrate that using the CLIFF scheme can reproduce a diverse range of dimeric interaction energy patterns with only a small training set. The overall errors for each SAPT energy component, as well as the SAPT total energy, are all well below the desired chemical accuracy of ~1 kcal/mol.

Intermolecular Non-Bonded Interactions from Machine Learning Datasets

Accurate determination of intermolecular non-covalent-bonded or non-bonded interactions is the key to potentially useful molecular dynamics simulations of polymer systems. However, it is challenging to balance both the accuracy and computational cost in force field modelling. One of the main difficulties is properly representing the calculated energy data as a continuous force function. In this paper, we employ well-developed machine learning techniques to construct a general purpose intermolecular non-bonded interaction force field for organic polymers. The original ab initio dataset SOFG-31 was calculated by us and has been well documented, and here we use it as our training set. The CLIFF kernel type machine learning scheme is used for predicting the interaction energies of heterodimers selected from the SOFG-31 dataset. Our test results show that the overall errors are well below the chemical accuracy of about 1 kcal/mol, thus demonstrating the promising feasibility of machine learning techniques in force field modelling.

PESPIP: Software to fit complex molecular and many-body potential energy surfaces with permutationally invariant polynomials

We wish to describe a potential energy surface by using a basis of permutationally invariant polynomials whose coefficients will be determined by numerical regression so as to smoothly fit a dataset of electronic energies as well as, perhaps, gradients. The polynomials will be powers of transformed internuclear distances, usually either Morse variables, exp(-r_i,j/λ), where λ is a constant range hyperparameter, or reciprocals of the distances, 1/r_i,j. The question we address is how to create the most efficient basis, including (a) which polynomials to keep or discard, (b) how many polynomials will be needed, (c) how to make sure the polynomials correctly reproduce the zero interaction at a large distance, (d) how to ensure special symmetries, and (e) how to calculate gradients efficiently. This article discusses how these questions can be answered by using a set of programs to choose and manipulate the polynomials as well as to write efficient Fortran programs for the calculation of energies and gradients. A user-friendly interface for access to monomial symmetrization approach results is also described. The software for these programs is now publicly available.

Hydration dynamics and IR spectroscopy of 4-fluorophenol

Halogenated groups are relevant in pharmaceutical applications and potentially useful spectroscopic probes for infrared spectroscopy. In this work, the structural dynamics and infrared spectroscopy of para-fluorophenol (F-PhOH) and phenol (PhOH) is investigated in the gas phase and in water using a combination of experiment and molecular dynamics (MD) simulations. The gas phase and solvent dynamics around F-PhOH and PhOH is characterized from atomistic simulations using empirical energy functions with point charges or multipoles for the electrostatics, Machine Learning (ML) based parametrizations and with full ab initio (QM) and mixed Quantum Mechanical/Molecular Mechanics (QM/MM) simulations with a particular focus on the CF- and OH-stretch region. The CF-stretch band is heavily mixed with other modes whereas the OH-stretch in solution displays a characteristic high-frequency peak around 3600 cm-1 most likely associated with the -OH group of PhOH and F-PhOH together with a characteristic progression below 3000 cm-1 due to coupling with water modes which is also reproduced by several of the simulations. Solvent and radial distribution functions indicate that the CF-site is largely hydrophobic except for simulations using point charges which renders them unsuited for correctly describing hydration and dynamics around fluorinated sites. The hydrophobic character of the CF-group is particularly relevant for applications in pharmaceutical chemistry with a focus on local hydration and interaction with the surrounding protein.

The MD17 datasets from the perspective of datasets for gas-phase “small” molecule potentials

There has been great progress in developing methods for machine-learned potential energy surfaces. There have also been important assessments of these methods by comparing so-called learning curves on datasets of electronic energies and forces, notably the MD17 database. The dataset for each molecule in this database generally consists of tens of thousands of energies and forces obtained from DFT direct dynamics at 500 K. We contrast the datasets from this database for three “small” molecules, ethanol, malonaldehyde, and glycine, with datasets we have generated with specific targets for the potential energy surfaces (PESs) in mind: a rigorous calculation of the zero-point energy and wavefunction, the tunneling splitting in malonaldehyde, and, in the case of glycine, a description of all eight low-lying conformers. We found that the MD17 datasets are too limited for these targets. We also examine recent datasets for several PESs that describe small-molecule but complex chemical reactions. Finally, we introduce a new database, “QM-22,” which contains datasets of molecules ranging from 4 to 15 atoms that extend to high energies and a large span of configurations.

Quantitative molecular simulations

All-atom simulations can provide molecular-level insights into the dynamics of gas-phase, condensed-phase and surface processes. One important requirement is a sufficiently realistic and detailed description of the underlying intermolecular interactions. The present perspective provides an overview of the present status of quantitative atomistic simulations from colleagues' and our own efforts for gas- and solution-phase processes and for the dynamics on surfaces. Particular attention is paid to direct comparison with experiment. An outlook discusses present challenges and future extensions to bring such dynamics simulations even closer to reality.

Double proton transfer in hydrated formic acid dimer: Interplay of spatial symmetry and solvent-generated force on reactivity

The double proton transfer (DPT) reaction in the hydrated formic acid dimer (FAD) is investigated at molecular-level detail. For this, a global and reactive machine learned (ML) potential energy surface (PES) is developed to run extensive (more than 100 ns) mixed ML/MM molecular dynamics (MD) simulations in explicit molecular mechanics (MM) solvent at MP2-quality for the solute. Simulations with fixed – as in a conventional empirical force field – and conformationally fluctuating – as available from the ML-based PES – charge models for FAD show a significant impact on the competition between DPT and dissociation of FAD into two formic acid monomers. With increasing temperature the barrier height for DPT in solution changes by about 10% (∼1 kcal mol⁻¹) between 300 K and 600 K. The rate for DPT is largest, ∼1 ns⁻¹, at 350 K and decreases for higher temperatures due to destabilisation and increased probability for dissociation of FAD. The water solvent is found to promote the first proton transfer by exerting a favourable solvent-induced Coulomb force along the O–H⋯O hydrogen bond whereas the second proton transfer is significantly controlled by the O–O separation and other conformational degrees of freedom. Double proton transfer in hydrated FAD is found to involve a subtle interplay and balance between structural and electrostatic factors.

Simulation of double proton transfer in formic acid dimer by reactive ML potential in explicit molecular mechanics water solvent.

Predicting properties of periodic systems from cluster data: A case study of liquid water

The accuracy of the training data limits the accuracy of bulk properties from machine-learned potentials. For example, hybrid functionals or wave-function-based quantum chemical methods are readily available for cluster data but effectively out of scope for periodic structures. We show that local, atom-centered descriptors for machine-learned potentials enable the prediction of bulk properties from cluster model training data, agreeing reasonably well with predictions from bulk training data. We demonstrate such transferability by studying structural and dynamical properties of bulk liquid water with density functional theory and have found an excellent agreement with experimental and theoretical counterparts.

Local Electronic Charge Transfer in the Helical Induction of Cis-Transoid Poly(4-carboxyphenyl)acetylene by Chiral Amines

Understanding the phenomena that lead to the formation of a specific helicity in helical polymers remains a challenge even today. Various polymers have been shown to assume different helical screw-senses depending on different stimuli. Acid-base chiral amines, for example, can induce helical conformations on cis-transoid poly(4-carboxyphenyl)acetylene yielding high-intensity circular dichroism signals. There have been many experimental attempts to elucidate the driving forces involved, but the induction process remains unclear. Here, we investigate the mechanism of helical polymer formation by both Molecular Dynamics (MD) and Density Functional Theory (DFT) approaches. We find that DFT calculations and the dissociation energies between 4 monomer polymers and amines show a clear trend in the affinity of R and S conformers with clockwise and counterclockwise polymer screw-senses, respectively. The charge analysis revealed that the local charge transfer effect plays a crucial role that leads to the helical polymer-amine induction.

Chemistry Dissolved in Ionic Liquids. A Theoretical Perspective

The theoretical treatment of ionic liquids must focus now on more realistic models while at the same time keeping an accurate methodology when following recent ionic liquids research trends or allowing predictability to come to the foreground. In this Perspective, we summarize in three cases of advanced ionic liquid research what methodological progress has been made and point out difficulties that need to be overcome. As particular examples to discuss we choose reactions, chirality, and radicals in ionic liquids. All these topics have in common that an explicit or accurate treatment of the electronic structure and/or intermolecular interactions is required (accurate methodology), while at the same time system size and complexity as well as simulation time (realistic model) play an important role and must be covered as well.

Providing direction for mechanistic inferences in radical cascade cyclization using Transformer model

Even in modern organic chemistry, predicting or proposing a reaction mechanism and speculating on reaction intermediates remains challenging. For example, it is challenging to predict the regioselectivity of radical attraction...

Multipolar Force Fields for Amide-I Spectroscopy from Conformational Dynamics of the Alanine Trimer

The dynamics and spectroscopy of N-methyl-acetamide (NMA) and trialanine in solution are characterized from molecular dynamics simulations using different energy functions, including a conventional point charge (PC)-based force field, one based on a multipolar (MTP) representation of the electrostatics, and a semiempirical DFT method. For the 1D infrared spectra, the frequency splitting between the two amide-I groups is 10 cm^-1 from the PC, 13 cm^-1 from the MTP, and 47 cm^-1 from self-consistent charge density functional tight-binding (SCC-DFTB) simulations, compared with 25 cm^-1 from experiment. The frequency trajectory required for the frequency fluctuation correlation function (FFCF) is determined from individual normal mode (INM) and full normal mode (FNM) analyses of the amide-I vibrations. The spectroscopy, time-zero magnitude of the FFCF C(t = 0), and the static component Δ₀² from simulations using MTP and analysis based on FNM are all consistent with experiments for (Ala)₃. Contrary to this, for the analysis excluding mode-mode coupling (INM), the FFCF decays to zero too rapidly and for simulations with a PC-based force field, the Δ₀² is too small by a factor of two compared with experiments. Simulations with SCC-DFTB agree better with experiment for these observables than those from PC-based simulations. The conformational ensemble sampled from simulations using PCs is consistent with the literature (including P_II, β, α_R, and α_L), whereas that covered by the MTP-based simulations is dominated by P_II with some contributions from β and α_R. This agrees with and confirms recently reported Bayesian-refined populations based on 1D infrared experiments. FNM analysis together with a MTP representation provides a meaningful model to correctly describe the dynamics of hydrated trialanine.

Machine Learning for Chemical Reactions

Machine learning (ML) techniques applied to chemical reactions have a long history. The present contribution discusses applications ranging from small molecule reaction dynamics to computational platforms for reaction planning. ML-based techniques can be particularly relevant for problems involving both computation and experiments. For one, Bayesian inference is a powerful approach to develop models consistent with knowledge from experiments. Second, ML-based methods can also be used to handle problems that are formally intractable using conventional approaches, such as exhaustive characterization of state-to-state information in reactive collisions. Finally, the explicit simulation of reactive networks as they occur in combustion has become possible using machine-learned neural network potentials. This review provides an overview of the questions that can and have been addressed using machine learning techniques, and an outlook discusses challenges in this diverse and stimulating field. It is concluded that ML applied to chemistry problems as practiced and conceived today has the potential to transform the way with which the field approaches problems involving chemical reactions, in both research and academic teaching.

CLIFF: A component-based, machine-learned, intermolecular force field

Computation of intermolecular interactions is a challenge in drug discovery because accurate ab initio techniques are too computationally expensive to be routinely applied to drug-protein models. Classical force fields are more computationally feasible, and force fields designed to match symmetry adapted perturbation theory (SAPT) interaction energies can remain accurate in this context. Unfortunately, the application of such force fields is complicated by the laborious parameterization required for computations on new molecules. Here, we introduce the component-based machine-learned intermolecular force field (CLIFF), which combines accurate, physics-based equations for intermolecular interaction energies with machine-learning models to enable automatic parameterization. The CLIFF uses functional forms corresponding to electrostatic, exchange-repulsion, induction/polarization, and London dispersion components in SAPT. Molecule-independent parameters are fit with respect to SAPT2+(3)δMP2/aug-cc-pVTZ, and molecule-dependent atomic parameters (atomic widths, atomic multipoles, and Hirshfeld ratios) are obtained from machine learning models developed for C, N, O, H, S, F, Cl, and Br. The CLIFF achieves mean absolute errors (MAEs) no worse than 0.70 kcal mol^-1 in both total and component energies across a diverse dimer test set. For the side chain-side chain interaction database derived from protein fragments, the CLIFF produces total interaction energies with an MAE of 0.27 kcal mol^-1 with respect to reference data, outperforming similar and even more expensive methods. In applications to a set of model drug-protein interactions, the CLIFF is able to accurately rank-order ligand binding strengths and achieves less than 10% error with respect to SAPT reference values for most complexes.

Site-selective dynamics of azidolysozyme

The spectroscopic response of and structural dynamics around all azido-modified alanine residues (AlaN₃) in lysozyme are characterized. It is found that AlaN₃ is a positionally sensitive probe for the local dynamics, covering a frequency range of ∼15 cm^-1 for the center frequency of the line shape. This is consistent with findings from selective replacements of amino acids in PDZ2, which reported a frequency span of ∼10 cm^-1 for replacements of Val, Ala, or Glu by azidohomoalanine. For the frequency fluctuation correlation functions, the long-time decay constants τ₂ range from ∼1 to ∼10 ps, which compares with experimentally measured correlation times of 3 ps. Attaching azide to alanine residues can yield dynamics that decays to zero on the few ps time scale (i.e., static component Δ₀ ∼ 0 ps^-1) or to a remaining, static contribution of ∼0.5 ps^-1 (corresponding to 2.5 cm^-1), depending on the local environment on the 10 ps time scale. The magnitude of the static component correlates qualitatively with the degree of hydration of the spectroscopic probe. Although attaching azide to alanine residues is found to be structurally minimally invasive with respect to the overall protein structure, analysis of the local hydrophobicity indicates that the hydration around the modification site differs for modified and unmodified alanine residues, respectively.

Dynamics and Infrared Spectrocopy of Monomeric and Dimeric Wild Type and Mutant Insulin

The infrared spectroscopy and dynamics of -CO labels in wild type and mutant insulin monomer and dimer are characterized from molecular dynamics simulations using validated force fields. It is found that the spectroscopy of monomeric and dimeric forms in the region of the amide-I vibration differs for residues B24-B26 and D24-D26, which are involved in dimerization of the hormone. Also, the spectroscopic signatures change for mutations at position B24 from phenylalanine, which is conserved in many organisms and is known to play a central role in insulin aggregation, to alanine or glycine. Using three different methods to determine the frequency trajectories (solving the nuclear Schrödinger equation on an effective 1-dimensional potential energy curve, using instantaneous normal modes, and using parametrized frequency maps) leads to the same overall conclusions. The spectroscopic response of monomeric WT and mutant insulin differs from that of their respective dimers, and the spectroscopy of the two monomers in the dimer is also not identical. For the WT and F24A and F24G monomers, spectroscopic shifts are found to be ∼20 cm^-1 for residues (B24-B26) located at the dimerization interface. Although the crystal structure of the dimer is that of a symmetric homodimer, dynamically the two monomers are not equivalent on the nanosecond time scale. Together with earlier work on the thermodynamic stability of the WT and the same mutants, it is concluded that combining computational and experimental infrared spectroscopy provides a potentially powerful way to characterize the aggregation state and dimerization energy of modified insulins.

Complex reaction processes in combustion unraveled by neural network-based molecular dynamics simulation

Combustion is a complex chemical system which involves thousands of chemical reactions and generates hundreds of molecular species and radicals during the process. In this work, a neural network-based molecular dynamics (MD) simulation is carried out to simulate the benchmark combustion of methane. During MD simulation, detailed reaction processes leading to the creation of specific molecular species including various intermediate radicals and the products are intimately revealed and characterized. Overall, a total of 798 different chemical reactions were recorded and some new chemical reaction pathways were discovered. We believe that the present work heralds the dawn of a new era in which neural network-based reactive MD simulation can be practically applied to simulating important complex reaction systems at ab initio level, which provides atomic-level understanding of chemical reaction processes as well as discovery of new reaction pathways at an unprecedented level of detail beyond what laboratory experiments could accomplish.

Gaining insights into combustion processes is challenging due to the complex reactions involved. The present work proposes a neural network potential model trained to ab initio data that enables to simulate the combustion of methane by predicting reactants, products and reaction intermediates.