Permutationally Invariant Fitting of Many-Body, Non-covalent Interactions with Application to Three-Body Methane–Water–Water

MBX: A many-body energy and force calculator for data-driven many-body simulations

Many-Body eXpansion (MBX) is a C++ library that implements many-body potential energy functions (PEFs) within the "many-body energy" (MB-nrg) formalism. MB-nrg PEFs integrate an underlying polarizable model with explicit machine-learned representations of many-body interactions to achieve chemical accuracy from the gas to the condensed phases. MBX can be employed either as a stand-alone package or as an energy/force engine that can be integrated with generic software for molecular dynamics and Monte Carlo simulations. MBX is parallelized internally using Open Multi-Processing and can utilize Message Passing Interface when available in interfaced molecular simulation software. MBX enables classical and quantum molecular simulations with MB-nrg PEFs, as well as hybrid simulations that combine conventional force fields and MB-nrg PEFs, for diverse systems ranging from small gas-phase clusters to aqueous solutions and molecular fluids to biomolecular systems and metal-organic frameworks.

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.

Δ-Machine Learned Potential Energy Surfaces and Force Fields

There has been great progress in developing machine-learned potential energy surfaces (PESs) for molecules and clusters with more than 10 atoms. Unfortunately, this number of atoms generally limits the level of electronic structure theory to less than the "gold standard" CCSD(T) level. Indeed, for the well-known MD17 dataset for molecules with 9-20 atoms, all of the energies and forces were obtained with DFT calculations (PBE). This Perspective is focused on a Δ-machine learning method that we recently proposed and applied to bring DFT-based PESs to close to CCSD(T) accuracy. This is demonstrated for hydronium, N-methylacetamide, acetyl acetone, and ethanol. For 15-atom tropolone, it appears that special approaches (e.g., molecular tailoring, local CCSD(T)) are needed to obtain the CCSD(T) energies. A new aspect of this approach is the extension of Δ-machine learning to force fields. The approach is based on many-body corrections to polarizable force field potentials. This is examined in detail using the TTM2.1 water potential. The corrections make use of our recent CCSD(T) datasets for 2-b, 3-b, and 4-b interactions for water. These datasets were used to develop a new fully ab initio potential for water, termed q-AQUA.

Data-Driven Many-Body Potential Energy Functions for Generic Molecules: Linear Alkanes as a Proof-of-Concept Application

We present a generalization of the many-body energy (MB-nrg) theoretical/computational framework that enables the development of data-driven potential energy functions (PEFs) for generic covalently bonded molecules, with arbitrary quantum mechanical accuracy. The "nearsightedness of electronic matter" is exploited to define monomers as "natural building blocks" on the basis of their distinct chemical identity. The energy of generic molecules is then expressed as a sum of individual many-body energies of incrementally larger subsystems. The MB-nrg PEFs represent the low-order n-body energies, with n = 1-4, using permutationally invariant polynomials derived from electronic structure data carried out at an arbitrary quantum mechanical level of theory, while all higher-order n-body terms (n > 4) are represented by a classical many-body polarization term. As a proof-of-concept application of the general MB-nrg framework, we present MB-nrg PEFs for linear alkanes. The MB-nrg PEFs are shown to accurately reproduce reference energies, harmonic frequencies, and potential energy scans of alkanes, independently of their length. Since, by construction, the MB-nrg framework introduced here can be applied to generic covalently bonded molecules, we envision future computer simulations of complex molecular systems using data-driven MB-nrg PEFs, with arbitrary quantum mechanical accuracy.

Graph Theoretic Molecular Fragmentation for Multidimensional Potential Energy Surfaces Yield an Adaptive and General Transfer Machine Learning Protocol

Over a series of publications we have introduced a graph-theoretic description for molecular fragmentation. Here, a system is divided into a set of nodes, or vertices, that are then connected through edges, faces, and higher-order simplexes to represent a collection of spatially overlapping and locally interacting subsystems. Each such subsystem is treated at two levels of electronic structure theory, and the result is used to construct many-body expansions that are then embedded within an ONIOM-scheme. These expansions converge rapidly with many-body order (or graphical rank) of subsystems and have been previously used for ab initio molecular dynamics (AIMD) calculations and for computing multidimensional potential energy surfaces. Specifically, in all these cases we have shown that CCSD and MP2 level AIMD trajectories and potential surfaces may be obtained at density functional theory cost. The approach has been demonstrated for gas-phase studies, for condensed phase electronic structure, and also for basis set extrapolation-based AIMD. Recently, this approach has also been used to derive new quantum-computing algorithms that enormously reduce the quantum circuit depth in a circuit-based computation of correlated electronic structure. In this publication, we introduce (a) a family of neural networks that act in parallel to represent, efficiently, the post-Hartree-Fock electronic structure energy contributions for all simplexes (fragments), and (b) a new k-means-based tessellation strategy to glean training data for high-dimensional molecular spaces and minimize the extent of training needed to construct this family of neural networks. The approach is particularly useful when coupled cluster accuracy is desired and when fragment sizes grow in order to capture nonlocal interactions accurately. The unique multidimensional k-means tessellation/clustering algorithm used to determine our training data for all fragments is shown to be extremely efficient and reduces the needed training to only 10% of data for all fragments to obtain accurate neural networks for each fragment. These fully connected dense neural networks are then used to extrapolate the potential energy surface for all molecular fragments, and these are then combined as per our graph-theoretic procedure to transfer the learning process to a full system energy for the entire AIMD trajectory at less than one-tenth the cost as compared to a regular fragmentation-based AIMD calculation.

Breaking covalent bonds in the context of the many-body expansion (MBE). I. The purported "first row anomaly" in XHn (X = C, Si, Ge, Sn; n = 1-4)

We present a new, novel implementation of the Many-Body Expansion (MBE) to account for the breaking of covalent bonds, thus extending the range of applications from its previous popular usage in the breaking of hydrogen bonds in clusters to molecules. A central concept of the new implementation is the in situ atomic electronic state of an atom in a molecule that casts the one-body term as the energy required to promote it to that state from its ground state. The rest of the terms correspond to the individual diatomic, triatomic, etc., fragments. Its application to the atomization energies of the XHn series, X = C, Si, Ge, Sn and n = 1-4, suggests that the (negative, stabilizing) 2-B is by far the largest term in the MBE with the higher order terms oscillating between positive and negative values and decreasing dramatically in size with increasing rank of the expansion. The analysis offers an alternative explanation for the purported "first row anomaly" in the incremental Hn-1X-H bond energies seen when these energies are evaluated with respect to the lowest energy among the states of the XHn molecules. Due to the "flipping" of the ground/first excited state between CH2 (3B1 ground state, 1A1 first excited state) and XH2, X = Si, Ge, Sn (1A1 ground state, 3B1 first excited state), the overall picture does not exhibit a "first row anomaly" when the incremental bond energies are evaluated with respect to the molecular states having the same in situ atomic states.

Graph-Theory-Based Molecular Fragmentation for Efficient and Accurate Potential Surface Calculations in Multiple Dimensions

We present a multitopology molecular fragmentation approach, based on graph theory, to calculate multidimensional potential energy surfaces in agreement with post-Hartree-Fock levels of theory but at the density functional theory cost. A molecular assembly is coarse-grained into a set of graph-theoretic nodes that are then connected with edges to represent a collection of locally interacting subsystems up to an arbitrary order. Each of the subsystems is treated at two levels of electronic structure theory, the result being used to construct many-body expansions that are embedded within an ONIOM scheme. These expansions converge rapidly with the many-body order (or graphical rank) of subsystems and capture many-body interactions accurately and efficiently. However, multiple graphs, and hence multiple fragmentation topologies, may be defined in molecular configuration space that may arise during conformational sampling or from reactive, bond breaking and bond formation, events. Obtaining the resultant potential surfaces is an exponential scaling proposition, given the number of electronic structure computations needed. We utilize a family of graph-theoretic representations within a variational scheme to obtain multidimensional potential surfaces at a reduced cost. The fast convergence of the graph-theoretic expansion with increasing order of many-body interactions alleviates the exponential scaling cost for computing potential surfaces, with the need to only use molecular fragments that contain a fewer number of quantum nuclear degrees of freedom compared to the full system. This is because the dimensionality of the conformational space sampled by the fragment subsystems is much smaller than the full molecular configurational space. Additionally, we also introduce a multidimensional clustering algorithm, based on physically defined criteria, to reduce the number of energy calculations by orders of magnitude. The molecular systems benchmarked include coupled proton motion in protonated water wires. The potential energy surfaces and multidimensional nuclear eigenstates obtained are shown to be in very good agreement with those from explicit post-Hartree-Fock calculations that become prohibitive as the number of quantum nuclear dimensions grows. The developments here provide a rigorous and efficient alternative to this important chemical physics problem.

A CCSD(T)-Based 4-Body Potential for Water

High-level, ab initio calculations find that the 4-body (4-b) interaction is needed to account for near-100% of the total interaction energy for water clusters as large as the 21-mer. Motivated by this, we report a permutationally invariant polynomial potential energy surface (PES) for the 4-body interaction. This machine-learned PES is a fit to 2119 symmetry-unique, CCSD(T)-F12a/haTZ 4-b interaction energies. Configurations for these come from tetramer direct-dynamics calculations, fragments from an MD water simulation at 300 K, and tetramer fragments in a variety of water clusters. The PIP basis is purified to ensure that the PES goes rigorously to zero in monomer+trimer and dimer+dimer dissociations. The 4-b energies of isomers of the hexamer calculated with the new PES are shown to be in better agreement with benchmark CCSD(T) results than those from the MB-pol potential. Tests on larger clusters further validate the high-fidelity of the PES. The PES is shown to be fast to evaluate, taking 2.4 s for 10⁵ evaluations on a single core of 2.4 GHz Intel Xeon processor, and significantly faster using a parallel version of the PES.

General Many-Body Framework for Data-Driven Potentials with Arbitrary Quantum Mechanical Accuracy: Water as a Case Study

We present a general framework for the development of data-driven many-body (MB) potential energy functions (MB-QM PEFs) that represent the interactions between small molecules at an arbitrary quantum-mechanical (QM) level of theory. As a demonstration, a family of MB-QM PEFs for water is rigorously derived from density functionals belonging to different rungs across Jacob's ladder of approximations within density functional theory (MB-DFT) and from Møller-Plesset perturbation theory (MB-MP2). Through a systematic analysis of individual MB contributions to the interaction energies of water clusters, we demonstrate that all MB-QM PEFs preserve the same accuracy as the corresponding ab initio calculations, with the exception of those derived from density functionals within the generalized gradient approximation (GGA). The differences between the DFT and MB-DFT results are traced back to density-driven errors that prevent GGA functionals from accurately representing the underlying molecular interactions for different cluster sizes and hydrogen-bonding arrangements. We show that this shortcoming may be overcome, within the MB formalism, by using density-corrected functionals (DC-DFT) that provide a more consistent representation of each individual MB contribution. This is demonstrated through the development of a MB-DFT PEF derived from DC-PBE-D3 data, which more accurately reproduce the corresponding ab initio results.

Permutationally Invariant Polynomial Expansions with Unrestricted Complexity

A general strategy is presented for constructing and validating permutationally invariant polynomial (PIP) expansions for chemical systems of any stoichiometry. Demonstrations are made for three categories of gas-phase dynamics and kinetics: collisional energy-transfer trajectories for predicting pressure-dependent kinetics, three-body collisions for describing transient van der Waals adducts relevant to atmospheric chemistry, and nonthermal reactivity via quasiclassical trajectories. In total, 30 systems are considered with up to 15 atoms and 39 degrees of freedom. Permutational invariance is enforced in PIP expansions with as many as 13 million terms and 13 permutationally distinct atom types by taking advantage of petascale computational resources. The quality of the PIP expansions is demonstrated through the systematic convergence of in-sample and out-of-sample errors with respect to both the number of training data and the order of the expansion, and these errors are shown to predict errors in the dynamics for both reactive and nonreactive applications. The parallelized code distributed as part of this work enables the automation of PIP generation for complex systems with multiple channels and flexible user-defined symmetry constraints and for automatically removing unphysical unconnected terms from the basis set expansions, all of which are required for simulating complex reactive systems.

Guest-Host Interactions in Clathrate Hydrates: Benchmark MP2 and CCSD(T)/CBS Binding Energies of CH4, CO2, and H2S in (H2O)20 Cages

We present benchmark binding energies of naturally occurring gas molecules CH₄, CO₂, and H₂S in the small cage, namely, the pentagonal dodecahedron (5¹²) (H₂O)₂₀, which is one of the constituent cages of the 3 major lattices (structures I, II, and H) of clathrate hydrates. These weak interactions require higher levels of electron correlation and converge slowly with an increasing basis set to the complete basis set (CBS) limit, necessitating the use of large basis sets up to the aug-cc-pV5Z and subsequent correction for basis set superposition error (BSSE). For the host hollow (H₂O)₂₀ cages, we have identified a most stable isomer with binding energy of -200.8 ± 2.1 kcal/mol at the CCSD(T)/CBS limit (-199.2 ± 0.5 kcal/mol at the MP2/CBS limit). Additionally, we report converged second order Møller-Plesset (MP2) CBS binding energies for the encapsulation of guests in the (H₂O)₂₀ cage of -4.3 ± 0.1 for CH₄@(H₂O)₂₀, -6.6 ± 0.1 for CO₂@(H₂O)₂₀, and -8.5 ± 0.1 kcal/mol for H₂S@(H₂O)₂₀, respectively. For CH₄@(H₂O)₂₀, exhibiting the weakest encapsulation affinity among the three, we report CCSD(T)/aug-cc-pVTZ binding energies and, based on them, a CCSD(T)/CBS estimate of -4.75 ± 0.1 kcal/mol. To the best of our knowledge, the CCSD(T)/aug-cc-pVTZ calculation for CH₄@(H₂O)₂₀ is the largest one reported to date (168 valence electrons, 1978 basis functions, and the correlation of 84 doubly occupied and 1873 virtual orbitals) and required a scalable implementation of the (T) module on 6144 nodes (350 208 cores) of the "Cori" supercomputer at the National Energy Research Supercomputing Center (NERSC) for a total execution time of 195 min (for the (T) part). These efficient scalable implementations of highly correlated methods offer the capability to obtain long-lasting benchmarks of intermolecular interactions in complex systems. They also provide a path toward parametrizing classical potentials needed to study the dynamical and transport properties in these complex systems as well as assess the accuracy of lower scaling electronic structure methods such as density functional theory (DFT) and MP2 including its spin-biased variants.

Full-dimensional potential energy surface for acetylacetone and tunneling splittings

New, full-dimensional potential energy surface for acetylacetone allows for description of H-tunneling dynamics and characterization of stationary points.

Efficient Generation of Permutationally Invariant Potential Energy Surfaces for Large Molecules

An efficient method is described for generating a fragmented, permutationally invariant polynomial basis to fit electronic energies and, if available, gradients for large molecules. The method presented rests on the fragmentation of a large molecule into any number of fragments while maintaining the permutational invariance and uniqueness of the polynomials. The new approach improves on a previous one reported by Qu and Bowman by avoiding repetition of polynomials in the fitting basis set and speeding up gradient evaluations while keeping the accuracy of the PES. The method is demonstrated for CH₃–NH–CO–CH₃ (N-methylacetamide) and NH₂–CH₂–COOH (glycine).

Assessing the Importance of the H2-H2O-H2O Three-Body Interaction on the Vibrational Frequency Shift of H2 in the sII Clathrate Hydrate and Comparison with Experiment

The vibrational frequency shift of H₂ in the 5¹² cage of the sII clathrate hydrate with and without surrounding water molecules is reported at 0 K, using diffusion Monte Carlo calculations for the ground and first excited vibrational states of H₂. Approximate 1d calculations of the frequency shift are also reported with the H₂ at the equilibrium position in the clathrate hydrate. These calculations make use of full-dimensional potential energy surfaces for the H₂-H₂O 2-body and H₂-H₂O-H₂O 3-body interactions. The inclusion of the 3-body interaction is shown to make roughly a 33% contribution to the frequency shift and to bring the calculated value of -40 ± 4 cm^-1 to within just 3 cm^-1 of the experimental value at 20 K. This level of agreement with experiment may be somewhat fortuitous; however, the importance of the 3-body interaction is firmly established by these calculations. The frequency shift reported here with 2-body interactions does not agree with a previously reported calculation using just 2-body interactions from a different ab initio potential energy surface and with a different method to obtain the frequency shift. A similar 1d calculation of the frequency shift using that potential is reported and agrees to within roughly 10% of the one previously reported. Therefore, this suggests that the difference between the present calculations and the previous one using just 2-body interactions is mainly due to differences in the potential energy surfaces.

Quantum approaches to vibrational dynamics and spectroscopy: is ease of interpretation sacrificed as rigor increases?

The subject of this Perspective is quantum approaches, beyond the harmonic approximation, to vibrational dynamics and IR spectroscopy.

Low temperature reaction dynamics for CH3OH + OH collisions on a new full dimensional potential energy surface

Is the rise of the rate constant measured in laval expansion experiments of OH with organic molecules at low temperatures due to the reaction between the reactants or due to the formation of complexes with the buffer gas? This question has importance for understanding the evolution of prebiotic molecules observed in different astrophysical objects. Among these molecules methanol is one of the most widely observed, and its reaction with OH has been studied by several groups showing a fast increase in the rate constant under 100 K. Transition state theory doesn't reproduce this behavior and here dynamical calculations are performed on a new full dimensional potential energy surface developed for this purpose. The calculated classical reactive cross sections show an increase at low collision energies due to a complex forming mechanism. However, the calculated rate constant at temperatures below 100 K remains lower than the observed one. Quantum effects are likely responsible for the measured behavior at low temperatures.

"Divide and conquer" semiclassical molecular dynamics: A practical method for spectroscopic calculations of high dimensional molecular systems

We extensively describe our recently established "divide-and-conquer" semiclassical method [M. Ceotto, G. Di Liberto, and R. Conte, Phys. Rev. Lett. 119, 010401 (2017)] and propose a new implementation of it to increase the accuracy of results. The technique permits us to perform spectroscopic calculations of high-dimensional systems by dividing the full-dimensional problem into a set of smaller dimensional ones. The partition procedure, originally based on a dynamical analysis of the Hessian matrix, is here more rigorously achieved through a hierarchical subspace-separation criterion based on Liouville's theorem. Comparisons of calculated vibrational frequencies to exact quantum ones for a set of molecules including benzene show that the new implementation performs better than the original one and that, on average, the loss in accuracy with respect to full-dimensional semiclassical calculations is reduced to only 10 wavenumbers. Furthermore, by investigating the challenging Zundel cation, we also demonstrate that the "divide-and-conquer" approach allows us to deal with complex strongly anharmonic molecular systems. Overall the method very much helps the assignment and physical interpretation of experimental IR spectra by providing accurate vibrational fundamentals and overtones decomposed into reduced dimensionality spectra.

Full dimensional potential energy surface and low temperature dynamics of the H2CO + OH → HCO + H2O reaction

A new method is proposed to analytically represent the potential energy surface of reactions involving polyatomic molecules capable of accurately describing long-range interactions and saddle points, needed to describe low-temperature collisions. It is based on two terms, a reactive force field term and a many-body term. The reactive force field term accurately describes the fragments, long-range interactions among them and the saddle points for reactions. The many-body term increases the desired accuracy everywhere else. This method has been applied to the OH + H2CO → H2O + HCO reaction, giving a barrier of 27.4 meV. The simulated classical rate constants with this potential are in good agreement with recent experimental results [Ocaña et al., Astrophys. J., 2017, submitted], showing an important increase at temperatures below 100 K. The reaction mechanism is analyzed in detail here, and explains the observed behavior at low energy by the formation of long-lived collision complexes, with roaming trajectories, with a capture observed for very long impact parameters, >100 a.u., determined by the long-range dipole-dipole interaction.

The TensorMol-0.1 model chemistry: a neural network augmented with long-range physics

We construct a robust chemistry consisting of a nearsighted neural network potential, TensorMol-0.1, with screened long-range electrostatic and van der Waals physics. It is offered in an open-source Python package and achieves millihartree accuracy and a scalability to tens-of-thousands of atoms on ordinary laptops.

Traditional force fields cannot model chemical reactivity, and suffer from low generality without re-fitting. Neural network potentials promise to address these problems, offering energies and forces with near ab initio accuracy at low cost. However a data-driven approach is naturally inefficient for long-range interatomic forces that have simple physical formulas. In this manuscript we construct a hybrid model chemistry consisting of a nearsighted neural network potential with screened long-range electrostatic and van der Waals physics. This trained potential, simply dubbed “TensorMol-0.1”, is offered in an open-source Python package capable of many of the simulation types commonly used to study chemistry: geometry optimizations, harmonic spectra, open or periodic molecular dynamics, Monte Carlo, and nudged elastic band calculations. We describe the robustness and speed of the package, demonstrating its millihartree accuracy and scalability to tens-of-thousands of atoms on ordinary laptops. We demonstrate the performance of the model by reproducing vibrational spectra, and simulating the molecular dynamics of a protein. Our comparisons with electronic structure theory and experimental data demonstrate that neural network molecular dynamics is poised to become an important tool for molecular simulation, lowering the resource barrier to simulating chemistry.

Semiclassical "Divide-and-Conquer" Method for Spectroscopic Calculations of High Dimensional Molecular Systems

A new semiclassical "divide-and-conquer" method is presented with the aim of demonstrating that quantum dynamics simulations of high dimensional molecular systems are doable. The method is first tested by calculating the quantum vibrational power spectra of water, methane, and benzene-three molecules of increasing dimensionality for which benchmark quantum results are available-and then applied to C_{60}, a system characterized by 174 vibrational degrees of freedom. Results show that the approach can accurately account for quantum anharmonicities, purely quantum features like overtones, and the removal of degeneracy when the molecular symmetry is broken.

Intrinsic Bond Energies from a Bonds-in-Molecules Neural Network

Neural networks are being used to make new types of empirical chemical models as inexpensive as force fields, but with accuracy similar to the ab initio methods used to build them. In this work, we present a neural network that predicts the energies of molecules as a sum of intrinsic bond energies. The network learns the total energies of the popular GDB9 database to a competitive MAE of 0.94 kcal/mol on molecules outside of its training set, is naturally linearly scaling, and applicable to molecules consisting of thousands of bonds. More importantly, it gives chemical insight into the relative strengths of bonds as a function of their molecular environment, despite only being trained on total energy information. We show that the network makes predictions of relative bond strengths in good agreement with measured trends and human predictions. A Bonds-in-Molecules Neural Network (BIM-NN) learns heuristic relative bond strengths like expert synthetic chemists, and compares well with ab initio bond order measures such as NBO analysis.

On-the-Fly ab Initio Semiclassical Calculation of Glycine Vibrational Spectrum

We present an on-the-fly ab initio semiclassical study of vibrational energy levels of glycine, calculated by Fourier transform of the wavepacket correlation function. It is based on a multiple coherent states approach integrated with monodromy matrix regularization for chaotic dynamics. All four lowest-energy glycine conformers are investigated by means of single-trajectory semiclassical spectra obtained upon classical evolution of on-the-fly trajectories with harmonic zero-point energy. For the most stable conformer I, direct dynamics trajectories are also run for each vibrational mode with energy equal to the first harmonic excitation. An analysis of trajectories evolved up to 50 000 atomic time units demonstrates that, in this time span, conformers II and III can be considered as isolated species, while conformers I and IV show a pretty facile interconversion. Therefore, previous perturbative studies based on the assumption of isolated conformers are often reliable but might be not completely appropriate in the case of conformer IV and conformer I for which interconversion occurs promptly.

The many-body expansion combined with neural networks

Fragmentation methods such as the many-body expansion (MBE) are a common strategy to model large systems by partitioning energies into a hierarchy of decreasingly significant contributions. The number of calculations required for chemical accuracy is still prohibitively expensive for the ab initio MBE to compete with force field approximations for applications beyond single-point energies. Alongside the MBE, empirical models of ab initio potential energy surfaces have improved, especially non-linear models based on neural networks (NNs) which can reproduce ab initio potential energy surfaces rapidly and accurately. Although they are fast, NNs suffer from their own curse of dimensionality; they must be trained on a representative sample of chemical space. In this paper we examine the synergy of the MBE and NN's and explore their complementarity. The MBE offers a systematic way to treat systems of arbitrary size while reducing the scaling problem of large systems. NN's reduce, by a factor in excess of 10⁶, the computational overhead of the MBE and reproduce the accuracy of ab initio calculations without specialized force fields. We show that for a small molecule extended system like methanol, accuracy can be achieved with drastically different chemical embeddings. To assess this we test a new chemical embedding which can be inverted to predict molecules with desired properties. We also provide our open-source code for the neural network many-body expansion, Tensormol.

High-level ab initio potential energy surface and dynamics of the F- + CH3I SN2 and proton-transfer reactions

Bimolecular nucleophilic substitution (S_N2) and proton transfer are fundamental processes in chemistry and F^- + CH₃I is an important prototype of these reactions. Here we develop the first full-dimensional ab initio analytical potential energy surface (PES) for the F^- + CH₃I system using a permutationally invariant fit of high-level composite energies obtained with the combination of the explicitly-correlated CCSD(T)-F12b method, the aug-cc-pVTZ basis, core electron correlation effects, and a relativistic effective core potential for iodine. The PES accurately describes the S_N2 channel producing I^- + CH₃F via Walden-inversion, front-side attack, and double-inversion pathways as well as the proton-transfer channel leading to HF + CH₂I^-. The relative energies of the stationary points on the PES agree well with the new explicitly-correlated all-electron CCSD(T)-F12b/QZ-quality benchmark values. Quasiclassical trajectory computations on the PES show that the proton transfer becomes significant at high collision energies and double-inversion as well as front-side attack trajectories can occur. The computed broad angular distributions and hot internal energy distributions indicate the dominance of indirect mechanisms at lower collision energies, which is confirmed by analyzing the integration time and leaving group velocity distributions. Comparison with available crossed-beam experiments shows usually good agreement.

Influence of denticity and combined soft–hard strategy on the interaction of picolinic-type ligands with NpO2+

The denticity of the ligands and the combined hard–soft donor strategy work cooperatively in the coordination of NpO₂⁺ with ligands.

A quantum chemical study on ˙Cl-initiated atmospheric degradation of acrylonitrile

Degradation of acrylonitrile (CH₂CHCN) by reaction with atomic chlorine was studied using quantum chemical methods.