Interatomic Energy Research Articles

New Angles on Standard Force Fields: Toward a General Approach for Treating Atomic-Level Anisotropy.

Nearly all standard force fields employ the "sum-of-spheres" approximation, which models intermolecular interactions purely in terms of interatomic distances. Nonetheless, atoms in molecules can have significantly nonspherical shapes, leading to interatomic interaction energies with strong orientation dependencies. Neglecting this "atomic-level anisotropy" can lead to significant errors in predicting interaction energies. Herein, we propose a simple, transferable, and computationally efficient model (MASTIFF) whereby atomic-level orientation dependence can be incorporated into ab initio intermolecular force fields. MASTIFF includes anisotropic exchange-repulsion, charge penetration, and dispersion effects, in conjunction with a standard treatment of anisotropic long-range (multipolar) electrostatics. To validate our approach, we benchmark MASTIFF against various sum-of-spheres models over a large library of intermolecular interactions between small organic molecules. MASTIFF achieves quantitative accuracy, with respect to both high-level electronic structure theory and experiment, thus showing promise as a basis for "next-generation" force field development.

Manifestations of structural phase transition in ab initio molecular dynamics of (C3N2H5)2SbF5 crystal

Structural and electronic properties of the ferroelastic crystal (C3N2H5)2SbF5 characterized by first-order phase transition were studied by ab initio methods in the framework of density functional theory. The molecular dynamics calculations were performed at different temperatures in the range TC - 70 ÷ TC + 70° containing the phase transition point TC. In this approach, atomic scale (microscopic) manifestations of this transition were obtained. The quasi continuous temperature changes of some microscopic properties in the relatively wide temperature range around TC were observed in spite of sharp experimental temperature dependences of several macroscopic properties of (C3N2H5)2SbF5 near the first order phase transition point TC (latent heat flow, dielectric permittivity). The latter peculiarities may be regarded as the microscopic precursors of the first order phase transition in (C3N2H5)2SbF5. Different specific kinetic energies (energy per one atom) for five constituting chemical elements (C, N, H, Sb and F) of the crystal have been detected for the first time, indicating for different abilities of the interatomic energy exchange.

Covalent Bonding in the Hydrogen Molecule.

This work addresses the continuing disagreement between two schools of thought concerning the mechanism of covalent bonding. According to Hellmann, Ruedenberg, and Kutzelnigg, covalent bonding is a quantum mechanical phenomenon whereby lowering of the kinetic energy associated with electron sharing, i.e., delocalization, is the key stabilization mechanism. The opposing view of Slater, Feynman, and Bader has maintained that the source of stabilization is electrostatic potential energy lowering due to electron density redistribution to binding regions between nuclei. Following our study of H2+ we present an analogous detailed study of H2 where bonding involves an electron pair with repulsion and correlation playing a significant role in its properties. We use a range of different computational approaches to study and reveal the relevant contributions to bonding as seen in the electron density and corresponding kinetic and potential energy distributions. The energetics associated with the more complex electronic structure of H2, when examined in detail, clearly agrees with the analysis of Ruedenberg; i.e., covalent bonding is due to a decrease in the interatomic kinetic energy resulting from electronic delocalization. Our results support the view that covalent bonding is a quantum dynamical phenomenon requiring a properly quantized kinetic energy to be used in its description.

An interacting quantum atom study of model SN 2 reactions (X- ···CH3 X, X = F, Cl, Br, and I).

The quantum chemical topology method has been used to analyze the energetic profiles in the X– + CH3X → XCH3 + X–SN2 reactions, with X = F, Cl, Br, and I. The evolution of the electron density properties at the BCPs along the reaction coordinate has been analysed. The interacting quantum atoms (IQA) method has been used to evaluate the intra‐atomic and interatomic energy variations along the reaction path. The different energetic terms have been examined by the relative energy gradient method and the ANANKE program, which enables automatic and unbiased IQA analysis. Four of the six most important IQA energy contributions were needed to reproduce the reaction barrier common to all reactions. The four reactions considered share many common characteristics but when X = F a number of particularities occur. © 2017 Wiley Periodicals, Inc.

Energetic Analysis of Conjugated Hydrocarbons Using the Interacting Quantum Atoms Method.

A number of aromatic, antiaromatic, and nonaromatic organic molecules was analyzed in terms of the contributions to the electronic energy defined in the quantum theory of atoms in molecules and the interacting quantum atoms method. Regularities were found in the exchange and electrostatic interatomic energies showing trends that are closely related to those of the delocalization indices defined in the theory. In particular, the CC interaction energies between bonded atoms allow to rationalize the energetic stabilization associated with the bond length alternation in conjugated polyenes. This approach also provides support to Clar's sextet rules devised for aromatic systems. In addition, the H⋯H bonding found in some of the aromatic molecules studied was of an attractive nature, according to the stabilizing exchange interaction between the bonded H atoms. © 2017 Wiley Periodicals, Inc.

Resonance interatomic energy in a Schwarzschild spacetime

We study, in the Schwarzschild spacetime, the resonance interatomic energy (RIE) of two static identical atoms with an interatomic separation $L$ along the radial direction and correlated by a symmetric/antisymmetric entangled state. The atoms are assumed to be coupled to massless scalar fields in the Boulware, Unruh, and Hartle-Hawking vacua, and approximate analytical results are obtained both at infinity and near the horizon. Our results show that at infinity, the RIE approaches that in a flat spacetime, while, near the horizon, they can deviate dramatically from each other. Besides, different from other atomic radiative properties such as the Lamb shift of a single atom or the interatomic energy between two uncorrelated atoms, which can be obviously affected by the thermal character of quantum fields, the RIE of two atoms in a symmetric/antisymmetric entangled state in the Boulware, Unruh, and Hartle-Hawking vacua are exactly the same as a result of the fact that the RIE of two such atoms depends only on the atomic self-reaction, i.e., it does not feel the vacuum fluctuations. This suggests that the RIE of two static atoms in a symmetric/antisymmetric entangled state outside a black hole is oblivious to the Hawking radiation, in contrast to those uncorrelated atoms.

Effect of the allotropic transition in titanium on its interatomic interaction energy

The variation of interatomic interaction energy during allotropic transition in titanium is established by analyzing the stress and temperature dependences of durability. This energy is ≈458 kJ/mol in bodycentered β-Ti at a temperature of T > 1155 K, which agrees well with the titanium sublimation heat, and ≈305 kJ/mol in hexagonal close-packed α-Ti at T < 1155 K. Literature data confirming the conclusions drawn are discussed.

A multipolar approach to the interatomic covalent interaction energy.

Interatomic exchange-correlation energies correspond to the covalent energetic contributions to an interatomic interaction in real space theories of the chemical bond, but their widespread use is severely limited due to their computationally intensive character. In the same way as the multipolar (mp) expansion is customary used in biomolecular modeling to approximate the classical Coulomb interaction between two charge densities ρA(r) and ρB(r), we examine in this work the mp approach to approximate the interatomic exchange-correlation (xc) energies of the Interacting Quantum Atoms method. We show that the full xc mp series is quickly divergent for directly bonded atoms (1-2 pairs) albeit it works reasonably well most times for 1- n (n > 2) interactions. As with conventional perturbation theory, we show numerically that the xc series is asymptotically convergent and that, a truncated xc mp approximation retaining terms up to l1+l2=2 usually gives relatively accurate results, sometimes even for directly bonded atoms. Our findings are supported by extensive numerical analyses on a variety of systems that range from several standard hydrogen bonded dimers to typically covalent or aromatic molecules. The exact algebraic relationship between the monopole-monopole xc mp term and the inter-atomic bond order, as measured by the delocalization index of the quantum theory of atoms in molecules, is also established. © 2017 Wiley Periodicals, Inc.

Interatomic bond energy and analytical scale of hardness

Based on detailed models of interatomic cohesion and the well-developed structural-thermodynamic approach, the interatomic bond energy has been determined for some covalent and metallic crystals and it has been found to agree with experimental data. Using the proposed analytical relationship for the degree of covalency of crystals the author has elaborated a generalized model that describes experimental hardness of supersclerometer materials (diamond, cBN, SiC, and others), minerals, refractory compounds, semiconductors, ionic crystals and metals. On the basis of the mechanical-chemical approach to (nano)flow a dislocation model of crystal-mechanical anisotropy of yield strength has been put forward for monocrystalline diamond and lonsdaleite; the model makes it possible to draw a conclusion on a slight difference in their sclerometric characteristics. The experimental relationships that govern high-temperature high-pressure plasticity in some covalent crystals are discussed.

Geometric method for large Morse clusters formation

This paper describes a geometrically founded method for constructing the initial configuration of a complete icosahedral structure of an atomic cluster. The method finds a global minimum of the cluster energy as a result of a single local optimization procedure. The method is based on the proposed algorithm for the stratified accommodation of atom centers, that allows one to form structural configurations commonly found among the clusters with global minimum of interatomic interaction energy. This algorithm provides the ability to build a spatial configuration of the dense packing of spheres for the formation of icosahedral and decahedral structures, as well as building complete icosahedrons with a large number of atoms. With the proposed method, we have reached the global minima for large Morse clusters (N = 817, 923, and 1415), which is a record for Morse clusters with r = 6.

COMPUTER SIMULATION OF FUNCTIONALIZED CARBON NANOTUBES AND GRAPHENE

Nanomaterials based on carbon nanotubes (CNT) and graphenes attract a lot of attention of researchers as the materials capable to raise the development of various industries to the new level, and first of all, of the chemical and electronic sectors. In addition to known experimental methods, new nanosystems are widely studied using advanced tools of quantum-chemical approaches. Modern theoretical methods are of great interest due to their ability to interpret known experimental facts and predict properties of non-synthesized compounds yet. This paper reviews results of theoretical studies performed using the density functional theory (DFT) methods to obtain data on the structure and electronic properties of single-walled CNT and graphene, modified with various impurities, with covalent-ionic and non-covalent binding mechanisms. New computational methods are briefly described that are currently employed to treat the dispersion interaction and enhance possibilities of DFT tools in systems where the van der Waals forces play a significant role. Particular attention is paid to the characteristics of carbon nanomaterials containing technologically important hydroxyl, carboxyl and amino groups. It is shown that the specific peculiarity of band structures of discussed in the literature CNT functionalized by OH, COOH, NHn and CONH2 groups is the partially occupied band in the neighborhood of the Fermi level, which directly affects the CNT conductivity. Modification of graphene layers is analyzed that interact with hydrogen, fluorine, bases of nucleic acids and the metal substrate surface. We also provide accuracy estimates for the calculations of interatomic bond lengths, interaction energy and band gap carried out in the literature using a variety of DFT approximations.

Exponential Relationships Capturing Atomistic Short-Range Repulsion from the Interacting Quantum Atoms (IQA) Method.

A topological atom is a quantum object with a well-defined intra-atomic energy, which includes kinetic energy, Coulomb energy, and exchange energy. In the context of intermolecular interactions, this intra-atomic energy is calculated from supermolecular wave functions, by using the topological partitioning. This partitioning is parameter-free and invokes only the electron density to obtain the topological atoms. In this work, no perturbation theory is used; instead, a single wave function describes the behavior of all van der Waals complexes studied. As the monomers approach each other, frontier atoms deform, which can be monitored through a change in their shape and volume. Here we show that the corresponding atomic deformation energy is very well described by an exponential function, which matches the well-known Buckingham repulsive potential. Moreover, we recover a combination rule that enables the interatomic repulsion energy between topological atoms A and B to be expressed as a function of the interatomic repulsion energy between A and A on one hand, and between B and B on the other hand. As a result a link is established between quantum topological atomic energies and classical well-known interatomic repulsive potentials.

Theoretical study for misfit dislocation formation at InAs/GaAs(001) interface

The formation of misfit dislocations (MDs) at InAs/GaAs(001) interface is theoretically investigated using empirical interatomic potentials and ab initio calculations. The calculated cohesive energy using empirical interatomic potentials demonstrate that InAs/GaAs(001) system with 5/7 MD core structure is stabilized compared with coherently grown system when the thickness of InAs wetting layer is larger than 1 monolayer (ML). This result suggests that lattice strain is relaxed by incorporating MD to proceed the growth of InAs wetting layers. The estimated critical thickness of MD formation and dislocation formation energy for InAs/GaAs(001) are 0.5 ML and 1.51eV/Å, respectively, which are favorably compared with those of InAs/GaAs(110) interface. Using the calculated results of MDs by empirical interatomic potentials and surface energies by ab initio calculations, we furthermore evaluate growth modes of InAs on GaAs(001) substrate on the basis of macroscopic theories. The estimation of free energies reveals that two-dimensional growth with MDs and Stranski-Krastanov coherent growth simultaneously appear around 0.6 ML. These results suggest that the formation MDs at InAs/GaAs(001) interface is crucial for the wetting layer growth on GaAs(001) substrate.

Torquoselectivity in Cyclobutene Ring Openings and the Interatomic Interactions That Control Them.

Torquoselectivity has explained diasteromeric preferences of a number electrocyclic ring openings. The quantum theory of atoms in molecules (QTAIM), the electron localizability indicator (ELI-D), and the interacting quantum atoms (IQA) energy partition method are used to evaluate qualitatively and quantitatively the atomic interactions behind the torquoselectivity of a series of 3-substituted cyclobutenes. ELI-D topology and IQA energies show that the interaction between the distal terminus carbon atom of cyclobutene (C4) with the substituent at C3 (R5) in the transition state governs torquoselectivities. In the case of 3-borylcyclobutene, this interaction is so strong that a protocovalent bond is actually formed between B5 and C4. The evaluation of the interatomic energies allowed us to identify an additional interaction that contribute to a minor extent to the stabilization of the TS. Despite the fact that C4,R5 interaction is the main cause of the torquoselectivity, a bonding path (BP) between these two atoms was not observed. However, the lack of a BP between C4 and R5 does not mean that the topology of the electron density was not affected by the interaction of these two atoms. Surprisingly, we found a strong correlation between the density at the bond critical point (BCP) and the BP shape of C3-C4 breaking bond with the observed activation energies and torquoselectivities.

FEREBUS: Highly parallelized engine for kriging training.

FFLUX is a novel force field based on quantum topological atoms, combining multipolar electrostatics with IQA intraatomic and interatomic energy terms. The program FEREBUS calculates the hyperparameters of models produced by the machine learning method kriging. Calculation of kriging hyperparameters (θ and p) requires the optimization of the concentrated log-likelihood L̂(θ,p). FEREBUS uses Particle Swarm Optimization (PSO) and Differential Evolution (DE) algorithms to find the maximum of L̂(θ,p). PSO and DE are two heuristic algorithms that each use a set of particles or vectors to explore the space in which L̂(θ,p) is defined, searching for the maximum. The log-likelihood is a computationally expensive function, which needs to be calculated several times during each optimization iteration. The cost scales quickly with the problem dimension and speed becomes critical in model generation. We present the strategy used to parallelize FEREBUS, and the optimization of L̂(θ,p) through PSO and DE. The code is parallelized in two ways. MPI parallelization distributes the particles or vectors among the different processes, whereas the OpenMP implementation takes care of the calculation of L̂(θ,p), which involves the calculation and inversion of a particular matrix, whose size increases quickly with the dimension of the problem. The run time shows a speed-up of 61 times going from single core to 90 cores with a saving, in one case, of ∼98% of the single core time. In fact, the parallelization scheme presented reduces computational time from 2871 s for a single core calculation, to 41 s for 90 cores calculation. © 2016 The Authors. Journal of Computational Chemistry Published by Wiley Periodicals, Inc.

Incorporation of local structure into kriging models for the prediction of atomistic properties in the water decamer.

Machine learning algorithms have been demonstrated to predict atomistic properties approaching the accuracy of quantum chemical calculations at significantly less computational cost. Difficulties arise, however, when attempting to apply these techniques to large systems, or systems possessing excessive conformational freedom. In this article, the machine learning method kriging is applied to predict both the intra‐atomic and interatomic energies, as well as the electrostatic multipole moments, of the atoms of a water molecule at the center of a 10 water molecule (decamer) cluster. Unlike previous work, where the properties of small water clusters were predicted using a molecular local frame, and where training set inputs (features) were based on atomic index, a variety of feature definitions and coordinate frames are considered here to increase prediction accuracy. It is shown that, for a water molecule at the center of a decamer, no single method of defining features or coordinate schemes is optimal for every property. However, explicitly accounting for the structure of the first solvation shell in the definition of the features of the kriging training set, and centring the coordinate frame on the atom‐of‐interest will, in general, return better predictions than models that apply the standard methods of feature definition, or a molecular coordinate frame. © 2016 The Authors. Journal of Computational Chemistry Published by Wiley Periodicals, Inc.

The prediction of topologically partitioned intra-atomic and inter-atomic energies by the machine learning method kriging

The construction of a novel protein force field called FFLUX, which uses topological atoms, is founded on high-rank and fully polarizable multipolar electrostatics. The machine learning method kriging successfully predicts multipole moments of a given atom with as only input the nuclear coordinates of the atoms surrounding this given atom. Thus, trained kriging models accurately capture the polarizable multipolar electrostatics of amino acids. Here we show that successful kriging models can also be constructed for non-electrostatic energy contributions. As a result, the full potential energy surface of the (molecular) system trained for can be predicted by the corresponding set of atomic kriging models. In particular, we report on the performance of kriging models for each atom’s (A) (1) total atomic energy (E IQA ), (2) intra-atomic energy (E intra ) (both kinetic and potential energy), (3) exchange energy ( $$V_{XC}^{{AA^{\prime } }}$$ ) and (4) electrostatic energy ( $$V_{\text{cl}}^{{AA^{{\prime }} }}$$ ) of atom A with the rest of the system (A′), and (5) interatomic energy ( $$V_{\text{inter}}^{{AA^{{\prime }} }}$$ ). The total molecular energy can be reconstructed from the kriging predictions of these atomic energies. For the three case studies investigated (i.e. methanol, N-methylacetamide and peptide-capped glycine), the molecular energies were produced with mean absolute errors under 0.4, 0.8 and 1.1 kJ mol−1, respectively.

Interaction of Hydrogen with Au Modified by Pd and Rh in View of Electrochemical Applications

Hydrogen interaction with bimetallic Au(Pd) and Au(Rh) systems are studied with the density functional theory (DFT)-based periodic approach. Several bimetallic configurations with varying concentrations of Pd and Rh atoms in the under layer of a gold surface(111) were considered. The reactivity of the doped Au(111) toward hydrogen adsorption and absorption was related to the property modifications induced by the presence of metal dopants. DFT-computed quantities, such as the energy stability, the inter-atomic and inter-slab binding energies between gold and dopants, and the charge density were used to infer the similarities and differences between both Pd and Rh dopants in these model alloys. The hydrogen penetration into the surface is favored in the bimetallic slab configurations. The underlayer dopants affect the reactivity of the surface gold toward hydrogen adsorption in the systems with a dopant underlayer, covered by absorbed hydrogen up to a monolayer. This indicates a possibility to tune the gold surface properties of bimetallic electrodes by modulating the degree of hydrogen coverage of the inner dopant layer(s).

Nature of beryllium bonds in view of interacting quantum atoms and natural energy decomposition analysis

In the light of interacting quantum atoms (IQA) and natural energy decomposition analysis (NEDA) the nature of different types of beryllium bonds is studied. IQA intra-atomic (self) energies indicate that, in most of the traditional beryllium bonds (in which the Lewis base is a lone pair donor), π-Be bonds (Lewis base is an unsaturated molecule) and also the Be–Ng (noble gases) interactions, the beryllium atom is stabilized upon complex formations. According to IQA inter-atomic energy components, the Be⋯Y bonds (Y is an atom in the Be-bond acceptor that is connected directly to the beryllium atom) have a dominant classical electrostatic character. However, in the IQA partitioning of total inter-molecular interactions, the contributions of non-classical (exchange–correlation) terms are non-negligible. Natural energy decomposition analysis of traditional and π-Be bonds indicate that the attractive interactions come from both the electrical and charge transfer terms. The electrical term in the Be–Ng bonds is negligibly small and the charge transfer is the most dominant contributor in the interaction energy.

An analytical model of interfacial energy based on a lattice-matching interatomic energy

We develop an explicit model for the interfacial energy in crystals that emphasizes the geometric origin of the cusps in the energy profile. We start by formulating a general class of interatomic energies that are reference-configuration-free but explicitly incorporate the lattice geometry of the ground state. In particular, away from the interface the energy is minimized by a perfect lattice. We build these attributes into the energy by locally matching, as best as possible, a perfect lattice to the atomic positions and then quantifying the local energy in terms of the inevitable remaining mismatch, hence the term lattice-matching used to describe the resulting interatomic energy. Based on this general energy, we formulate a simpler rigid-lattice model in which the atomic positions on both sides of the interface coincide with perfect, but misoriented, lattices. In addition, we restrict the lattice-matching operation to a binary choice between the perfect lattices on both sides of the interface. Finally, we prove an L2-bound on the interatomic energy and use that bound as a basis for comparison with experiment. We specifically consider symmetric tilt grain boundaries (STGB), symmetric twist grain boundaries (STwGB) and asymmetric twist grain boundaries (ATwGB) in face-centered cubic (FCC) and body-centered cubic (BCC) crystals. Two or more materials are considered for each choice of crystal structure and boundary class, with the choice of materials conditioned by the availability of molecular dynamics data. Despite the approximations made, we find very good overall agreement between the predicted interfacial energy structure and that calculated by molecular dynamics. In particular, the positions of the cusps are predicted well, and therefore, although surface reconstruction and faceting are not included in the model, the dominant orientations of the facets are correctly predicted by our geometrical model.