Intra-atomic Energy Research Articles

A simple efficient algorithm for molecular simulations of constant potential electrodes.

Increasingly, society requires high power, high energy storage devices for applications ranging from electric vehicles to buffers on the electric grid. Supercapacitors are a promising contribution to meeting these demands, though there still remain unsolved practical problems. Molecular dynamics simulations can shed light on the relevant molecular level processes in electric double layer capacitors, but these simulations are computationally very demanding. Our focus here is on the algorithmic complexity of the constant potential method (CPM), which uses dedicated electrostatics solvers to maintain a fixed potential difference between two conducting electrodes. We show how any standard electrostatics solver-capable of calculating the energies and forces on all atoms-can be used to implement CPM with a minimum of coding. As an example, we compare our generalized implementation of CPM, based on invocations of the particle-particle-particle-mesh routine of the Large-scale Atomic/Molecular Massively Parallel Simulator, with a traditional implementation based on a dedicated re-implementation of Ewald summation. Both methods yield comparable results on four test systems, with the former achieving a substantial gain in speed and improved scalability. The step from dedicated electrostatic solvers to generic routines is made possible by noting that CPM's traditional narrow Gaussian point-spread of atomic charges on the electrodes effectively endows point-like atoms with chemical hardness, i.e., an intra-atomic energy quadratic in the charge.

Atoms and interatomic bonding synergism inherent in molecular electronic wave functions.

The chemical model of matter consists of atoms held together by bonds. The success of this model implies that the physical interactions of the electrons and nuclei in molecules combine into compound interactions that create the bonding. In the quantum mechanical description, the modified atoms in molecules and the bonding synergism are contained in the molecular electronic wave function. So far, only part of this information has been recovered from the wave function. Notably, the atoms have remained unidentified in the wave function. One reason is that conventional energy decomposition analyses formulate separate model wave functions, independent of the actual wave function, to represent "prepared atoms" and preconceived interactions and, then, intuitively catenate the parts. In the present work, the embedded modified atoms and the inherent physical synergisms between them are determined by a unified derivation entirely from the actual molecular valence space wave function. By means of a series of intrinsic orbital and configurational transformations of the wave function, the energy of formation of a molecule is additively resolved in terms of intra-atomic energy changes, interference energies, and quasi-classical, non-classical, and charge-transfer Coulombic interactions. The analysis furnishes an algorithm for the quantitative resolution of the energy of formation, which enables analyses elucidating reaction energies.

Intra-atomic exchange energy quantified

An article in Physical Review X reports the first experimental measurement of the intra-atomic exchange interaction in rare-earth atoms.

Measuring the Intra-Atomic Exchange Energy in Rare-Earth Adatoms

We present the first experimental determination of the intra-atomic exchange energy between the inner 4f and the outer 6s5d shells in rare-earth elements. Inelastic electron tunneling spectroscopy ...

Why is Si2H2 Not Linear? An Intrinsic Quasi-Atomic Bonding Analysis.

The molecular energy of Si2H2 geometric structures increases in the order dibridged < trans-bent < linear, in contrast to acetylene, C2H2, for which the linear structure is the global minimum. In this study, the intra-atomic (antibonding) and bonding contributions to the total molecular energy of these valence isoelectronic molecules are computed by expressing the density matrices of the full valence space multiconfiguration self-consistent field wave function in terms of quasi-atomic orbitals. The analysis shows that the intra-atomic contributions to the molecular energy become less favorable in the order dibridged → trans-bent → linear for both C2H2 and Si2H2. By contrast, the inter-atomic bonding contributions become energetically more favorable in that order for both C2H2 and Si2H2. The two systems differ as follows. For Si2H2, the antibonding intra-atomic energy changes that occur when the dibridged molecule reconstructs into the trans-bent and linear structures prevail over the interatomic interactions that induce bond formation. In contrast, for C2H2, the interatomic interactions that create bonds prevail over the intra-atomic energy changes that occur when the dibridged molecule reconstructs into the trans-bent and linear structures. The intra-atomic energy changes that occur in these systems are related to the hybridization of the heavy atoms in an analogous manner to the hybridization of C in CH4 from (2s)2(2p)2 to sp3 hybrid orbitals.

An Interacting Quantum Atoms (IQA) and Relative Energy Gradient (REG) Study of the Halogen Bond with Explicit Analysis of Electron Correlation

Energy profiles of seven halogen-bonded complexes were analysed with the topological energy partitioning called Interacting Quantum Atoms (IQA) at MP4(SDQ)/6–31 + G(2d,2p) level of theory. Explicit interatomic electron correlation energies are included in the analysis. Four complexes combine X2 (X = Cl or F) with HCN or NH3, while the remaining three combine ClF with HCN, NH3 or N2. Each complex was systematically deformed by translating the constituent molecules along its central axis linking X and N, and reoptimising its remaining geometry. The Relative Energy Gradient (REG) method (Theor. Chem. Acc. 2017, 136, 86) then computes which IQA energies most correlate with the total energy during the process of complex formation and further compression beyond the respective equilibrium geometries. It turns out that the covalent energy (i.e., exchange) of the halogen bond, X…N, itself drives the complex formation. When the complexes are compressed from their equilibrium to shorter X…N distance then the intra-atomic energy of N is in charge. When the REG analysis is restricted to electron correlation then the interatomic correlation energy between X and N again drives the complex formation, and the complex compression is best described by the destabilisation of the through-space correlation energy between N and the “outer” halogen.

Does the Intra-atomic Deformation Energy of Interacting Quantum Atoms Represent Steric Energy?

Invited for this month's cover picture is the group of Paul L. A. Popelier from Manchester Institute of Biotechnology (UK). The cover picture shows the quantum topological atoms in a configuration of the complex HF⋅⋅⋅OH2, where F is green and O is red. Read the full text of their Full Paper at 10.1002/open.201800275.

Does the Intra-Atomic Deformation Energy of Interacting Quantum Atoms Represent Steric Energy?

We show that the mutual, through‐space compression of atomic volume experienced by approaching topological atoms causes an exponential increase in the intra‐atomic energy of those atoms, regardless of approach orientation. This insight was obtained using the modern energy partitioning method called interacting quantum atoms (IQA). This behaviour is consistent for all atoms except hydrogen, which can behave differently depending on its environment. Whilst all atoms experience charge transfer when they interact, the intra‐atomic energy of the hydrogen atom is more vulnerable to these changes than larger atoms. The difference in behaviour is found to be due to hydrogen's lack of a core of electrons, which, in heavier atoms, consistently provide repulsion when compressed. As such, hydrogen atoms do not always provide steric hindrance. In accounting for hydrogen's unusual behaviour and demonstrating the exponential character of the intra‐atomic energy in all other atoms, we provide evidence for IQA's intra‐atomic energy as a quantitative description of steric energy.

When hydroquinone meets methoxy radical: Hydrogen abstraction reaction from the viewpoint of interacting quantum atoms

Interacting Quantum Atoms methodology is used for a detailed analysis of hydrogen abstraction reaction from hydroquinone by methoxy radical. Two pathways are analyzed, which differ in the orientation of the reactants at the corresponding transition states. Although the discrepancy between the two barriers amounts to only 2 kJ/mol, which implies that the two pathways are of comparable probability, the extent of intra-atomic and inter-atomic energy changes differs considerably. We thus demonstrated that Interacting Quantum Atoms procedure can be applied to unravel distinct energy transfer routes in seemingly similar mechanisms. Identification of energy components with the greatest contribution to the variation of the overall energy (intra-atomic and inter-atomic terms that involve hydroquinone's oxygen and the carbon atom covalently bound to it, the transferring hydrogen and methoxy radical's oxygen), is performed using the Relative energy gradient method. Additionally, the Interacting Quantum Fragments approach shed light on the nature of dominant interactions among selected fragments: both Coulomb and exchange-correlation contributions are of comparable importance when considering interactions of the transferring hydrogen atom with all other atoms, whereas the exchange-correlation term dominates interaction between methoxy radical's methyl group and hydroquinone's aromatic ring. This study represents one of the first applications of Interacting Quantum Fragments approach on first order saddle points. © 2018 Wiley Periodicals, Inc.

Unfavorable regions in the ramachandran plot: Is it really steric hindrance? The interacting quantum atoms perspective.

Accurate description of the intrinsic preferences of amino acids is important to consider when developing a biomolecular force field. In this study, we use a modern energy partitioning approach called Interacting Quantum Atoms to inspect the cause of the φ and ψ torsional preferences of three dipeptides (Gly, Val, and Ile). Repeating energy trends at each of the molecular, functional group, and atomic levels are observed across both (1) the three amino acids and (2) the φ/ψ scans in Ramachandran plots. At the molecular level, it is surprisingly electrostatic destabilization that causes the high‐energy regions in the Ramachandran plot, not molecular steric hindrance (related to the intra‐atomic energy). At the functional group and atomic levels, the importance of key peptide atoms (Oi –1, Ci, Ni, Ni +1) and some sidechain hydrogen atoms (Hγ) are identified as responsible for the destabilization seen in the energetically disfavored Ramachandran regions. Consistently, the Oi –1 atoms are particularly important for the explanation of dipeptide intrinsic behavior, where electrostatic and steric destabilization unusually complement one another. The findings suggest that, at least for these dipeptides, it is the peptide group atoms that dominate the intrinsic behavior, more so than the sidechain atoms. © 2017 The Authors. Journal of Computational Chemistry Published by Wiley Periodicals, Inc.

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.

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.

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.

Hermitian “chemical” Hamiltonian: an alternative ab initio method

Some previous results of the present author are combined in order to develop a Hermitian version of the “Chemical Hamiltonian Approach.” In this framework the second quantized Born–Oppenheimer Hamiltonian is decomposed into one- and two-center components, if some finite basis corrections are omitted. (No changes are introduced into the one- and two-center integrals, while projective expansions are used for the three- and four-center ones, which become exact only in the limit of complete basis sets.) The total molecular energy calculated with this Hamiltonian can then presented as a sum of the intraatomic and diatomic energy terms which were introduced in our previous “chemical energy component analysis” scheme. The corresponding modified Hartree–Fock–Roothaan equations are also derived; they do not contain any three- and four-center integrals, while the non-empirical character of the theory is conserved. This scheme may be useful also as a “layer” in approaches like ONIOM.

Resonant photoemission spectroscopy study of the d and f states in GdNi5 − x Cu x intermetallics

The electronic structure of the GdNi5 − xCux (x = 0, 1, and 2) compounds is studied by resonant photoemission spectroscopy, the main regularities of the electronic strucutre transformation upon substitution of copper for nickel are established, and the energies of the d and f states that form its valence bands are measured. X-ray absorption and resonant photoemission spectra at the gadolinium M4, 5 and N4, 5 edges and nickel and copper L2, 3 edges are recorded. It is shown that a core photohole and an excited electron in gadolinium decay along the elastic channel; in the final state, one hole forms in the valence band and Gd 4f photoemission is enhanced tenfold. Since the inelastic Auger-type relaxation channel dominates in the transition elements with the formation of two holes in the valence band, the resonant photoemission spectrum allows us to measure the energy of two-particle interactions. The intra-atomic repulsion energy in nickel and copper is found to be ∼7 eV.

Hydrogen-hydrogen interaction in planar biphenyl: a theoretical study based on the interacting quantum atoms and Hirshfeld atomic energy partitioning methods.

The nature of H-H interaction between ortho-hydrogen atoms in planar biphenyl is investigated by two different atomic energy partitioning methods, namely fractional occupation iterative Hirshfeld (FOHI) and interacting quantum atoms (IQA), and compared with the traditional virial-based approach of quantum theory of atoms in molecules (QTAIM). In agreement with Bader's hypothesis of H-H bonding, partitioning the atomic energy into intra-atomic and interatomic terms reveals that there is a net attractive interaction between the ortho-hydrogens in the planar biphenyl. This falsifies the classical view of steric repulsion between the hydrogens. In addition, in contrast to the traditional QTAIM energy analysis, both FOHI and IQA show that the total atomic energy of the ortho-hydrogens remains almost constant when they participate in the H-H interaction. Although, the interatomic part of atomic energy of the hydrogens plays a stabilizing role during the formation of the H-H bond, it is almost compensated by the destabilizing effects of the intra-atomic parts and consequently, the total energy of the hydrogens remains constant. The trends in the changes of intra-atomic and interatomic energy terms of ortho-hydrogens during H-H bond formation are very similar to those observed for the H2 molecule.

Covalent bonds are created by the drive of electron waves to lower their kinetic energy through expansion.

An analysis based on the variation principle shows that in the molecules H2 (+), H2, B2, C2, N2, O2, F2, covalent bonding is driven by the attenuation of the kinetic energy that results from the delocalization of the electronic wave function. For molecular geometries around the equilibrium distance, two features of the wave function contribute to this delocalization: (i) Superposition of atomic orbitals extends the electronic wave function from one atom to two or more atoms; (ii) intra-atomic contraction of the atomic orbitals further increases the inter-atomic delocalization. The inter-atomic kinetic energy lowering that (perhaps counter-intuitively) is a consequence of the intra-atomic contractions drives these contractions (which per se would increase the energy). Since the contractions necessarily encompass both, the intra-atomic kinetic and potential energy changes (which add to a positive total), the fact that the intra-atomic potential energy change renders the total potential binding energy negative does not alter the fact that it is the kinetic delocalization energy that drives the bond formation.

The prediction of atomic kinetic energies from coordinates of surrounding atoms using kriging machine learning

A novel design of a next-generation force field considers not only the electronic inter-atomic energy but also intra-atomic energy. This strategy promises a faithful mapping between the force field and the quantum mechanics that underpins it. Quantum chemical topology provides an energy partitioning in which atoms have well- defined electronic kinetic energies, and we are interested in capturing how they respond to changes in the positions of surrounding atoms. A machine learning method called kriging successfully creates models from a training set of molecular configurations that can then be used to predict the atomic kinetic energies occurring in previously unseen molecular configurations. We present a proof-of-concept based on four molecules of increasing complexity (meth- anol, N-methylacetamide, glycine and triglycine). We test how well the atomic kinetic energies can be modelled with respect to training set size, molecule size and elemental composition. For all atoms tested, the mean atomic kinetic energy errors fall below 1.5 kJ mol -1 , and far below this in most cases. This represents errors all under 0.5 % and thus the kinetic energies are well modelled using the kriging method, even when using modest-to-small training set sizes.

Transition metal atoms in cubic configurations

Matrix Hartree–Fock calculations are reported for 3d transition metals in a configuration chosen to represent, as closely as is possible with integral occupation numbers, an atom in an fcc metal. The cubic symmetry shell (3dt)6 is assumed to be fully occupied, and electrons are successively removed from the (3de)4 shell to represent atoms from Cu to Mn. A single 4s orbital is included, with independent calculations for the two possible choices of relative spin of the 4s orbital and 3de shell. Orbital energies are computed for each of the nonequivalent 4s and 3d orbitals, and the relationship of these quantities with transition metal energy bands is discussed. Intra-atomic orbital energy splittings are found to be comparable in magnitude to energy band splittings. Radial densities of the 4sα and 4sβ orbitals are computed. These densities are found to be compatible with a proposed explanation of recently observed negative magnetization regions within the unit cell of ferromagnetic transition metals.

Effect of the magnetism of impurities on their diffusion in metals: Bulk diffusion of iron, cobalt, and rhodium in iridium single crystals

The coefficients and parameters of the temperature dependences of the coefficients of bulk diffusion of Fe, Co, Rh, and Au atomic probes (APs) in iridium single crystals (mono-Ir) have been determined from the diffusion profiles obtained using secondary-ion mass spectrometry of the diffusion zones. The enthalpies of activation of diffusion of Fe, Co, and Rh APs are considerably lower than the enthalpy of activation of selfdiffusion in mono-Ir. This is caused by the negative contributions of the intraatomic exchange energy and energy of relaxation of the environment of the d transition APs to the enthalpy of interaction of magnetically active APs with the vacancies in the iridium lattice. The interaction energy of partners in such complexes and the relationships between the magnetic moments of d transition APs in complexes with vacancies have been estimated. The Rh APs in complexes with vacancies in iridium possess stable magnetic moments.