Force field for copper clusters and nanoparticles

An atomic force field for simulating copper clusters and nanoparticles is developed. More than 2000 cluster configurations of varying size and shape are used to constrain the parametrization of the copper force field. Binding energies for these training clusters were computed using density functional theory. Extensive testing shows that the copper force field is fast and reliable for near‐equilibrium structures of clusters, ranging from only a few atoms to large nanoparticles that approach bulk structure. Nonequilibrium dissociation and compression structures that are included in the training set are also well described by the force field. Implications for molecular dynamics simulations and extensions to other metallic and covalent systems are discussed. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2009     

Atomic Partitioning of the MPn (n = 2, 3, 4) Dynamic Electron Correlation Energy by the Interacting Quantum Atoms Method: A Fast and Accurate Electrostatic Potential Integral Approach

Recently, the quantum topological energy partitioning method called interacting quantum atoms (IQA) has been extended to MPn (n = 2, 3, 4) wave functions. This enables the extraction of chemical insight related to dynamic electron correlation. The large computational expense of the IQA-MPn approach is compensated by the advantages that IQA offers compared to older nontopological energy decomposition schemes. This expense is problematic in the construction of a machine learning training set to create kriging models for topological atoms. However, the algorithm presented here markedly accelerates the calculation of atomically partitioned electron correlation energies. Then again, the algorithm cannot calculate pairwise interatomic energies because it applies analytical integrals over whole space (rather than over atomic volumes). However, these pairwise energies are not needed in the quantum topological force field FFLUX, which only uses the energy of an atom interacting with all remaining atoms of the system that it is part of. Thus, it is now feasible to generate accurate and sizeable training sets at MPn level of theory. © 2019 The Authors. Journal of Computational Chemistry published by Wiley Periodicals, Inc.     

Prediction of conformationally dependent atomic multipole moments in carbohydrates

The conformational flexibility of carbohydrates is challenging within the field of computational chemistry. This flexibility causes the electron density to change, which leads to fluctuating atomic multipole moments. Quantum Chemical Topology (QCT) allows for the partitioning of an “atom in a molecule,” thus localizing electron density to finite atomic domains, which permits the unambiguous evaluation of atomic multipole moments. By selecting an ensemble of physically realistic conformers of a chemical system, one evaluates the various multipole moments at defined points in configuration space. The subsequent implementation of the machine learning method kriging delivers the evaluation of an analytical function, which smoothly interpolates between these points. This allows for the prediction of atomic multipole moments at new points in conformational space, not trained for but within prediction range. In this work, we demonstrate that the carbohydrates erythrose and threose are amenable to the above methodology. We investigate how kriging models respond when the training ensemble incorporating multiple energy minima and their environment in conformational space. Additionally, we evaluate the gains in predictive capacity of our models as the size of the training ensemble increases. We believe this approach to be entirely novel within the field of carbohydrates. For a modest training set size of 600, more than 90% of the external test configurations have an error in the total (predicted) electrostatic energy (relative to ab initio) of maximum 1 kJ mol^?1 for open chains and just over 90% an error of maximum 4 kJ mol^?1 for rings. © 2015 Wiley Periodicals, Inc.     

The interaction of slow positrons with organic moecules above and below positronium formation thresholds

A review is given of the ionization of organic moecules by monoenergetic positrons having energies in the range of 0.5–15 eV. Two mechanisms, unique to positrons, are described. If the kinetic energy of the positron is above the positronium formation threshold, such that electrons can be removed from the molecules to form free positronium atoms, the ionization/fragmentation behavior can be explained qualitatively by a modification of the Ore gap theory. To explain how positrons can ionize and fragment molecules when their kinetic energies are below the positronium formation threshold, it is necessary to assume that energy is transferred to the molecule by the annihilation process. Ionization cross sections for positrons having kinetic energies below the positronium formation threshold are sensitive to molecular size, structure and bond types. Continuing work involves a search for positronium compound formation and measurements of the kinetic energy distributions of ions.     

Accuracy and tractability of a kriging model of intramolecular polarizable multipolar electrostatics and its application to histidine

We propose a generic method to model polarization in the context of high‐rank multipolar electrostatics. This method involves the machine learning technique kriging, here used to capture the response of an atomic multipole moment of a given atom to a change in the positions of the atoms surrounding this atom. The atoms are malleable boxes with sharp boundaries, they do not overlap and exhaust space. The method is applied to histidine where it is able to predict atomic multipole moments (up to hexadecapole) for unseen configurations, after training on 600 geometries distorted using normal modes of each of its 24 local energy minima at B3LYP/apc‐1 level. The quality of the predictions is assessed by calculating the Coulomb energy between an atom for which the moments have been predicted and the surrounding atoms (having exact moments). Only interactions between atoms separated by three or more bonds (“1, 4 and higher” interactions) are included in this energy error. This energy is compared with that of a central atom with exact multipole moments interacting with the same environment. The resulting energy discrepancies are summed for 328 atom–atom interactions, for each of the 29 atoms of histidine being a central atom in turn. For 80% of the 539 test configurations (outside the training set), this summed energy deviates by less than 1 kcal mol^?1. © 2013 Wiley Periodicals, Inc.     

Photoionization dynamics in pure helium droplets

The photoionization and photoelectron spectroscopy of pure He droplets were investigated at photon energies between 24.6 eV (the ionization energy of He) and 28.0 eV. Time-of-flight mass spectra and photoelectron images were obtained at a series of molecular beam source temperatures and pressures to assess the effect of droplet size on the photoionization dynamics. At source temperatures below 16 K, where there is significant production of clusters with more than 10(4) atoms, the photoelectron images are dominated by fast electrons produced via direct ionization, with a small contribution from very slow electrons with kinetic energies below 1 meV arising from an indirect mechanism. The fast photoelectrons from the droplets have as much as 0.5 eV more kinetic energy than those from atomic He at the same photon energy. This result is interpreted and simulated within the context of a "dimer model", in which one assumes vertical ionization from two nearest-neighbor He atoms to the attractive region of the He2+ potential energy curve. Possible mechanisms for the slow electrons, which were also seen at energies below IE(He), are discussed, including vibrational autoionizaton of Rydberg states comprising an electron weakly bound to the surface of a large HeN+ core.     

Improving the performance of the coupled reference interaction site model-hyper-netted chain (RISM-HNC)/simulation method for free energy of solvation

The coupled reference interaction site model-hyper-netted chain (RISM-HNC)/ simulation methodology determines solvation free energies as a function of the set of all radial distribution functions of solvent atoms about atomic solute sites. These functions are determined from molecular dynamics (MD) or Monte Carlo (MC) simulations rather than from solving the RISM and HNC equations iteratively. Previous applications of the method showed that it can predict relative free energies of solvation for small solutes accurately. However, the errors scale with the system size. In this study, we propose the use of the hard-sphere free energy as the reference and a linear response approximation to improve the performance, i.e., accuracy and robustness, of the method, particularly removing the size dependency of the error. The details of the new formalism are presented. To validate the proposed formalism, solvation free energies of N-methylacetamide and methylamine are computed using the new RISM-HNC-based expressions in addition to a linear response expression, which are compared to previous thermodynamic integration and thermodynamic perturbation results performed with the same force field. Additionally, free energies of solvation for cyclohexane, pyridine, benzene and derivatives, and other small organic molecules are calculated and compared to experimental values.     

Theoretical study of atoms by the electronic kinetic energy density and stress tensor density

The electronic structure of atoms in the first, second, and third periods were analyzed using the electronic kinetic energy density and stress tensor density, which are local quantities motivated by quantum field theoretic consideration, specifically the rigged quantum electrodynamics. The zero surfaces of the electronic kinetic energy density, which are called as the electronic interfaces, of the atoms were computed. It was found that their sizes exhibited clear periodicity and were comparable to the conventional atomic and ionic radii. The electronic stress tensor density and its divergence, tension density, of the atoms, were also computed and how their electronic structures were characterized by them was discussed. © 2016 Wiley Periodicals, Inc.     

Effective polarization energy of the naphthalene molecular crystal: a study on the polarizable force field

polarization energy of the localized charge in organic solids consists of electronic polarization energy, permanent electrostatic interactions, and inter/intra molecular relaxation energies. The effective electronic polarization energies for an electron/hole carrier were successfully estimated by AMOEBA polarizable force field in naphthalene molecular crystals. Both electronic polarization energy and permanent electrostatic interaction were in agreement with the preview experimental values. In addition, the influence of the multipoles from different distributed mutipole analysis (DMA) fitting options on the electrostatic interactions are discussed in this paper. We found that the multipoles obtained from Gauss-Hermite quadrature without diffuse function or grid-based quadrature with 0.325 Å H atomic radius will give reasonable electronic polarization energies and permanent interactions for electron and hole carriers.     

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.     

Grid-based energy density analysis: implementation and assessment

Grid-based energy density analysis (grid-EDA) that decomposes the total energy into atomic energies by a space-partitioning function is proposed. The kinetic energy, nuclear attraction, and exchange-correlation functional are evaluated on grid points and are split into atomic contributions. To reduce numerical errors in the conventional scheme of numerical integration, the electronic Coulomb and HF exchange interactions are evaluated by the pseudospectral method, which was first applied to an ab initio method by Friesner [Chem. Phys. Lett. 116, 39 (1985)], and are decomposed into atomic contributions. Grid-EDA using the pseudospectral method succeeds in ensuring less than 1 kcalmol error in total energies for small molecules and providing reliable atomic energy contributions for the problematic lithium cluster, which exhibits a strong basis-set dependence for Mulliken-type EDA. Also, site-dependent atomization energies are estimated by grid-EDA for cluster models such as Li(48), C(41)H(60), and Mg(32)O(32). Grid-EDA reveals that these models imitate crystal environments reasonably because atomization energies estimated from the inner atoms of the models are close to the experimental cohesive energies.     

The electronic structure of thorium monoxide: Ligand field assignment of states in the range 0–5 eV

Configuration interaction ligand field theory (CI LFT) calculations of the electronic energy levels of ThO were performed by treating the molecular electronic states as Th ^{2 +} free-ion levels perturbed by the ligand field of O²⁻. Twenty nine experimentally characterized ThO v = 0 energy levels, together with the energy difference between the v = 0 levels of the Y and W states were fitted using a CI LFT model that included Th ^{2 +} 7s ² , 6d7s, 6d², 7s7p, 6d7p, 5f7s, and 7p² configurations. Predictions from these calculations were used to provide tentative assignments for 171 out of 250 ThO band heads listed by Gatterer et al. [“Molecular Spectra of Metallic Oxides”, Specola Vaticana (1957)]. Term energies for 30 electronic states have been determined based on these assignments. Subsequently, the CI LFT model was refined by fitting to a set of 59 electronic term energies. The inclusion of CI effects together with integer valence, atomic-in-molecule, ionic bonding ideas reveals atomic energy level patterns that are multiply replicated in the molecular energy level patterns of six Th ^{2 +} O²⁻ atomic ion configurations (6d7s, 6d², 7s7p, 6d7p, 5f7s, and 7p²) revealing the underlying atomic ion structure that gives rise to the complex and seemingly erratic unassigned bands reported in the Vatican Atlas. © 2018 Wiley Periodicals, Inc.     

Polarizable empirical force field for sulfur‐containing compounds based on the classical Drude oscillator model

Condensed‐phase computational studies of molecules using molecular mechanics approaches require the use of force fields to describe the energetics of the systems as a function of structure. The advantage of polarizable force fields over nonpolarizable (or additive) models lies in their ability to vary their electronic distribution as a function of the environment. Toward development of a polarizable force field for biological molecules, parameters for a series of sulfur‐containing molecules are presented. Parameter optimization was performed to reproduce quantum mechanical and experimental data for gas phase properties including geometries, conformational energies, vibrational spectra, and dipole moments as well as for condensed phase properties such as heats of vaporization, molecular volumes, and free energies of hydration. Compounds in the training set include methanethiol, ethanethiol, propanethiol, ethyl methyl sulfide, and dimethyl disulfide. The molecular volumes and heats of vaporization are in good accordance with experimental values, with the polarizable model performing better than the CHARMM22 nonpolarizable force field. Improvements with the polarizable model were also obtained for molecular dipole moments and in the treatment of intermolecular interactions as a function of orientation, in part due to the presence of lone pairs and anisotropic atomic polarizability on the sulfur atoms. Significant advantage of the polarizable model was reflected in calculation of the dielectric constants, a property that CHARMM22 systematically underestimates. The ability of this polarizable model to accurately describe a range of gas and condensed phase properties paves the way for more accurate simulation studies of sulfur‐containing molecules including cysteine and methionine residues in proteins. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010     

Theoretical determination of standard oxidation and reduction potentials of chlorophyll-a in acetonitrile

QM/MM calculations were performed on ethyl chlorophyllide-a and its radical cation and anion, by using the density functional (DF) B3LYP method to determine the molecular characteristics, and a molecular mechanics (MM) method to simulate the solvating medium. The presence of the solvent was accounted for during the optimization of the geometry of the 85-atom chlorophyll-a system by using an ONIOM methodology. A total of 24 solvent molecules were explicitly considered during the optimization process, and these were treated by the universal force field (UFF) method. Initially, the split-valence 3-21G basis set was used for optimizing the geometry of the 85-atom species, neutral, cation and anion. Electronic energies were then determined for the optimized species by making use of the polarized 6-31G(d) basis set. The ionization energy calculated (6.0 eV) is in very good agreement with the observed one (6.1 eV). The MM+ force field was used to investigate the dynamics of the acetonitrile molecules around the neutral species as well as the radical ions of chlorophyll. The required atomic charges on all the atoms were obtained from calculations on all involved molecules at the DFT/6-31G(d) level. Randomly sampled configurations were used to determine the first solvation layer contribution to the free energy of solvation of various species. A truncated 46-atom model of ethyl chlorophyllide-a was used to evaluate the thermal energies of neutral chlorophyll molecule relative to its two radical ions in the gas phase. Born energy, Onsager energy, and the Debye-Huckel energy of the chlorophyll-solvent aggregate were added as perturbative corrections to the free energy of solvation that was initially obtained through molecular dynamics method for the same complex. These calculations yield the oxidation potential as 0.75 +/- 0.32 V and the reduction potential -1.18 +/- 0.31 V at 298.15 K. The calculated values are in good agreement with the experimental midpoint potentials of +0.76 and -1.04 V, respectively.     

Electronic configurations of the d- and f-block elements follow the simple rules of energy ordering which were considered to be anomalous,previously

The existing set of principles used for the explanation of electronic configurations, has not been able to explain the electronic configurations of all the d- and f-block elements, systematically. This study proposes a new theory based on two principles, the relative decrease in the energies of the outermost atomic orbitals and the pairing energies of the electrons in different atomic orbitals for the explanation of the electronic configurations of the elements. The theory for the first time has been able to address the anomalies of the electronic configurations of the all the d- and f-block elements, systematically.     

Atoms-in-molecules in momentum space: a Hirshfeld partitioning of electron momentum densities

A direct application of the Hirshfeld atomic partitioning (HAP) scheme is implemented for molecular electron momentum densities (EMDs). The momentum density contributions of individual atoms in diverse molecular systems are analyzed along with their topographical features and the kinetic energies of the atomic partitions. The proposed p-space HAP-based charge scheme does seem to possess the desirable attributes expected of any atoms in molecules partitioning. In addition to this, the main strength of the p-space HAP is the exact knowledge of the kinetic energy functional and the inherent ease in computing the kinetic energy. The charges derived from HAP in momentum space are found to match chemical intuition and the generally known chemical characteristics such as electronegativity, etc.     

Shell and subshell periodic structures of icosahedral nickel nanoclusters

Using the modified analytic embedded atom method and molecular dynamics, the binding energies and their second order finite differences (stability functions) of icosahedral Ni clusters with shell and subshell periodicity are studied in detail via atomic evolution. The results exhibit shell and subshell structures of the clusters with atoms from 147 to 250,000, and the atomic numbers corresponding to shell or subshell structures are in good agreement with the experimental magic numbers obtained in time-of-flight mass spectra of threshold photoionization, and Martin's theoretical proposition of progressive formation of atomic umbrellas. Clusters with size from 147 to 561 atoms are energetically investigated via one-by-one atomic evolution and their magic numbers are theoretically proved. For medium-size Ni clusters with 561 to 2057 atoms, the prediction of magic numbers with atomic numbers is performed on the basis of umbrella-like subshell growth in near face-edge-vertex order. The similarity of the energy curves makes it possible to extend the prediction to even larger Ni nanoclusters in hierarchical Mackay icosahedral configurations.     

Derivation of class II force fields. VIII. Derivation of a general quantum mechanical force field for organic compounds

A class II valence force field covering a broad range of organic molecules has been derived employing ab initio quantum mechanical "observables." The procedure includes selecting representative molecules and molecular structures, and systematically sampling their energy surfaces as described by energies and energy first and second derivatives with respect to molecular deformations. In this article the procedure for fitting the force field parameters to these energies and energy derivatives is briefly reviewed. The application of the methodology to the derivation of a class II quantum mechanical force field (QMFF) for 32 organic functional groups is then described. A training set of 400 molecules spanning the 32 functional groups was used to parameterize the force field. The molecular families comprising the functional groups and, within each family, the torsional angles used to sample different conformers, are described. The number of stationary points (equilibria and transition states) for these molecules is given for each functional group. This set contains 1324 stationary structures, with 718 minimum energy structures and 606 transition states. The quality of the fit to the quantum data is gauged based on the deviations between the ab initio and force field energies and energy derivatives. The accuracy with which the QMFF reproduces the ab initio molecular bond lengths, bond angles, torsional angles, vibrational frequencies, and conformational energies is then given for each functional group. Consistently good accuracy is found for these computed properties for the various types of molecules. This demonstrates that the methodology is broadly applicable for the derivation of force field parameters across widely differing types of molecular structures. Copyright 2001 John Wiley & Sons, Inc. J Comput Chem 22: 1782-1800, 2001