Valence–Bond Order (VBO): A New Approach to Modeling Reactive Potential Energy Surfaces for Complex Systems, Materials, and Nanoparticles

Abstract

The extension of molecular mechanics to reactive systems, metals, and covalently bonded clusters with variable coordination numbers requires new functional forms beyond those popular for organic chemistry and biomolecules. Here we present a new scheme for reactive molecular mechanics, which is denoted as the valence-bond order model, for approximating reactive potential energy surfaces in large molecules, clusters, nanoparticles, solids, and other condensed-phase materials, especially those containing metals. The model is motivated by a moment approximation to tight binding molecular orbital theory, and we test how well one can approximate potential energy surfaces with a very simple functional form involving only interatomic distances with no explicit dependence on bond angles or dihedral angles. For large systems the computational requirements scale linearly with system size, and no diagonalizations or iterations are required; thus the method is well suited to large-scale simulations. The method is illustrated here by developing a force field for particles and solids composed of aluminum and hydrogen. The parameters were optimized against both interaction energies and relative interaction energies. The method performs well for pure aluminum clusters, nanoparticles, and bulk lattices and reasonably well for pure hydrogen clusters; the mean unsigned error per atom for the aluminum-hydrogen clusters is 0.1 eV/atom.

Polarized Molecular Orbital Model Chemistry 3. The PMO Method Extended to Organic Chemistry

“…48,57,58 The absolute errors in the reaction energies are given in Table S7 (Supporting Information), and Table S8 contains errors in barrier heights. For the reaction energies, PMO2 shows a relatively high MUE compared with the other semiempirical methods.…”

Benchmarking the Performance of the ReaxFF Reactive Force Field on Hydrogen Combustion Systems

“…Alternatively, empirical methods including reactive force fields 39,[42][43][44][45][46][47] and tight binding [48][49][50] offer a computationally more feasible approach to larger and longer simulations, though potentially with a loss of accuracy. The former allow for the nanosecond scale simulations on thousands of atoms.…”

Analytic Force Field for Clusters and Nanoparticles of Aluminum and Its Hydride

“…It is recommended that only the exponential EA PEF be considered for use in molecular dynamics simulations that include hydrides. It is also noteworthy that the MUE for the VBO method [21] is found to be 0.1 eV=atom. Therefore, the exponential EA PEF appears to be the most reliable; however, the training set (and definition of MUE) are different in the two studies, so it is not possible to make this claim with certainty.…”

“…Whereas aluminum clusters and nanoparticles have been investigated through first-principle calculations by various researchers [12][13][14][15][16][17][18][19][20], studies of binary compounds such as aluminum hydrides are less numerous. One important study [21] introduces a new valence-bond order (VBO) approach for modeling reactive potential energy surfaces. The VBO method is related to an EA method, and the initial application of the method to aluminum hydrides contains no explicit dependence on the bond angle or Coulombic terms in order to test and develop a simple functional form which would be well suited for large-scale simulations.…”

“…Likewise, one of the motivations of the present study is to investigate the interactions between aluminum and hydrogen in the formation of aluminum hydrides so as to characterize and develop a general PEF form that properly accounts for both covalent and metallic bonding interactions. As in the previous study [21], the starting point for this investigation is to compute the energies for a large set of stable and metastable aluminum and aluminum hydride structures using first-principle DFT. These structures may then be used as a training set for determining the model parameters and testing the reliability of the FF for a variety of conditions.…”