Chemical Pressure Maps of Molecules and Materials: Merging the Visual and Physical in Bonding Analysis.

The characterization of bonding interactions in molecules and materials is one of the major applications of quantum mechanical calculations. Numerous schemes have been devised to identify and visualize chemical bonds, including the electron localization function, quantum theory of atoms in molecules, and natural bond orbital analysis, whereas the energetics of bond formation are generally analyzed in qualitative terms through various forms of energy partitioning schemes. In this Article, we illustrate how the chemical pressure (CP) approach recently developed for analyzing atomic size effects in solid state compounds provides a basis for merging these two approaches, in which bonds are revealed through the forces of attraction and repulsion acting between the atoms. Using a series of model systems that include simple molecules (H2, CO2, and S8), extended structures (graphene and diamond), and systems exhibiting intermolecular interactions (ice and graphite), as well as simple representatives of metallic and ionic bonding (Na and NaH, respectively), we show how CP maps can differentiate a range of bonding phenomena. The approach also allows for the partitioning of the potential and kinetic contributions to the interatomic interactions, yielding schemes that capture the physical model for the chemical bond offered by Ruedenberg and co-workers.

Progress in Visualizing Atomic Size Effects with DFT-Chemical Pressure Analysis: From Isolated Atoms to Trends in AB5 Intermetallics.

The notion of atomic size poses an important challenge to chemical theory: empirical evidence has long established that atoms have spatial requirements, which are summarized in tables of covalent, ionic, metallic, and van der Waals radii. Considerations based on these radii play a central role in the design and interpretation of experiments, but few methods are available to directly support arguments based on atomic size using electronic structure methods. Recently, we described an approach to elucidating atomic size effects using theoretical calculations: the DFT-Chemical Pressure analysis, which visualizes the local pressures arising in crystal structures from the interactions of atomic size and electronic effects. Using this approach, a variety of structural phenomena in intermetallic phases have already been understood in terms that provide guidance to new synthetic experiments. However, the applicability of the DFT-CP method to the broad range of the structures encountered in the solid state is limited by two issues: (1) the difficulty of interpreting the intense pressure features that appear in atomic core regions and (2) the need to divide space among pairs of interacting atoms in a meaningful way. In this article, we describe general solutions to these issues. In addressing the first issue, we explore the CP analysis of a test case in which no core pressures would be expected to arise: isolated atoms in large boxes. Our calculations reveal that intense core pressures do indeed arise in these virtually pressure-less model systems and allow us to trace the issue to the shifts in the voxel positions relative to atomic centers upon expanding and contracting the unit cell. A compensatory grid unwarping procedure is introduced to remedy this artifact. The second issue revolves around the difficulty of interpreting the pressure map in terms of interatomic interactions in a way that respects the size differences of the atoms and avoids artificial geometrical constraints. In approaching this challenge, we have developed a scheme for allocating the grid pressures to contacts inspired by the Hirshfeld charge analysis. Here, each voxel is allocated to the contact between the two atoms whose free atom electron densities show the largest values at that position. In this way, the differing sizes of atoms are naturally included in the division of space without resorting to empirical radii. The use of the improved DFT-CP method is illustrated through analyses of the applicability of radius ratio arguments to Laves phase structures and the structural preferences of AB5 intermetallics between the CaCu5 and AuBe5 structure types.

First-Principles Elucidation of Atomic Size Effects Using DFT-Chemical Pressure Analysis: Origins of Ca36Sn23's Long-Period Superstructure.

The space requirements of atoms are empirically known to play key roles in determining structure and reactivity across compounds ranging from simple molecules to extended solid state phases. Despite the importance of this concept, the effects of atomic size on stability remain difficult to extract from quantum mechanical calculations. Recently, we outlined a quantitative yet visual and intuitive approach to the theoretical analysis of atomic size in periodic structures: the DFT-Chemical Pressure (DFT-CP) analysis. In this Article, we describe the methodological details of this DFT-CP procedure, with a particular emphasis on refinements of the method to make it useful for a wider variety of systems. A central improvement is a new integration scheme with broader applicability than our earlier Voronoi cell method: contact volume space-partitioning. In this approach, we make explicit our assumption that the pressure at each voxel is most strongly influenced by its two closest atoms. The unit cell is divided into regions corresponding to individual interatomic contacts, with each region containing all points that share the same two closest atoms. The voxel pressures within each contact region are then averaged, resulting in effective interatomic pressures. The method is illustrated through the verification of the role of Ca-Ca repulsion (deduced earlier from empirical considerations by Corbett and co-workers) in the long-period superstructure of the W5Si3 type exhibited by Ca36Sn23.

Tris(oxazolinyl)boratomagnesium-catalyzed cross-dehydrocoupling of organosilanes with amines, hydrazine, and ammonia.

We report magnesium-catalyzed cross-dehydrocoupling of Si-H and N-H bonds to give Si-N bonds and H(2). A number of silazanes are accessible using this method, as well as silylamines from NH(3) and silylhydrazines from N(2)H(4). Kinetic studies of the overall catalytic cycle and a stoichiometric Si-N bond-forming reaction suggest nucleophilic attack by a magnesium amide as the turnover-limiting step.

Algorithms for sampling a quantum microcanonical ensemble of harmonic oscillators at potential minima and conical intersections.

Algorithms are presented for sampling quantum microcanonical ensembles for a potential energy minimum and for the conical intersection at the minimum energy crossing point of two coupled electronic states. These ensembles may be used to initialize trajectories for chemical dynamics simulations. The unimolecular dynamics of a microcanonical ensemble about a potential energy minimum may be compared with the dynamics predicted by quantum Rice-Ramsperger-Kassel-Marcus (RRKM) theory. If the dynamics is non-RRKM, it will be of particular interest to determine which states have particularly long lifetimes. Initializing a microcanonical ensemble for the electronically excited state at a conical intersection is a model for electronic nonadiabatic dynamics. The trajectory surface-hopping approach may be used to study the ensuing chemical dynamics. A strength of the model is that zero-point energy conditions are included for the initial nonadiabatic dynamics at the conical intersection.