The Local Theory for Regular Systems in the Context of t-Bonded Sets

The main goal of the local theory for crystals developed in the last quarter of the 20th Century by a geometry group of Delone (Delaunay) at the Steklov Mathematical Institute is to find and prove the correct statements rigorously explaining why the crystalline structure follows from the pair-wise identity of local arrangements around each atom. Originally, the local theory for regular and multiregular systems was developed with the assumption that all point sets under consideration are (r,R) role= presentation \u3e(r,R) -systems or, in other words, Delone sets of type (r,R) role= presentation \u3e(r,R) in d-dimensional Euclidean space. In this paper, we will review the recent results of the local theory for a wider class of point sets compared with the Delone sets. We call them t-bonded sets. This theory, in particular, might provide new insight into the case for which the atomic structure of matter is a Delone set of a “microporous” character, i.e., a set that contains relatively large cavities free from points of the set

Self-Replication and Self-Assembly for Manufacturing

It has been argued that a central objective of nanotechnology is to make products inexpensively, and that self-replication is an effective approach to very low-cost manufacturing. The research presented here is intended to be a step towards this vision. We describe a computational simulation of nanoscale machines floating in a virtual liquid. The machines can bond together to form strands (chains) that self-replicate and self-assemble into user-specified meshes. There are four types of machines and the sequence of machine types in a strand determines the shape of the mesh they will build. A strand may be in an unfolded state, in which the bonds are straight, or in a folded state, in which the bond angles depend on the types of machines. By choosing the sequence of machine types in a strand, the user can specify a variety of polygonal shapes. A simulation typically begins with an initial unfolded seed strand in a soup of unbonded machines. The seed strand replicates by bonding with free machines in the soup. The child strands fold into the encoded polygonal shape, and then the polygons drift together and bond to form a mesh. We demonstrate that a variety of polygonal meshes can be manufactured in the simulation, by simply changing the sequence of machine types in the seed

Self-Replicating Strands that Self-Assemble into User-Specified Meshes

It has been argued that a central objective of nanotechnology is to make products inexpensively, and that self-replication is an effective approach to very low-cost manufacturing. The research presented here is intended to be a step towards this vision. In previous work (JohnnyVon 1.0), we simulated machines that bonded together to form self-replicating strands. There were two types of machines (called types 0 and 1), which enabled strands to encode arbitrary bit strings. However, the information encoded in the strands had no functional role in the simulation. The information was replicated without being interpreted, which was a significant limitation for potential manufacturing applications. In the current work (JohnnyVon 2.0), the information in a strand is interpreted as instructions for assembling a polygonal mesh. There are now four types of machines and the information encoded in a strand determines how it folds. A strand may be in an unfolded state, in which the bonds are straight (although they flex slightly due to virtual forces acting on the machines), or in a folded state, in which the bond angles depend on the types of machines. By choosing the sequence of machine types in a strand, the user can specify a variety of polygonal shapes. A simulation typically begins with an initial unfolded seed strand in a soup of unbonded machines. The seed strand replicates by bonding with free machines in the soup. The child strands fold into the encoded polygonal shape, and then the polygons drift together and bond to form a mesh. We demonstrate that a variety of polygonal meshes can be manufactured in the simulation, by simply changing the sequence of machine types in the seed

From ab initio quantum chemistry to molecular dynamics: The delicate case of hydrogen bonding in ammonia

The ammonia dimer (NH3)2 has been investigated using high--level ab initio quantum chemistry methods and density functional theory (DFT). The structure and energetics of important isomers is obtained to unprecedented accuracy without resorting to experiment. The global minimum of eclipsed C_s symmetry is characterized by a significantly bent hydrogen bond which deviates from linearity by about 20 degrees. In addition, the so-called cyclic C_{2h} structure is extremely close in energy on an overall flat potential energy surface. It is demonstrated that none of the currently available (GGA, meta--GGA, and hybrid) density functionals satisfactorily describe the structure and relative energies of this nonlinear hydrogen bond. We present a novel density functional, HCTH/407+, designed to describe this sort of hydrogen bond quantitatively on the level of the dimer, contrary to e.g. the widely used BLYP functional. This improved functional is employed in Car-Parrinello ab initio molecular dynamics simulations of liquid ammonia to judge its performance in describing the associated liquid. Both the HCTH/407+ and BLYP functionals describe the properties of the liquid well as judged by analysis of radial distribution functions, hydrogen bonding structure and dynamics, translational diffusion, and orientational relaxation processes. It is demonstrated that the solvation shell of the ammonia molecule in the liquid phase is dominated by steric packing effects and not so much by directional hydrogen bonding interactions. In addition, the propensity of ammonia molecules to form bifurcated and multifurcated hydrogen bonds in the liquid phase is found to be negligibly small.Comment: Journal of Chemical Physics, in press (305335JCP

Tuning ion coordination preferences to enable selective permeation

Potassium (K-) channels catalyze K+ ion permeation across cellular membranes while simultaneously discriminating their permeation over Na+ ions by more than a factor of a thousand. Structural studies show bare K+ ions occupying the narrowest channel regions in a state of high coordination by all 8 surrounding oxygen ligands from the channel walls. As in most channels, the driving force for selectivity occurs when one ion is preferentially stabilized or destabilized by the channel compared to water. In the common view of mechanism, made vivid by textbook graphics, the driving force for selectivity in K- channels arises by a fit, whereby the channel induces K+ ions to leave water by offering an environment like water for K+, in terms of both energy and local structure. The implication that knowledge of local ion coordination in a liquid environment translates to design parameters in a protein ion channel, producing similar energetic stabilities, has gone unchallenged, presumably due in part to lack of consensus regarding ion coordination structures in liquid water. Growing evidence that smaller numbers and different arrangements of ligands coordinate K+ ions in liquid water, however, raises new questions regarding mechanism: how and why should ion coordination preferences change, and how does that alter the current notions of ion selectivity? Our studies lead to a new channelcentric paradigm for the mechanism of K+ ion channel selectivity. Because the channel environment is not liquid-like, the channel necessarily induces local structural changes in ion coordination preferences that enable structural and energetic differentiation between ions.Comment: Main manuscript: 12 pages, 6 figures. Supplementary information: 10 pages, 7 figure