Calculating the number of Hamilton cycles in layeredpolyhedral graphs

We describe a method for computing the number of Hamilton cycles in cubic polyhedral graphs. The Hamilton cycle counts are expressed in terms of a finite-state machine, and can be written as a matrix expression. In the special case of polyhedral graphs with repeating layers, the state machines become cyclic, greatly simplifying the expression for the exact Hamilton cycle counts, and let us calculate the exact Hamilton cycle counts for infinite series of graphs that are generated by repeating the layers. For some series, these reduce to closed form expressions, valid for the entire infinite series. When this is not possible, evaluating the number of Hamiltonian cycles admitted by the series' k-layer member is found by computing a (k - 1)th matrix power, requiring O(log(2)(k)) matrix-matrix multiplications. We demonstrate our technique for the two infinite series of fullerene nanotubes with the smallest caps. In addition to exact closed form and matrix expressions, we provide approximate exponential formulas for the number of Hamilton cycles.Peer reviewe

Novel hollow all-carbon structures

A new family of cavernous all-carbon structures is proposed. These molecular cage structures are constructed by edge subdivisions and leapfrog transformations from cubic polyhedra or their duals. The obtained structures were then optimized at the density functional level. These hollow carbon structures represent a new class of carbon allotropes which could lead to many interesting applications.Peer reviewe

A method for designing a novel class of gold-containing molecules

We propose a novel class of gold-containing molecules, which have been designed using conjugated carbon structures as templates. The sp-hybridized carbons of C-2 moieties are replaced with a gold atom and one of the adjacent carbons is replaced by nitrogen. Applying the procedure to hexadehydro[12]annulene yields the well-known cyclic trinuclear gold(i) carbeniate complex. Planar, tubular and cage-shaped complexes can be obtained by taking similar sp-hybridized carbon structures as the starting point.Peer reviewe

Recent progress and perspectives of space electric propulsion systems based on smart nanomaterials

Miniaturized spacecraft built from advanced nanomaterials are poised for unmanned space exploration. In this review, the authors examine the integration of nanotechnology in electric propulsion systems and propose the concept of self-healing and adaptive thrusters

Biasing molecular modelling simulations with experimental residual dipolar couplings

In this thesis two different models, that is levels of abstraction, are used to explore specific classes of molecular structures and their properties. In part I, fullerenes and other all-carbon cages are investigated using graphs as a representation of their molecular structure. By this means the large isomer space, simple molecular properties as well as pure graph theoretical aspects of the underlying graphs are explored. Although chemical graphs are used to represent other classes of molecules, cavernous carbon molecules are particularly well suited for this level of abstraction due to their large number of isomers with only one atom type and uniform hybridisation throughout the molecule. In part II, a force field for molecular dynamics, that is the step wise propagation of a molecular structure in time using Newtonian mechanics, is complemented by an additional term that takes into account residual dipolar couplings that are experimentally measured in NMR experiments. Adding this force term leads to more accurate simulated dynamics which is especially important for proteins whose functionality in many cases crucially depends on their dynamics. Large biomolecules are an example of chemical systems that are too large for treatment with quantum chemical methods but at the same time have an electronic structure that is simple enough for accurate simulations with a forcefield