Achieving plane wave accuracy in linear-scaling density functional theory applied to periodic systems: a case study on crystalline silicon

Linear-scaling methods for density functional theory promise to revolutionize the scope and scale of first-principles quantum mechanical calculations. Crystalline silicon has been the system of choice for exploratory tests of such methods in the literature, yet attempts at quantitative comparisons under linear-scaling conditions with traditional methods or experimental results have not been forthcoming. A detailed study using the ONETEP code is reported here, demonstrating for the first time that plane wave accuracy can be achieved in linear-scaling calculations on periodic systems.     

2,5‐Dichloro‐2,5‐dihydro­thio­phene 1‐oxide: determinaton of the complete stereochemistry

The title five‐membered heterocycle, C₄H₄Cl₂OS, adopts an envelope conformation with the S atom at the tip of the flap. All three ring substituents, viz. the sulfoxide O atom and the two Cl atoms, are cis to each other. The two C atoms α to the sulfoxide group are also bonded to chlorine. The electron‐withdrawing chlorine substituents give rise to weak C—H·O hydrogen bonds with the sulfoxide O atom of a symmetry‐related mol­ecule [H·O = 2.44 (2) and 2.61 (2) Å, C·O = 3.143 (3) and 3.302 (2) Å and C—H·O = 129.9 (19) and 135.1 (19)°]. There is also a possible weak C—H·Cl inter­action. Chains of mol­ecules held together by these weak inter­actions run parallel to the a axis.     

A Numerical Study of Blowup in the Harmonic Map Heat Flow Using the MMPDE Moving Mesh Method

The numerical solution of the harmonic heat map flow problems with blowup in finite or infinite time is considered using an adaptive moving mesh method. A properly chosen monitor function is derived so that the moving mesh method can be used to simulate blowup and produce accurate blowup profiles which agree with formal asymptotic analysis. Moreover, the moving mesh method has finite time blowup when the underlying continuous problem does. In situations where the continuous problem has infinite time blowup, the moving mesh method exhibits finite time blowup with a blowup time tending to infinity as the number of mesh points increases. The inadequacy of a uniform mesh solution is clearly demonstrated.     

Computationally Efficient Changepoint Detection for a Range of Penalties

In the multiple changepoint setting, various search methods have been proposed, which involve optimizing either a constrained or penalized cost function over possible numbers and locations of changepoints using dynamic programming. Recent work in the penalized optimization setting has focused on developing an exact pruning-based approach that, under certain conditions, is linear in the number of data points. Such an approach naturally requires the specification of a penalty to avoid under/over-fitting. Work has been undertaken to identify the appropriate penalty choice for data-generating processes with known distributional form, but in many applications the model assumed for the data is not correct and these penalty choices are not always appropriate. To this end, we present a method that enables us to find the solution path for all choices of penalty values across a continuous range. This permits an evaluation of the various segmentations to identify a suitable penalty choice. The computational complexity of this approach can be linear in the number of data points and linear in the difference between the number of changepoints in the optimal segmentations for the smallest and largest penalty values. Supplementary materials for this article are available online.     

Partitioning the Vertices of a Graph into Two Total Dominating Sets

A total dominating set in a graph G is a set S of vertices of G such that every vertex in G is adjacent to a vertex of S. We study graphs whose vertex set can be partitioned into two total dominating sets. In particular, we develop several sufficient conditions for a graph to have a vertex partition into two total dominating sets. We also show that with the exception of the cycle on five vertices, every selfcomplementary graph with minimum degree at least two has such a partition.     

Vertex-edge domination in graphs

In this paper we study graph parameters related to vertex-edge domination, where a vertex dominates the edges incident to it as well as the edges adjacent to these incident edges. First, we present new relationships relating the ve-domination to some other domination parameters, answering in the affirmative four open questions posed in the 2007 PhD thesis by Lewis. Then we provide an upper bound for the independent ve-domination number in terms of the ve-domination number for every nontrivial connected K_1,k-free graph, with k ≥ 3, and we show that the independent ve-domination number is bounded above by the domination number for every nontrivial tree. Finally, we establish an upper bound on the ve-domination number for connected C₅-free graphs, improving a recent bound given for trees.     

Density functional study of the reaction of carbon surface oxides: the behavior of ketones

The reactions of a ketone surface oxide group have been studied on two forms of the zigzag edge and the armchair edge of a model char using density functional theory at the B3LYP/6-31G(d) level of theory. Rearrangement and surface migration reactions were found to occur much more rapidly than desorption reactions on both the zigzag and armchair edges. A number of desorption pathways characterized here go some way toward explaining the experimentally observed broad activation energy profile for CO desorption. Three separate desorption processes were characterized; on the zigzag surface two were found with activation energies of 275 and 367 kJ mol(-1), while on the armchair surface one was found with an activation energy of 296 kJ mol(-1). The activation energies for these processes were found to be insensitive to increasing the size of the char fragment. On a larger char fragment, however, an extra desorption process was found to be possible, with an activation energy of 160 kJ mol(-1).     

Radiochemical studies of free radical vinyl polymerizations—IV. Polymerizations of esters of methacrylic acid

[¹⁴C]Azoisobutyronitrile has been used to initiate the polymerizations of methyl, ethyl, n-butyl, i-butyl, t-butyl, dodecyl, phenyl and cyclohexyl esters of methacrylic acid at 60°. Rates and efficiencies of initiation were measured and the mode of bimolecular termination of polymer radicals determined. Termination was predominantly by disproportionation in every case. No correlation could be found between n (the average number of initiator fragments per polymer molecule) and specific polar or steric effects for the ester groups but a possible correlation was detected between n and the ratio $\text{k}{}_{\mathrm{t}}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{/k}{}_{\mathrm{p}}$.