Aromaticity of Even-Number Cyclo[n]carbons (n = 6–100)

Nanotubes: Number of Kekulé Structures and Aromaticity

Carbon nanotubes (CNTs) are composed of cylindrical graphite sheets consisting of sp(2) carbons. Due to their structure CNTs are considered to be aromatic systems. In this work the number of Kekulé structures (K) in "armchair" CNTs was estimated by using the transfer matrix technique. All Kekulé structures of the cyclic variants of naphthalene and benzo[c]phenanthrene have been generated and th...

Local aromaticity of [n]acenes, [n]phenacenes, and [n]helicenes (n = 1-9).

The local aromaticity of the six-membered rings in three series of benzenoid compounds, namely, the [n]acenes, [n]phenacenes, and [n]helicenes for n = 1-9, has been assessed by means of three probes of local aromaticity based on structural, magnetic, and electron delocalization properties. For [n]acenes our analysis shows that the more reactive inner rings are more aromatic than the outer rings...

Stability and aromaticity of nH2@B12N12 (n=1–12) clusters

Standard ab initio and density functional calculations are carried out to determine the structure, stability, and reactivity of B(12)N(12) clusters with hydrogen doping. To lend additional support, conceptual DFT-based reactivity descriptors and the associated electronic structure principles are also used. Related cage aromaticity of this B(12)N(12) and nH(2)@B(12)N(12) are analyzed through the...

ON THE NUMBER OF EVEN AND ODD STRINGS ALONG THE OVERPARTITIONS OF n

A partition of a non-negative integer n is a non-increasing sequence of positive integers whose sum is n. For example, The 5 partitions of 4 are 4, 3 + 1, 2 + 2, 2 + 1 + 1, and 1 + 1 + 1 + 1. To explain Ramanujan’s famous three partition congruences, the partition statistics, the rank (resp. the crank) were introduced by Dyson [8] (resp. Andrews and Garvan [3]). Atkin and Garvan [5] initiated t...

FPGA controller for rearrangeable Log2(N, 0, p) fabrics with an even number of stages