Topological Ring-Currents in Condensed Benzenoid Hydrocarbons

Topological ring-currents are defined as being pi-electron ring-current intensities in condensed, benzenoid hydrocarbons that (i) are calculated by the simplest Hückel-London-Pople- McWeeny method, (ii) are based on a molecular geometry of regular hexagons of carbon atoms, and (iii) are expressed as a ratio to the corresponding ring-current intensity calculated, by the same method, for benzene. Once a particular benzenoid hydrocarbon has been specified, such topological ring-currents are predetermined and do not further depend on any subjective (or other) parameters; they are, therefore, purely graph-theoretical indices, reliant solely on knowledge of a vertex-adjacency matrix for the graph representing the connectivity of the carbon atoms in the benzenoid molecule under study. For convenient reference, tables of all known topological ring-current intensities – some published, and others so-far unpublished – are presented for future evaluation and possible comparison with other graph-theoretical indices that characterise the individual rings of a condensed, benzenoid hydrocarbon

Graphical Study of Heteroconjugated Molecules

A graphical (graph-theoretical) approach, which has previously been applied systematically only to conjugated hydrocarbon systems, extended to include consideration of the (rooted) graphs representing certaJin conjugated molecules which contain a restricted class of heteroatoms. The use of the modified Sachs formula for rooted graphs is discussed

Graphical Study of Heteroconjugated Molecules

A graphical (graph-theoretical) approach, which has previously been applied systematically only to conjugated hydrocarbon systems, extended to include consideration of the (rooted) graphs representing certaJin conjugated molecules which contain a restricted class of heteroatoms. The use of the modified Sachs formula for rooted graphs is discussed

Proof of the Formulae for the Molecular Orbitals and Energy Levels of Mobius Annulenes, Based on the Theory of Skew-Circulant Matrices

The formulae for the molecular orbitals and corresponding energy-levels that arise in a Huckel molecular-orbital (HMO) treatment of Miobius systems are derived by appeal to the theory of skew-circulant matrices. The approach adopted is analogous to that previously used to obtain the orbital energies and HMO\u27s of \u27Huckel\u27 annulenes from the theory of circulant matrices

Precision Measurement of 11Li moments: Influence of Halo Neutrons on the 9Li Core

The electric quadrupole moment and the magnetic moment of the 11Li halo nucleus have been measured with more than an order of magnitude higher precision than before, |Q| = 33.3(5)mb and mu=3.6712(3)mu_N, revealing a 8.8(1.5)% increase of the quadrupole moment relative to that of 9Li. This result is compared to various models that aim at describing the halo properties. In the shell model an increased quadrupole moment points to a significant occupation of the 1d orbits, whereas in a simple halo picture this can be explained by relating the quadrupole moments of the proton distribution to the charge radii. Advanced models so far fail to reproduce simultaneously the trends observed in the radii and quadrupole moments of the lithium isotopes.Comment: 4 pages, 4 figures, 1 tabl

Effects of candesartan cilexetil on carotid remodeling in hypertensive diabetic patients: the MITEC study

In hypertension and diabetes, early structural changes of the arterial wall precede or support atherosclerosis. There is evidence that some antihypertensive drugs exert an antiathero-sclerotic effect. Over 36 months, we investigated the effect of candesartan cilexetil (CC) on the common carotid intima-media thickness (IMT) vs amlodipine besylate (AML) in patients with type 2 diabetes and mild to moderate essential hypertension. After a 4-week wash-out period, 209 patients were randomized to either CC 8 mg or AML 5 mg once daily for a minimum of 1 month, after which, if BP was not normalized, the dosage was doubled, followed by the addition of hydrochlorothiazide 12.5 mg if necessary. No significant differences were observed between the two groups for change in IMT at M12 (−0.001 vs −0.027 mm/year for CC and AML respectively, p = 0.425), at M24 (−0.033 vs −0.019 mm per year respectively, p = 0.442), and at the last visit (−0.016 vs −0.039 mm per year respectively, p = 0.549). Within the group, comparisons did not show a significant difference in changes in IMT from baseline to the three visits. At the last visit, IMT regression was observed in 52.2% of patients receiving CC and in 51.3% of those receiving AML (p = 0.908). The augmentation in carotid lumen diameter from baseline was statistically greater in the AML group at the last visit (p = 0.034). BP variations during the study were similar in the two groups. The results of this study show that CC and AML treatments may alter identically the natural progression of carotid IMT in hypertensive type 2 diabetic patients

Comparisons of π-Electron Ring-Current and Bond-Current Patterns Calculated by Topological (‘HLPM’) and Ab Initio (‘Ipso-Centric’) Formalisms for Two Isomeric Conjugated Hydrocarbons, Corazulene and Cornaphthalene

The π-electron ring-currents and bond-currents associated with the isomeric structures corazulene (1) and cornaphthalene (2) are calculated by means of the rudimentary topological Hückel–London–Pople–McWeeny (HLPM) method (which is entirely equivalent to the recently named ‘graph-theoretical CD–HL’ approach).These currents are compared with analogous quantities computed by Lillington et al. by use of the more-sophisticated ipso–centric ab initio approach. The simple HLPM method is seen to exhibit a remarkable ability to reproduce complex patterns of current in large polycyclic hydrocarbons — the successful prediction of which, ostensibly, might naïvely be expected to be the preserve only of more sophisticated, and much less intuitive, ab initio calculations. This conclusion is entirely consistent with findings from contemporary work on other structures by the present, and other, authors

Rationalisation of Relative »Ring-Current« Sizes in Polycyclic, Conjugated Hydrocarbons

A theoretical basis is established for relating the incidence of relatively \u27high\u27 and \u27low\u27 »ring-current« intensities (as encountered, for example, in the central rings of peropyrene (I) and perylene (II), respectively) to intuitive Valence-Bond Resonance- Theory (VB-RT) ideas about \u27bond fixation\u27. In the present treatment, this aim is not achieved by devising a »ring-current« formalism that is itself actually based on a VB-RT wave-function: the philosophy adopted here is (a) to identify, and classify, those occasions on which simple Molecular-Orbital (MO) theory predicts specific rings in conjugated hydrocarbons to have exceptionally high and low »ring-currents«, and then (b) to use topological arguments that rely simply on the carbon-atom connectivity of the conjugated system in question to show that the situations identified in (a), above, are just those in which the absence, or presence, of VB-RT \u27bond-fixation\u27 is to be expected

Ring Currents and the PCP Rule

According to the recently discovered PCP rule, the intensity of cyclic conjugation in the fivemembered rings of polycyclic conjugated hydrocarbons related to acenaphthylene and fluoranthene increases with the number of phenyl-cyclopentadienyl (PCP) fragments present in the molecule. The validity of this regularity was first observed by studying the energy effects of cyclic conjugation in the fivemembered rings of these systems. In order to show that the PCP rule is not an artifact of the method employed, it is necessary to confirm its validity by other approaches. We now show that the PCP rule is in perfect agreement with calculated topological π-electron ring-currents, ostensibly an independent, quantitative, theoretical – albeit, it is here argued, likewise also graph-theoretical – measure of cyclic conjugation in the individual rings of polycyclic π-electron systems. In addition, we show that the molecularstructure dependency of the ring currents in acenaphthylene and fluoranthene congeners also agrees with other, earlier-established, regularities for cyclic conjugation