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For convenient reference, tables of all known topological ring-current intensities – some published, and others so-far unpublished – are presented for future evaluation and possible comparison with other graph-theoretical indices that characterise the individual rings of a condensed,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

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

All that glisters is not gold: a comparison of electronic monitoring versus filled prescriptions – an observational study

BACKGROUND: Poor compliance with antihypertensive medication is assumed to be an important reason for unsatisfactory control of blood pressure. Poor compliance is difficult to detect. Each method of measuring compliance has its own strengths and weaknesses. The aim of the present study was to compare patient compliance with antihypertensive drugs as measured by two methods, electronic monitoring versus refill compliance. METHODS: 161 patients with a diagnosis of hypertension for at least a year prior to inclusion, and inadequate blood pressure control (systolic blood pressure ≥ 160 mmHg and/or diastolic blood pressure ≥ 95 mmHg) despite the use of antihypertensive drugs, were included. Patients' pharmacy records from 12 months prior to inclusion were obtained. Refill compliance was calculated as the number of days for which the pills were prescribed divided by the total number of days in this period. After inclusion compliance was measured with an electronic monitor that records time and date of each opening of the pillbox. Agreement between both compliance measures was calculated using Spearman's correlation coefficient and Cohen's kappa coefficient. RESULTS: There was very little agreement between the two measures. Whereas refill compliance showed a large range of values, compliance as measured by electronic monitoring was high in almost all patients with estimates between 90% and 100%. Cohen's kappa coefficient was 0.005. CONCLUSION: While electronic monitoring is often considered to be the gold standard for compliance measurements, our results suggest that a short-term electronic monitoring period with the patient being aware of electronic monitoring is probably insufficient to obtain valid compliance data. We conclude that there is a strong need for more studies that explore the effect of electronic monitoring on patient's compliance

2007 Guidelines for the management of arterial hypertension: The Task Force for the Management of Arterial Hypertension of the European Society of Hypertension (ESH) and of the European Society of Cardiology (ESC)

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