Time-Dependent Density Functional Molecular Orbital and Excited State Calculations on Bis(porphyrinyl)butadiynes in the Monocationic, Neutral, Monoanionic, and Dianionic Oxidation States

We report a theoretical study of the multiple oxidation states (1+, 0, 1−, and 2−) of a meso,meso-linked diporphyrin, namely bis[10,15,20-triphenylporphyrinatozinc(II)-5-yl]butadiyne (4), using Time-Dependent Density Functional Theory (TDDFT). The origin of electronic transitions of singlet excited states is discussed in comparison to experimental spectra for the corresponding oxidation states of the close analogue bis{10,15,20-tris[3‘,5‘-di-tert-butylphenyl]porphyrinatozinc(II)-5-yl}butadiyne (3). The latter were measured in previous work under in situ spectroelectrochemical conditions. Excitation energies and orbital compositions of the excited states were obtained for these large delocalized aromatic radicals, which are unique examples of organic mixed-valence systems. The radical cations and anions of butadiyne-bridged diporphyrins such as 3 display characteristic electronic absorption bands in the near-IR region, which have been successfully predicted with use of these computational methods. The radicals are clearly of the “fully delocalized” or Class III type. The key spectral features of the neutral and dianionic states were also reproduced, although due to the large size of these molecules, quantitative agreement of energies with observations is not as good in the blue end of the visible region. The TDDFT calculations are largely in accord with a previous empirical model for the spectra, which was based simplistically on one-electron transitions among the eight key frontier orbitals of the C4 (1,4-butadiyne) linked diporphyrins.

Quantitative electroencephalographic comodulation : an investigation of patterns in chronic fatigue syndrome

Introduction. This is a pilot study of quantitative electro-encephalographic (QEEG) comodulation analysis, which is used to assist in identifying regional brain differences in those people suffering from chronic fatigue syndrome (CFS) compared to a normative database. The QEEG comodulation analysis examines spatial-temporal cross-correlation of spectral estimates in the resting dominant frequency band. A pattern shown by Sterman and Kaiser (2001) and referred to as the anterior posterior dissociation (APD) discloses a significant reduction in shared functional modulation between frontal and centro-parietal areas of the cortex. This research attempts to examine whether this pattern is evident in CFS. Method. Eleven adult participants, diagnosed by a physician as having CFS, were involved in QEEG data collection. Nineteen-channel cap recordings were made in five conditions: eyes-closed baseline, eyes-open, reading task one, math computations task two, and a second eyes-closed baseline. Results. Four of the 11 participants showed an anterior posterior dissociation pattern for the eyes-closed resting dominant frequency. However, seven of the 11 participants did not show this pattern. Examination of the mean 8-12 Hz amplitudes across three cortical regions (frontal, central and parietal) indicated a trend of higher overall alpha levels in the parietal region in CFS patients who showed the APD pattern compared to those who did not have this pattern. All patients showing the pattern were free of medication, while 71% of those absent of the pattern were using antidepressant medications. Conclusions. Although the sample is small, it is suggested that this method of evaluating the disorder holds promise. The fact that this pattern was not consistently represented in the CFS sample could be explained by the possibility of subtypes of CFS, or perhaps co-morbid conditions. Further, the use of antidepressant medications may mask the pattern by altering the temporal characteristics of the EEG. The results of this pilot study indicate that further research is warranted to verify that the pattern holds across the wider population of CFS sufferers.

High body mass index is not a barrier to physical activity: Analysis of international rugby players' anthropometric data

Recent data indicate that levels of overweight and obesity are increasing at an alarming rate throughout the world. At a population level (and commonly to assess individual health risk), the prevalence of overweight and obesity is calculated using cut-offs of the Body Mass Index (BMI) derived from height and weight. Similarly, the BMI is also used to classify individuals and to provide a notional indication of potential health risk. It is likely that epidemiologic surveys that are reliant on BMI as a measure of adiposity will overestimate the number of individuals in the overweight (and slightly obese) categories. This tendency to misclassify individuals may be more pronounced in athletic populations or groups in which the proportion of more active individuals is higher. This differential is most pronounced in sports where it is advantageous to have a high BMI (but not necessarily high fatness). To illustrate this point we calculated the BMIs of international professional rugby players from the four teams involved in the semi-finals of the 2003 Rugby Union World Cup. According to the World Health Organisation (WHO) cut-offs for BMI, approximately 65% of the players were classified as overweight and approximately 25% as obese. These findings demonstrate that a high BMI is commonplace (and a potentially desirable attribute for sport performance) in professional rugby players. An unanswered question is what proportion of the wider population, classified as overweight (or obese) according to the BMI, is misclassified according to both fatness and health risk? It is evident that being overweight should not be an obstacle to a physically active lifestyle. Similarly, a reliance on BMI alone may misclassify a number of individuals who might otherwise have been automatically considered fat and/or unfit.

A Petrov-Galerkin method for a singularly perturbed ordinary differential equation with non-smooth data

In this paper, a singularly perturbed ordinary differential equation with non-smooth data is considered. The numerical method is generated by means of a Petrov-Galerkin finite element method with the piecewise-exponential test function and the piecewise-linear trial function. At the discontinuous point of the coefficient, a special technique is used. The method is shown to be first-order accurate and singular perturbation parameter uniform convergence. Finally, numerical results are presented, which are in agreement with theoretical results.