Hyperaromatic stabilization of arenium ions: cyclohexa- and cycloheptadienyl cations-experimental and calculated stabilities and ring currents

Measurements of pK(R) show that the cycloheptadienyl cation is less stable than the cyclohexadienyl (benzenium) cation by 18 kcal mol(-1). This difference is ascribed here to "hyperaromaticity" of the latter. For the cycloheptadienyl cation a value of K(R) = [ROH][H(+)]/[R(+)] is assigned by combining a rate constant for reaction of the cation with water based on the azide clock with a rate constant for the acid-catalyzed formation of the cation accompanying equilibration of cycloheptadienol with its trifluoroethyl ether in TFE-water mixtures. Comparison of pK(R) = -16.1 with pK(R) = -2.6 for the cyclohexadienyl cation yields the difference in stabilities of the two ions. Interpretation of this difference in terms of hyperconjugative aromaticity is supported by the effect of benzannelation in reducing pK(R) for the benzenium ion: from -2.6 down to -3.5 for the 1H-naphthalenium and -6.0 for the 9H-anthracenium ions, respectively. MP2/6-311+G** and G3MP2 calculations of hydride ion affinities of benzenium ions show an order of stabilities for substituents at the methylene group consistent with their hyperconjugative abilities, i.e., (H(3)Si)(2) > cyclopropyl > H(2) > Me(2)> (HO)(2) > F(2). Calculations of ring currents show a similar ordering. No conventional ring current is seen for the cycloheptadienyl cation, whereas currents in the F(2)-substituted benzenium ion are consistent with antiaromaticity. Arenium ions where the methylene group is substituted with a single OH group show characteristic energy differences between conformations, with C-H or C-OH bonds respectively occupying or constrained to axial positions favorable to hyperconjugation. The differences were found to be 8.8, 6.3, 2.4, and 0.4 kcal mol(-1) for benzenium, naphthalenium, phenanthrenium, and cyclohexenyl cations, respectively.     

Dynamically arrested states of matter

We outline current developments in our understanding of dynamical arrest, that phenomenon in which many particles stop moving in a collective manner. However in addition to the question of true dynamical arrest itself, we emphasize the development of new tools that can describe relatively sharp changes in the way that ergodic systems may be explored. We discuss the concept of new order parameters (dynamically available volume), and indicate how they may be applied to understand dramatic slowing phenomena present in particle systems, and other arenas of soft and complex matter.     

Clarification of the bootstrap percolation paradox

We study the onset of the bootstrap percolation transition as a model of generalized dynamical arrest. Our results apply to two dimensions, but there is no significant barrier to extending them to higher dimensionality. We develop a new importance-sampling procedure in simulation, based on rare events around "holes", that enables us to access bootstrap lengths beyond those previously studied. By framing a new theory in terms of paths or processes that lead to emptying of the lattice we are able to develop systematic corrections to the existing theory and compare them to simulations. Thereby, for the first time in the literature, it is possible to obtain credible comparisons between theory and simulation in the accessible density range.     

Everyday episodic memory in amnestic mild cognitive impairment: a preliminary investigation

Background

In humans, rapid eye movements (REM) density during REM sleep plays a prominent role in psychiatric diseases. Especially in depression, an increased REM density is a vulnerability marker for depression. In clinical practice and research measurement of REM density is highly standardized. In basic animal research, almost no tools are available to obtain and systematically evaluate eye movement data, although, this would create increased comparability between human and animal sleep studies.

Methods

We obtained standardized electroencephalographic (EEG), electromyographic (EMG) and electrooculographic (EOG) signals from freely behaving mice. EOG electrodes were bilaterally and chronically implanted with placement of the electrodes directly between the musculus rectus superior and musculus rectus lateralis. After recovery, EEG, EMG and EOG signals were obtained for four days. Subsequent to the implantation process, we developed and validated an Eye Movement scoring in Mice Algorithm (EMMA) to detect REM as singularities of the EOG signal, based on wavelet methodology.

Results

The distribution of wakefulness, non-REM (NREM) sleep and rapid eye movement (REM) sleep was typical of nocturnal rodents with small amounts of wakefulness and large amounts of NREM sleep during the light period and reversed proportions during the dark period. REM sleep was distributed correspondingly. REM density was significantly higher during REM sleep than NREM sleep. REM bursts were detected more often at the end of the dark period than the beginning of the light period. During REM sleep REM density showed an ultradian course, and during NREM sleep REM density peaked at the beginning of the dark period. Concerning individual eye movements, REM duration was longer and amplitude was lower during REM sleep than NREM sleep. The majority of single REM and REM bursts were associated with micro-arousals during NREM sleep, but not during REM sleep.

Conclusions

Sleep-stage specific distributions of REM in mice correspond to human REM density during sleep. REM density, now also assessable in animal models through our approach, is increased in humans after acute stress, during PTSD and in depression. This relationship can now be exploited to match animal models more closely to clinical situations, especially in animal models of depression.