Adsorption of organic molecules at the TiO2(110) surface: the effect of van der Waals interactions

Understanding the interaction of organic molecules with TiO2 surfaces is important for a wide range of technological applications. While density functional theory (DFT) calculations can provide valuable insight about these interactions, traditional DFT approaches with local exchange-correlation functionals suffer from a poor description of non-bonding van der Waals (vdW) interactions. We examine here the contribution of vdW forces to the interaction of small organic molecules (methane, methanol, formic acid and glycine) with the TiO2 (110) surface, based on DFT calculations with the optB88-vdW functional. The adsorption geometries and energies at different configurations were also obtained in the standard generalized gradient approximation (GGA-PBE) for comparison. We find that the optB88-vdW consistently gives shorter surface adsorbate-to-surface distances and slightly stronger interactions than PBE for the weak (physisorbed) modes of adsorption. In the case of strongly adsorbed (chemisorbed) molecules both functionals give similar results for the adsorption geometries, and also similar values of the relative energies between different chemisorption modes for each molecule. In particular both functionals predict that dissociative adsorption is more favourable than molecular adsorption for methanol, formic acid and glycine, in general agreement with experiment. The dissociation energies obtained from both functionals are also very similar, indicating that vdW interactions do not affect the thermodynamics of surface deprotonation. However, the optB88-vdW always predicts stronger adsorption than PBE. The comparison of the methanol adsorption energies with values obtained from a Redhead analysis of temperature programmed desorption data suggests that optB88-vdW significantly overestimates the adsorption strength, although we warn about the uncertainties involved in such comparisons.

A proof of van Aubel's theorem using orthogonal vectors

We show how two linearly independent vectors can be used to construct two orthogonal vectors of equal magnitude in a simple way. The proof that the constructed vectors are orthogonal and of equal magnitude is a good exercise for students studying properties of scalar and vector triple products. We then show how this result can be used to prove van Aubel's theorem that relates the two line segments joining the centres of squares on opposite sides of a plane quadrilateral.

Aberrant brain responses to emotionally valent words is normalised after cognitive behavioural therapy in female depressed adolescents

AbstractBackground Depression in adolescence is debilitating with high recurrence in adulthood, yet its pathophysiological mechanism remains enigmatic. To examine the interaction between emotion, cognition and treatment, functional brain responses to sad and happy distractors in an affective go/no-go task were explored before and after Cognitive Behavioural Therapy (CBT) in depressed female adolescents, and healthy participants. Methods Eighty-two Depressed and 24 healthy female adolescents, aged 12 to 17 years, performed a functional magnetic resonance imaging (fMRI) affective go/no-go task at baseline. Participants were instructed to withhold their responses upon seeing happy or sad words. Among these participants, 13 patients had CBT over approximately 30 weeks. These participants and 20 matched controls then repeated the task. Results At baseline, increased activation in response to happy relative to neutral distractors was observed in the orbitofrontal cortex in depressed patients which was normalized after CBT. No significant group differences were found behaviourally or in brain activation in response to sad distractors. Improvements in symptoms (mean: 9.31, 95% CI: 5.35-13.27) were related at trend-level to activation changes in orbitofrontal cortex. Limitations In the follow-up section, a limited number of post-CBT patients were recruited. Conclusions To our knowledge, this is the first fMRI study addressing the effect of CBT in adolescent depression. Although a bias toward negative information is widely accepted as a hallmark of depression, aberrant brain hyperactivity to positive distractors was found and normalised after CBT. Research, assessment and treatment focused on positive stimuli could be a future consideration. Moreover, a pathophysiological mechanism distinct from adult depression may be suggested and awaits further exploration.