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.

Prevalence and nonrandom distribution of exonic mutations in interferon regulatory factor 6 in 307 families with Van der Woude syndrome and 37 families with popliteal pterygium syndrome

Purpose: Interferon regulatory factor 6 encodes a member of the IRF family of transcription factors. Mutations in interferon regulatory factor 6 cause Van der Woude and popliteal pterygium syndrome, two related orofacial clefting disorders. Here, we compared and contrasted the frequency and distribution of exonic Mutations in interferon regulatory factor 6 between two large geographically distinct collections of families with Van der Woude and between one collection of families with popliteal pterygium syndrome. Methods: We performed direct sequence analysis of interferon regulatory factor 6 exons oil samples from three collections, two with Van der Woude and one with popliteal pterygium syndrome. Results: We identified mutations in interferon regulatory factor 6 exons in 68% of families in both Van der Woude collections and in 97% of families with popliteal pterygium syndrome. In sum, 106 novel disease-causing variants were found. The distribution of mutations in the interferon regulatory factor 6 exons in each collection was not random; exons 3, 4, 7, and 9 accounted for 80%. In the Van der Woude collections, the mutations were evenly divided between protein truncation and missense, whereas most mutations identified in the popliteal pterygium syndrome collection were missense. Further, the missense mutations associated with popliteal pterygium syndrome were localized significantly to exon 4, at residues that are predicted to bind directly to DNA. Conclusion: The nonrandom distribution of mutations in the interferon regulatory factor 6 exons suggests a two-tier approach for efficient mutation screens for interferon regulatory factor 6. The type and distribution of mutations are consistent with the hypothesis that Van der Woude is caused by haploinsufficiency of interferon regulatory factor 6. Oil the other hand, the distribution of popliteal pterygium syndrome-associated mutations suggests a different, though not mutually exclusive, effect oil interferon regulatory factor 6 function. Genet Med 2009:11(4):241-247.

Diagnostisering av elever i geometri : En studie med utgångspunkt i van Hieles teori

Detta är en studie som har sin utgångspunkt i Pierre M. van Hieles teori om lärande i geometri, som presenterades 1986 i boken Structure and Insight. Van Hiele har i boken vidareutvecklat sin och Dina van Hiele-Geldofs ursprungliga lärandeteori från 1955. Vår studie har som syfte att se om van Hieles teori går att tillämpa i en individuell, skriftlig diagnos för att nivåbestämma elever i årskurs 1 på gymnasiet.