# Annual Meeting of the Belgian Physical Society 2016

Wednesday May 18th was a good day for our little family. Since my girlfriend an I both are physicists by training, we attended the annual meeting of the Belgian Physical Society in Ghent, together. What made this event even more special was the fact that both of us had an oral presentation at the same conference, which never happened before. 🙂

Sylvia talked about an example of indeterminism in Newtonian mechanics, and showed how the indeterminism can be clarified by using non-standard analysis. The example considers the Norton Dome, a hill with a specifically designed shape ( $y(x)=-2/3(1-(1-3/2|x|)^{2/3})^{3/2}$ ). When considering a point mass, experiencing only gravitational force, there are two solutions for the equation of motion: (1) the mass is there, and remains there forever (r(t)=0) and (2) the mass was rolling uphill with a non-zero speed which becomes exactly zero at the top, and continues over the top ( $r(t)=\frac{1}{144} (t-T)^4$ with T the time the top is reached). Here, r refers to the arc length as measured along the dome (0 at the top). In addition, there also exists a family of solutions taking the first solution at t<T, while taking the second solution at t>T. (As the first and second derivatives of these latter solutions are continuous, Newton will not complain.) This leads to indeterminism in a Newtonian system; for instance, you start with a mass on the top of the hill, and at a random point in time it starts to roll off without the presence of an external something putting it into motion. Using infinitesimals, Sylvia shows that the probability for the mass to start rolling off the dome immediately is infinitesimally close to one.

My own talk was on the use of computational materials science as a means for understanding and explaining experimental observations. I presented results on the pressure-induced breathing of the MIL-47(V) MOF, showing how the experimentally observed S-shape of the transition-pressure-curve can be explained by the spin interactions of the unpaired vanadium-d electrons: it turns out that regions with only ferromagnetic chains compress already at 85 MPa, while the addition of higher and higher percentages of anti-ferromagnetic chains increases the pressure at which the pores collapse, up to 125 MPa for the regions containing 100% anti-ferromagnetic chains. As a second topic, I showed how the electronic band structure of the linker-functionalized UiO-66(Zr) MOF changes. When one or two -OH or -SH groups are added to the benzene ring of the linker, part of the valence band is split off and moves into the band gap. In semiconductors, this would be called a gap state; however, in this case, since every linker in the material contributes

Top left: I am presenting computational results on MOFs. Top Right: Sylvia presents the Norton Dome. Bottom: Group picture at the central garden in “Het Pand”. (Photos: courtesy of Sylvia Wenmackers (TL), Philippe Smet (TR), and Michael Tytgat (B) )

a single electron state to this gap state, it practically becomes the valence band top. As a consequence, the color of such functionalized MOF’s changes from white to yellow and orange. As a third topic, I discussed the COK-69(Ti) MOF. In this MOF the electrons in the titaniumoxide clusters are strongly correlated, just as for pure titaniumoxide. Because such systems are poorly described with standard DFT, we used the DFT+U approach, which allowed us to discern between Ti3+ and Ti4+ ions. The latter was practically done by partitioning the electron density using the Hirshfeld-I scheme.