9 problems

Linear-molecule conjecture. The presence of a strong magnetic field can lead to the formation of linear molecules (linear chains) situated along magnetic lines.

For two rigid molecules with orientations and separation encoded by $\tau=(L,U,V)$, let $\mathcal{E}(\tau)$ be the Born–Oppenheimer ground-state energy. In the limit $L\to\infty$,…

In the neutral Born–Oppenheimer model, suppose a mountain-pass construction produces a transition state $(\tilde Y,\tilde\Psi)$ at the mountain-pass level $c$, with $\tilde Y$ a nu…

Let $N=|Z|$ be the neutral case, let $\bar Y_0$ and $\bar Y_1$ be two local minima of $Y\mapsto E_N(Y,Z)$, and define … Assume $c>\max\{E_N(\bar Y_0,Z),E_N(\bar Y_1,Z)\}$. Compactn…

Let $Z=(Z_1,Z_2)$ describe two rigid molecular subsystems and let $N$ electrons be distributed as $N_1+N_2=N$. In the dissociation limit, the energy is the minimum over all such di…

An isomerization is a chemical reaction connecting two stable molecular configurations with the same atoms, within the Born–Oppenheimer approximation; its activation energy is the…

Generalized ionization conjecture for molecules. The large-$Z$ upper and lower limits of the homonuclear diatomic Born–Oppenheimer curve satisfy

Let $Z$ be the nuclear charge and $B$ the magnetic-field strength. Consider the actual molecule modelled by the Pauli Hamiltonian, and let its equilibrium distance be denoted by…

Effective error-term conjecture. The remainder $o(Z^2)$ can be replaced by $O(Z^{2-\eta})$ for some $\eta>0$, with the constant in the error term depending only on $r_{min}$ and…