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Extra info for A Ghost - Free Axiomatization of Quantum Mechanics
2b there is nothing unusual about the aromatic system, but the nuclei of the two ﬂuorine atoms in the ‘‘Fjord region’’ are linked by a bond path  closing a seven-membered ring which has quite an unusual topology – it gives rise to two ring critical points and a cage critical point . We have, thus, recently reported the ﬁrst example of an actual molecular system in which a cage is bounded by only two ring surfaces . Such a CCP (enclosed by two ring surfaces) arises in all the studied derivatives of 1,12-diﬂuorohelicenes .
002 au isodensity envelope. The zeroﬂux surfaces are denoted by the vertical bars between the atomic symbols. Large spheres represent the nuclei of the ﬂuorine atoms (golden) and of the boron atom (blue–gray). The lines linking the nuclei represent the bond paths. The BCPs are denoted by the small red dots. A BCP always lies on the zero-ﬂux surface shared by the two bonded atoms. basins constitute proper open quantum systems and are therefore termed ‘‘pseudoatoms’’. e. share a common interatomic zero-ﬂux surface, a bond critical point, and a bond path) to atoms and other pseudo-atoms in a molecule.
Will vanish only for systems bounded by a zero-ﬂux surface satisfying Eq. (6) (or for the whole system, because the Laplacian integrated over the entire space also vanishes). Thus only the total system and proper open sub-systems will have a deﬁnite kinetic energy. A proper open system (one bounded by a zero-ﬂux surface and/or inﬁnity) will be referred to as W to distinguish it from an arbitrary bounded region of space o. For such a proper open system one has: KðWÞ ¼ GðWÞ ¼ TðWÞ ð32Þ and, because the integral of the Laplacian vanishes over W, the integral of the local statement of the virial theorem (Eq.