A unified molecular force field via a model theory of isoelectronic diatomic molecules

Abstract

Electronic energy curves for diatomic molecules come in a wide variety of shapes. More categorically, these correspond to stable, metastable or repulsive states. We propose that a great deal of this apparently diverse behavior might in fact be contained in a single isoelectronic energy surface E(R,Z,Z′). That is, each kind of curve can be thought of as a particular cross section of the surface corresponding to some range of the nuclear charges Z and Z′. Analytic representations for these surfaces have been given and their properties examined. We have found that they are folded and contain critical points. These features put limits on the number of isoelectronic species that can exist in a sequence and interconnect their properties. By this we understand that data gathered on even the repulsive states of one molecule of an isoelectronic sequence contains information about the stable and metastable members of that sequence.

The δ point interaction two‐center system

“…Based on the point interaction model (1), stability bounds for one-electron molecular systems in strong magnetic fields have been predicted by perturbation calculations [13] and found surprisingly sharp by subsequent accurate variational [25] and finite elements computations [26]. Qualitatively, for the δ-model (1) we encounter the same stability scenario as analyzed in detail in the related Coulomb system [27,28]. Thus, upon growing charges or asymmetry (as expressed by the ratio Z 1 /Z 2 ), the initial stability against fragmentation is turned into metastability where dissociation becomes possible by tunneling.…”

“…for all a ∈ (0, 1), thus demonstrating positivity of (27) for all R > 0. For homonuclear systems Z 1 = Z 2 = Z > 0, it is well-known [13][14][15] that the condition (16) permits explicit solutions in terms of the Lambert function W [20], viz.,…”

“…Plotted are also the boundaries of the metastable region governed by the behavior of the corresponding critical charges Z (m) . By using in addition (27) but proceeding otherwise in the same way as for Z (c) , one can show that…”

“…guaranteeing strict negativity of (27). To simplify the calculations, for negative Z 2 with −Z 1 ≤ Z 2 < 0 we employ the scaling properties of e[R; Z] to restrict our attention to Z 1 = 1.…”

Building blocks for electron density in free molecules and in condensed matter phases

“…By means of Thomas-Fermi-like approximations [equivalent to the neglect of density gradient "corrections" in Eq. (ll)], Laurenzi [19] has argued that the second term on the rhs of Eq. (14) correlates strongly with the first term and indeed cancels two-thirds of it to yield…”