The Structure Lacuna

Abstract

Molecular symmetry is intimately connected with the classical concept of three-dimensional molecular structure. In a non-classical theory of wave-like interaction in four-dimensional space-time, both of these concepts and traditional quantum mechanics lose their operational meaning, unless suitably modified. A required reformulation should emphasize the importance of four-dimensional effects like spin and the symmetry effects of space-time curvature that could lead to a fundamentally different understanding of molecular symmetry and structure in terms of elementary number theory. Isolated single molecules have no characteristic shape and macro-biomolecules only develop robust three-dimensional structure in hydrophobic response to aqueous cellular media.

Valence atom with bohmian quantum potential: the golden ratio approach

“…(25d); however, changing the sign to negative radii as surpassing the threshold 21/5 and fixing in fact the limit N bonding =4, is consistent with maximum bond order met in Nature; it is also not surprising this self-released limit connects with golden ratio by the golden-spiral optimization of bond-order [51]; more subtle, it connects also with the 4 π symmetry of two spherical valence atoms making a chemical bond (Figure 2, inset): such “spinning” reminds of the graviton symmetry [52] (the highest spherical symmetry in Nature, with spin equal 2) and justifies the recent treatments of chemical bonding by means of the quasi-particles known as bondons [10,53], as well as the use of the 4D complex projective geometry in modeling the chemical space as a non-Euclidian one, eventually with a time-space metrics including specific “gravitational effects” describing the bonding [51];…”

“…( 25d ), while marking the double golden ratio 2 τ gap between the bonding lengths of the second and third bonding order, as well as the forbidden chemical bonding region for N bonding ≥21/5 for the electrons participating in the same bonding. Further connection of chemical bonding and the 4D space to model it is suggested by the inset picture illustrating the 2-fold (4 π ) spinning symmetry of the adduct atom respecting the bonding direction, after [51]. …”