Chemistry by Number Theory

Abstract

Aspects of elementary number theory pertaining to the golden ratio and the golden spiral are shown to be related to and therefore of importance in the simulation of chemical phenomena. Readily derived concepts include atomic structure, electronegativity, bond order, the theory of covalent interaction and aspects of molecular chirality. The physical interpretation of the results implicates the 4D structure of space-time as a fundamental consideration. The implied classical nature of 3D molecular structure identifies molecular mechanics as an ideal method for structure optimization, and it is shown that the parameters may be related to number theory. All results point at a 4D wave structure of electrostatic charge.

On New Formulas of Fibonacci and Lucas Numbers Involving Golden Ratio Associated with Atomic Structure in Chemistry

“…The limiting of the above ratio Z N for stable nuclides is equal to the golden ratio α. That is, [3,4]). Due to Equation ( 19), it well-known that the golden ratio occurs in periodic table.…”

“…He gave many results between the proton-neutron ratio and the golden ratio. Boeyens et al [3,4]) have studied chemistry and its application using number theory involving the Fibonacci numbers, the Lucas numbers, and the golden ratio. They gave some basic aspects of the golden helix related to the simulation of chemical events.…”

“…It is well known that the Fibonacci numbers and other special numbers are also used in mathematical models that frequently appear in theory of chemistry theory involving the structure of the elements, the periodic table of the elements, and their symmetrical and crystalline structures (cf. [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]).…”

“…They concluded that molecular mechanics is an ideal method for structure optimization based on parameters obtained by number theory (cf. [3,4]).…”

“…There are many applications of the generating functions for the Fibonacci numbers and the Lucas numbers (cf. [3][4][5][6][7][8][9][10][11][12][13][14]).…”