Why do molecules echo atomic periodicity?

Abstract

Franck-Condon factors are investigated for sequences of free main-group diatomic molecules. Theory-based Condon loci (parabolas) and Morse-potential loci are plotted on Deslandres tables to verify if they, indeed, follow the largest Franck-Condon factors. Then, the inclination angles of the Condon loci are determined. Thus, entire band systems are quantified by one variable, the angle. For all available isoelectronic sequences, this angle increases from a central minimum toward magic-number molecular boundaries. The theory for the Condon locus gives the angle in terms of the ratio of the upper-state to the lowerstate force constants. It is concluded that the periodicity is caused due to the fact that this ratio becomes larger as rare-gas molecules are approached, a trend that probably points to the extreme cases of the rare-gas molecules themselves. Thus, molecular periodicity echoes atomic periodicity in that data plots have extrema at molecules with magic-number atoms, yet it does not echo the details of atomic periodicity in series between those molecules.

Do triatomic molecules echo atomic periodicity?

“…Gas-phase main-group diatomics AB display this periodic behavior dramatically and allow some reasonably precise predictions to be made. [1,2] The properties that have been studied include internuclear separations r e [3], vibration frequencies ω e [3], spring constants k 1 [4], ionization potentials [3], and entire Deslandres tables of band-system Frank-Condon factors [5]. Kong [6] found this same periodicity among contracted internuclear distances of free linear/bent triatomic molecules (Figure 1).…”

Periodic trends in constants of triatomic molecules

“…Hefferlin and Tatum have extended the development of diatomic periodicity using Deslandres tables of band‐system Franck–Condon factors.…”

“…Such behavior points to a new kind of periodicity across many possible permutations of diatomic molecules. Theoretical motivation for the dynamics in question, as derived in the equations of both the Morse and parabolic fits, permits “An understanding of molecular periodicity that has a basis in quantum states…”…”

“…Work done by Hefferlin and Kong over the past forty years has shown that diatomic and triatomic molecules share many periodic properties with the Mendeleev's periodic table of elements. This work acts as a direct extension from the periodic systems of atoms to triatomic molecules.…”

“…Organization of this data into a detailed, highly symmetric, multidimensional coordinate system allows for robust graphical and statistical analysis of all constants and associated trends, which in turn permits rapid identification of suspect data to be rechecked. All collected empirical and computational data, along with several interactive visualizations highlighting these results, is available online.Hefferlin and Tatum [2,8] have extended the development of diatomic periodicity using Deslandres tables of band-system Franck-Condon factors.They found in most cases that the most probable transitions occurred along the edges of a diagonal, nearly perfectly parabolic path, behavior repeated across all diatomic species with associated known Franck-Condon factors, for a given isoelectronic series. Such behavior points to a new kind of periodicity across many possible permutations of diatomic molecules.…”