The r-centroid concept revisited

Abstract

The r-centroid concept, was proposed the in 1950s to permit factoring of the band strength integral Sυ',υ'' into the product of the Franck–Condon factor qυ',υ'', and of the square of the electronic transition moment Re (r), when taken at the r-centroid value of the internuclear separation, r = [Formula: see text]υ',υ'', which is the most likely value r at which the υ' « υ'' transition will occur. It has been much used since then in the interpretation of intensity measurements on many band systems of importance in astrophysics, atmospheric physics, space physics, and chemical physics to determine the variation of the electronic transition moment with internuclear separation, and thereby to derive band strengths, and other molecular transition probability parameters. It has been somewhat less used in recent years in the study of individual band systems, since the development of powerful computing facilities now allow for exact ab initio numerical studies to be made of individual molecules and their radiative transitions. Nevertheless the r-centroid concept, and some of its recent developments, provide much insight into the general systematics of diatomic molecular band systems and their spectra. This partly tutorial paper reviews the origins, properties, applications, and recent developments of the r-centroid concept. PACS No.: 33.70

Franck-Condon Factors and r-Centroids for Several Systems of CoF Molecule

“…Some bands are found to be roughly equal in magnitude such as [(0,2), (2,0), (3,1)]and [(2,1), (4,1), (5,2)] bands which indicate that these bands of comparable intensities. FCFs for the bands (1,2), (3,3), (3,5), (4,4), (4,6), (6,2) and (6,3) are likely to be intense, hence one expects that these bands may be observed experimentally where as other bands, having small FCFs may not be observed experimentally. Refer to Fig.2.…”

“…The FCFs are also useful in the studies of radiative transfer in the atmospheres of stellar and other astronomical objects, which contain molecular species [2]. On the other hand, the r-centroid [3][4][5] also has been found of much importance as it is used in the interpretation of intensity measurements of many band systems of astrophysically important molecules and, to determine the variation of the electronic transition moment with inter-nuclear separation, and thereby to derive band strengths, and other molecular transition probability parameters [6].…”

State-Resolved Dynamics of the CN(B2Σ+) and CH(A2Δ) Excited Products Resulting from the VUV Photodissociation of CH3CN

“…P v ‘ (Λ‘) is determined from a modified Boltzmann equation using the T vib values determined from the experimental data. S v ‘ v ‘ ‘ (Λ‘) is the band strength of a transition between the vibrational levels v ‘ and v ‘ ‘ in an excited electronic state Λ‘ that is given by where R̄ e 2 and q v ‘ v ‘ ‘ are the average electronic transition moment and the Franck−Condon factor, respectively, for the selected band. Incorporation of S v ‘ v ‘ (Λ‘) into eq 6 permits scaling of the data derived from the CH(A 2 Δ−X 2 Π) and CN(B 2 Σ + −X 2 Σ + ) spectra.…”

Franck-Condon Factors and r-Centroids for Several Systems of CoF Molecule

“…The FCFs are also useful in the studies of radiative transfer in the atmospheres of stellar and other astronomical objects, which contain molecular species [2]. On the other hand, the r-centroid [3][4][5] also has been found of much importance as it is used in the interpretation of intensity measurements of many band systems of astrophysically important molecules and, to determine the variation of the electronic transition moment with inter-nuclear separation, and thereby to derive band strengths, and other molecular transition probability parameters [6].…”