An algorithm for the estimation of anharmonicity from a Morse potential
Abstract The wavefunctions of the ground and first excited state in a Morse potential are calculated and plotted, and the expectation values of the bond lengths
On the Existence of Conformers of Cyclobutyl Monohalides. III. Assignments of the Fundamentals of Bromocyclobutane and Chlorocyclobutane
The infrared spectra of the liquid and the vapor and the Raman spectra of the liquid of bromocyclobutane and chlorocyclobutane are reported. The 30 fundamentals of each halide are assigned and an approximate picture of the motions of those atoms, which are mainly involved in the fundamental modes, is given. There is one‐to‐one correlation between the fundamentals of bromocyclobutane with the fundamentals of chlorocyclobutane. This signifies that the amount of interaction between different modes is generally of the same order of magnitude in both halides, in contrast to the corresponding cyclopropyl halides. There is little symmetry correlation between the fundamentals of the cyclobutyl halides and cyclobutane; the out‐of‐plane ring‐bending (ring‐puckering) mode is an exception. In the Appendix, computer calculations of A‐ and C‐type band envelopes are presented and compared with observations; the computations include vibration—rotation interaction.
Live birth in the Devonian period
The extinct placoderm fishes were the dominant group of vertebrates throughout the Middle Palaeozoic era, yet controversy about their relationships within the gnathostomes (jawed vertebrates) is partly due to different interpretations of their reproductive biology. Here we document the oldest record of a live-bearing vertebrate in a new ptyctodontid placoderm, Materpiscis attenboroughi gen. et sp. nov., from the Late Devonian Gogo Formation of Australia (approximately 380 million years ago). The new specimen, remarkably preserved in three dimensions, contains a single, intra-uterine embryo connected by a permineralized umbilical cord. An amorphous crystalline mass near the umbilical cord possibly represents the recrystallized yolk sac. Another ptyctodont from the Gogo Formation, Austroptyctodus gardineri, also shows three small embryos inside it in the same position. Ptyctodontids have already provided the oldest definite evidence for vertebrate copulation, and the new specimens confirm that some placoderms had a remarkably advanced reproductive biology, comparable to that of some modern sharks and rays. The new discovery points to internal fertilization and viviparity in vertebrates as originating earliest within placoderms.