An Atlas of Forecasted Molecular Data. 1. Internuclear Separations of Main-Group and Transition-Metal Neutral Gas-Phase Diatomic Molecules in the Ground State

Abstract

Needed spectroscopic data on diatomic molecules can often be found in the superb critical tables of Huber and Herzberg or in the literature published since 1979. Unfortunately, these sources apply to only a fraction of the diatomic species that can exist and so investigators have had to rely on interpolation, additivity, or ad hoc rules to estimate needed values, all of which require other information that is often lacking. This Atlas presents 1001 additional internuclear separations for use until critical tables are available to fill the needs more precisely. The Atlas was produced by mining the data from Huber and Herzberg for trends with least-squares analysis and with neural network software. There are 162 molecules about whose data Huber and Herzberg had no qualifications and whose data were employed for this work; 248 copies of data with low and high magnitudes were added to reduce the effects of frequency. Internuclear separations for 1001 species not found in Huber and Herzberg are presented, and least-squares predictions supplement some of them. The results, i.e., the Atlas, are presented as Table A, Supporting Information. The average error, based on the average of the absolute differences between the predicted values and tabulated values for the molecules having Huber and Herzberg data, is 0.074 A; if each error is expressed as a percent of the forecast to which it pertains, the average of these errors is 2.94%. There are 25 "questionable" data from Huber and Herzberg, not used in the preparation of the Atlas, for which predictions are included in the Atlas. Of these, 14 agree with the predicted internuclear separations to within twice the stated errors. Additional atlases for other properties of diatomic molecules are in preparation.

Kronecker-Product Periodic Systems of Small Gas-Phase Molecules and the Search for Order in Atomic Ensembles of Any Phase

“…Still further improvement was attained when the duplication of entries for molecules like CO and OC (the original assumption) was abandoned. 1,001 r e data [52] and 1,920 e data [53] not found in critical tables were predicted. Comparisons with some values gleaned from the literature showed that the predictions have sufficiently good accuracies to be adequate for preliminary studies of, say, stellar atmospheres.…”

An Atlas of Forecasted Molecular Data. 2. Vibration Frequencies of Main-Group and Transition-Metal Neutral Gas-Phase Diatomic Molecules in the Ground State

“…If the en's are equal, then A is the atom with the higher period number R . In early trials, we had symmetrized the data as in ref , but this procedure is here reconsidered, for the following reason: the effect of the symmetrization is that for almost all points in the multidimensional space (i.e., the locations of heteronuclear molecules) there are two different sets of coordinates associated with exactly the same datum. Given that there are relatively few nodes with connections to adjust, this makes the problem of finding a solution in the space much more difficult and time-consuminga crucial factor for ω e , which has a far larger range of magnitudes than the internuclear separations …”

“…The training data were sorted in order of increasing magnitude. Their numbers per unit vibration frequency increase (with negative curvature) from low values of ω e to a long, rather linear, region and then move up (with positive curvature) to high-value ω e valuesvery much as shown in Figure 2 of ref . To eliminate poor performance at the low and high ends due to the deficits, 1346 duplicate values of the vectors were introduced in the following way to form a larger training set of 1550 vectors:…”

“…The results for these molecules are presented as in Table , which is an excerpt of the Atlas, Supporting Information. The molecules appear alphabetically in column 1, just as in ref (e.g., BaRh, BAs, BaSe) except that homonuclear molecules contain both atomic names, as in AgAg. Atom A in molecule AB is the one with the smaller Pauling en or with the greater period number if the en's are equal.…”

“…This atlas of diatomic-molecular vibration frequencies (ω e ) and the preceding Atlas of Internuclear Separations seek to provide forecasts that should be useful, for instance, in studies of species found in stellar atmospheres. Studies of spectroscopic data, even of moderate accuracy, provide tests of models of stellar interiors and nucleogenesis.…”