Isospectral and Subspectral Molecules

Isospectral molecules are non-identical structures which possess the same spectrum of eigenvalues. Methods for recognizing isospectrality, procedures of Heilbronner, Herndon and .Zivkovic for constructing new isospectral mates, and the specification of the relationship among the eigenvectors of the adjacency matrix of isospectral pairs are discussed here. Instances of isospectral graphs are relatively rare. There are many cases, however, in which the spectrum of one molecular graph contains the spectrum of a second, smaller graph. In such cases, the larger, composite, graph and the smaller, component graph are said to be subspectral. Methods of McClelland, Hall and D\u27Amato for determining subspectrality of graphs are reviewed in detail. It appears that all known cases of subspectral molecules, but one, can be explained by various decomposition or factorization schemes. No chemical evidence is found so far that shows a relationship among the measured properties of isospectral or subspectral molecules. However, the existence of isospectral and subspectral molecules prevented the use of characteristic polynomial for the unique characterization of molecules in various classification schemes and in computerized chemical documentation

Structure, Energy, and Vibrational Frequencies of Oxygen Allotropes On (n ≤ 6) in the Covalently Bound and van der Waals Forms: Ab Initio Study at the CCSD(T) Level

Recent experiments on the UV and electron beam irradiation of solid O2 reveals a series of IR features near the valence antisymmetric vibration band of O3 which are frequently interpreted as the formation of unusual On allotropes in the forms of weak complexes or covalently bound molecules. In order to elucidate the question of the nature of the irradiation products, the structure, relative energies, and vibrational frequencies of various forms of On (n = 1−6) in the singlet, triplet, and, in some cases, quintet states were studied using the CCSD(T) method up to the CCSD(T,full)/cc-pCVTZ and CCSD(T,FC)/aug-cc-pVTZ levels. The results of calculations demonstrate the existence of stable highly symmetric structures O4(D3h), O4 (D2d), and O6 (D3d) as well as the intermolecular complexes O2·O2, O2·O3, and O3·O3 in different conformations. The calculations show that the local minimum corresponding to the O3···O complex is quite shallow and cannot explain the ν3 band features close to 1040 cm−1, as was proposed previously. For the ozone dimer, a new conformer was found which is more stable than the structure known to date. The effect of the ozone dimer on the registered IR spectra is discussed

Evaluating bone biopsy quality by technique in an animal model

Rationale and Objectives: Powered bone biopsy technique is popular due to its ease of use. However, there is conflicting evidence regarding the diagnostic quality of the samples. The purpose of this study is to evaluate the diagnostic adequacy of different bone biopsy devices and techniques as it relates to the frequency of sample artifacts. Materials and Methods: Bone biopsy was performed on same-day processed lamb femora using the following techniques: manual, pulsed powered and full powered. Ten samples were collected using each method by a single musculoskeletal-trained radiologist and were reviewed by 3 blinded pathologists. Samples were compared across multiple categories: length, bone dust, thermal/crush artifact, cellular morphology, fragmentation, and diagnostic acceptability. Bayesian Multilevel Nonlinear Regression models were performed assessing the association between the techniques across the categories. Results: Statistical analysis revealed that the manual technique outperformed any powered technique across all categories: decreased thermal/crush artifact (P = 0.014), decreased bone dust (p<0.001), better cellular morphology (P = 0.005), less fragmentation (P < 0.0001) and better diagnostic acceptability (P < 0.0001). Conclusion: Manually obtained bone biopsy samples generally produce a more diagnostic sample as compared to powered techniques in an animal model. Given these results, manual bone biopsy methods should be encouraged after consideration for lesion composition, difficulty of access and the patient's overall condition