Raman scattering in C_{60} and C_{48}N_{12} aza-fullerene: First-principles study

We carry out large scale {\sl ab initio} calculations of Raman scattering activities and Raman-active frequencies (RAFs) in ${\rm C}_{48}{\rm N}_{12}$ aza-fullerene. The results are compared with those of ${\rm C}_{60}$. Twenty-nine non-degenerate polarized and 29 doubly-degenerate unpolarized RAFs are predicted for ${\rm C}_{48}{\rm N}_{12}$. The RAF of the strongest Raman signal in the low- and high-frequency regions and the lowest and highest RAFs for ${\rm C}_{48}{\rm N}_{12}$ are almost the same as those of ${\rm C}_{60}$. The study of ${\rm C}_{60}$ reveals the importance of electron correlations and the choice of basis sets in the {\sl ab initio} calculations. Our best calculated results for ${\rm C}_{60}$ with the B3LYP hybrid density functional theory are in excellent agreement with experiment and demonstrate the desirable efficiency and accuracy of this theory for obtaining quantitative information on the vibrational properties of these molecules.Comment: submitted to Phys.Rev.

A mathematical and computational review of Hartree-Fock SCF methods in Quantum Chemistry

We present here a review of the fundamental topics of Hartree-Fock theory in Quantum Chemistry. From the molecular Hamiltonian, using and discussing the Born-Oppenheimer approximation, we arrive to the Hartree and Hartree-Fock equations for the electronic problem. Special emphasis is placed in the most relevant mathematical aspects of the theoretical derivation of the final equations, as well as in the results regarding the existence and uniqueness of their solutions. All Hartree-Fock versions with different spin restrictions are systematically extracted from the general case, thus providing a unifying framework. Then, the discretization of the one-electron orbitals space is reviewed and the Roothaan-Hall formalism introduced. This leads to a exposition of the basic underlying concepts related to the construction and selection of Gaussian basis sets, focusing in algorithmic efficiency issues. Finally, we close the review with a section in which the most relevant modern developments (specially those related to the design of linear-scaling methods) are commented and linked to the issues discussed. The whole work is intentionally introductory and rather self-contained, so that it may be useful for non experts that aim to use quantum chemical methods in interdisciplinary applications. Moreover, much material that is found scattered in the literature has been put together here to facilitate comprehension and to serve as a handy reference.Comment: 64 pages, 3 figures, tMPH2e.cls style file, doublesp, mathbbol and subeqn package

Agricultural, architectural and archaeological evidence for the role and ecological adaptation of a scattered mountain oasis in Oman

The original publication is available at www.elsevier.co

Evaluating the Effects of Different Requirements Representations on Writing Test Cases

Context and MotivationOne must test a system to ensure that the requirements are met, thus, tests are often derived manually from requirements. However, requirements representations are diverse; from traditional IEEE-style text, to models, to agile user stories, the RE community of research and practice has explored various ways to capture requirements. Question/problemBut, do these different representations influence the quality or coverage of test suites? The state-of-the-art does not provide insights on whether or not the representation of requirements has an impact on the coverage, quality, or size of the resulting test suite. ResultsIn this paper, we report on a family of three experiment replications conducted with 148 students which examines the effect of different requirements representations on test creation. We find that, in general, the different requirements representations have no statistically significant impact on the number of derived tests, but specific affordances of the representation effect test quality, e.g., traditional textual requirements make it easier to derive less abstract tests, whereas goal models yield less inconsistent test purpose descriptions. ContributionOur findings give insights on the effects of requirements representation on test derivation for novice testers. Our work is limited in the use of students

Scaling and Confinement in Ultrathin Chalcogenide Films as Exemplified by GeTe

Chalcogenides such as GeTe, PbTe, Sb2Te3, and Bi2Se3 are characterized by an unconventional combination of properties enabling a plethora of applications ranging from thermo-electrics to phase change materials, topological insulators, and photonic switches. Chalcogenides possess pronounced optical absorption, relatively low effective masses, reasonably high electron mobilities, soft bonds, large bond polarizabilities, and low thermal conductivities. These remarkable characteristics are linked to an unconventional bonding mechanism characterized by a competition between electron delocalization and electron localization. Confinement, that is, the reduction of the sample dimension as realized in thin films should alter this competition and modify chemical bonds and the resulting properties. Here, pronounced changes of optical and vibrational properties are demonstrated for crystalline films of GeTe, while amorphous films of GeTe show no similar thickness dependence. For crystalline films, this thickness dependence persists up to remarkably large thicknesses above 15 nm. X-ray diffraction and accompanying simulations employing density functional theory relate these changes to thickness dependent structural (Peierls) distortions, due to an increased electron localization between adjacent atoms upon reducing the film thickness. A thickness dependence and hence potential to modify film properties for all chalcogenide films with a similar bonding mechanism is expected