Analytical Potential Energy Function for the Ground State X^{1} Sigma^+ of LaCl

The equilibrium geometry, harmonic frequency and dissociation energy of lanthanum monochloride have been calculated at B3LYP, MP2, QCISD(T) levels with energy-consistent relativistic effective core potentials. The possible electronic state and reasonable dissociation limit for the ground state are determined based on atomic and molecular reaction statics. Potential energy curve scans for the ground state X^{1} Sigma^+ have been carried out with B3LYP and QCISD(T) methods due to their better performance in bond energy calculations. We find the potential energy calculated with QCISD(T) method is about 0.5 eV larger than dissociation energy when the diatomic distance is as large as 0.8 nm. The problem that single-reference ab initio methods don't meet dissociation limit during calculations of lanthanide heavy-metal elements is analyzed. We propose the calculation scheme to derive analytical Murrell-Sorbie potential energy function and Dunham expansion at equilibrium position. Spectroscopic constants got by standard Dunham treatment are in good agreement with results of rotational analyses on spectroscopic experiments. The analytical function is of much realistic importance since it is possible to be applied to predict fine transitional structure and study reaction dynamic process.Comment: 10 pages, 1 figure, 3 table

Calculations of surface effects on phonon modes and Raman intensities of Ge quantum dots

Phonon modes and Raman intensities of Ge quantum dots (QDs) with two different types of surfaces, a free standing surface or a fixed surface, in a size range from five atoms to 7 nm in diameter, are calculated by using a microscopic valence force field model. The results are compared, and the effects of surfaces on phonon properties of QDs are investigated. It is found that phonon modes and Raman intensities of QDs with these two different types of surfaces have obvious differences which clearly reveal the effects of the surfaces of QDs. The calculated results agree with existing experimental observations. We expect that our calculations will stimulate more experimental measurements on phonon properties and Raman intensities of QDs

Phonons of single quintuple Bi2Te3 and Bi2Se3 films and bulk materials

Phonons of single quintuple films of Bi2Te3 and Bi2Se3 and corresponding bulk materials are calculated in detail by MedeA (a trademark of Materials Design) and Vienna ab initio simulation package (VASP). The calculated results with and without spin-orbit couplings are compared, and the important roles that the spin-orbit coupling plays in these materials are discussed. A symmetry breaking caused by the anharmonic potentials around Bi atoms in the single quintuple films is identified and discussed. The observed Raman intensity features in Bi2Te3 and Bi2Se3 quintuple films are explained

Microscopic investigation of phonon modes in SiGe alloy nanocrystals

Phonon modes in spherical silicon germanium alloy (SiGe) nanocrystals containing up to 1147 atoms (3.6 nm) have been investigated as a function of the Si concentration. Microscopic details of phonon modes, including phonon frequencies and vibrational amplitudes, phonon density-of-states are calculated directly from the dynamic matrices. In particular, the dependence of phonon frequency on the configuration (such as a different ratio of Si to Ge atoms), and location (surface or interior) of clusters of atoms in SiGe alloy nanocrystals have been investigated. Low frequency surface phonons that are related to the spheroidal and torsional modes of a continuum sphere are identified and their frequency dependence on alloy concentration elucidated. The calculated results are compared with measured Raman spectra in bulk, thin films, and superlattices of SiGe alloy reported in the literature. Insights into the behavior of Raman peaks usually identified as Ge-Ge, Si-Si, and Ge-Si optical phonon modes are presented

Theoretical investigation of the surface vibrational modes in germanium nanocrystals

We have used a microscopic lattice dynamical model to study phonon modes in germanium (Ge) NC with size varying between 47 to 7289 atoms (diametersimilar to6.8 nm). By separating these atoms into bulk and surface atoms we have found that surface modes can exist in Ge NC both at low frequencies (\u3c50\u3ecm(-1)) and at high frequency (similar to260 cm(-1)). The latter mode is a resonant mode which occurs in the pseudogap between the acoustic and optical phonon branches in bulk Ge. From the low frequency surface modes we have been able to reconstruct the spheroidal and torsional Lamb modes which have been used to interpret experimental results. Finally, we found that the Lamb model starts to deviate from the lattice dynamical results for Ge NC with diameternm

Stacking Group Structure of Fermionic Symmetry-Protected Topological Phases

In the past decade, there has been a systematic investigation of symmetry-protected topological (SPT) phases in interacting fermion systems. Specifically, by utilizing the concept of equivalence classes of finite-depth fermionic symmetric local unitary (FSLU) transformations and the decorating symmetry domain wall picture, a large class of fixed-point wave functions have been constructed for fermionic SPT (FSPT) phases. Remarkably, this construction coincides with the Atiyah-Hirzebruch spectral sequence, enabling a complete classification of FSPT phases. However, unlike bosonic SPT phases, the stacking group structure in fermion systems proves to be much more intricate. The construction of fixed-point wave functions does not explicitly provide this information. In this paper, we employ FSLU transformations to investigate the stacking group structure of FSPT phases. Specifically, we demonstrate how to compute stacking FSPT data from the input FSPT data in each layer, considering both unitary and anti-unitary symmetry, up to 2+1 dimensions. As concrete examples, we explictly compute the stacking group structure for crystalline FSPT phases in all 17 wallpaper groups using the fermionic crystalline equivalence principle. Importantly, our approach can be readily extended to higher dimensions, offering a versatile method for exploring the stacking group structure of FSPT phases

Collaborative filtering with diffusion-based similarity on tripartite graphs

Collaborative tags are playing more and more important role for the organization of information systems. In this paper, we study a personalized recommendation model making use of the ternary relations among users, objects and tags. We propose a measure of user similarity based on his preference and tagging information. Two kinds of similarities between users are calculated by using a diffusion-based process, which are then integrated for recommendation. We test the proposed method in a standard collaborative filtering framework with three metrics: ranking score, Recall and Precision, and demonstrate that it performs better than the commonly used cosine similarity.Comment: 8 pages, 4 figures, 1 tabl