A semi-analytical approach for calculating the equilibrium structure and radial breathing mode frequency of single-walled carbon nanotubes

A semi-analytical model for determining the equilibrium configuration and the radial breathing mode (RBM) frequency of single-wall carbon nanotubes (CNTs) is presented. By taking advantage of the symmetry characteristics, a CNT structure is represented by five independent variables. A line search optimization procedure is employed to determine the equilibrium values of these variables by minimizing the potential energy. With the equilibrium configuration obtained, the semi-analytical model enables an efficient calculation of the RBM frequency of the CNTs. The radius and radial breathing mode frequency results obtained from the semi-analytical approach are compared with those from molecular dynamics (MD) and ab initio calculations. The results demonstrate that the semi-analytical approach offers an efficient and accurate way to determine the equilibrium structure and radial breathing mode frequency of CNTs.

Evolutionary Dynamics Modeling of Symbolic Social Network Structure Equilibrium

The use of symbol attributes on the side of symbolic social networks to analyze,understand,and predict the topology,function,and dynamic behaviour of complex networks,and has important theoretical significance for personalized recommendations,attitude prediction,user feature analysis,and clustering and application value.However,due to the huge scale of online social networks,this poses a challenge to traditional symbolic social network analysis methods.Based on the theory of structural equilibrium,this paper studies the evolutionary dynamics of symbolic social networks,proposes the energy function of weak structural equilibrium theory,and uses the evolution of evolutionary algorithms to obtain the weak imbalance of the network.The simulation experiment results show that the calculation method in this paper can get the optimal solution faster.It provides an idea for the study of real and complex social networks.

Ab Initio Studies on the Structure and Binding Interaction of M^+CO_2(M=Sc,Ti…Zn)

The geometry and binding interaction of M+CO2 (M represents the firstrow transition metals) were studied using ab initio methods. In some cases the frequency calculations and basis set superposition error corrections were included. For all the complexes under the study, the linear structures were found to be the equilibrium structure. The distances of M+—O in R(M+—O) in which M has 4s electrons are obvious longer than those in which M has no 4s electrons, and from Sc to Zn the change trend is decreased, accompanied with some oscillation. The binding energy has an opposite change trend to that of the R(M+—O). Linear M+CO2 has the same spin as M+, while Tshape structures may have different spins. The static electronic interaction was found to be about 80% of the total binding energy.

Structures and electronic properties of Mo_(2n)N_n(n=1-5):a density functional study

The lowest-energy structures and the electronic properties of Mo2nNn （n=1-5） clusters have been studied by using the density functional theory （DFT） simulating package DMol3 in the generalized gradient approximation （GGA）. The resulting equilibrium geometries show that the lowest-energy structures are dominated by central cores which correspond to the ground states of Mon （n = 2, 4, 6, 8, 10） clusters and nitrogen atoms which surround these cores. The average binding energy, the adiabatic electron affinity （AEA）, the vertical electron affinity （VEA）, the adiabatic ionization potential （AIP） and the vertical ionization potential （VIP） of Mo2nNn （n=1-5） clusters have been estimated. The HOMO LUMO gaps reveal that the clusters have strong chemical activities. An analysis of Mulliken charge distribution shows that charge-transfer moves from Mo atoms to N atoms and increases with cluster size.

Assignment of Photoelectron Spectra of MC2 （M= V, Cr, Fe, and Co）

Hybrid density functional theory （DFT） calculations are performed to study MC2 （M= V, Cr, Fe and Co） clusters in the neutral and anionic charge states. We find that the equilibrium geometries of MC2 and their anions are all cyclic structures with C2v symmetry, which agrees well with the previous theoretical studies. The Mulliken charge and spin populations of MC2 clusters and their anions are also calculated, and it is found that the electron charge transformations from anions to neutral molecules mainly take place on the M atoms. Time-dependent DFT is used to calculate the excited states, and a theoretical assignment for the features in the experimental photoelectron spectrum is given, which are in good agreement with the available experimental data.

Ab initio calculations of the ionization spectrum of SO_2

The ionization spectrum of sulfur dioxide has been successfully studied by using the symmetry-adapted-cluster configuration-interaction （SAC-CI） general-R and SD-R methods and the basis set correlation-consistent polarized valence triple-zeta （cc-pVTZ）. The SAC-CI general-R method reproduces the experimental spectrum well for both the main peaks and the satellite peaks of ionization spectrum of SO2. The sequence of ionic states corresponding to main peaks of SO2 has been re-determined according to the SAC-CI conclusions and it is reordered as X^2A1, A^2B2, B2A2, C^2B1,D^2A1, E^2B2 and F^2A1. Besides, the equilibrium structures and adiabatic ionization potentials （AIPs） of ionic states of main peaks of SO2 are calculated by using the SAC-CI SD-R method.

Structural, electronic and vibrational properties of indium oxide clusters

Geometric, electronic and vibrational properties of the most stable and energetically favourable configurations of indium oxide clusters InmOn （1 ≤m, n ≤ 4） are investigated using density functional theory. The lowest energy geometries prefer the planar arrangement of the constituent atoms with a trend to maximize the number of ionic In-O bonds. Due to the charge transfer from In to O atoms, the electrostatic repulsion occurs between the atoms with the same kind of charge. The minimization of electrostatic repulsion and the maximization of In O bond number compete between each other and determine the location of the isometric total energy. The most stable linear In-O-In-O structure of In2O2 cluster is attributed to the reduced electrostatic repulsive energy at the expense of In-O bond number, while the lowest energy rhombus-like structure of In2O3 cluster reflects the maximized number of In O bonds. Furthermore, the vibrational frequencies of the lowest energy clusters are calculated and compared with the available experimental results. The energy gap and the charge density distribution for clusters with varying oxygen/indium ratio are also discussed.

Modification of the Drawing Behavior of 08VTiRe Steel

The uneven amount of globular structure in a very low carbon, low alloy steel in annealed state is studied. After the examination of TEM and EPMA, it is considered that this globular structure arranging in chains and in grain boundaries is carbide and is formed, due to the falling to the pseudo eutectoid zone, in the quick cooling process after hot rolling. In addition, the alloying addition of Ti, V and rare earth element also aggravates the precipitation of carbide. In order to limit the quantity and size of the carbide so as to improve the drawing behavior of the material, the annealing temperature is properly raised to get the equilibrium structure.

Site preference of Ti and Nb in L1-(2)-ordered Co-Al-W phase and their effect on the properties of the alloy:first-principles study

In this work,the equilibrium structure,electronic and elastic properties of L1_(2)-ordered Co-Al-W and Co-Al-W-X(X=Ti and Nb)phase were calculated,using first-principles calculations.Among six nonequivalent sites(Al_(1),Al_(2),Co_(3),Co_(4),W_(5),W_(6)),Ti and Nb prefer to occupy the W_(6)site,since the formation enthalpy of the system is lowest when Ti and Nb occupy the W。site.Both Ti and Nb most affect the density of states of Al atoms.Compared with the Al_(2) site,which is the sub-preference site of Ti and Nb,the density of states of Al atoms is higher with the addition of Ti and Nb in the W_(6)site,which means that the latter system is more stable.According to the bulk modulus B,shear modulus G,Young's modulus E,hardness Hv and Poisson's ratioσ,for Co_(3)(AI,W)alloy,the addition of Ti and Nb in the W_(6)site decreases its hardness hut increases its duetility.This work cnnfirms that Ti and Nh can stahilize the Cag(Al,W)alloy and have a positive effect in solving the relatively poor ductility of this alloy,which has important implications for the development of cobalt.based alloys.