Spin–orbit coupling in oxygen containing diradicals

Intermediate diradicals which occur in the Paterno–Büchi photocycloaddition and in the Norrish type I photoreactions have been calculated taking into account the spin–orbit coupling (SOC) between the singlet (S) and triplet (T) states. Reaction paths for the photocycloaddition of formaldehyde to ethene and the diradical products of the α-cleavage of cyclohexanone have been optimized by the MNDO CI method for a number of different singlet and triplet states. SOC integrals are calculated by an effective one-electron approximation. Intermediate diradicals in the Paterno–Büchi reaction and the SOC effects are also studied ab initio with CAS SCF geometry optimization in a TZV basis set. Both methods predict a large SOC matrix element between the S and T states in the course of the C–C attack, while the SOC integral is two orders of magnitude smaller for the diradical produced in the C–O attack. In the Norrish type I photoreaction the oxygen atom also produces some nonzero contribution to the SOC integral which governs intersystem crossing in a ·C–C· diradical. For the diradicals produced by the α-cleavage of cyclohexanone a vibronic interaction is responsible for the SOC mixing between the lowest S and T states. The importance of one-center versus two-center SOC contributions in diradicals is briefly discussed.     

人造地球卫星运动方程的代数动力学算法数值解

代数动力学算法首次被用于求人造地球卫星运动方程的数值解，在四阶算法下，与Runge-Kutta算法和辛算法的计算结果作了比较.结果表明，代数动力学算法对于人造地球卫星长期轨道的计算有较高的精度.并讨论了地球四极和八极带谐项对卫星轨道的影响. 关键词： 人造地球卫星运动方程 代数动力学算法数值解 地球四极和八极带谐项对卫星轨道的影响     

Full four‐component relativistic calculations of the one‐bond 77Se–13C spin‐spin coupling constants in the series of selenium heterocycles and their parent open‐chain selenides

Four‐component relativistic calculations of ⁷⁷Se–¹³C spin–spin coupling constants have been performed in the series of selenium heterocycles and their parent open‐chain selenides. It has been found that relativistic effects play an essential role in the selenium–carbon coupling mechanism and could result in a contribution of as much as 15–25% of the total values of the one‐bond selenium–carbon spin‐spin coupling constants. In the overall contribution of the relativistic effects to the total values of ¹J(Se,C), the scalar relativistic corrections (negative in sign) by far dominate over the spin‐orbit ones (positive in sign), the latter being of less than 5%, as compared to the former (ca 20%). A combination of nonrelativistic second‐order polarization propagator approach (CC2) with the four‐component relativistic density functional theory scheme is recommended as a versatile tool for the calculation of ¹J(Se,C). Solvent effects in the values of ¹J(Se,C) calculated within the polarizable continuum model for the solvents with different dielectric constants (ε 2.2–78.4) are next to negligible decreasing negative ¹J(Se,C) in absolute value by only about 1 Hz. The use of the locally dense basis set approach applied herewith for the calculation of ⁷⁷Se–¹³C spin‐spin coupling constants is fully justified resulting in a dramatic decrease in computational cost with only 0.1–0.2‐Hz loss of accuracy. Copyright © 2014 John Wiley & Sons, Ltd.     

True spin and pseudo spin entanglement around Dirac Points in graphene with Rashba spin–orbit interaction

We analytically obtained the Schmidt decomposition of the entangled state between the pseudo spin and the true spin in graphene with Rashba spin–orbit coupling. The entangled state has the standard form of the Bell state, where the SU(2) spin symmetry is broken. These states can be explicitly expressed as the superposition of two nonorthogonal, but mirror symmetrical spin states entangled with the pseudo spin states. Because of the closely locking between the pseudo spin and the true spin, it is found that the orbit curve in the spin-polarization parameter space for the fixed equi-energy contour around Dirac points has the same shape as the $\delta \overrightarrow{k}$-contour. Due to the spin–orbit coupling that cause the topological transition in the local geometry of the dispersion relation, the new equi-energy contours around the new emergent Dirac Points can be obtained by squeezing the one around the original Dirac point. The spin texture in the momentum space around the Dirac points is analyzed under the Rashba spin–orbit interaction and it is found that the orientation of the spin polarization at each crystal momentum $\overrightarrow{k}$ is independent of the Rashba coupling strength.     

Existence of heteroclinic orbits in a novel three-order dynamical system

In this paper,we design a novel three-order autonomous system.Numerical simulations reveal the complex chaotic behaviors of the system.By applying the undetermined coefficient method,we find a heteroclinic orbit in the system.As a result,the Si’lnikov criterion along with some other given conditions guarantees that the system has both Smale horseshoes and chaos of horseshoe type.     

Carlsson's rank conjecture and a conjecture on square-zero upper triangular matrices

Let k be an algebraically closed field and A the polynomial algebra in r variables with coefficients in k. In case the characteristic of k is 2, Carlsson [9] conjectured that for any DG-A-module M of dimension N as a free A-module, if the homology of M is nontrivial and finite dimensional as a k-vector space, then $2^r\le N$. Here we state a stronger conjecture about varieties of square-zero upper triangular $N\times N$ matrices with entries in A. Using stratifications of these varieties via Borel orbits, we show that the stronger conjecture holds when $N<8$ or $r<3$ without any restriction on the characteristic of k. As a consequence, we obtain a new proof for many of the known cases of Carlsson's conjecture and give new results when $N>4$ and $r=2$.     

Sensitivity analysis for a type of statically stable sailcrafts

Two types of sensitivities are proposed for statically stable sailcrafts.One type is the sensitivities of solar-radiation-pressure force with respect to position of the center of mass,and the other type is the sensitivities of solar-radiation-pressure force with respect to attitude.The two types of sensitivities represent how the solar-radiationpressure force changes with the position of mass center and the attitude.Sailcrafts with larger sensitivities undergo larger error of the solar-radiation-pressure force,leading to larger orbit error,as demonstrated by simulation.Then as a case study,detailed formulas are derived to calculate the sensitivities for sailcrafts with four triangular sails.According to these formulas,in order to reduce both types of sensitivities,the angle between opposed sails should not be too large,and the center of mass should be as close to the axis of symmetry of the four sails as possible and as far away from the center of pressure of the sailcraft as possible.     

Electron transport of a quantum wire with spatially periodic spin–orbit coupling

Electron transport properties of an ideal one-dimensional (1D) quantum wire are studied including spatially periodic Rashba spin–orbit coupling (SOC) and Dresselhaus SOC. By comparing with the previous work [S.J. Gong, Z.Q. Yang, J. Phys. Condens. Matter 19 (2007) 446209], two transmission gaps appear in the transmission probability of electrons and their widths are also broadened dramatically. Moreover, it is found that their widths are sensitive not only to the strength of SOCs but also to the length ratio of SOCs segment and non-SOCs segment. In addition, a ‘circle-type’ transmission behavior has been found by tuning the strength of SOCs continuously. Our results may extend the previous work and provide an more effective method to manipulate the current in nanoelectric devices.     

Application of the multireference equation of motion coupled cluster method,including spin–orbit coupling,to the atomic spectra of Cr,Mn, Fe and Co

The recently introduced multireference equation of motion (MR-EOM) approach is combined with a simple treatment of spin–orbit coupling, as implemented in the ORCA program. The resulting multireference equation of motion spin–orbit coupling (MR-EOM-SOC) approach is applied to the first-row transition metal atoms Cr, Mn, Fe and Co, for which experimental data are readily available. Using the MR-EOM-SOC approach, the splittings in each L-S multiplet can be accurately assessed (root mean square (RMS) errors of about 70 cm^?1). The RMS errors for J-specific excitation energies range from 414 to 783 cm^?1 and are comparable to previously reported J-averaged MR-EOM results using the ACESII program. The MR-EOM approach is highly efficient. A typical MR-EOM calculation of a full spin–orbit spectrum takes about 2 CPU hours on a single processor of a 12-core node, consisting of Intel XEON 2.93 GHz CPUs with 12.3 MB of shared cache memory.