Software package SIMPRE—Revisited

This article elucidates the pitfalls identified in the software package SIMPRE recently developed by Baldoví et al. (J. Comput. Chem. 2013, 34, 1961) for modeling the spectroscopic and magnetic properties of single ion magnets as well as single‐molecule magnets. Analysis of the methodology used therein reveals that the crystal field parameters (CFPs), expressed nominally in the Stevens formalism, exhibit features characteristic for the CFPs expressed in the Wybourne notation. The resemblance of the two types of CFPs introduces a serious confusion that may lead to wrong comparisons of the CFPs taken from various sources. To clarify this confusion, the properties of the CFPs ( , ) associated with the Stevens operators ( X = S , J , or L ), which belong to the class of the tesseral‐tensor operators, are contrasted with those of the CFPs B_kq associated with the Wybourne operators , which belong to the class of the spherical‐tensor operators. Importantly, the confused properties of Stevens and Wybourne operators may bear on reliability of SIMPRE calculations. To consider this question independent calculations are carried out using the complete approach and compared with those of the restricted approach utilized earlier. It appears that the numerical results of the package SIMPRE are formally acceptable, however, the meaning of the CFPs must be properly reformulated. Several other conceptual problems arising from misinterpretations of the crucial notions and the CFP notations identified therein are also discussed and clarified. © 2014 Wiley Periodicals, Inc.     

Improved measurements and analysis of the far-infrared spectrum of methanol-D1 (CH2DOH) arising from trans- (e0) to gauche- (e1 & o1) states

In this work the millimeter-wave (MMW) and far infrared (FIR) absorption spectrum for the asymmetrically deuterated Methanol (CH₂DOH) species measured recently at a temperature of −60 °C with better accuracy and signal/noise (S/N) ratio than known before has been assigned for transitions originating at the lowest lying trans- to gauche-states. The entire spectrum for 50–1200 cm⁻¹ has been re-recorded recently using the Synchrotron Radiation Source coupled with the Bruker Fourier Transform Infrared (FTIR) spectrometer with a resolution of about 0.001 cm⁻¹ or better. Complete spectrum has not been exploited a great deal but it helped to entangle overlapping lines in the present work. This also fills the gap remaining in the usual FTIR in the range 400–500 cm⁻¹. Hence it is expected to help the interacting partner for the Coriolis interaction encountered earlier. The assigned transitions mostly for the axial rotational angular momentum quantum number K + 1 ← K, both for R- and Q-sub bands for wide range of rotational angular momentum quantum number. The MMW spectrum has been recalibrated and assigned for a number of Q-branches. The assignments are confirmed rigorously using closed loop residual technique. The assigned ^rR and ^rQ lines have been analyzed in terms of polynomial expansion parameters. The new assignments are presented for about 750 transitions and a grand atlas of more than 1000 lines has been prepared which will be made available through the open source server at “research gate”. The present work should be useful in the area of astrophysical detection and further understanding of the energy relaxation pathways in the molecule.     

Exploring artificial neural networks to model interatomic and intermolecular potential energy surfaces

We demonstrate how a back-propagation artificial neural network can be trained to represent a potential energy surface (PES) in a formless manner with limited data points and exploited to predict interaction energies for configurations not included in the training set. A similar exercise is undertaken for predicting the eigenvalues and eigenvectors of a model Hamiltonian matrix that delicately depends on parameters and exhibits crossing of eigen values.     

A Lagrangian for Hamiltonian vector fields on singular Poisson manifolds

On a manifold equipped with a bivector field, we introduce for every Hamiltonian a Lagrangian on paths valued in the cotangent space whose stationary points project onto Hamiltonian vector fields. We show that the remaining components of those stationary points tell whether the bivector field is Poisson or at least defines an integrable distribution—a class of bivector fields generalizing twisted Poisson structures that we study in detail.     

Conservative numerical methods for the Full von Kármán plate equations

This article is concerned with the numerical solution of the full dynamical von Kármán plate equations for geometrically nonlinear (large‐amplitude) vibration in the simple case of a rectangular plate under periodic boundary conditions. This system is composed of three equations describing the time evolution of the transverse displacement field, as well as the two longitudinal displacements. Particular emphasis is put on developing a family of numerical schemes which, when losses are absent, are exactly energy conserving. The methodology thus extends previous work on the simple von Kármán system, for which longitudinal inertia effects are neglected, resulting in a set of two equations for the transverse displacement and an Airy stress function. Both the semidiscrete (in time) and fully discrete schemes are developed. From the numerical energy conservation property, it is possible to arrive at sufficient conditions for numerical stability, under strongly nonlinear conditions. Simulation results are presented, illustrating various features of plate vibration at high amplitudes, as well as the numerical energy conservation property, using both simple finite difference as well as Fourier spectral discretizations. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 1948–1970, 2015     

极性晶体中强耦合表面磁极化子特性

研究极性晶体中表面磁极化子的特性。采用Huybrechts线性组合算符和幺正变换方法,导出了晶体中强耦合表面磁极化子处于基态的振动频率和有效哈密顿量,讨论了坐标z的两种极限情况,对RbCl晶体进行了数值计算。结果表明:振动频率和平行有效哈密顿量随磁场的增加而增大。     

Yb3+掺杂稀土钽铌酸盐的晶体场从头计算研究

Yb³⁺掺杂晶体材料是重要的激光材料,在超短脉冲激光、大功率激光等领域有重要应用前景,但长期以来很难通过实验拟合确定Yb3+晶体场参数,尤其是低对称体系,从头计算是解决此问题的重要途经.本文介绍了适合计算稀土离子掺杂晶体的从头计算DV-Xα方法和有效哈密顿量模型,用该方法计算了Yb³⁺掺杂M型和M'型钽铌酸盐的晶场参数和旋轨耦合参数,得到的能级结构和实验能很好地符合,并发现了Yb³⁺掺杂钽铌酸盐的晶场强度参数随稀土原子序数呈现规律变化.表明结合DV-Xα计算和有效哈密顿量方法是计算Yb³⁺掺杂低对称钽铌酸盐晶体场的有效途径,结果显示Yb3+掺杂钽铌酸盐晶体有望成为新型全固态激光工作物质.     

Hamiltonian nature of monopole dynamics

Classical electromagnetism with magnetic monopoles is not a Hamiltonian field theory because the Jacobi identity for the Poisson bracket fails. The Jacobi identity is recovered only if all of the species have the same ratio of electric to magnetic charge or if an electron and a monopole can never collide. Without the Jacobi identity, there are no local canonical coordinates or Lagrangian action principle. To build a quantum field of magnetic monopoles, we either must explain why the positions of electrons and monopoles can never coincide or we must resort to new quantization techniques.     

New solution system for circular sector plate bending and its application

Instead of the biharmonic type equation, a set of new governing equations and solving method for circular sector plate bending is presented based on the analogy between plate bending and plane elasticity problems. So the Hamiltonian system can also be applied to plate bending problems by introducing bending moment functions. The new method presents the analytical solutions for the circular sector plate. The results show that the new method is effective. Project supported by National Natural Science Foundation (No. 19732020) and the Doctoral Research Foundation of China.