Inorganic Molecular Electride Mg4O3: Structure,Bonding, and Nonlinear Optical Properties

Growing demands of material science and, in particular, in the field of nonlinear optics (NLO) encourage us to look for stable highly polarizable molecules with excess diffuse electrons. An unusual class of compounds called electrides comply with these requirements. Many attempts have been made, yet only few electrides have been synthesized as solids and none of them as molecular species. In this paper, a new theoretically designed molecular species with electride characteristics is reported. The idea of this molecular electride comes from the formation of electride-like features in the MgO crystal with defect F-centers. The geometry of the investigated molecule can be described as a Mg₄O₄ cube with one oxygen atom removed. In Mg₄O₃, two 3s electrons are pushed out from the inner area of the molecule forming a diffuse electride multicentered bond. Our calculations show that this electride-like cluster possesses a noticeably large first hyperpolarizability β=5733 au. At the same time, a complete cube Mg₄O₄ and Mg₄O₃²⁺ without electride electron pair have much smaller β: 0 au and 741 au, respectively. This fact indicates the decisive role of the electride electron pair in NLO properties. Additionally, vertical detachment energies of isomers (VDE), excitation energies ΔE, polarizabilities α, and IR spectra were calculated. These properties, including β, are supposed to be observable experimentally and can serve as indirect evidence of the stable molecular electride formation.     

Improved third‐order weighted essentially nonoscillatory scheme

A new third‐order WENO scheme is proposed to achieve the desired order of convergence at the critical points for scalar hyperbolic equations. A new reference smoothness indicator is introduced, which satisfies the sufficient condition on the weights for the third‐order convergence. Following the truncation error analysis, we have shown that the proposed scheme achieves the desired order accurate for smooth solutions with arbitrary number of vanishing derivatives if the parameter ε satisfies certain conditions. We have made a comparative study of the proposed scheme with the existing schemes such as WENO‐JS, WENO‐Z, and WENO‐N3 through different numerical examples. The result shows that the proposed scheme (WENO‐MN3) achieves better performance than these schemes.     

Adaptive Neuro-Fuzzy Inference System and a Multilayer Perceptron Model Trained with Grey Wolf Optimizer for Predicting Solar Diffuse Fraction

The accurate prediction of the solar diffuse fraction (DF), sometimes called the diffuse ratio, is an important topic for solar energy research. In the present study, the current state of Diffuse irradiance research is discussed and then three robust, machine learning (ML) models are examined using a large dataset (almost eight years) of hourly readings from Almeria, Spain. The ML models used herein, are a hybrid adaptive network-based fuzzy inference system (ANFIS), a single multi-layer perceptron (MLP) and a hybrid multi-layer perceptron grey wolf optimizer (MLP-GWO). These models were evaluated for their predictive precision, using various solar and DF irradiance data, from Spain. The results were then evaluated using frequently used evaluation criteria, the mean absolute error (MAE), mean error (ME) and the root mean square error (RMSE). The results showed that the MLP-GWO model, followed by the ANFIS model, provided a higher performance in both the training and the testing procedures.     

基于局部加密纯无网格法非线性Cahn-Hilliard方程的模拟

为数值求解描述不同物质间相位分离现象的高阶非线性Cahn-Hilliard(C-H)方程,发展了一种基于局部加密纯无网格有限点集法(local refinement finite pointset method,LR-FPM).其构造过程为:1)将C-H方程中四阶导数降阶为两个二阶导数,连续应用基于Taylor展开和加权最小二乘法的FPM离散空间导数;2)对区域进行局部加密和采用五次样条核函数以提高数值精度;3)局部线性方程组求解中准确施加含高阶导数Neumann边值条件.随后,运用LR-FPM求解有解析解的一维/二维C-H方程,分析粒子均匀分布/非均匀分布以及局部粒子加密情况的误差和收敛阶,展示了LR-FPM较网格类算法在非均匀布点情况下的优点.最后,采用LR-FPM对无解析解的一维/二维C-H方程进行了数值预测,并与有限差分结果相比较.数值结果表明,LR-FPM方法具有较高的数值精度和收敛阶,比有限差分法更易数值实现,能够准确展现不同类型材料间相位分离非线性扩散现象随时间的演化过程.     

L1-type smoothness indicators based weighted essentially nonoscillatory scheme for Hamilton-Jacobi equations

This article presents an improved fifth-order finite difference weighted essentially nonoscillatory (WENO) scheme to solve Hamilton-Jacobi equations. A new type of nonlinear weights is introduced with the construction of local smoothness indicators on each local stencil that are measured with the help of generalized undivided differences in L¹-norm. A novel global smoothness measurement is also constructed with the help of local measurements from its linear combination. Numerical experiments are conducted in one- and two-dimensions to demonstrate the performance enhancement, resolution power, numerical accuracy for the proposed scheme, and compared it with the classical WENO scheme.     

基于特征正交分解的一类瞬态非线性热传导问题的新型快速分析方法

提出了一种基于特征正交分解(POD)和有限元法的瞬态非线性热传导问题的模型降阶快速分析方法, 建立了导热系数随温度变化的一类瞬态非线性热传导问题有限元格式的POD降阶模型. 在隐式时间推进方法的基础上有效结合单元预转换方法和多级线性化方法发展了一种加速求解瞬态非线性热传导降阶模型的新型计算方法,并通过二维和三维算例验证了该方法的准确性和高效性. 研究结果表明: (1)降阶模型解的均方根误差在经过初始时段轻微的脉动后稳定于0.01%以下, 而其计算效率比有限元全阶模型提高2$\sim $3个数量级, 并且自由度数量(DOFs)愈大提高的幅度也愈加显著; (2)新型算法解决了常规算法在计算非线性降阶模型时加速性能差的问题, 即使是在DOFs比较小的时候也能够明显提高计算效率; (3)常数边界条件下得到的POD模态可以用来建立相同求解域在各种复杂时变边界条件下的瞬态非线性热传导降阶模型, 并对其传热过程和温度场进行快速准确的分析与预测, 具有很好的工程应用价值.      

Nonlinear Jordan Higher Derivations of Triangular Algebras

In this paper, we prove that any nonlinear Jordan higher derivation on triangular algebras is an additive higher derivation. As a byproduct, we obtain that any nonlinear Jordan derivation on nest algeb...     

Prediction of 195Pt NMR chemical shifts of dissolution products of H2[Pt(OH)6] in nitric acid solutions by DFT methods: how important are the counter‐ion effects?

¹⁹⁵Pt NMR chemical shifts of octahedral Pt(IV) complexes with general formula [Pt(NO₃)_n(OH)_{6 ? n}]^2?, [Pt(NO₃)_n(OH₂)_{6 ? n}]^{4 ? n} (n = 1–6), and [Pt(NO₃)_{6 ? n ? m}(OH)_m(OH₂)_n]^{?2 + n ? m} formed by dissolution of platinic acid, H₂[Pt(OH)₆], in aqueous nitric acid solutions are calculated employing density functional theory methods. Particularly, the gauge‐including atomic orbitals (GIAO)‐PBE0/segmented all‐electron relativistically contracted–zeroth‐order regular approximation (SARC–ZORA)(Pt) ∪ 6–31G(d,p)(E)/Polarizable Continuum Model computational protocol performs the best. Excellent second‐order polynomial plots of δ_calcd(¹⁹⁵Pt) versus δ_exptl(¹⁹⁵Pt) chemical shifts and δ_calcd(¹⁹⁵Pt) versus the natural atomic charge Q_Pt are obtained. Despite of neglecting relativistic and spin orbit effects the good agreement of the calculated δ ¹⁹⁵Pt chemical shifts with experimental values is probably because of the fact that the contribution of relativistic and spin orbit effects to computed σ^{iso 195}Pt magnetic shielding of Pt(IV) coordination compounds is effectively cancelled in the computed δ ¹⁹⁵Pt chemical shifts, because the relativistic corrections are expected to be similar in the complexes and the proper reference standard used. To probe the counter‐ion effects on the ¹⁹⁵Pt NMR chemical shifts of the anionic [Pt(NO₃)_n(OH)_{6 ? n}]^2? and cationic [Pt(NO₃)_n(OH₂)_{6 ? n}]^{4 ? n} (n = 0–3) complexes we calculated the ¹⁹⁵Pt NMR chemical shifts of the neutral (PyH)₂[Pt(NO₃)_n(OH)_{6 ? n}] (n = 1–6; PyH = pyridinium cation, C₅H₅NH⁺) and [Pt(NO₃)_n(H₂O)_{6 ? n}](NO₃)_{4 ? n} (n = 0–3) complexes. Counter‐anion effects are very important for the accurate prediction of the ¹⁹⁵Pt NMR chemical shifts of the cationic [Pt(NO₃)_n(OH₂)_{6 ? n}]^{4 ? n} complexes, while counter‐cation effects are less important for the anionic [Pt(NO₃)_n(OH)_{6 ? n}]^2? complexes. The simple computational protocol is easily implemented even by synthetic chemists in platinum coordination chemistry that dispose limited software availability, or locally existing routines and knowhow. Copyright © 2016 John Wiley & Sons, Ltd.