利用Sagnac干涉仪实现光子轨道角动量分束器

光子轨道角动量量子态具有高维和光学涡旋特性, 在经典和量子领域展示出了巨大的应用潜力, 目前对其的研究已成为物理学的一个热点. 本实验研究了利用Sagnac干涉仪干涉的方法将具有不同轨道角动量的光束无破坏地分离到不同的路径, 即实现光子轨道角动量分束器. 实验中利用此分束器验证了对几种不同轨道角动量态(包含叠加态)的分离, 得到了与理论预期相符的实验结果. 这种对轨道角动量态的区分的方法相比已有的其他区分方法具有较好的稳定性, 而且可用于区分叠加态, 也可以达到单光子水平, 最重要的是实现了不同的轨道角动量本征态无破坏的与路径比特耦合. 这种新方法对高密度通信、量子纠缠、量子保密通信、量子计算与量子信息等方面有着重要的意义.     

Chem1D: a software package for electronic structure calculations on one-dimensional systems

We present a preliminary version of a software package, Chem1D, that performs molecular orbital calculations on one-dimensional atoms and molecules using the unadorned Coulomb operator 1/|x₁ ? x₂|. We describe methods for computing the necessary one- and two-electron integrals and outline the overall structure of the package. We use Chem1D to perform calculations on a set of small molecules and show that one-dimensional chemistry differs in a number of interesting ways from three-dimensional chemistry.     

在动量空间讨论二氯乙烯的同分异构性

通过量化计算得到了二氯乙烯偏式、顺式和反式三种同分异构体的几何结构参数, 并利用电子动量谱学方法计算了二氯乙烯偏式、顺式和反式同分异构体的四个芯轨道的动量密度二维分布图和动量谱线. 对比不同异构体的四个芯轨道在坐标空间和动量空间的电子分布情况发现, 在坐标空间无法体现的原子轨道间的相互干涉作用在动量空间被放大了, 表现为动量曲线具有多峰结构和一定的周期性. 通过计算周期值可以求出不同异构体相邻原子间的间距; 通过判断周期轴的方向能够得到三种异构体的分子轴取向.     

FIXED POINT WITH ORBITAL DIAMETRAL FUNCTION

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Understanding the Uniqueness of 2p Elements in Periodic Tables

The Periodic Table, and the unique chemical behavior of the first element in a column (group), were discovered simultaneously one and a half centuries ago. Half a century ago, this unique chemistry of the light homologs was correlated to the then available atomic orbital (AO) radii. The radially nodeless 1s, 2p, 3d, 4f valence AOs are particularly compact. The similarity of r (2s)≈r(2p) leads to pronounced sp-hybrid bonding of the light p-block elements, whereas the heavier p elements with n≥3 exhibit r (ns) ≪ r (np) of approximately −20 to −30 % . Herein, a comprehensive physical explanation is presented in terms of kinetic radial and angular, as well as potential nuclear-attraction and electron-screening effects. For hydrogen-like atoms and all inner shells of the heavy atoms, r (2s) ≫ r (2p) by +20 to +30 % , whereas r (3s)≳r(3p) ≳r(3d), since in Coulomb potentials radial motion is more radial orbital expanding than angular motion. However, the screening of nuclear attraction by inner core shells is more efficient for s than for p valence shells. The uniqueness of the 2p AO is explained by this differential shielding. Thereby, the present work paves the way for future physical explanations of the 3d, 4f, and 5g cases.     

Why is N···Be distance of NH3H+···DBeH shorter than that of NH3D+···HBeH? paradoxical geometrical isotope effects for partially isotope‐substituted dihydrogen‐bonded isotopomers

The partial isotope substitution for the change of geometrical parameters, interaction energies, and nuclear magnetic shielding tensors (σ) of dihydrogen‐bonded NH₃X⁺···YBeH (X, Y = H, D, and T) systems is analyzed. Based on the theoretical calculation, the distance between heavy atoms R_N···Be of NH₃H⁺···DBeH is clearly found to be shorter than that in NH₃D⁺···HBeH. Such apparently paradoxical geometrical isotope effect (GIE) on R_N···Be is revealed by the cooperative effect of two kinds of (1) primary covalent‐bonded GIE and (2) secondary dihydrogen‐bonded one. We have demonstrated that (1) the covalent bond lengths become shorter by heavier isotope‐substitution and (2) the dihydrogen‐bonded distance R_X···Y becomes shorter by heavier Y and lighter X isotope‐substitution due to the difference of electronic structure reflected by the nuclear distribution. We have also found that interaction energy of NH₃H⁺···DBeH is stronger than that of NH₃D⁺···HBeH and isotopic deshielding effect of magnetic shielding becomes large in lighter isotope. © 2013 Wiley Periodicals, Inc.     

Reactivity index based on orbital energies

This study shows that the chemical reactivities depend on the orbital energy gaps contributing to the reactions. In the process where a reaction only makes progress through charge transfer with the minimal structural transformation of the reactant, the orbital energy gap gradient (OEGG) between the electron‐donating and electron‐accepting orbitals is proven to be very low. Using this relation, a normalized reaction diagram is constructed by plotting the normalized orbital energy gap with respect to the normalized intrinsic reaction coordinate. Application of this reaction diagram to 43 fundamental reactions showed that the majority of the forward reactions provide small OEGGs in the initial stages, and therefore, the initial processes of the forward reactions are supposed to proceed only through charge transfer. Conversely, more than 60% of the backward reactions are found to give large OEGGs implying very slow reactions associated with considerable structural transformations. Focusing on the anti‐activation‐energy reactions, in which the forward reactions have higher barriers than those of the backward ones, most of these reactions are shown to give large OEGGs for the backward reactions. It is also found that the reactions providing large OEGGs in the forward directions inconsistent with the reaction rate constants are classified into S_N2, symmetric, and methyl radical reactions. Interestingly, several large‐OEGG reactions are experimentally established to get around the optimum pathways. This indicates that the reactions can take significantly different pathways from the optimum ones provided no charge transfer proceeds spontaneously without the structural transformations of the reactants. © 2014 Wiley Periodicals, Inc.     

Canonical two‐range addition theorem for slater‐type orbitals

The radial Slater‐type orbitals (STO) ${r^\mu }{e^{ - \alpha r}}$ can be simply obtained by repeated parametric differentiation of the Yukawa Potential $({e^{ - \alpha r}}/r)$ with respect to α. A new compact two‐range addition theorem (AdT) for the STO is herein derived by explicit parametric differentiation of the well‐known Yukawa AdT. The resulting addition formula is combined with the single‐range AdT for solid spherical harmonics $({r^l}Y_l^m(\hat r))$ to present a new AdT for three‐dimensional spherical coordinate STOs. We advance the proposition that this formula is “canonical” in the same sense that the Laplace expansion of the Coulomb potential is considered canonical. We demonstrate how this procedure can be employed for all exponential‐type orbitals. © 2012 Wiley Periodicals, Inc.     

Pyridine adsorption on small Nin‐cluster (n = 2,3,4): A study of geometry and electronic structure

Adsorption of pyridine on Ni_n‐clusters (with n = 2,3,4) is studied by quantum chemical calculations at B3LYP/LANL2DZ and B3LYP/6‐311G^** levels. First, Ni_n‐clusters are investigated for accessible structure and electronic states. The lowest electronic state with four unpaired electrons is predicted for Ni₄‐cluster based on geometry and electronic structure, showing that the cluster stability nicely depends on number of unpaired electrons. Correction for basis set superposition error of metal‐metal bond is appreciable and has increasing effect on cluster binding energy. Next, adsorption of pyridine in planar and vertical adsorption modes is investigated on rhombus Ni₄‐cluster. The vertical mode is found (at B3LYP/6‐311G^** level) as the most favorable adsorption mode. Adsorption energy (ΔE_ads) depends on cluster size; adsorption on Ni₄‐cluster is most favorable with ΔE_ads = ?207.33 kJ/mol. The natural bond orbital analysis reveals the charge transfer in adsorbate/metal‐cluster. Results of investigations for the Ni₂‐ and Ni₃‐cluster are also presented. © 2012 Wiley Periodicals, Inc.     

Structures,energetics, and isomerism of [Be,C,O,S]: Stability of triply bonded sulfur

Multiply bonded sulfur has continued to attract attention both experimentally and theoretically. Triply sulfur‐bonded compounds are still rare, due to either the lack of suitable generation precursors or the conversion instability toward doubly sulfur‐bonded structures. A detailed computational study was performed on the structures and stability of various [Be,C,O,S] isomers at the coupled cluster singles doubles (triple excitations) (CCSD(T))/aug‐cc‐pVTZ//B3LYP/6‐311+G(d)+ZPVE level to predict intrinsically stable isomers with triply bonded sulfur. The molecular orbital, bond distance, and harmonic vibrational frequency analysis were carried out at aug‐cc‐pVTZ‐B3LYP, M06‐2X, and CCSD(T) levels to investigate the bonding nature of linear structures. It was shown that two low‐lying isomers are linear SBeCO 01 (0.0 kcal/mol) and SBeOC 02 (15.7 kcal/mol), both of which possess the SBe triple bonding. The Lewis acid–base association of SBe + CO can barrierlessly form 01 and 02, with the former more abundant, while the insertion reaction of SCO + Be might generate more 02 than 01 via photochemical processes. By contrast, formation of the SC‐bearing isomer SCBeO 04 (39.4 kcal/mol) seems unlikely due to its higher energy and less kinetic competition than that of 01 and 02, via either simple association or insertion reactions. The new stable isomers SBeCO 01 and SBeOC 02 add to the number of SBe triply bonded species. Their unique structures and varied branching ratios under association and insertion processes deserve future experimental study. © 2013 Wiley Periodicals, Inc.