A decomposition theorem for SU(n) and its application to CP-violation through quark mass diagonalisation

It is proved that the groupG=SU(n) has a decompositionG=FCF whereF is a maximal abelian subgroup andC is an (n − 1)² parameter subset of matrices. The result is applied to the problem of absorbing the maximum possible number of phases in the mass-diagonalising matrix of the charged weak current into the quark fields; i.e., of determining the exact number of CP-violating phases for arbitrary number of generations. The inadequacies of the usual way of solving this problem are discussed. Then=3 case is worked out in detail as an example of the constructive procedure furnished by the proof of the decomposition theorem.     

An efficient solver for large structured eigenvalue problems in relativistic quantum chemistry

ABSTRACT

We report an efficient program for computing the eigenvalues and symmetry-adapted eigenvectors of very large quaternionic (or Hermitian skew-Hamiltonian) matrices, using which structure-preserving diagonalisation of matrices of dimension N > 10, 000 is now routine on a single computer node. Such matrices appear frequently in relativistic quantum chemistry owing to the time-reversal symmetry. The implementation is based on a blocked version of the Paige–Van Loan algorithm, which allows us to use the Level 3 BLAS subroutines for most of the computations. Taking advantage of the symmetry, the program is faster by up to a factor of 2 than state-of-the-art implementations of complex Hermitian diagonalisation; diagonalising a 12, 800 × 12, 800 matrix took 42.8 (9.5) and 85.6 (12.6) minutes with 1 CPU core (16 CPU cores) using our symmetry-adapted solver and Intel Math Kernel Library's ZHEEV that is not structure-preserving, respectively. The source code is publicly available under the FreeBSD licence.     

Zero-width resonances in the context of Fano's configuration interaction formalism

ABSTRACT

We examine how to link two approaches for resonance width calculations, in a situation of crossing of two diatomic molecular potentials. One is the semiclassical formalism of Child. The other is Fano's configuration interaction approach leading to the Fermi golden rule. We build a case where the vanishing of the width in the two formalisms can be reduced to the same conditions.     

Analytic variationally optimized internally orthogonalized modified Laguerre orbitals in accurate atomic configuration interaction calculation

An analytic configuration interaction method based on variationally optimized internally orthogonalized modified Laguerre orbitals is presented. We have developed the corresponding computer code. For application, we study the 1s2s $^{1}S$ isoelectronic sequence from helium to neon, and compare with other methods. By taking into account the Eckart upper-bound theorem, we obtained more accurate and more intuitively understandable results than Hartree--Fock and multi-configuration Hartree--Fock reported results.     

Method of configuration interaction in calculations of the spectral characteristics of atoms and molecules

For He, Be, Ne, and Mg atoms and their isoelectronic series, calculations of the dipole dynamic polarizability, energies, and strengths of the oscillators of the lowest electronic transitions are made within the scope of the method of configuration interaction. This very method is also used to calculate the dipole dynamic polarizability of a number of molecules of hydrides and N₂ and CO₂ molecules. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 67, No. 4, pp. 427–432, July–August, 2000.     

强组态相互作用对Sn离子谱线分布的影响

本文利用多组态Dirac-Fock(MCDF)方法,计算了Sn离子在不同离化度下（从SnVI到SnXIII）所产生的4p64dn-14f+4p64dn-15p+4p54dn+1 - 4p64dn的跃迁光谱,给出了组态平均能量随电离度的变化规律和理论预言的辐射光谱,并分析了组态相互作用对其的影响。     

钡原子6s~2、5d~2、6p~2组合的电子相关效应及其组合相互作用

用模型势方法和斯莱特-高登(Slater-Condon)理论计算了钡原子偶宇称6s~2,5d~2,6p~2电子组合、角动量J=0,1,2的双激发能级的激发能和组合相互作用(configuration interaction)。结果表明,6s~2,5d~2和6p~2组合在~1S_0态中强烈地混合,使常规能级标识符号失去意义。另外,我们的结果也从理论上证明了曾引起争议的6p~(21)S_0能级是位于第一电离势之上的自由离能级。     

Multireference configuration interaction potential curve and analytical potential energy function of the ground and low-lying excited states of CdSe

The potential energy curves (PECs) of the ground state ($^{3}\Pi )$ and three low-lying excited states ($^{1}\Sigma $, $^{3}\Sigma $,$^{ 1}\Pi )$ of CdSe dimer have been studied by employing quasirelativistic effective core potentials on the basis of the complete active space self-consistent field method followed by multireference configuration interaction calculation. The four PECs are fitted to analytical potential energy functions using the Murrel--Sorbie potential function. Based on the PECs, the vibrational levels of the four states are determined by solving the Schr\"{o}dinger equation of nuclear motion, and corresponding spectroscopic constants are accurately calculated. The equilibrium positions as well as the spectroscopic constants and the vibrational levels are reported. By our analysis, the $^{3}\Pi $ state, of which the dissociation asymptote is Cd($^{1}$S) + Se($^{3}$P), is identified as a ground state of CdSe dimer, and the corresponding dissociation energy is estimated to be 0.39\,eV. However, the first excited state is only 1132.49\,cm$^{ - 1}$ above the ground state and the $^{3}\Sigma $ state is the highest in the four calculated states.     

A comparison of various approaches in internally contracted multireference configuration interaction: the carbon dimer as a test case

Various variational spaces deriving from different contraction schemes of the first-order interacting space have been examined and their performances have been tested on the carbon dimer. The contraction schemes stemming from the strongly contracted and from the partially contracted approach of the n-electron valence state perturbation theory have been analysed along with the mixed approach of Werner and Knowles as well as with the totally uncontracted approach where the full dimensionality of the first-order interacting space is taken into account. The results are very similar for all the spaces considered, despite their widely varying dimensionality. A comparison with the second-order and the third-order results of NEVPT is also reported.     

氦原子sp组态的自旋-轨道相互作用精细结构参数

本文借助不可约张量理论,导出了通常由光谱实验数据确定的氦原子sp组态自旋-轨道相互作用精细结构参数A的理论计算式,在推导过程中完成所有角向积分和自旋求和计算.     

多组态Dirac-Fock方法与准相对论组态相互作用方法的比较研究

利用多组态Dirac-Fock(MCDF)方法与准相对论组态相互作用方法,分别详细计算了低Z、中Z和高Z原子(离子)各个壳层上电子的束缚能、平均轨道半径、总束缚能、激发能、精细结构能级以及类Ne等电子系列离子的2p53s 1,3P1-2p6 1S0跃迁能,并且对这两种方法的结果进行了数值比较.     

Investigation of the multiplet features of SrTiO3 in X‐ray absorption spectra based on configuration interaction calculations

Synchrotron‐based L_2,3‐edge absorption spectra show strong sensitivities to the local electronic structure and chemical environment. However, detailed physical information cannot be extracted easily without computational aids. Here, using the experimental Ti L_2,3‐edges absorption spectrum of SrTiO₃ as a fingerprint and considering full multiplet effects, calculations yield different energy parameters characterizing local ground state properties. The peak splitting and intensity ratios of the L₃ and L₂ set of peaks are carefully analyzed quantitatively, giving rise to a small hybridization energy around 1.2 eV, and the different hybridization energy values reported in the literature are further addressed. Finally, absorption spectra with different linearly polarized photons under various tetragonal crystal fields are investigated, revealing a non‐linear orbital–lattice interaction, and a theoretical guidance for material engineering of SrTiO₃‐based thin films and heterostructures is offered. Detailed analysis of spectrum shifts with different tetragonal crystal fields suggests that the e_g crystal field splitting is a necessary parameter for a thorough analysis of the spectra, even though it is not relevant for the ground state properties.     

多参考组态相互作用方法计算研究XOn(X=S,Cl; n=0,±1)的解析势能函数和光谱常数

采用从头计算的多参考组态相互作用方法和含扩散基的3个基组aug-cc-PVXZ(X=D,T,Q)计算了SO和ClO分子及其分子离子的势能曲线,确定了平衡几何结构、离解能,并采用Feller拟合递推方法得到了基函数为无穷大计算水平值.确定了SO-,ClO ,ClO-分子离子的基态.通过Murrell-Sorbie势能函数和最小二乘法拟合得到了解析势能函数.基于所得的势能函数,通过解核运动的薛定谔方程得到振动能级,精确计算了相应的光谱常数,并与现有的理论值和实验值进行了比较.     

Ab initio multi-reference configuration interaction of the low-lying states of the AsP molecule

Nine low-lying electronic states of the AsP molecule, including Σ , Ⅱ, and △ symmetries with singlet, triplet, and quintet spin multiplicities, are studied using multi-reference configuration interaction method.The potential energy curves and the spectroscopic constants of these nine states are determined, and compared with the experimental observed data as well as other theoretical works available at present.Three quintet states are reported for the first time.Furthermore, the analytical potential energy functions of these states are fitted using Murrell-Sorbie function and least square fitting method.     

多参考组态相互作用方法计算研究XOn(X=S,Cl；n=0,±1)的解析势能函数和光谱常数

采用从头计算的多参考组态相互作用方法和含扩散基的3个基组aug-cc-PVXZ (X=D,T,Q) 计算了SO和ClO分子及其分子离子的势能曲线，确定了平衡几何结构、离解能，并采用Feller拟合递推方法得到了基函数为无穷大计算水平值. 确定了SO^－，ClO⁺，ClO^-分子离子的基态. 通过Murrell-Sorbie势能函数和最小二乘法拟合得到了解析势能函数. 基于所得的势能函数，通过解核运动的薛定谔方程得到振 关键词： 多参考组态相互作用 势能曲线 解析势能函数 光谱常数     

The quadrupole plus pairing interaction model in large configuration space for W,Os and Pt nuclei

The equilibrium deformations of tungsten, osmium and platinum nuclei are studied with the self-consistent quadrupole plus pairing interaction model by considering all the nucleons in nucleus explicitly. It is shown that similar results can be obtained by performing calculations with or without the assumption of an inert core. The only difference is in the strength of the quadrupole and pairing interactions to be employed in the respective calculations. The experimental static quadrupole moments and theB (E2) values are correctly reproduced by performing calculations with bare nucleon charge for all the nucleons.     

A novel configuration model for random graphs with given degree sequence

Recently, random graphs in which vertices are characterized by hidden variables controlling the establishment of edges between pairs of vertices have attracted much attention. This paper presents a specific realization of a class of random network models in which the connection probability between two vertices (i,j) is a specific function of degrees ki and kj. In the framework of the configuration model of random graphs, we find the analytical expressions for the degree correlation and clustering as a function of the variance of the desired degree distribution. The obtained expressions are checked by means of numerical simulations. Possible applications of our model are discussed.     

The influence of CH … π interaction on coupling constants across N … H–F hydrogen bond in a substituted T-shaped configuration: a theoretical study

For studying the influence of CH?…?π interaction on coupling constants across N?…?H–F hydrogen bond in a substituted T-shaped configuration, X-benzene⊥(FH?…?pyrazine?…?HF) complexes are chosen as a working model. NMR calculations are performed at B3LYP/6-311++G(d,p) and PBE0/6-311++G(d,p) levels. Here, correlations between energetic, geometrical and topological parameters and coupling constants are investigated. The results indicate that direct correlations exist between strength of N?…?H hydrogen bond, electron-donating power of substituents and |^2hJ_N?F|. Also, |^2hJ_N?F| increases as cooperative and synergistic energies become more negative. These behaviours are reversed for ^1hJ_N?H. Due to contradictory behaviours of FC and PSO terms, an irregular trend is observed for ¹J_H?F.     

相对论多组态相互作用方法计算Mg~+离子同位素位移

采用相对论多组态相互作用方法研究了Mg~+离子3s~2S_(1/2)—3s~2P_(1/2)和3s~2S_(1/2)—3s~2P_(3/2)两条跃迁谱线的特殊质量位移系数和场位移因子,并计算了中子数8≤N≤20的Mg~+离子的同位素位移.计算结果与其他理论的计算值符合得比较好,与最新的实验测量结果比较,相对误差在0.13%到0.28%范围,是目前最接近Mg~+离子同位素位移实验测量的理论计算结果.该计算结果可为Mg~+离子同位素位移实验和理论研究提供参考,能够用于Mg~+离子的短寿命同位素的光谱测量实验以及利用Mg~+离子开展幻中子数N=8和N=20附近的奇异原子核特性研究等.所用的计算方法和电子激发模式也可以推广到其他核外电子数为11的多电子体系,用于开展相应的原子光谱结构计算和同位素位移的理论研究.