Behind the success of modified coupled-cluster methods: addition by subtraction

ABSTRACT

Modified coupled-cluster (CC) methods such as linearized coupled-cluster doubles (LinCCD), approximate coupled pair (ACP D14), 2CC (from nCC family), parameterized CCSD (pCCSD) and distinguishable cluster (DCSD) can have their advantages over general CC methods. Though these methods include connected clusters of single and double excitations at most, distinguishable cluster, parameterized CC and approximate coupled pair methods, in particular, have been shown to produce quantitatively correct results in benchmark studies. To put these methods on a stronger foothold, it is essential to understand the rationale for their success: mimicking the effect of connected triple excitations. We exploit the relation between CC and many body perturbation theory (MBPT) in general, and between CCSD and MBPT(4)/MP4 in particular, to take a step towards bringing clarity to this persisting conundrum. Our aim here is to look for numerical signs of ‘addition by subtraction’ or ‘inclusion by deletion’ effect that is likely behind the success of these modified CCD or CCSD methods. We achieve this by revisiting well-studied examples of single and multiple bond dissociation and comparing the performance of these modified CCSD methods with higher-level CC methods. Though our results are qualitative in nature, we hope this would lead to more rigorous analysis in future studies.     

Unitary units in modular group algebras of 2-groups

We study the unitary subgroupV _?(F₂ G) in the group algebras F₂ Gof 2-groups of maximal class over the field F₂of two elements. We show that there does not exist a normal complement to Gin V _?(F₂ G) if and only if Gis the dihedral group of order 2ⁿ(n≥ 5) or the semidihedral group of order 2ⁿ(n≥5). We also describe V _?(F₂ G) when the subgroup Ghas order 8 and 16 and in this case there exist a normal complement of Gin V _?(F₂ G).     

Moufang sets of mixed type F4

Moufang sets were introduced by Jacques Tits in order to understand isotropic linear algebraic groups of relative rank one, but the notion is more general. We describe a new class of Moufang sets, arising from so‐called mixed groups of type ${\mathsf{F}}_4$ in characteristic 2, obtained as the fixed point set under a suitable involution.     

一类单调算子的新不动点定理

利用单调迭代法、数学归纳法以及序差距的性质,在半序Banach空间中探究不具有紧性、连续性以及任何凹凸性的单调算子不动点存在以及惟一性问题,得出其新不动点定理,这些结果对相关结论进行了推广,使其适用范围更广,同时将该结论应用于求解Volterra型积分方程组问题中.     

A Family of Integrable Rational Semi-Discrete Systems and Its Reduction

Within framework of zero curvature representation theory, a family of integrable rational semi-discrete systems is derived from a matrix spectral problem. The Hamiltonian forms of obtained semi-discrete systems are constructed by means of the discrete trace identity. The Liouville integrability for the obtained family is demonstrated. In the end, a reduced family of obtained semi-discrete systems and its Hamiltonian form are worked out.     

A simple method for evaluation of the self-consistency of the radial distribution functions and the orientation of water molecules in the first coordination sphere from the results of molecular dynamics calculations

A simple method for determination of the angular orientation of water molecules in the first coordination sphere from the radial distribution functions is proposed. A comparative analysis of the ability of the model potentials of pair interaction to take into account the effects of manybody interactions (MBI) was performed. The responses of the model pair potentials to the MBI effects in the first and second coordination spheres were found to be poorly correlated with each other. It was concluded that it is necessary to derive a new analytical type of potential functions of pair interaction. Published inIzvestiya Akademii Nauk. Seriya Khimicheskaya. No. 11, pp. 1842–1846. November. 2000.     

Investigation of copper-azamacrocyclic complexes by high-performance liquid chromatography

The use of copper radioisotopes in imaging and therapy has prompted an increased interest in chelators which form stable copper complexes, such as Cu(II)-azamacrocyclic complexes. The effects of charge, stability and the size of the macrocyclic backbone of the Cu(II)-azamacrocyclic complexes on biological behavior have been evaluated. Here we report a reversed-phase high-performance liquid chromatography (HPLC) method to separate several Cu(II)-azamacrocyclic complexes, including Cu(II) complexes of 1,4,8,11-tetraazacyclotetradecane-1,4,8,11-tetraacetic acid (TETA), 4,11-bis(carboxymethyl)-1,4,8,11-tetraazabicyclo[6.6.2]hexadecane (CB-TE2A) and 4,10-bis(carboxymethyl)-1,4,7,10-tetraazabicyclo[5.5.2]tetradecane (CB-DO2A). Absorbance at 280 nm was used to monitor the complexes as they eluted from the reversed-phase column. The effects of the concentration of the buffer, the pH of the buffered mobile phase and the concentration of the organic modifier, methanol, on the separation were investigated. Separation of these copper complexes by ion-pair HPLC with the use of a mass spectrometry-compatible ion-pair reagent, triethylammonium acetate, in the mobile phase at pH 6.3 is also presented. The reversed-phase chromatographic conditions utilized also allow the pK(a)s of Cu-TETA and the log(k'w) values of Cu-CB-TE2A, Cu-TETA and Cu-CB-DO2A to be estimated.     

Twist‐dependent stacking energy of base‐pair steps in B‐DNA geometry: A density functional theory approach

Stacking energy of all the 10 unique DNA base‐pair steps (bp step) are calculated using density functional theory within the ultrasoft pseudopotential plane wave method and local density approximation for the exchange‐correlation functional. We have studied the dependence of stacking energy on twist angle, an aspect found difficult to explain using classical theory. We have found that the twist angle for different bp steps at stacking energy minimum matches extremely well with the values of average twist obtained from B‐DNA crystal structure data. This indicates that the use of a proper quantum chemical method to calculate the π‐π electronic interactions may explain stacking energy without incorporating hydrophobic interaction through solvent or effect of backbone through pseudobond. From the twist angle‐dependent stacking energy profile, we have also generated the probability distributions of twist for all the bp steps and calculated the variance of the distribution. Our calculated variances show similar trend to that of the experimental data for which sufficient numbers of data are available. The TA, AT, and CG doublets show large variances among the 10 possible bp steps, indicating their maximum flexibility. This might be the case of unusual deformation observed at the TATA‐box while binding to TBP protein. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

顾客导向视觉下物流服务质量的集对分析

结合物流服务的特点,从顾客感知角度建立物流服务质量评价指标体系,利用熵值法确定各指标的权重,基于集对分析方法构建物流服务质量评价模型,并以湖州市某第三方物流企业为例验证该模型的实用性和可行性,实例表明集对分析方法的评价结果较为合理,且具有概念清晰、计算方法简洁、可操作性强的优点,对其他研究的评价具有一定的借鉴意义。     

机构公共约束辨识及自由度计算“拆闭副法”

本文论证了闭环机构公共约束m_i与开环机构末杆约束m′_i的差异,提出关系式:m_i=m′_i f′_i。澄清长期以来在机构自由度计算中关于公共约束的疑难。指出И·И·Артоболевский统一结构公式中的m_i,若定义为开环末杆约束m′_i,则在自由度计算中,运动副的级有确定的统一定义。阿氏公式与F·Freudenstein公式等效。作者建议取А·П·Мальищев型修正公式:W=6n-sum from k=1kp_k sum from i=1 m_i作为统一结构公式;并提出确定末杆约束的拆闭副法;指出应用刚体运动分解原理考察各运动副对末杆产生的独立运动时,必须考虑末杆的约束条件。文中列举若干计算例题,并与常用计算方法进行对比分析。