The matrix theory of electron spin multiplets for atoms and molecules

In this article a matrix method for the construction of spin multiplets (spinconfigurations) is suggested in order to solve the multielectron problem for atoms and mulecules by means of configuration interaction.A simple graphical way is given to enumerate configurations and to break their set into subsets of configurations related to the given projection of the total spin of a system S _z . It is found that all matrices in the theory of spin multiplets are convex and in cases of two, three, and four electrons are broken into blocks of an order no higher than 3.The model of the solution of the multielectron Schrödinger equation, in which the total spin of core electrons is zero, is considered. In this model the construction of linear combinations of configurations is reduced to the construction of those for but valence electrons.     

3,4-聚异戊二烯的磺化反应及其离聚体的结构研究

本工作合成了磺化的3,4-聚异戊二烯及其离子聚合体,IR和NMR谱图证明对3,4-聚异戊二烯的磺化反应是成功的,并且磺酸基团主要与3,4-链节的侧基双键发生反应。WAXD对磺化3,4-聚异戊二烯及其离聚体的研究表明,磺化度的增加使离聚体的结晶能力降低,SAXS结果表明,在离子含量为3.29mol％的离聚体中,未观察到离子簇聚集,只观察到多重离子对的散射。     

Anomalous values of 〈Ŝ2〉 before and after annihilation of the first spin contaminant in UHF wave function

We present a number of molecular systems for which the average values 〈?²〉 before and after annihilation of the first spin contaminant in the wave function of the unrestricted Hartree-Fock method are anomalously large (they substantially exceed the expected value S (S + 1)). An example of such systems is N@C₂₀, for the doublet state of which the 〈?²〉 values are equal to 4.2595 before and 13.1390 after annihilation, respectively (calculated by UHF/6-31G* method). We show that four, at the least, spin multiplets (S′ = S, S + 1, S + 2, S + 3) contribute comparatively to the wave function of such systems. The relations are derived allowing one to estimate the contributions of the highest multiplets basing on the average values of 〈?²〉 before and after annihilation of the first spin contaminant.     

A marriage made in torsional space: using GALAHAD models to drive pharmacophore multiplet searches

Pharmacophore multiplets are useful tools for 3D database searching, with the queries used ordinarily being derived from ensembles of random conformations of active ligands. It seems reasonable to expect that their usefulness can be augmented by instead using queries derived from single ligand conformations obtained from aligned ligands. Comparisons of pharmacophore multiplet searching using random conformations with multiplet searching using single conformations derived from GALAHAD (a genetic algorithm with linear assignment for hypermolecular alignment of datasets) models do indeed show that, while query hypotheses based on random conformations are quite effective, hypotheses based on aligned conformations do a better job of discriminating between active and inactive compounds. In particular, the hypothesis created from a neuraminidase inhibitor model was more similar to half of 18 known actives than all but 0.2% of the compounds in a structurally diverse subset of the World Drug Index. Similarly, a model developed from five angiotensin II antagonists yielded hypotheses that placed 65 known antagonists within the top 0.1–1% of decoy databases. The differences in discriminating power ranged from 2 to 20-fold, depending on the protein target and the type of pharmacophore multiplet used.     

Interlocked multiplets in anisotropically scattering medium with exponential Planck function

The equation of transfer for interlocked multiplets in anisotropically scattering atmosphere with planetary phase function has been considered. The Planck function is considered as exponential function of optical depth. The diffusely reflected intensity and emergent intensity in nth approximation has been obtained. Attempt has been made to get exact diffusely reflected intensity and emergent intensity.     

Measurement of long‐range proton–carbon coupling constants from pure in‐phase 1D multiplets

The SELective INverse detection of carbon–proton CORrelation pulse sequence that yields a 1D spectrum of a proton directly bonded to a selected carbon resonance has been converted into a proton and carbon double‐selective variant that provides a ¹H spectrum of a selected proton that is long‐range coupled to a specific carbon resonance. The resulting 1D proton multiplet exhibits a pure absorptive in‐phase lineshape for precise measurement of specific long‐range proton–carbon coupling constants in small organic molecules at natural abundance. Copyright © 2011 John Wiley & Sons, Ltd.     

Kinetic energy analysis of atomic multiplets

Summary A kinetic energy analysis of total energy differences in atomic multiplets arising fromf ^m (m=2–12) electronic configurations is performed within the nonrelativistic restricted Hartree-Fock framework. For these 1290 multiplets of 22 lanthanoid (Ce to Er) and actinoid (Th to Fm) atoms, a very good linear correlation between the total energy difference and the kinetic energy difference of the outermostf-electrons is found. The present results, together with our previous ones for the multiplets arising froms ^mpⁿ (m=1,2;n=2–4) ands ^mdⁿ (m=0–2;n=2–8) electronic configurations, demonstrate that the kinetic energy difference of electrons in open subshells is an excellent predictor of total energy differences among atomic multiplet states.     

On the possibilities of high-resolution continuum source graphite furnace atomic absorption spectrometry for the simultaneous or sequential monitoring of multiple atomic lines

This paper explores the potential of commercially available high-resolution continuum source graphite furnace atomic absorption spectrometry instrumentation for the simultaneous or sequential monitoring of various atomic lines, in an attempt to highlight the analytical advantages that can be derived from this strategy. In particular, it is demonstrated how i) the monitoring of multiplets may allow for the simple expansion of the linear range, as shown for the measurement of Ni using the triplet located in the vicinity of 234.6 nm; ii) the use of a suitable internal standard may permit improving the precision and help in correcting for matrix-effects, as proved for the monitoring of Ni in different biological samples; iii) direct and multi-element analysis of solid samples may be feasible on some occasions, either by monitoring various atomic lines that are sufficiently close (truly simultaneous monitoring, as demonstrated in the determination of Co, Fe and Ni in NIST 1566a Oyster tissue) or, alternatively, by opting for a selective and sequential atomization of the elements of interest during every single replicate. Determination of Cd and Ni in BCR 679 White cabbage is attempted using both approaches, which permits confirming that both methods can offer very similar and satisfactory results. However, it is important to stress that the second approach provides more flexibility, since analysis is no longer limited to those elements that show very close atomic lines (closer than 0.3 nm in the ultraviolet region) with a sensitivity ratio similar to the concentration ratio of the analytes in the samples investigated.     

Runge-Lenz vector, accidental SU(2) symmetry, and unusual multiplets for motion on a cone

We consider a particle moving on a cone and bound to its tip by 1/r or harmonic oscillator potentials. When the deficit angle of the cone divided by 2π is a rational number, all bound classical orbits are closed. Correspondingly, the quantum system has accidental degeneracies in the discrete energy spectrum. An accidental SU(2) symmetry is generated by the rotations around the tip of the cone as well as by a Runge-Lenz vector. Remarkably, some of the corresponding multiplets have fractional “spin” and unusual degeneracies.     

Short and Long SU(2, 2/4) Multiplets in the AdS/CFT Correspondence

We analyze short and long multiplets which appear in the OPE expansion of chiral primary operators in N=4 Super Yang–Mills theory. Among them, higher spin long and new short multiplets appear having the interpretation in the AdS/CFT correspondence of string states and supergravity multiparticle states, respectively. We also analyze the decomposition of long multiplets under N=1 supersymmetry as a possible tool exploring other supersymmetric deformations of IIB string on AdS₅×S₅.