A mathematical discussion of Pons Viver's implementation of Löwdin's spin projection operator

Recently, the molecular electronic structure theories for efficiently treating static (or strong) correlation in a black-box manner have attracted much attention. In these theories, a spin projection operator is used to recover the spin symmetry of a broken-symmetry Slater determinant. Very recently, Pons Viver proposed the practical and exact implementation of Löwdin's spin projection operator (Int. J. Quantum Chem. 2019, 119, e25770). In the present study, we attempt to supply mathematical proofs to Pons Viver's proposals and show a condition for establishing Pons Viver's implementation. Moreover, we explicitly derive the (spin projected) extended Hartree-Fock (EHF) equations on the basis of the model of common orbitals (ie, closed-shell orbitals used in the restricted open-shell Hartree-Fock (ROHF) method), which was combined by Pons Viver with the EHF method.     

Enhancement of Ion Pairing of Sr(II) and Ba(II) Salts by a Tritopic Ion-Pair Receptor in Solution

Tritopic ion-pair receptors can bind bivalent salts in solution; yet, these salts have a tendency to form ion-pairs even in the absence of receptors. The extent to which such receptors can enhance ion pairing has however remained elusive. Here, we study ion pairing of M²⁺ (Ba²⁺, Sr²⁺) and X⁻ (I⁻, ClO₄⁻) in acetonitrile with and without a dichlorooxacalix[2]arene[2]triazine-related receptor containing a pentaethylene-glycol moiety. We find marked ion association already in receptor-free solutions. When present, most of the MX⁺ ion-pairs are bound to the receptor and the overall degree of ion association is enhanced due to coordinative, hydrogen-bonding, and anion-π interactions. The receptor shows higher selectivity for iodides but also stabilizes perchlorates, despite the latter are often considered as weakly coordinating anions. Our results show that ion-pair binding is strongly correlated to ion pairing in these solutions, thereby highlighting the importance of taking ion association in organic solvents into account.     

自旋涨落与非常规超导配对

铜氧化物高温超导、铁基高温超导、重费米子超导和κ-型层状有机超导等超导体的超导态都与磁性有序态相邻,且超导能隙在动量空间一般存在变号.因此,这些超导体的超导机理被认为有别于常规BCS超导中的电子交换声子导致的各向同性s-波配对.在这些非常规超导中,自旋涨落被认为是导致电子形成库珀对的主要起源之一.本文主要以铜基和铁基高...     

基于交通量均分的城市道路网络定向研究

为减少城市交通拥挤,从交通量均分的角度出发,提出了综合反映道路网络局部和整体性质的k最优定向,并且利用奇度点配对的思想为定向问题设计了启发式算法。     

Absorption and fluorescence emission spectroscopic characters of naphtho‐homologated yy‐DNA bases and effect of methanol solution and base pairing

A comprehensive theoretical study of electronic transitions of naphtho‐homologated base analogs, namely, yy‐T , yy‐C , yy‐A , and yy‐G , was performed. The nature of the low‐lying excited states is discussed, and the results are compared with those from experiment and also with those of y‐bases. Geometrical characteristics of the lowest excited singlet ππ* and nπ* states were explored using the CIS method, and the effects of methanol solution and paring with their complementary natural bases on the relevant absorption and emission spectra of these modified bases were examined. The calculated excitation and emission energies agree well with the measured data, where experimental results are available. In methanol solution, the fluorescence from yy‐A and yy‐G would be expected to occur around 539 and 562 nm, respectively, suggesting that yy‐A is a green‐colored fluorophore, whereas yy‐G is a yellow‐colored fluorophore. The methanol solution was found to red‐shift both the absorption and emission maxima of yy‐A , yy‐T , and yy‐C , but blue‐shift those for yy‐G . Generally, though base pairing has no significant effects on the absorption and fluorescence maxima of yy‐A , yy‐C , and yy‐T , it blue‐shifts those for yy‐G . © 2009 Wiley Periodicals, Inc. J Comput Chem 2010     

Independence of Yang-Mills Equations with Respect to the Invariant Pairing in the Lie Algebra

It is proved that the Euler–Lagrange equations of a Yang-Mills type Lagragian is independent with respect to the chosen pairing in the Lie algebra. Moreover, the Hamilton-Cartan equations of these Lagrangians are obtained and proved to be also independent with respect to the pairing. PACS Numbers 2003: 02.20.Qs, 02.20.Sv, 02.20.Tw, 02.40.Ma, 02.40.Vh, 11.10.Ef, 11.15.Kc Mathematics Subject Classification 2000: Primary 70S15, Secondary 58A20, 58E15, 58E30, 70S05, 70S10, 81T13     

Proton Orbital [541]1/2 and Backbending in 178W

The microscopic mechanism of nine experimentally observed bands in ^178W is investigated using the particle-number conserving method of the cranked shell model with monopole and quadrupole paring interactions. The experimental results, including the moments of inertia and angular momentum alignments of nine bands in ^178W, are reproduced well by the particle-number conserving calculations, in which no free parameter is involved. Calculations demonstrate that occurrence of sharp backbending comes mainly from the contribution of high-j intruder orbitals vi13/2 or πh11/2 and their interference effect with orbitals near the Fermi surface. Theω variation of the occupation probability of each cranked orbital and the contribution to moment of inertia from each cranked orbital are analyzed.     

Solvent and temperature effects on the conformational equilibria of a dihydrobenzo[h]quinolinium fluoroborate

Spectra of the N‐phenyl‐5,6‐dihydro‐2,4‐diphenylbenzo[h]quinolinium tetrafluoroborate (1) and of the N‐phenyl‐5,6,8,9‐tetrahydro‐7‐phenyldibenzo[c,h]acridinium tetrafluoroborate (2) were recorded in various solvents and temperatures. The analysis of the ¹H‐NMR spectra of the tetrafluoroborate salt 1, recorded in acetone, acetonitrile, 1,1,2,2‐tetrachloroethane and chloroform, revealed the existence of an equilibrium between two conformers in solution. Tight ion‐pairing in chloroform led to a smaller barrier for interconversion between the two conformers. In more polar solvents, where the dihydrobenzoquinolinium exists as a free cation, theoretical calculations predicted larger barriers. The spectra of 1 in 1,1,2,2‐tetrachloroethane also varied with temperature, resembling at higher temperatures the spectrum in CDCl₃ and at 300K spectra in more polar media. Spectra of 2 did not vary with the solvent or the temperature, in an indication of a much higher barrier to conformational interconversion, because of a greater steric hindrance between the N‐phenyl substituent and the dihydrobenzo rings. Copyright © 2009 John Wiley & Sons, Ltd.     

Defocus and binocular vision based stereo particle pairing method for 3D particle tracking velocimetry

We propose a new method, based on the depth-from-defocus technique and binocular vision, for solving the stereo particle pairing problem in 3D particle tracking velocimetry (PTV). Firstly, the apparent particle depth is measured with a single camera, using the depth-from-defocus technique. Secondly, a strict mathematical model of the particle-to-particle correspondence relationship between the left and right images, taking into account the refractions at the interfaces in the optical path, is presented, with the assumption that the apparent particle depth is measured. Thirdly, based on the apparent particle depth and particle-to-particle correspondence relationship, the epipoplar line is truncated into a short line segment by cutting off, where the apparent particle depth extends beyond its estimated range. For the first time, the range of the blur circle radius is employed as an additional stereo particle pairing constraint. Finally, the optimal pairing particle is selected by applying the epipolar line segment and blur circle radius constraints. The experimental results show that the rate of correct pairing is significantly improved compared with the epipolar line nearest neighbor analysis, especially when the particle density is increasing.