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11.
Eugene Strahov 《Advances in Mathematics》2007,212(1):109-142
Normalized irreducible characters of the symmetric group S(n) can be understood as zonal spherical functions of the Gelfand pair (S(n)×S(n),diagS(n)). They form an orthogonal basis in the space of the functions on the group S(n) invariant with respect to conjugations by S(n). In this paper we consider a different Gelfand pair connected with the symmetric group, that is an “unbalanced” Gelfand pair (S(n)×S(n−1),diagS(n−1)). Zonal spherical functions of this Gelfand pair form an orthogonal basis in a larger space of functions on S(n), namely in the space of functions invariant with respect to conjugations by S(n−1). We refer to these zonal spherical functions as normalized generalized characters of S(n). The main discovery of the present paper is that these generalized characters can be computed on the same level as the irreducible characters of the symmetric group. The paper gives a Murnaghan-Nakayama type rule, a Frobenius type formula, and an analogue of the determinantal formula for the generalized characters of S(n). 相似文献
12.
13.
Eric Cancès Renaud Keriven François Lodier Andreas Savin 《Theoretical chemistry accounts》2004,111(2-6):373-380
Efficient formulas for computing the probabilities of finding exactly electrons in an arbitrarily chosen volume 3 for Hartree–Fock wavefunctions are presented. These formulas allow the use of shape optimization techniques, such as level set methods, for optimizing with respect to various criteria involving such probabilities. The criterion defined as the difference between the Hartree–Fock and the independent-particle model probabilities of finding electrons in stresses the quantum effects due to the Pauli principle. We have implemented a 2D level set method for optimizing this criterion in order to study spatial separation of electron pairs in linear molecules. The method is described and the illustrative example of the BH molecule is reported.Contribution to the Jacopo Tomasi Honorary Issue 相似文献
14.
W. Kunz J. Barthel L. Klein T. Cartailler P. Turq B. Reindl 《Journal of solution chemistry》1991,20(9):875-891
A variety of methods has been used for the study of lithium bromide solutions in acetonitrile yielding by their combination reliable information on different levels of approximation. Osmotic coefficients based on precise vapor pressure measurements are reproduced by CM (chemical model) and HNC (hypernetted chain) calculations and by BD (brownian dynamics) simulations. The results of neutron scattering experiments are treated with the help of HNC and BD methods. Hartree-Fock calculations on isolated LiBr pairs and solvated lithium ions yield reliable particle distances and reveal the geometry of the lithium solvation sphere. 相似文献
15.
Studies of the vibrational spectra of matrix-isolated M+NO
3
–
ion pairs have been extended to glassy aprotic solvents. The deuterated form of the solvents DMSO, THF, and ACN have windows through the 7- nitrate ionv
3(e) mode infrared region, so it was possible to clearly observe the splitting of the degeneracy of this mode,v
3, produced by the contacting, but solvated, alkali metal cation. Primary attention has been directed to the extent to which this splitting is reduced relative to the argon matrix values. This reduction, which reflects electron-density transfer from the solvating molecules to the ion pairs, is comparable to that observed for H2O and NH3 matrices as the splitting is reduced to 20–35% of the argon-matrix values. The extent of reduction ofv
3 for the different solvents has been related to Gutmann's donicity number scale with the correlation holding well for solvent molecules of comparable size, DMSO, THF and DMF, but breaking down for the smaller linear ACN, apparently because of more molecules in the cation solvation sphere. The matrix data have also been used, through comparison with spectra for saturated liquid solutions of Li+NO
3
–
, to show that the contact ion pair is the dominant species in liquid THF and ACN, whereas the ions are largely solvent separated in DMSO. 相似文献
16.
17.
Johannes Smid 《Journal of polymer science. Part A, Polymer chemistry》2004,42(15):3655-3667
The discovery and implications of the existence of two kinds of ion pairs in solutions of carbanion salts is described. Also discussed are the factors controlling tight–loose ion pair equilibrium: the nature of the carbanion and its counterion, temperature, pressure, solvent, and cation‐complexing additives. A few examples are presented of the effect of these ionic species on the mechanisms of anionic polymerization and proton transfer. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 3655–3667, 2004 相似文献
18.
Ion Association and Hydration in Aqueous Solutions of Nickel(II) and Cobalt(II) Sulfate 总被引:1,自引:0,他引:1
Ting?Chen Glenn?HefterEmail author Richard?Buchner 《Journal of solution chemistry》2005,34(9):1045-1066
Aqueous solutions of nickel(II) and cobalt(II) sulfate have been investigated at 25 ∘C by dielectric relaxation spectroscopy (DRS) over a wide range of frequencies (0.2 ≤ ν (GHz) ≤ 89) and salt concentrations
(0.025 ≤ c(mol-L−1) ≤ 1.4). The spectra indicate, as for MgSO4(aq) studied previously, the simultaneous presence of double solvent-separated, solvent-shared and contact ion pairs in both
NiSO4(aq) and CoSO4(aq). The stepwise formation constants for each ion-pair type and the overall association constant, obtained from the data
are in good agreement with ultrasonic relaxation and other estimates. The DR spectra at higher concentrations (c ≥ 0.5 mol-L−1) suggest the existence of a nonlinear triple ion M2SO42+(aq). Consistent with the very strong hydration of the salts, which have ‘effective’ hydration numbers approaching 27 at infinite
dilution, there are no significant differences in any of the relaxation or thermodynamic parameters for NiSO4(aq) and CoSO4(aq), except that the triple ion appears to be somewhat more stable for the latter. 相似文献
19.
G. Papanastasiou A. Papoutsis M. Tsirtou I. Ziogas 《Journal of solution chemistry》1996,25(2):203-217
The kinetics of the reaction between sodium ethoxide and methyl iodide has been studied at 25°C in various cyclohexane-ethanol solvent mixtures with a cyclohexane content of 10 to 50% per volume. The determination of the rate constants att=0 were carried out by a new iterative method proposed in this investigation. The obtained results show that the reaction rate decreases with the increasing cyclohexane content. This behavior can be attributed to various solute-solvent interactions of electrostatic nature. On the other hand, the variation of ion and ion pairs rate constants with solvent composition permits the various solvation effects to be taken into account. 相似文献
20.
Anthony J. D'Aristotile 《Journal of Theoretical Probability》1995,8(2):321-346