Force Constants and Bond Orders of Nitrogen Bonds

The force constants and the corresponding bond orders of nitrogen bonds have been calculated from the vibrational spectra (infrared and Raman spectra) of a great number of nitrogen compounds. Plotting the maximum bond order of stable nitrogen bonds against the sum of Pauling's electronegativities of the bonding partners (Σx) leads to one continuous curve for the N? X bonds where X represents elements of the first and the second short period of the periodic table. Furthermore, when the bonds formed between these elements are arranged in a coordinate system in such a way that the position of each bond is determined by the difference between the electronegativities of the bonding partners (Δx along the ordinate) and the sum of the electronegativities of the bonding partners (Σx along the abscissa), the bonding partners capable of forming multiple bonds all lie within a closed domain, where their position can be correlated with their polymerizability and other reactivities of the multiple bonds. Also discussed are the orders of bonds between nitrogen and some transition elements. In an appendix, the present methods used to calculate force constants and bond orders are surveyed.     

Comparison of the Hartree-Fock,Møller-Plesset,and Hartree-Fock-Slater method with respect to electrostatic properties of small molecules

Summary The results of various quantum chemical calculations, the Hartree-Fock (HF) method, the Møller-Plesset perturbation theory (MP2), and the Hartree-Fock-Slater (HFS) method are compared. Atomic charges, dipole moments, topological properties of the electron density distribution and polarizabilities, and first hyperpolarizabilities are calculated. Atomic charges obtained with the HFS method are found to be very close to those calculated with the MP2 method, from which we conclude that the HFS method describes to some extent electron correlation effects. Performing an MP2 calculation after an HF calculation improves the molecular dipole moments considerably, yielding values close to the experimental ones. HFS calculations are computationally less demanding than MP2 and yield comparable results for the electron density distributions, dipole moments and polarizabilities.     

On the theory of solvent effects

A simple electrostatic analysis is given of the virtual charge (solvaton) model to represent the environment effect on the electronic wave function of a solute immersed in a polarizable surrounding. New features of this model are found. The classical aspects are discussed and secondly the quantal implications are considered. A correct Hartree-Fock-like operator is derived which represents an electron in a molecular orbital subjected to the average effect of the other electrons and to the reaction field produced by the virtual charges on the atomic centers.A general formalism based on the preceding model is presented in appendix. The final equations have a form similar to Newton's equation to represent a solvated electron. Unlike some other theories in this field, there is no cut-off involved in the evaluation of the molecular integrals.     

氮杂冠醚研究Ⅶ、双仲胺型氮杂冠醚对过渡金属离子的选择性萃取作用

合成了五种新型双仲胺型氦杂冠醚，研究了它们对过渡金属离子进行液—液萃取，并用原子吸收法测定其浓度。实验结果表明：这类冠醚对Ａｇ￣＋、Ｐｄ￣（２＋）、和Ｐｔ￣（４＋）等贵金属离子有较强的选择配位性能，对选择性分离这些金属离子有重要的意义。     

The Hellmann-Feynman theorem applied to long-range forces

The relations between the Hellmann-Feynman forces in laboratory fixed (L-) and relative (R-) coordinate systems are clarified. In the usualL-coordinate system, the force is interpreted as force on nucleus, while in theR-coordinate system, it means force on whole particles consisting of the electrons and nuclei of each interacting subsystem. From a perturbation theoretical viewpoint, the concept of the force on whole particles correctly corresponds to the perturbation energy and is superior to the force on the nucleus.     

An experiment to test an explanation of a possible violation of quantum theory

An experiment to test a possible explanation of the Schmidt backwards causation results is suggested. The experiment might distinguish between many- and one- world interpretations of quantum theory.     

Moment closure hierarchies for kinetic theories

This paper presents a systematicnonperturbative derivation of a hierarchy of closed systems of moment equations corresponding to any classical kinetic theory. The first member of the hierarchy is the Euler system, which is based on Maxwellian velocity distributions, while the second member is based on nonisotropic Gaussian velocity distributions. The closure proceeds in two steps. The first ensures that every member of the hierarchy is hyperbolic, has an entropy, and formally recovers the Euler limit. The second involves modifying the collisional terms so that members of the hierarchy beyound the second also recover the correct Navier-Stokes behavior. This is achieved through the introduction of a generalization of the BGK collision operator. The simplest such system in three spatial dimensions is a 14-moment closure, which also recovers the behavior of the Grad 13-moment system when the velocity distributions lie near local Maxwellians. The closure procedure can be applied to a general class of kinetic theories.     

Essential spectrum and -solutions of one-dimensional Schrödinger operators

In 1949, Hartman and Wintner showed that if the eigenvalue equations of a one-dimensional Schrödinger operator possess square integrable solutions, then the essential spectrum is nowhere dense. Furthermore, they conjectured that this statement could be improved and that under this condition the essential spectrum might always be void. This is shown to be false. It is proved that, on the contrary, every closed, nowhere dense set does occur as the essential spectrum of Schrödinger operators which satisfy the condition of existence of -solutions. The proof of this theorem is based on inverse spectral theory.

     

Salting coefficients for gases in seawater from scaled-particle theory

Experimental values of the salting coefficients for He, Ne, Ar, O₂, and N₂ in seawater are compared with values calculated from scaled-particle theory. The agreement is reasonably good; the average difference between calculated and observed values at 25°C is 0.007. Scaled-particle theory predicts correctly thatk _s should decrease as the temperature increases and that this effect should be most pronounced at low temperatures. However, the predicted magnitude ofdK _s/dt is only about half of that observed.     

Swelling of physically cross-linked copolymers in water vapour

A general thermodynamic equation for the swelling of a cross-linked polymer system in the vapour of a swelling agent has been derived under isothermal and isobaric conditions. The equation is used to describe the equilibrium uptake of water by elastomers Arnitel^® (DSM), which are hard-soft-segment block copolymers in which the hard segments poly(butylene terephthalate) crystallise and are responsible for a physical cross-linking. The gravimetrically determined degrees of swelling of different elastomers in water vapour of various partial pressures are analysed and discussed by the application of an extended semi-empirical swelling equation of Flory-Huggins-Staverman-van Santen.