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.     

Atom-probe field ion microscopy

The atom probe field ion microscope (AP-FIM) is a combination of a field ion microscope and a time-of-flight mass spectrometer with a single ion detection sensivity. With the field ion microscope topology of a surface, surface reactions and surface modifications can be studied in atomic detail. By time-of-flight measurements surface layers and interface layers can be chemically analyzed atom by atom and atomic layer by atomic layer. Compositional variations according to surface or interface segregation, precipitations, or surface changes in corrosion or in electrochemical layer formation etc. can be studied quantitatively on a subnanometer scale. Some of our studies on related problems will be decribed briefly.     

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.     

A case study in conformation design: learning by doing

Efforts are described to design simple, fully flexible but conformationally preorganised omega-hydroxy-nonanoic acids that could serve as the conformation controlling unit in analogues of the potent protein-kinase C activator aplysiatoxin. Such analogues are macrodilactones incorporating the designed omega-hydroxy-nonanoic acid and 3,4-dihydroxy-pentanoic acid, which contains the pharmacophoric groups. The design process (replacement of CH(2) groups by an oxygen atom, annelation of a six-membered ring and placement of alkyl substituents) of the omega-hydroxy-nonanoic acids was monitored by force-field calculations. In the end of this process simple analogues of aplysiatoxin are proposed in which the proper disposition of the pharmacophoric groups is secured by a conformationally flexible but preorganised template structure as part of the macrodilactone ring.     

On the mathematical formulation and interpretation of LACO MO theory

The mathematical basis of LCAO MO theory is studied, both within the Hartree-Fock approximation and in more exact formulations. The basic LCAO expansion for molecular orbitals ¦> in terms of atomic orbitals ¦x> is conveniently written ¦> = ¦x> S ^–1 B where S is the overlap matrix for atomic orbitals and B is the matrix of atomic orbital-molecular orbital overlaps. It is suggested that matrices P and Q, defined by P=B B and Q=BnB where n is the matrix of molecular orbital occupation numbers, are appropriate to the interpretation of molecular calculations in terms of atomic orbital components, electronic populations and the degree of bonding. Implications for Hartree-Fock calculations are investigated.     

Evaluation of Multicenter Electronic Attraction, Electric Field and Electric Field Gradient Integrals with Screened and Nonscreened Coulomb Potentials over Integer and Noninteger n Slater Orbitals

By the use of complete orthonormal sets of -exponential-type orbitals, where ( = 1, 0, –1, –2,...) the multicenter electronic attraction (EA), electric field (EF) and electric field gradient (EFG) integrals of nonscreened and Yukawa-like screened Coulomb potentials are expressed through the two-center overlap integrals with the same screening constants and the auxiliary functions introduced in our previous paper (I.I. Guseinov, J. Phys. B, 3 (1970) 1399). The recurrence relations for auxiliary functions are useful for the calculation of multicenter EA, EF and EFG integrals for arbitrary integer and noninteger values of principal quantum numbers, screening constants, and location of slater-type orbitals. The convergence of the series is tested by calculating concrete cases.