Compressed Atoms

This result becomes important as the wave function of the valence electron of compressed atoms. 

Ph. Marteau. Far infrared induced absorption in highly compressed atomic and molecular systems. In G. Birnbaum, ed., Phenomena Induced by Intermodular Interactions, pp. 415-436, Plenum Press, New York, 1985. 

The compressibility of tellurium at 25° C. between 100 and 500 megabars12 is 5-00 x 10-6 per megabar, a value which falls on the smooth compressibility - atomic volume curve for the elements.13... 

Actual calculations of compressed-atom densities, performed with suitably modified SCF software, show that the increased pressure raises all electronic energy levels, at different rates that depend on the shell structure. The effect is more pronounced on those levels of highest effective quantum number l and it is not uncommon for levels of different l to cross during compression. The interpretation of photoelectron spectra in terms of free-atom electron configurations may therefore be misleading in the study of surface chemistry and catalytic effects, for which they are routinely used. 

The only remaining problem is calculation of the electron-density function, which cannot be done classically. However, for molecules in condensed phases the influence of the environment introduces another simplification. It has been shown that valence-state wave functions of compressed atoms are simpler, than hydrogenic free-atom functions. Core levels are largely unaffected and a nodeless valence-state wave function, which allows chemical distortion of electron density, can be defined. We return to this topic at a later stage. 

An example of an electron in a phase-locked cavity has been encountered in the study of compressed atoms [76, 24]. Isotropic compression of an atom, simulated by imposing a finite boundary condition on the electronic wave function, i.e. linv xpe = 0, r0 < oo, raises electronic energy levels, until an electron is decoupled from the core at a characteristic atomic ionization radius. This electron then exists in a field-free cavity with a spherical Bessel wave function. In the ground state... 

The key to the understanding of molecular geometry is in the definition of an holistic molecule described by one of the factors in a product function, equation 5.7. This factor represents the molecular wave function for the molecule of interest and defines non-local entanglement within a limited region of space that varies as a function of the environment. The relative confinement of the molecule means that the boundary conditions on the molecular wave function are variable, in the same sense as for the compressed atom. Different solutions are therefore found in different settings and particularly in different states of aggregation. Any structure revealed by the wave functions must likewise be a function of the surroundings. 

Michels et al. and de Groot and ten Seldam have attempted to represent the effect of short-range electron repulsion by a compressed-atom model. Although thdr model leads to negative corrections to iP at very high pressures, it is not clear how these corrections relate to Bg since the model considers single atoms compressed uniformly. Several authors have developed expressions for the polarizability of a molecule in a condensed-phase environment, which indicate it to be less than ao> These models, however, involve many-body interactions, and, as in the previous case, it is not clear how they can be related to Bg. 

P.O. Froman, S. Yngve, N. Froman, The energy levels and the corresponding normalized wave functions for a model of a compressed atom, J. Math. Phys. 28 (8) (1987) 1813-1826. 

Atomic orbitals have a disadvantage in that they are diffuse. In solids, large molecules or clusters that are the size of the orbitals are compressed due to the interaction with the neighbors. A measure for the distance between neighbors is given by the so-called covalent radius, r0, and is empirically determined for all atoms. Therefore, it is wise to use orbitals that somehow incorporate this information. To enhance this effect, an additional harmonic potential is added to the atomic Kohn-Sham equations that leads to compressed atomic orbitals, or optimized atomic orbitals (O-LCAO) ... 

They state that the purpose of their work (carried out in Richards laboratory) was to test Richards theory of compressible atoms. They rightly point out that the above value is some 500 cals, less than is required by my Heat Theorem 15,014, according to p. 115). 

Band theory provides a picture of electron distribution in crystalline solids. The theory is based on nearly-free-electron models, which distinguish between conductors, insulators and semi-conductors. These models have much in common with the description of electrons confined in compressed atoms. The distinction between different types of condensed matter could, in principle, therefore also be related to quantum potential. This conjecture has never been followed up by theoretical analysis, and further discussion, which follows, is purely speculative. 

J.C.A. Boeyens, Ionization radii of compressed atoms, J. Chem. Soc. Faraday Trans., 1994 (90) 3377-3381. 

Gottingen (where he was offered a professorship in 1901). He became full professor at Harvard in 1901, being appointed in 1912 to the Erving professorship on the retirement of Prof. Jackson. Besides atomic weights, Richards worked on the compressibility of solid elements (which led him to the idea of compressible atoms ) and on the thermodynamics of galvanic cells (see p. 620). All his work is characterised by great accuracy and originality. ... 

Velocity of a shear wave propagated perpendicular to the c-axis with polarization parallel to the c-axis = Adiabatic compressibility Isothermal compressibility Atomic volume... 

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