Electronic theory criticisms

Whether the number of electrons per atom is integral or nonintegral, the concept of a critical interatomic separation for collective-electron versus localized-electron theories seems to have physical significance. Further, two tentative conclusions are suggested ... 

The justification of jr-electron theories has been repeatedly questioned during recent years indeed, it has become almost fashionable to emphasize the shortcomings of the cr—it separation and the non-validity of the theories based upon it. These are, in fact, approximations and cannot be expected to lead to unconditionally reliable conclusions. However, the numerical results that have provoked the criticisms in question are not a necessary consequence of the a—it separation and the related approximations. Therefore, we shall begin by restating and clarifying the basic concepts on which the whole question of the a—it separation rests. We shall consider the conditions under which the electrons of a molecule can be classified into a and it electrons and indicate what should be understood be a—7i separation and what are the limitations of this approximation. We shall show that the most important part of th e a—n interaction is usually taken into accound within the a—n separation scheme and, finally, discuss whether the a—it interaction has a significant effect on the theoretical predictions made for the physical properties of unsaturated molecules (ionization potentials, electronic spectra, charge densities and dipole moments etc.). 

The Interstitial-Electron Theory has been applied to the structure of metals, alloys and interstitial compounds, to their magnetic and superconducting properties, as well as to a range of surface phenomena. This work has seemingly not come to the attention of the wider scientific community perhaps because it was published only in Japanese journals. It merits wider recognition and a critical evaluation. 

Mercury electrodeposition is a model system for experimental studies of electrochemical phase formation. On the one hand, the product obtained is a liquid drop, corresponding very well with the liquid drop model of classical nucleation theory. Besides, electron transfer is fast [61] and therefore the growth of nuclei is controlled by mass transport to the electrode surface [44]. On the other hand, the properties of the mercuryjaqueous solution interface have been the object of study for over a century and hence are fairly well understood. The high overpotential for proton reduction onto both mercury and vitreous carbon favor the study of the process over a wide range of overpotentials. In spite of the complications introduced by the equilibrium between the Hg +, Hg2 " ", and Hg species, this system offers an excellent opportunity to verily the fundamental postulates of the electrochemical nucleation theory. In fact, the dependence of the nucleation rate on the oxidation state of the electrodepositing species is fiiUy consistent with theory critical nuclei appear with similar sizes and onto similar number densities of active sites... 

Some criticisms of the importance of the electronic theory influencing the intrinsic adhesion have already been raised and other comments on its general... 

Acoustical Measurement Analog-Signal Electronic Circuits Circuit Theory Critical Data IN Physics and Chemistry Electromagnetic Compatibility Signal Processing, Digital Superconductivity... 

The simple metals, whose conduction bands correspond to s and p shells in isolated atoms, include the alkali metals, the divalent metals Be, Mg, Zn, Cd, and Hg, the trivalent metals Al, Ga, In, and Tl, and the tetravalent metals (white) Sn and Pb. Almost all of their properties which are related to electronic band structure are explicable by nearly-free-electron theory using pseudopotentials (Sections 3.5 and 3.6). The extent to which they conform in detail to this generalization varies from one case to another. For all the metals cited simple pseudopotential theory is fairly successful in predicting or fitting Fermi surface properties. This will be evident from a consideration of the comparisons of theoretical and fitted pseudopotential parameters already shown in Figure 12. However, the use of perturbation theory is not very critical in this context [i.e., the contribution of screening to the values of v q) which are of interest is not large]. In other contexts the validity of perturbation theory is more critical, and indeed the use of pseudopotential-perturbation theory is then not always so successful. An example is the calculation of phonon dispersion relations by such methods, which has enjoyed remarkable success for Na, Mg, and j(i2i,i22) jjjjQ difficulties for the heavier metals and those... 

R F W Bader s theory of atoms in molecules [Bader 1985] provides an alternative way to partition the electrons between the atoms in a molecule. Bader s theory has been applied to many different problems, but for the purposes of our present discussion we will concentrate on its use in partitioning electron density. The Bader approach is based upon the concept of a gradient vector path, which is a cuiwe around the molecule such that it is always perpendicular to the electron density contours. A set of gradient paths is drawn in Figure 2.14 for formamide. As can be seen, some of the gradient paths terminate at the atomic nuclei. Other gradient paths are attracted to points (called critical points) that are... 

The theory and appHcation of SF BDV and COV have been studied in both uniform and nonuniform electric fields (37). The ionization potentials of SFg and electron attachment coefficients are the basis for one set of correlation equations. A critical field exists at 89 kV/ (cmkPa) above which coronas can appear. Relative field uniformity is characterized in terms of electrode radii of curvature. Peak voltages up to 100 kV can be sustained. A second BDV analysis (38) also uses electrode radii of curvature in rod-plane data at 60 Hz, and can be used to correlate results up to 150 kV. With d-c voltages (39), a similarity rule can be used to treat BDV in fields up to 500 kV/cm at pressures of 101—709 kPa (1—7 atm). It relates field strength, SF pressure, and electrode radii to coaxial electrodes having 2.5-cm gaps. At elevated pressures and large electrode areas, a faH-off from this rule appears. The BDV properties ofHquid SF are described in thehterature (40—41). 

In Chapter 2 you were introduced to atoms and in Chapter 6 they were described in more detail. You were told that the atom contains charged particles, that it has a nucleus made up of neutrons and protons, and that the nucleus is surrounded by electrons. The atom is incredibly small but the nucleus is even smaller. But also you were told that every theory (including the atomic theory) should be thought about and criticized—the evidence upon which it is based should be examined and understood. It is one thing to ask Do we believe in atoms and quite another to ask Why do we believe in atoms In this chapter we shall try to answer this last, harder question. 

Thus the orbitals and r electrons lie in the outermost part of the valence shell of ethane. They should play a critical role in determining the chemical properties of the molecule. Some theories have ascribed the barrier to internal rotation to these orbitals. It should be noted that the existence of r electrons in ethane is not a novelty, and was first pointed out by Mullikcn in 1935. 

For many years, the lectures of Yngve Ohrn on the theory of chemical bonding have been models of clarity and incisiveness to graduate students at the University of Florida and at various topical schools. Their success in introducing the assumptions and conclusions of molecular orbital theory, group theory, electron correlation methods and related subjects has engendered a critical, but liberal attitude toward competing doctrines. 

However, the direct dynamics calculations are computationally expensive, and cannot employ particularly high levels of electron correlation or large basis sets. If certain regions of the potential cannot be treated to within the required accuracy using a computationally affordable level of theory, the results may have unacceptably large errors. Nevertheless, direct dynamics calculations have played and will play a critical role in the discovery and analysis of competing pathways in chemical reactions. 

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