Quantum entities

Widespread disagreement on the understanding of chemical matter can, to a large extent, be traced back to the confusion over the nature of the electron. The intuitive concept of elementary particles completely dominates theoretical thinking, although the ultimate quantum entity, the photon, is a particle in name only. The carrier of the electromagnetic field is defined unequivocally by Maxwell s field equations, of the form... 

The results of this thought experiment and the way it is described in the present approach deny validity (pertinence) to the common statement quantum entities can behave like particles or waves depending on how they are observed. 

Quantum mechanics is about quantum states and their (parametric) time evolution. They are related to material substrates in real space, no doubt, but as such (quantum states) they belong to Hilbert space. In this latter space, pictorial descriptions originated in our real-world perceptions do not make sense. There are no quantum entities that can behave like particles or waves see the comments made by R Knight in [20]. From the perspective displayed in Section 5.3, it is not difficult to see that when real-space and Hilbert space descriptions are not distinguished properly, whenever a particle description is used to examine quantum-mechanical outcomes, weirdness would pop up. It is the way one understands quantum states, that is, at stake. More to the point it is the classical particle/wave picture that is part of the problem. 

The quantum potential can now be identified as a surface effect that exists close to any interface, in this case the vacuum interface. The non-local effects associated with the quantum potential also acquire a physical basis in the form of the vacuum interface, now recognized as the agent responsible for mediating the holistic entanglement of the universe. The causal interpretation of Bohmian mechanics finds immediate support in the postulate of a vacuum interface. There is no difference between classical and quantum entities, apart from size. Logically therefore, the quantum limit depends on... 

This chapter has clearly shown molecular quantum similarity to be a worthy field of research with a large range of appHcations. It allows quantification of the similarity between any pair of atoms or molecules, and it can be used by chemists for all quantum entities for which a density probability function is available. Consequently, molecular similarity can be extended far beyond the traditional approaches that address mainly congeneric molecules, or molecules differing in substituent composition. 

If this view of the quantum world is accepted, quantum entities do not exist until they are observed, If the standard commonsense view of the macro world is accepted, things continue to exist regardless of whether they are being observed. One way of seeing the macro world is that existence or reality can be seen as a relationship between the observer, the conditions of observation and the observed. Such a relative view would appear to reflect the facts... 

Neutrons are quantum entities, so they exhibit both particle-like and wave-like properties. For INS spectroscopy, the particle-like properties are relevant since the neutron- sample interaction occurs on a femtosecond timescale and the interaction can be considered to be analogous to billiard-ball scattering. 

The temporal behavior of molecules, which are quantum mechanical entities, is best described by the quantum mechanical equation of motion, i.e., the time-dependent Schrdd-inger equation. However, because this equation is extremely difficult to solve for large systems, a simpler classical mechanical description is often used to approximate the motion executed by the molecule s heavy atoms. Thus, in most computational studies of biomolecules, it is the classical mechanics Newtonian equation of motion that is being solved rather than the quantum mechanical equation. 

Quantum mechanics explains how entities like electrons have both particle-like and wave-like characteristics. The SchrOdinger equation describes the wavefunction of a particle ... 

The original Hohenberg-Kohn theorem was directly applicable to complete systems [14], The first adaptation of the Hohenberg-Kohn theorem to a part of a system involved special conditions the subsystem considered was a part of a finite and bounded entity regarded as a hypothetical system [21], The boundedness condition, in fact, the presence of a boundary beyond which the hypothetical system did not extend, was a feature not fully compatible with quantum mechanics, where no such boundaries can exist for any system of electron density, such as a molecular electron density. As a consequence of the Heisenberg uncertainty relation, molecular electron densities cannot have boundaries, and in a rigorous sense, no finite volume, however large, can contain a complete molecule. 

From the preceding discussion, it is quite clear that p(r) is indeed a fundamental quantum mechanical entity of no less significance than the wave function and that p(r) generates numerous attractive and transparent models of chemical behavior. How does one calculate p(r) One way would of course be to calculate it from the normalized occupied orbital densities, viz.,... 

Similarity between quantum systems, such as atoms and molecules, plays a very important role throughout chemistry. Probably the best example is the ubiquitously known periodic system of the elements. In this system, elements are arranged both horizontally and vertically in such a way that in both directions, elements have a high similarity to their neighbors. Another closely related idea is that of transferability. In chemistry, one speaks of transferability of an entity when its properties remain similar between different situations. An example is the transferability of the properties of a functional group between one molecule and another. The main motto of using similarity in chemistry is the assumption that similar molecules have similar properties. 

The relationship of the wheel-rim-type structure of 62 to the metal can be demonstrated by a 30° rotation of the two centered Alg rings followed by a shift of the six rings towards each other (cf. Figure 2.3-13) [92], The other possibility of the formation of an Al14 polyhedron with point symmetry by displacement of the two naked central atoms in the direction of a polyhedral entity has been shown to be energetically unfavorable by quantum chemical calculations i.e., the observed metalloid structure (Figure 2.3-13) is favored over the anticipated polyhedral structure as described by Wade-Mingos [5, 96] (see Chapter 1.1.2). 

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