Quantum, definition

Bader R. F. W., The zero-flux surface and the topological and quantum definitions of an atom in a molecule, Theor. Chem. Acc. 105 (2001) pp. 276-283. 

The coincidence of the topological and quantum definitions of an atom means that the topological atom is an open quantum subsystem, free to exchange charge and momentum with its environment across boundaries which are defined in real space and which, in general, change with time. It should be emphasized that the zero-flux surface condition is universal— it applies equally to an isolated atom or to an atom bound in a molecule. The approach of two initially free atoms causes a portion of their surfaces to be shared in the creation of an interatomic surface. Atomic surfaces undergo continuous deformations as atoms move relative to one another. They are, however, not destroyed as atoms separate. 

One might imagine that, with the advent of quantum mechanics and its application to chemistry, Dalton s atomic theory would have been reinforced. This has not happened. Quantum mechanics has been shown to account for the properties of isolated atoms and for the total properties of a molecular system. The increased understanding that would result from the discovery of a firm theoretical basis for Dalton s theory has not been obtained because of the lack of a quantum definition of an atom in a molecule. This is not to say that the concepts of atoms,and bonds do not appear in the quantum mechanical treatments of chemical systems. They do, but in the reverse manner to that described above. Rather than finding its quantum basis, the... 

The condition, started in eqn (8.113), that the atomic action integral vanish for all time intervals may be taken as the quantum definition of an atom. It is a direct consequence of the topological definition of an atom as the union of... 

We are now in a position to perform a generalized variation of the action integral for an open system to demonstrate that Schwinger s principle of stationary action can be extended in such a manner as to provide a quantum definition of an atom in a molecule. We shall be considering the change in the atomic action integral 2] of eqn (8.111) ensuing from variations... 

The system first used to introduce the quantum definition of pressure consists of a linear chain of hydrogen molecules compressed between a pair of Ne atoms [12]. The vise is depicted in Figure 7 for the compression of five H2 molecules, the system Ne Hio Ne. The calculations were performed at the SCF/SCVS level using the 6-311G basis. The effect of electron correlation on the calculated pressure and on the variation of properties with pressure is found to be minimal, amounting to a few per cent, as determined in... 

While Pendas makes no attempt to disprove the quantum definition of pressure obtained through the scaling procedure of Marc and McMillan [22] as presented here, he does state that "the use of electron-only scaling to study stressed situations, where the virials due to the nuclear system cannot be neglected, is not a very consistent procedure." In reality, the physics of an open system does not neglect the virials due to the nuclear system, they are included in the total virial that is defined by taking the virial of the Ehrenfest force, see for example Equation (13). The virial theorem illustrates... 

Woolley, R. 1998. Is there a Quantum Definition of a Molecule Journal of Mathematical Chemistry 23 3-12. 

Though Eq. (32) provides a rigorous quantum definition of the cumulative reaction probability, it is not helpful in a practical sense because a complete state-to-state reactive scattering calculation is required to obtain the S matrix. We seek a more direct (and thus presumably more efficient) route to N(E), but without approximation, to which approximations can be incorporated later as needed in specific applications. 

Therefore, the classical treatment of the Borrmann effect has the quality of the immediate interpretation of the recorded fluorescence spectra (see Putz, 2014) but does not fully respond to what is happening with this energy, intimate-dynamically manifested in the anomalous absorption. Here s why, the quantum view can causally present the dififaction phenomenology in d5mamic evolution, where the asymmetrical propagation naturally derives fi om the quantum definition itself of diflBaction the coherent (dynamic) photonic transfer derivedfrom the dynamic localization, (5.312) and (5.313). 

In this respect all the presently considered reactivity indices, i.e., polarizability, electronegativity, and chemical hardness, have equally consecrated quantum definitions as well as atomic and molecular representations (Putz, 2008b, 2012b). 

The topological definition of an atom and the associated ideas of structure and structural stability are introduced in Section 2. These ideas can be presented in a pictorial and qualitative manner. The quantum definition of an open system and its identification with the topological atom are presented in Section 3. The consequences of this identification are explored without presenting its derivation, the approach that must necessarily be followed in this general introduction to the theory. 

In the past there have been many failed attempts to define an atom in a molecule and its contributions or those of a functional group to the properties of the molecule. There was, and for some there remains, a prevailing belief that a unique definition is not possible. Consider, for example, the following statement that appeared in the Journal of the American Chemical Society in 1994 The atom (or functional group) in a molecule is not easily defined. There are always subjective factors for any definition, or strict partition of the molecule. What model one chooses is subject to one s particular needs. These comments are made without reference to the existing literature, and they represent the personal biases of the authors. Their remark that how one defines an atom is a matter of expediency is at variance with the practice of science wherein one s attempts at definition and understanding are necessarily guided by observation and by theory. Any definition that does not recover the essential observations that are associated with the concept of an atom in a molecule serves no useful purpose. Any definition that does not ultimately allow for the quantum definition of the atom s properties cannot be a physically admissible one. 

Woolley, 1998] R. G. Woolley. Is there a quantum definition of a molecule Journal of Mathematical Chemistry 23, 3-12, 1998. 

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