Non-classical system

Two Fused Five-membered Heterocyclic Rings (ii) Non-classical Systems... 

The weird properties that came to be associated with quantum systems, because of the probability doctrine, obscured the simple mathematical relationship that exists between classical and quantum mechanics. The lenghthy discussion of this aspect may be of less interest to chemical readers, but it may dispel the myth that a revolution in scientific thinking occured in 1925. Actually there is no break between classical and non-classical systems apart from the relative importance of Planck s action constant in macroscopic and microscopic systems respectively. Along with this argument goes the realization that even in classical mechanics, as in optics, there is a wave-like aspect associated with all forms of motion, which becomes more apparent, at the expense of particle behaviour, in the microscopic domain. 

Debating the relative merits of the partitioning schemes is a sterile exercise. Molecular cohesion is of strictly quantum-mechanical origin and therefore holistic. When this interaction is reduced to classically recognizable features the required abstraction destroys the holistic picture. Any abstraction is a classical approximation to a non-classical system. The essential difference between classical and non-classical descriptions of a molecule arises from the non-local basis of the latter (compare 3.4) which simultaneously depends on all particle coordinates. It is shaped by the complex wave function, which cannot be simulated by the superposition of real (classical) functions. The argument is therefore settled by this essential difference between quantum and classical theories [218]. The former is defined in the complex plane and the latter in real space, as shown in figure 2.7. 

References to ortho- and peri-fused systems other than [2.2.3]cyclazines have been made mainly in Volume 6 of CHEC-I. The spectroscopic properties of two fused-membered heterocyclic rings belonging to classical systems <84CHEC-I(6)973>, non-classical systems <84CHEC-I(6)1027>, and l,6,6ai -trithiapentalenes and related systems <84CHEC-I(6)1049> have been studied in detail. 

The non-classical system (182) has been synthesized, starting from 4,5-bis(chloromethyl)-l,2,5-thiadiazole, and characterized by the isolation of its dimer and adducts. The more complex but stable non-classical thiophens (183)—(185) have been prepared, starting from azomethine imine ylides, generated in situ from 1-aminopyridinium, 1-aminoquinolinium, or... 

The complex phase which is fundamental to gauge theory is commonly defined in terms of symmetry groups without consideration of its physical meaning, which emerges most clearly in its characterization of the quantum wave functions. Whereas phase relationships between point particles are hard to imagine, they appear naturally in wave structures. With respect to electrons and other chemical entities a wave model in terms of complex wave functions is therefore the most satisfactory physical model. The complex phase represents the fundamental attribute of non-classical systems and the major difference between classical particles and quantum waves. Simulation of chemical systems based on real basis sets is essentially classical. It is therefore wrong, although fashionable, to refer to such simulations as quantum chemistry. 

As shown in Table 5.2 the oxidation states of the tetrameres may also be formally rationalized considering they are built up of iron atoms with oxidation states + 3 and -h 2 which are the normal oxidation states for iron coordinated tetrahedrically by weak-field ligands. However as emphasized above, the system as a whole must be considered for proteins as well as for synthetic analogues as a mixed-valence system and in no case as a trapped-valence one constituted by distinguishable iron atoms with different oxidation states. This feature that determine that these tetrameric iron-sulfur species are the first non classical system known in biology is supported by spectroscopic techniques able to detect electronic states with half-life times in a wide range s) and at... 

---