Quantum Mechanical Properties

Electrons, protons and neutrons and all other particles that have s = are known as fennions. Other particles are restricted to s = 0 or 1 and are known as bosons. There are thus profound differences in the quantum-mechanical properties of fennions and bosons, which have important implications in fields ranging from statistical mechanics to spectroscopic selection mles. It can be shown that the spin quantum number S associated with an even number of fennions must be integral, while that for an odd number of them must be half-integral. The resulting composite particles behave collectively like bosons and fennions, respectively, so the wavefunction synnnetry properties associated with bosons can be relevant in chemical physics. One prominent example is the treatment of nuclei, which are typically considered as composite particles rather than interacting protons and neutrons. Nuclei with even atomic number tlierefore behave like individual bosons and those with odd atomic number as fennions, a distinction that plays an important role in rotational spectroscopy of polyatomic molecules. 

Thermodynamic properties such as heats of reaction and heats of formation can be computed mote rehably by ab initio theory than by semiempirical MO methods (55). However, the Hterature of the method appropriate to the study should be carefully checked before a technique is selected. Finally, the role of computer graphics in evaluating quantum mechanical properties should not be overlooked. As seen in Figures 2—6, significant information can be conveyed with stick models or various surfaces with charge properties mapped onto them. Additionally, information about orbitals, such as the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO), which ate important sites of reactivity in electrophilic and nucleophilic reactions, can be plotted readily. Figure 7 shows representations of the HOMO and LUMO, respectively, for the antiulcer dmg Zantac. 

Remarkably, although band stmcture is a quantum mechanical property, once electrons and holes are introduced, theit behavior generally can be described classically even for deep submicrometer geometries. Some allowance for band stmcture may have to be made by choosing different values of effective mass for different appHcations. For example, different effective masses are used in the density of states and conductivity (26). 

Weinhold, F. [1972] Upper and Lower Bounds to Quantum Mechanical Properties , Advances in Quantum Chemistry, 6, p. 299. 

The NMR signal arises from a quantum mechanical property of nuclei called spin . In the text here, we will use the example of the hydrogen nucleus (proton) as this is the nucleus that we will be dealing with mostly. Protons have a spin quantum number of V . In this case, when they are placed in a magnetic field, there are two possible spin states that the nucleus can adopt and there is an energy difference between them (Figure 1.1). 

Lanthanide ions have emerged as a very promising category of chemically accessible realizations of spin-based qubits. Their suitability for this task, which results from their physical, chemical and quantum mechanical properties, is discussed in the following sections. 

An approximation stating that the motion of nuclei in ordinary molecular vibrations is slow relative to the motions of electrons. Thus, the nuclei can be held in fixed positions when doing calculations of electronic states. Such an assumption is useful in determining potential energy surfaces and is central in studying the quantum mechanical properties of molecules. See also Adiabatic Photoreaction Diabatic Photoreaction... 

Spin is a quantum mechanical property that does not appear in classical mechanics. An electron can have one of two distinct spins, spin up or spin down. The full specification of an electron s state must include both its location and its spin. The Pauli exclusion principle only applies to electrons with the same spin state. 

Although based on a simplified parametric description of the electronic structure of the molecule and of the leads, the framework discussed in this section has the advantage of leading directly to the computation of measurable quantities (the I-V curves). Thus, it is possible to relate the experimental observations to the quantum-mechanical properties of the systems under investigation, e.g., the electronic energy-level structure of the molecule and the relation of such levels to the energy of the leads. A timely improvement in this direction will come from the implementation of manageable methods, which combine a parameter-free atomistic description of the electronic... 

QUANTUM MECHANICAL PROPERTIES 2.9.1 Nuclear Angular Momenta... 

The parity of a system is related to the symmetry properties of the spatial portion of the wave function. Another important quantum mechanical property of a system of two or more identical particles is the effect on the wave function of exchanging the coordinates of two particles. If no change in the wave function occurs when the spatial and spin coordinates are exchanged, we say the wave function is symmetric... 

The molecular electrostatic potential (MEP) is a rigorously defined quantum mechanical property. The electrostatic potential (EP) at a point r in the... 

This Chapter begins with a comprehensive review of the quantum-mechanical properties of organic molecules and how this affects their photon excitation. A series of detailed definitions and concepts are presented that are not normally found in biological treatises. These concepts are vital to an understanding of the mechanisms involved in the photochemistry of vision. 

The only way in which such molecules can be demonstrated to occur as linear vibrating pairs of atoms, is by confinement as guest species in crystals. Even this situation is contingent on directed interaction with the host lattice, in the absence of which the guest appears structureless, or disordered. The general conclusion must be that protons, like electrons, appear as point particles only in close confinement. Protons and neutrons must, like electrons, logically be considered as distortions of the aether as compressible and flexible fluids. Despite differences in mass and topological structure these different particles must therefore all have quantum-mechanical properties. In observation they would display the type of behaviour that seems to imply a dual wave-particle structure. 

Intramolecular cohesion evidently is a holistic quantum-mechanical property, which cannot be reduced to pairwise interactions. Molecules are formed during the interaction of atoms and/or radicals in their valence states, to be understood in terms of valence-state wave functions of appropriate symmetry. 

Nuclear spin, characterized by a spin quantum number I, is a quantum mechanical property possessed by some nuclei. This rotation of the nucleus around its spinning axis gives rise to an angular momentum, p, whose value is defined by... 

Models are applied to a system, or a portion of the observable universe separated by well-defined boundaries for the purpose of investigation. A chemical model is a theoretical construct that permits the calculation of chemical properties and processes, such as the thermodynamic, kinetic, or quantum mechanical properties of a system. A geochemical model is a chemical model developed for geologic systems. Geochemical models often incorporate chemical models such as ion association and aqueous speciation together with mineralogical data and assumptions about mass transfer to study water-rock interactions. 

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