State, electronic definition

Let us first seek to give a more rigorous and operational ab initio characterization of such units. The important physical idea underlying the above definitions is that of the connecting covalent bonds that link the nuclei. One can therefore recognize that a molecular unit is equivalently defined by the covalent-bond network that contiguously links the nuclei included in the unit. We can re-state the definition of a molecular unit in a way that emphasizes the electronic origin of molecular connectivity. 

A PWC function is defined as an (N — l)-electron bound parent state (atom or ion) with well-defined spin, parity, angular momentum and energy Ia = (Sa, na, La, Ea), coupled first to the spin-angular part of a single-particle state for the Nth electron, with definite orbital angular momentum la, to form a state with definite parity n, spin S, angular momentum L, and their projections L and M (for brevity, we indicate these global quantum numbers with the collective index T)... 

The partial wavefunctions I> Ey n) do not depend on the initial state they are exclusively governed by the dynamics in the excited electronic state. The definition in (2.70), on the the other hand, involves the overlap with the initial wavefunction and therefore tot(Ef) depends on the particular state of the parent molecule in the electronic ground state. tot has no practical advantage because its construction requires the dissociation amplitudes t(Ef,n) which already contain all the desired information. 

In view of current state of the art, namely, silicon-based technology, molecular electronics definitely exceed the expectations of a single product line. Going back, for instance, to 1960 silicon-based electronics were nearly exclusively considered as a simple replacement for the vacuum tube. However, it would have been myopic to limit the potential of silicon in that field of research. In fact, silicon constituted a technological platform, which evolved into the development of various products, most of them unfathomable at the time. Similarly, molecular electronics may be considered as a platform technology, rather than a single product line, which may give rise to many industrial products which are currently unforeseeable. 

When part of a delocalized aromatic molecule, the anion, after excited state electron transfer, gives rise to a not too reactive radical so that if one plays with the sequence of hydrogen abstraction from solvent followed by proton abstraction from the base, the initial anion may be restored and the solvent usefully replaces the sacrificial donor. This is the case with naphtholate as anion, certainly an interesting anionic sensitizer to test in other systems. Since the solvent is by definition at high concentration, its recovering role is played with a maximum efficiency reaction between the solvent and one of the radicals arising from the electron transfer is a good way to circumvent the back electron transfer. 

For systems which possess stereochemically active lone-pair electrons in the crystalline state, a definitive experimental answer to the title question is at least in principle available from difference density analysis of X-ray results where the potential for deriving electron distributions from elastic diffraction data is now being realized (13, 31, 104). In one application to subvalent molecules (164), (CH3)2TeCl2 was shown to possess a peak of 0.27 e/A3 centered at 0.9 A from the Te(IV) atom in the position expected for a lone pair of electrons (175). 

The simplest way of including the full interaction of the two final-state electrons is to use the impulse approximation. In its simplest plane-wave form this approximation is obtained from (10.14) by neglecting v and vi in the definition of the collision state T ( (k/,kj)). It retains the two-electron function (/> (k, r). In the spirit of this approximation it replaces x + (ko)) with a plane wave. We expect the plane-wave impulse approximation to describe kinematic regions where the two-electron collision dominates the reaction mechanism such as the higher-energy billiard-ball range. 

Electronic circular dichroism (CD) results from different absorption (molar absorption coefficient i and e ) of left- and right-circularly polarized light by the electronic subsystem of the molecule. CD has the same electronic origin as ordinary absorption. Therefore, CD spectra are interpreted in terms of the same concepts as absorption spectra, namely electronic transitions and excited states of definite chromophores For the discussions of electronic structures and excitations of complex chromophores molecular orbital (MO) theory provides an adequate framework. 

The traditional model of atomic structure has been the quantum-mechanical analogue of a solar system, with electrons perturbing each other only a little from their individual states of definite energy and angular momentum. On the other hand, the traditional model for molecular structure has been the quantum-mechanical counterpart of balls held together by springs in a fairly rigid, well-defined structure. These two pictures are so different and lend themselves to such different computational methods that they have remained as separated, almost unrelated fields within chemical physics. 

Suppose the chemical potential is not equalized then there are two points, ri and r2, with /r(r i) < p(r2). Consider these two points to be separate systems with N = p r )dr and N2 = p r2)dr electrons, respectively. From the definition of the local chemical potential [Eq. (105)] and the assumption that p(ri) < p(r2), it follows that the state with Ni + dN= [p(r0 + 8p(r)]dr and 7V2—dTV = [/9(r2)—8/9(r)]dr electrons has lower energy than the initial state. Electronic states, then, are stable only if the chemical potential is constant throughout the system. 

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