One-electron models

Cl calculations can be used to improve the quality of the wave-function and state energies. Self-consistent field (SCF) level calculations are based on the one-electron model, wherein each electron moves in the average field created by the other n-1 electrons in the molecule. Actually, electrons interact instantaneously and therefore have a natural tendency to avoid each other beyond the requirements of the Exclusion Principle. This correlation results in a lower average interelectronic repulsion and thus a lower state energy. The difference between electronic energies calculated at the SCF level versus the exact nonrelativistic energies is the correlation energy. 

The situation described here is based on a simple one-electron model which can hardly be expected to predict the behaviour of complex many-electron systems in quantitative detail. There can be no doubt however, that the qualitative picture is convincing and probably that the broad principles of electronic behaviour in solids have been identified. The most significant feature of the model is the band structure that makes no sense except in terms of the electron as a wave. Important, but largely unexplored aspects of solid-state reactions and heterogeneous catalysis must also relate to the nearly-free models of electrons in solids. 

Cu,Zn superoxide dismutase. Essentially, these observations support a stepwise one-electron model again. Interestingly, the oxidation state of copper does not change during the catalytic reaction, i.e. the sole kinetic role of the histidine coordinated metal center is to alter the electronic structures of the substrate and 02 in order to facilitate the electron transfer process between them. 

Given the ubiquitous character of molecular orbital concepts in contemporary discourse on electronic structure, ionization energies and electron affinities provide valuable parameters for one-electron models of chemical bonding and spectra. Electron binding energies may be assigned to delocalized molecular orbitals and thereby provide measures of chemical reactivity. Notions of hardness and softness, electronegativity,... 

For approximate wavefunctions, however, the various formulations give rise to different theoretical predictions. This has been demonstrated in detail, for example, by Hush and Williams (31) for large aromatic systems. Thus, when we wish to obtain exact values of J, we must be very careful in deciding which formalism to use. A final point here is that the one-electron model does not take into account configuration interaction. Calculations for relatively simple systems would be useful here. 

In fact, since the early developments of electron transfer theories, it has been recognized that the magnitude of T b is greatly enhanced if /a and (j/b are delocalized through the intercenter medium [54, 55]. In the framework of one-electron models, this delocalization can be described by a mixing of (pu and (Pa with the medium orbitals which leads to the so-called superexchange contribution. The origin of this contribution may be introduced as follows. If only one medium orbital cPm interacts with both (po and (Pa, the initial and final states may be written ... 

The indices are all defined in terms of the Hiickel molecular orbital method. This has been described on many occasions, and need not be discussed in detail here, but a brief statement of the basic equations is a necessary foundation for later sections. The method utilizes a one-electron model in which each tt electron moves in a effective field due partly to the a-bonded framework and partly to its averaged interaction with the other tt electrons. This corresponds conceptually to the Hartree-Fock approach (Section IX) but at this level no attempt is made to define more precisely the one-electron Hamiltonian h which contains the effective field. Instead, each 7r-type molecular orbital (MO) is approxi-... 

In the previous four sections, several solvent radical ions that cannot be classified as molecular ions ( a charge on a solvent molecule ) were examined. These delocalized, multimer radical ions are intermediate between the molecular ions and cavity electrons, thereby bridging the two extremes of electron (or hole) localization in a molecular liquid. While solvated electrons appear only in negative-EAg liquids, delocalized solvent anions appear both in positive and negative-EAg liquids. Actually, from the structural standpoint, trapped electrons in low-temperature alkane and ether glasses [2] are closer to the multimer anions because their stabilization requires a degree of polarization in the molecules that is incompatible with the premises of one-electron models. 

On Forming a One Electron Model - Mainly Concerning thed-Band. 58... 

Qualitatively, the most transparent type of model, as ever, would be a one-electron model that is capable of rendering both the ground state and, to a high degree, its excitation properties. However, in the present case, accommodations are called for, on both aspects, that are not trivial. These we will try to pursue and represent within the present one-electron-type framework as closely as possible. In seeking to develop the present model, we base it as firmly as possible on the available data, optical, photoemission, electrical, structural, etc. Much of this data is still open to interpretation, and many of the interpretations to follow are made in the light of experience gained with transition metal compounds (2). 

Near-range components. The dipole moments of three like atoms at near range were estimated using variational methods and a one-electron model. The results are believed to represent the qualitative features of the overlap-induced triatomic induced dipole, which is the dominant dipole at the spectroscopically important near range [1, 173], The triatomic overlap-induced dipoles were estimated to be just slightly weaker than the binary ones [1], The observation of very weak ternary absorption would then be a consequence of strong cancellations of long- and short-term induced dipole components [172]. 

In a 7r electron system the orbitals of an aromatic positive ion are similar to the corresponding orbitals of the neutral molecule. In contrast, in small molecules electronic rearrangement following excitation is often sufficiently important that changes in nuclear geometry, correlation energy, etc., are all essential to the correct interpretation of the excitation phenomenon. Because of the similarity in the orbital systems of neutral and positive ion aromatic compounds, we shall assume that it is possible to describe the photoionization of an aromatic molecule within the framework of a one-electron model. Given that the n and a electrons are describ-able by a set of separable equations of motion, we need consider only the initial and final orbitals of the most weakly bound electron to determine the ionization cross section near to the threshold of ionization. 

The microscopic electronic structure of the buckyonion can be derived using an effective one-electron model where the screening effects are treated within the random phase approximation (RPA). The particular spherical geometry of these... 

G. Hunter, Int.. Quantum Chem., 29, 197 (1986). The Exact One-Electron Model of Molecular Structure. 

The L2,3 edges of the 4th period transition metals are marked by prominent "white line" features due to excitations of the 2p3/2 (L3) and 2pi/2 (L2) levels, following the allowed dipole transitions, to unoccupied d states. On the basis of the (2j + 1) degeneracy in a one electron model, the L3/L2 intensity ratio should be 2 1, but wide departures from this ratio have been observed in transition metals and their oxides [21, 22, 29, 30]. Even though no single factor has been found to account for these observations, these extensive studies form the basis of an empirical catalogue of L3/L2 ratios to be used in future determinations of the oxidation states. Further, positive chemical shifts are also observed as a function of oxidation states for Tj 3+- Ti4+ (2 eV), Mn2+ - Mn4+ (2 eV), Fe2+... 

The vibronic Hamiltonian in the one-electron model is H = Hq + V. The kernels of these operators are... 

In our discussion of the dynamics of a single core hole we have so far used a simple one-electron model for the energy levels of the excited ionic state and also for the transition matrix elements leading to these states (Eq. (12)). 

The inconsistency between predictions made by MO REPEs and VB REPEs may be attributed to the different natures of simple MO and VB theories, i.e., the simple MO theory is a one-electron model, free of electron correlation, but VB theory is a many-electron, correlation model. This difference may result in the different topological dependence of -conjugation in MO and VB models, as illustrated by the [n]phenanthrene series. 

One-electron picture of molecular electronic structure provides electronic wavefunction, electronic levels, and ionization potentials. The one-electron model gives a concept of chemical bonding and stimulates experimental tests and predictions. In this picture, orbital energies are equal to ionization potentials and electron affinities. The most systematic approach to calculate these quantities is based on the Hartree-Fock molecular orbital theory that includes many of necessary criteria but very often fails in qualitative and quantitative descriptions of experimental observations. 

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