Half-electron technique

An advantage of the half-electron technique is its simplicity. IlyperChem can carry it out with only niin or m odificaiions of the usual calculation, . A disadvantage is that forces may not be accurate because of th e h alf electron approxim ation. ... 

You can think of the half-electron technique as a device to get reasonable orbitals to populate later with whole electrons. 

Semiempirical programs often use the half-electron approximation for radical calculations. The half-electron method is a mathematical technique for treating a singly occupied orbital in an RHF calculation. This results in consistent total energy at the expense of having an approximate wave function and orbital energies. Since a single-determinant calculation is used, there is no spin contamination. 

In Chapter 7, we noted that an electron in an atom can lie relatively far from the nucleus, so we commonly represent atoms as spheres in which the electrons spend 90% of their time. However, we often define atomic size in terms of how closely one atom lies next to another. In practice, we measure the distance between identical, adjacent atomic nuclei in a sample of an element and divide that distance in half. (The technique is discussed in Chapter 12.) Because atoms do not have hard surfaces, the size of an atom in a compound depends somewhat on the atoms near it. In other words, atomic size varies slightly from substance to substance. 

If one is interested in the kinetics of reactions that occur at very fast rates, having half-lives on the order of a fraction of a second or less, the methods that we have discussed previously for the determination of reaction rates are no longer applicable. Instead, measurements of the response of an equilibrium system to a perturbation are used to determine its relaxation time. The rate at which the system approaches its new equilibrium condition is observed using special electronic techniques. From an analysis of the system behavior and the equilibrium conditions, the form of the reaction rate expression can be determined. 

The alkali metals form a homogeneous group of extremely reactive elements which illustrate well the similarities and trends to be expected from the periodic classification, as discussed in Chapter 2. Their physical and chemical properties are readily interpreted in terms of their simple electronic configuration, ns, and for this reason they have been extensively studied by the full range of experimental and theoretical techniques. Compounds of sodium and potassium have been known from ancient times and both elements are essential for animal life. They are also major items of trade, commerce and chemical industry. Lithium was first recognized as a separate element at the beginning of the nineteenth eentury but did not assume major industrial importance until about 40 y ago. Rubidium and caesium are of considerable academic interest but so far have few industrial applications. Francium, the elusive element 87, has only fleeting existence in nature due to its very short radioactive half-life, and this delayed its discovery until 1939. 

Isotopes are also used to determine properties of the environment. Just as carbon-14 is used to date organic materials, geologists can determine the age of very old substances such as rocks by measuring the abundance in rocks of radioisotopes with longer half-lives. Uranium-238 (t1/2 = 4.5 Ga, 1 Ga = 10y years) and potassium-40 (t,/2 = 1.26 Ga) are used to date very old rocks. For example, potassium-40 decays by electron capture to form argon-40. The rock is placed under vacuum and crushed, and a mass spectrometer is used to measure the amount of argon gas that escapes. This technique was used to determine the age of rocks collected on the surface of the Moon they were found to be 3.5-4.0 billion years old, about the same age as the Earth. 

A number of the techniques that have been employed have the ability to directly monitor free-radical species either in vitro or in vivo [predominantly those involving electron spin resonance (e.s.r.) spectroscopy]. However, since many physiologically relevant free radicals have extremely short half-lives (e.g. 10 s for OH), the majority of the methods utilized detect products arising from their reactions with chemical components present (i.e. indirect methods). These indirect methods for... 

Despite their short half-lives, it is possible to detect free radicals in biological tissues by the addition of nonradicals such as nitrones or nitroso compounds, which act as spin traps by forming relatively stable free radicals on reaction with the endogenous radical species. Utilizing the technique of electron spin resonance (e.s.r.) spectroscopy, we have demonstrated ROM generation by human rheumatoid synovium when subjected to cycles of hypoxia/normoxia in vitro. Using 3,5-dibromo-4-nitroso-benzenesulphonate (DBNBS) as a spin trap, a... 

The binary borohydride species Zr( III 11)4 and U(BH4)4 have been investigated by quantum mechanical techniques and, for the zirconium case, also by gas-phase electron diffraction. All confirm that these simple molecules have a staggered conformation of borohydride ligands.15 In a related study, the hafnium analog Hf(BH4)4 has also been analyzed and is essentially isostructural.16 These studies show the molecules to possess tetrahedral symmetry with all of the BH4 ligands triply (i.e., if) bridging. Photoelectron spectra [He(i)] of the half and bent metallocene complexes Zr(7]S-CsHs)(BH4)4, M(7]S-CsHs)2(BH4)2 (M = Zr, Hf), and Ta(7]S-CsHs)2(BH4) have been determined.17... 

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