Orbital geometry, earth

Satellite instrumentation orbiting the earth view the stratosphere in limb and nadir viewing geometries. In addition both solar, lunar and stellar occulation have also been exploited very successfully. 

Group 2 complexes are formally electron deficient and conformationally floppy only small energies (often only 1-2 kcal mol-1) are required to alter their geometries by large amounts (e.g., bond angles by 20° or more). In such cases, the inclusion of electron-correlation effects becomes critical to an accurate description of the molecules structures. Both HF/MP2 and density functional theory (DFT) methods have been applied to organoalkaline earth compounds. DFT approaches, which implicitly incorporate electron correlation in a computationally efficient form, are generally the more widely used. Molecular orbital calculations that successfully reproduce bent... 

Donor-acceptor interactions also lead to strangely bent geometries in heavier F— M—F alkaline earth fluorides. Such bending can occur when strong ionic attractions force a filled fluoride pz orbital into proximity with an orthogonal metal pj orbital, for in this case symmetry-forbidden (pz)p —(p l)m interactions can turn on only when the strict a/n symmetry of a linear F—M—F arrangement is broken. 

Quantum chemical calculations on RE + /3-diketonate complexes are presently restricted to two approaches the effective core potential (ECP) and the SMLC/AMl method. The SMLC/AMl method is a very powerful addition to the semi-empirical molecular orbital method AMI in that it allows the prediction of geometric parameters of rare-earth /3-diketonate complexes of very difficult experimental determination. In this method the RE3+ ion is a sparkle represented by a -i-3e charge in the center of a repulsive spherical potential of the form exp(—ar). Recently, ab initio effective core potential calculations have also succeeded in reproducing the coordination polyhedron geometries of RE + /S-diketonate complexes with high accuracy . 

In the spin-forbidden transition > A2 there is no change in the geometry of the electronic orbitals and the equihbrium position of the ground and excited configuration is almost unchanged (see Fig. 2) the transition is sharp, the vibronic interaction weak and the situation of the R lines in ruby or alexandrite resembles that of rare earths. In contrast, the spin-allowed transition T2 -> A2 arises from the e set to the t2 set. Since... 

Ln = Pr, Nd, Pm, Sm, Dy, Ho, Er, and Tm X = F, Cl, Br, and I. Ground electronic states for all trihalides were established, assuming that the molecular symmetry was planar (Dsa) rather than pyramidal (Csv). Spin-orbit interaction was ignored. Comparison of calculated Ln-X bond lengths with experimental data showed that description of dynamic electron correlation was absolutely necessary for correct results. These studies on lanthanide systems were later extended to hydration models of trivalent rare-earth ions [253] for Y +, La +, Gd +, and Lu + geometry optimization was carried out at the MP2 level for hydrates containing from one to ten water molecules. In addition, ab initio molecular dynamics simulations (by following the dynamical reaction coordinate) for the systems with more water molecules, [M(H20)24] (M = Y, La) and [La(H20)64] ", were done and both radial distribution function and coordination number were obtained. 

Four ice age episodes were recognized in the Pleistocene Epoch that commenced about 2 million years ago and ended about 10,000 years ago. Each was succeeded by warmer episodes and there were an estimated 22 ice episodes during this time interval. Numerous possible causes for this last ice age and earlier ones have been put forward. One is a decrease in solar energy output. Another is variations in the geometry of the Earth s orbit and precessional cycle. 

For dipole forbidden transitions, e.g., from a p core state to a 4f final state, higher-order terms in the exponential expansion lead to a finite contribution to the cross section. This is in general small unless q 1/r, where is the core orbital radius, but such conditions may be satisfied both in transmission and reflection geometry (Schnatterly 1979, Grunes and Leapman 1980, Ludeke and Koma 1975), and will be of importance in rare earth electron loss spectroscopy. Thus even within the Born-Bethe regime monopole, quadrupole and octopole transitions may be prominent. 

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