Screening orbitals

Waber JT, Cromer DT (1965) Orbital radii of atoms and ions. J Chem Phys 42 4116-4123 Simons G, Bloch AN (1973) PauU-force model potential for sohds, Phys Rev 87 2754-2761 Zhang SB, Cohen ML, Phillips JC (1987) Relativistic screened orbital radii. Phys Rev 836 5861-5867... 

To understand the origin of low-energy satellites in the 3d spectra of light lanthanides, their implication for a dynamical picture of core level photoionization in the presence of semilocalized screening orbitals to establish their relation to the ground state electronic structure, see fig. 1 (Wertheim and Campagna 1978). 

You can use Lhe senii-empineal an tl ab initio Orbuals dialog box in IlyperChem Lo ret iies[ a con Lour ploL of any molecular orbital. When req nested, lhe orbital is con toured for a plane that is parallel lo lhe screen and which is specified by a subset selection and a plane offset, as described above. The index of the orbilal and its orbilal energy (in electron volts, eV) appears in the stains line. 

COSMO (conductor-like screening model) a method for including solvation effects in orbital-based calculations... 

The three signals are fed into an oscilloscope as vertical-, horizontal-, and external-intensity marker input. The keyphazor appears as a bright spot on the screen. In cases where the orbit obtained is completely circular, the maximum amplitude of vibration occurs in the direction of the keyphazor. To estimate the magnitude of the correction mass, a trial-and-error process is initiated. With the rotor perfectly balanced, the orbit finally shrinks to a... 

Finally, select acetone from the molecules on screen. Here, both the LUMO and the LUMO map are available under the Surfaces menu. First, select LUMO and display it as a Solid. It describes a 7U-type antibonding ( i ) orbital concentrated primarily on the earbonyl carbon and oxygen. Next, turn off this surface (select None under the LUMO sub-menu), and then seleet LUMO Map under the Surfaces menu. Display the map as a transpareni solid. Note the blue spot (maximum value of the LUMO) directly over the carbonyl carbon. This reveah the most likely site for nucleophilic attack. 

Exact solutions to the electronic Schrodinger equation are not possible for many-electron atoms, but atomic HF calculations have been done both numerically and within the LCAO model. In approximate work, and for molecular applications, it is desirable to use basis functions that are simple in form. A polyelectron atom is quite different from a one-electron atom because of the phenomenon of shielding", for a particular electron, the other electrons partially screen the effect of the positively charged nucleus. Both Zener (1930) and Slater (1930) used very simple hydrogen-like orbitals of the form... 

The self-consistent field function for atoms with 2 to 36 electrons are computed with a minimum basis set of Slater-type orbitals. The orbital exponents of the atomic orbitals are optimized so as to ensure the energy minimum. The analysis of the optimized orbital exponents allows us to obtain simple and accurate rules for the 1 s, 2s, 3s, 4s, 2p, 3p, 4p and 3d electronic screening constants. These rules are compared with those proposed by Slater and reveal the need for the screening due to the outside electrons. The analysis of the screening constants (and orbital exponents) is extended to the excited states of the ground state configuration and the positive ions. 

The reason usually cited for the great similarity in the properties of the lanthanides is that they have similar electronic configurations in the outermost 6s and 5d orbitals. This occurs because, at this point in the periodic table, the added electrons begin to enter 4f orbitals which are fairly deep inside the atom. These orbitals are screened quite well from the outside by outer electrons, so changing the number of 4/electrons has almost no effect on the chemical properties of the atom. The added electrons do not become valence electrons in a chemical sense—neither are they readily shared nor are they readily removed. 

When multi-electron atoms are combined to form a chemical bond they do not utilize all of their electrons. In general, one can separate the electrons of a given atom into inner-shell core electrons and the valence electrons which are available for chemical bonding. For example, the carbon atom has six electrons, two occupy the inner Is orbital, while the remaining four occupy the 2s and three 2p orbitals. These four can participate in the formation of chemical bonds. It is common practice in semi-empirical quantum mechanics to consider only the outer valence electrons and orbitals in the calculations and to replace the inner electrons + nuclear core with a screened nuclear charge. Thus, for carbon, we would only consider the 2s and 2p orbitals and the four electrons that occupy them and the +6 nuclear charge would be replaced with a +4 screened nuclear charge. 

The energies of orbitals are calculated today by solving the Schrodinger equation with computer software. The commercial software available is now so sophisticated that this approach can be as easy as typing in the name of the molecule or drawing it on screen. But these values are theoretical. How do we determine orbital energies experimentally ... 

Now many physical properties depend mainly on the behaviour of the electron in the outer part of its orbit. As an example we may mention the mole refraction or polarizability of an atom, which arises from deformation of the orbit in an external field. This deformation is greatest where the ratio of external field strength to atomic field strength is greatest that is, in the outer part of the orbit. Let us consider such a property which for hydrogen-like atoms is found to vary with nrZ t. Then a screening constant for this property would be such that... 

From this set of standard size screening constants it is possible to obtain screening constants for any atom or ion for any property dependent mainly on the behaviour of the electrons in the outer parts of their orbits. The constants can probably be trusted to be accurate to within about 10% of the quantum defect, for example, Ss values for M levels to within 1. In case that empirical data are available for some atoms or ions of a sequence it is well to use them to correct the screening constants. 

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