Orbital Screening

Figures, and show electron density plots of the = 1, a = 2, and a = 3 orbitals. We extract the shapes of the 12 p, and 3 d orbitals from these graphs. Then we add labels that summarize the screening properties of these orbitals. Screening is provided by small orbitals whose electron density is concentrated inside larger orbitals. In this case, 1 s screens both 2 p and 3 d 2 p screens 3 d, but not 1 s and 3 d screens neither 1 s nor 2 p. The screening patterns can be labeled as shown.

We know that the most important factor for orbital size is the value of tt and that small orbitals screen better than large ones, so the screening sequence makes sense. 

Relativistic effects are more pronounced for the actinides because of their higher nuclear charge. As a result, the s and p orbitals screen the charge of the nucleus better and the d and f orbitals expand, and are destabilized 2,3). The shielding of the 5/ orbitals by filled outer s and p orbitals is thus not as effective, and actinide ions form more covalent bonds and are found in higher oxidation states, at least at the beginning of the 5/ series. 

According to Slater, this is because electrons in the same quantum shell (here, the 3p orbitals) screen one another s view of the nuclear charge by only 0.35 unit. Thus, going from A1 to Si, the nuclear charge increases by +1.00, but the added electron screens only +0.35 of this. Electrons in lower shells screen the nuclear charge by essentially +1.00 unit, as seen by the outermost electrons. This same effect explains the lanthanide contraction— the steady shrinking of lanthanide(III) ion radii from 103 to 86 pm as we fill the 4/ quantum shell from La3+ (4/°) to Lu3+ (4/14). 

Spectroscopy is limited in a one semester course we have tried to use the relatively simple Bohr atom for examples of orbital screening and x-ray emission analysis to get as much meaning from the simple formula as possible. The treatment of chemical kinetics is split into a fundamental Chapter 7 and a more advanced Chapter 8 so that if time is running out in a one semester course, Chapter 8 can be skipped and delayed until the beginning of an elective second semester. A one semester sequence might be Introduction Mathematics and Physics Review, Chapters 1 through 7 and 9 with an elective second semester as Chapters 8, 10 through 15 with parts of 16, 17, 18, or 19. 

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 ... 

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