Atomic orbitals sequencing

The periodic table in block form, showing the filling sequence of the atomic orbitals. Filling proceeds from left to right across each row and from the right end of each row to the left end of the succeeding row. 

The molecular orbitals are labelled a and ir depending on whether they are symmetrical about the internuclear axis or have a nodal plane passing through the nuclei. The m.o. s are numbered in sequence of increasing energy, independent of the numbering of the atomic orbitals. This numbering serves to avoid any confusion in cases where atomic orbitals from different levels are combined, as in... 

Aufbau principle chem A description of the building up of the elements in which the structure of each in sequence is obtained by simultaneously adding one positive charge (proton) to the nucleus of the atom and one negative charge (electron) to an atomic orbital. auf.bau phn s3-pal)... 

Fig. 2-15.—The approximate sequence of energy values for atomic orbitals, the lowest circle representing the most stable orbital (Is). Each circle represents one atomic orbital, which can be ocoupied either by one electron or by two electrons with opposed spins.

It has not proved mathematically feasible to calculate the electron-electron repulsion that causes this change in orbital-energies for many-electron molecules. It is even difficult to rationalize the qualitative changes in sequence on the basis of the shapes of the 11orbitals. Greater success has been achieved by an approximate method which begins with orbitals characteristic of the isolated atoms present in the molecule, and assumes that molecular orbital wave functions can be obtained by taking linear combinations of atomic orbital wave functions (abbreviated L.C.A.O.). For... 

In any complete treatment of this molecule, we ought also to include further interaction with other configurations such as those built on the 2s or 2p atomic orbitals. This would depress all the levels slightly, but it is unlikely that their sequence would be changed. 

The same holds of course also for exponents. Here, however, the optimization is too difficult. Since we are forced to use for molecular calculations exponents optimum for atoms, the following questions may be asked. To what degree do atomic orbitals change when molecules are formed What sequence, combination and extent of optimization of the orbital exponents X for molecules is necessary and useful How many STO symmetry basis functions are needed to adequately represent each molecular orbital symmetry type What kind of functions (Is, 2s, 3s, 2p,. .. 3d, is needed and what number of each type should... 

A novel graphical representation of the. sequence of atomic orbitals is due to Theodor Bcnfcy (ca. I960). In this spiral form of the periodic table, reproduced in Fig. 9.7, the transition elements and lanthanides appear as spokes from a spiral rather than as detached horizontal rows. This has the advantage that elements with successive atomic numbers arc actually adjacent to one another. 

In what sequence do electrons fill the atomic orbitals related to a sublevel (5.3)... 

The Natural Bond Orbital analysis of Weinhold [Foster and Weinhold, 1980 Reed, Weinstock etal., 1985 Reed, Curtiss etal., 1988] generates, departing from canonical MOs, a set of localized one center (core, lone pairs) and two center (jt and a bonds) strongly occupied orbitals, and a set of one center (Rydberg) and two center (a, Jt ) weakly occupied orbitals the NBOs. The Natural Bond Orbitals (NBOs) are obtained by a sequence of transformations from the input basis to give, first, the Natural Atomic Orbitals (NAOs), then the Natural Hybrid Orbitals (NHOs), and finally the Natural Bond Orbitals (NBOs). For NAOs, atomic charges can be calculated as a summation of contributions given by orbitals localized on each atom moreover, from NBOs, bond order can be also calculated. 

From Rb to Xe, the general sequence of hlling orbitals is the same as that from K to Kr although there are once again irregularities in the distribution of electrons between and d atomic orbitals (see Table 1.3). 

Apply the aufbau principle using the atomic orbital energy sequence ... 

---