The atomic terms

It is obvious now that an atomic state has to be characterized not only by the electron distribution between energy levels (with Pauli exclusion principle validity), but also by moments total Lj, orbital and spin L, their mutual positions being taken into account. The range of quantum numbers J, L and S comprise the so-called atomic term. The symbolic presentation of the atomic term is given as A is characterized by the 

The number is called the term multiplicity it characterizes the number of acceptable states at fixed quantum number L. The multiphcity P is equal to25+lat5 L and 2L + 1 at S L. For example, for states with L = 1 and 5 = multiplicity is equal 2X +1=2 

The definite energy corresponds to each term. However, systans can often be degenerated. The external action can remove the degeneration, i.e., make each term have its own energy. 

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The CNDO/2 model came next (Pople and Segal, 1966). It differs from CNDO/1 in the way it handles Uu and Vab- The penetration term Fab is no longer calculated exactly, but taken as —Z Yab- The atomic terms become... 

Table 5 Review of the matrix elements between the atomic-term kets FvLMiSMs)...

Information about the symmetry of each energy level e, is contained in the eigenvector m, of the diagonalization matrix U. In a usual description, the transformation from the basis set of the atomic terms (AT) into the basis set... 

Second, we need to define a matrix representation between the atomic term functions for each symmetry operation, that depends upon three Euler angles [73]... 

The atomic terms U and A are determined from the atomic spectra of the corresponding isolated atom by selecting only those states which are of importance for bonding in molecules. Klopman 24> has achieved this by using barycenters of states correlated by means of a simplified Slater-Condon type equation of the form... 

The magnitudes of these quantities are written as /, L and S, which are known as quantum numbers for each of these quantities, and can be used to specify atomic states through the atomic term symbol... 

In 1996 a force field model was proposed in which geometry-dependent charges are calculated by EEM. This model, called consistent implementation of the electronegativity equalization method (CIEEM), combines a force field representation for the PES (e.g., Eq. [19]) with the EEM equation for the electronic energy (Eq. [7]) in such a way that the atomic terms of Eq. [7] explicitly enter the expression for the potential energy. Thus, within the CIEEM, the expression for the steric energy in the MM force field model will read... 

The atomic terms are characterized by the orbital angular momentum which is reflected in the value of the total orbital quantum number L. Just as the individual angular momenta are quantized, so are the resultants. For the example above, with = 1 for two p electrons, the maximum value of the resultant angular momentum is represented by the sum of the quantum numbers, and the minimum value is represented by the difference. Intermediate values are allowed too, provided they differ from the extremes by a whole number ... 

The atomic terms differ by their electron energies and can be characterized by the quantum numbers using the so-called term symbols ... 

Now the atomic terms are split into a set of multiplets. The number of multi-plets is (IS + 1), each one being labelled according to the quantum number... 

A non-zero contribution of the orbital angular momentum—a magnetic angular momentum—requires that the matrix elements of the atomic term functions 19/,) = L, ML, S, Ms) are non-zero... 

The spin-orbit interaction in free atoms alters the atomic terms l i) = L, ML, S, Ms) into atomic multiplets, denoted as L,S,J,Mj) = JM). The energies of the multiplets are given as follows... 

Interestingly, the formula for the molecular-state g-factor gs is similar to that obtained for the atomic-term g-factor gj when spin-orbit coupling was considered (Section 8.5.2) hence... 

Each molecular eigenfunction transforms as an irreducible representation, rh which is contained in the direct product of the atomic terms... 

In addition, the atomic terms Ef (qi) in many fluctuating-charge models are each assumed to be a quadratic polynomial of the form... 

The decision as to whether the atomic terms become positive or negative, odd or even, when combined to give molecular terms depends upon detailed prescriptions derivable from the wave equation. 

With Berzelius thoughts begins the quantification of chemical substances, in atomic proportions, while assessing to the atomic term a universal ontological signification (Berzelius, 1813-1814) ... 

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