Electron configurations defined

The coefficients indicate the composition of the electronic state in terms of a linear combination of the various electronic configurations defined earlier in the output. Here is an example from a 4,4 CAS showing the first two excited state configurations ... 

The fact that these HOMOs and LUMOs have a two-fold degeneracy implies that there are four isoenergetic one-electron transitions to yield the first excited states this complication is however resolved by the interaction of these one-electron excitations, and this is known as configuration interaction. The concept of configuration interaction (Cl) is somewhat similar to that of the interaction of atomic orbitals to form molecular orbitals. An electron configuration defines the distribution of electrons in the available orbitals, and an actual state is a combination of any number of such electron configurations, the state wavefunction being... 

We would normally write the electronic ground state electron configuration of a carbon atom as ls-2s 2p-. Despite the intellectual activity that has gone into defining mythical valence states for carbon atoms in different bonding situations, no one would include a d-orbital in the description of ground state carbon. 

Formation of the mono- and dinitrosyl complexes is a thermodynamically favorable process, which distinctly depends on the electronic configuration of the metal center. The adsorption energy, defined as A=. Eaddukt - ( mzsm-5+ no)> is shown in the form of a histogram in Figure 2.16. Formation of mononitrosyl complexes is exothermic... 

Fig. 8 The energy levels and wavefunotions for the r-orbitals of trans butadiene. The arrows define the electron configuration of the ground state.

Some of these approximate forms of wave function possess a character of particular theoretical interest. One such is the "uni-configurational wave function. This implies an appropriate linear combination of antisymmetrized products of molecular spin orbitals in which all antisymmetrized products belong to the same "electron configuration . The electron configuration of an antisymmetrized product is defined as the set of N spatial parts appearing in the product of spin orbitals. For instance, a uni-configurational wave function with N = 2, S = 0, Ms=0 is expressed as... 

In Equation 1.3, the radial function Rnl (r) is defined by the quantum numbers n and l and the spherical harmonics YJ" depend on the quantum numbers l and W . When the spin of the electron is taken into account, the normalized antisymmetric function is written as a Slater determinant. The corresponding eigenvalues depend only on n and l of each single electron, which determine the electronic configuration of the system. 

Multiplet structures are ignored completely and electronic configurations are defined only in terms of the occupation numbers of the various orbitals. Accordingly, the radial HFS wave equations for a free atom or ion are written in the form... 

We can now consider explicitly how configurations interact to produce electronic states. Our first task is to define the Hamiltonian operator. In order to simplify our analysis, we adopt a Hamiltonian which consists of only one electron terms and we set out to develop electronic states which arise from one electron configuration mixing. 

Define the functional U(Q [v[/])=q integration over the electronic configuration space is indicated as a sub-index. The variational principle applied [6] to the (spin-free) function space v /(q) leads to the Euler-Lagrange equation ... 

The valence electron configuration explains why groups define chemical families that exhibit similar chemical properties. Because it is the valence electrons that determine an element s chemical behavior, and groups have similar valence electron configurations, then elements in the same group display similar chemical behavior. The electron configuration also explains the... 

The Cupric, Cu2+ or Cu(II) State, 3d9 The most important and stable oxidation state for copper is divalent. There is a well-defined aqueous chemistry of the Cu2+ ion, which generates the familiar blue solution when complexed with water. A large number of copper coordination compounds exist and these have been studied extensively. A strong Jahn-Teller distortion is associated with the 3d9 electronic configuration of this ion. This implies that a regular tetrahedron or octahedron about the Cu2+ ion is never observed, except in the rare occurrence of a dynamic Jahn-Teller effect. The tetragonal distortion about an octahedron can lead to a square-planar coordination which is often observed in Cu(II) oxides. 

---