Total electron spin difference

Inclusion of Pauli s exclusion principle leads to the standard methods of ab initio computational chemistry. Within these methods, molecular systems containing the same nuclei and the same number of electrons, but having a different total electronic spin, can roughly speaking be said to be different systems. Thus, matrix elements of the Hamiltonian between Slater determinants corresponding to different spin states will all be zero, and they will not interact or mix at all. The wavefunctions obtained will be pure spin states. ... 

Electronic Spin-Spin Couplings. - For compounds with valence electrons that are well localized to the individual atoms and for which these electronic shells not are filled, one may ascribe a total electronic spin to the individual atoms. Moreover, these spins of different atoms may arrange themselves in an energetically favourable way which, e.g., for solids may lead to magnetic behaviour. But also for finite, molecular systems such couplings between the spins may exist and have important consequences for the overall properties of the system. 

The hyperfine coupling as measured, Aobs> is a composite of several factors described below. The intrinsic hyperfine interaction, Ajnt, depends on the distribution of electron spin on and near the atom of question. The observed hyperfine coupling may differ from the intrinsic value in a well-defined manner in a spin-coupled multinuclear center and/or when the total electron spin is greater than i... 

Lying at a lower energy than E2 is an energy level El- This energy level is due to an electron configuration in which two electrons are spin-paired, (tit ) A transition from Eq. 2 or E3 to Ei is not allowed under the total electron spin rule. None of these transitions would normally be involved in transitions that produce colour. However, in ruby, excited Cr ions in states E2 or 3 can lose energy to the crystal stmcture and drop down to level Ei. This process operates under different conditions from the optical transitions and is independent of spin. The energy is taken up in lattice vibrations and the ruby crystal warms up. This is called a radiationless or phonon-assisted transition. Typical rates of the transitions are ... 

Phosphorescence Spontaneous emission of light by a molecule from an electronically excited state that has a different total electronic spin from the ground state. 

We have described the spin of a single electron by the two spin functions a(this section we will discuss spin in more detail and consider the spin states of many-electron systems. We will describe restricted Slater determinants that are formed from spin orbitals whose spatial parts are restricted to be the same for a and p spins (i.e., xi = il iP ), Restricted determinants, except in special cases, are not eigenfunctions of the total electron spin operator. However, by taking appropriate linear combinations of such determinants we can form spin-adapted configurations which are proper eigenfunctions. Finally, we will describe unrestricted determinants, which are formed from spin orbitals that have different spatial parts for different spins (i.e., fjS ). 

As pointed out in the previous paragraph, the total wave function of a molecule consists of an electronic and a nuclear parts. The electrons have a different intrinsic nature from nuclei, and hence can be treated separately when one considers the issue of permutational symmetry. First, let us consider the case of electrons. These are fermions with spin and hence the subsystem of electrons obeys the Fermi-Dirac statistics the total electronic wave function... 

The total electron density is just the sum of the densities for the two types of electron. The exchange-correlation functional is typically different for the two cases, leading to a set of spin-polarised Kohn-Sham equations ... 

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