Rule of maximum spin

The result which we have just obtained may be generalized to all atoms or molecules Whenever the electron configuration of an atom or molecule is such that two or more unpaired electrons occupy different orbitals, the energy is not determined by the electron configuration alone, but depends on their spin functions. The lowest energy state is that in which all unpaired electrons have parallel spins. This statement is known as the rule of maximum spin. 

If the Hund rule of maximum spin is fulfilled, the above-mentioned 3d-levels are consistent with the experimental fact that the magnetic anisotropy of Fe ions is so large that they can be regarded, along the c-axis, as Ising spins. On the other hand, the Co ions do not seem so anisotropic magnetically (see sect. 6.2.4). Another evidence of the level scheme is the absence of the (1, l)-type... 

If an atom or molecule has n singly-occupied orthogonal (i.e. non-overlapping) orbitals, the lowest-energy arrangement of the spins for the n electrons is that for which the spins ate all parallel. This is a statement of Hund s rule of maximum spin multiplicity. The total spin quantum number is then S=nil. 

Hund s first rule The ground term will be one of maximum spin-multiplicity (maximum S)... 

The same phenomenon that leads to Hund s rule of maximum multiplicity in atoms (i.e., quantum-mechanical exchange stabilization) produces polarization of the electron spins in the C-H a bond. In a valence-bond treatment, the bond is comprised of one electron from a carbon sp2 orbital and another from a hydrogen Is orbital. Exchange forces act to polarize the sp2 electron so that its spin is parallel to the unpaired spin in the carbon 2p orbital this leaves the... 

With increasing atomic volume, one approaches the free atom limit where Hund s first rule postulates maximum spin, so that the individual spins of the electrons in a shell are aligned parallel. More generally, Pauli s exclusion principle implies that electrons with parallel spins have different spatial wavefunctions, reduces the Coulomb repulsion and is seen as exchange interaction. When the atoms are squeezed into a solid, some of the electrons are forced into common spatial wavefunctions, with antiparallel spins and reduction of the overall magnetic moment. At surfaces and interfaces, the reduced coordination reverses this effect, and a part of the atomic moment is recovered. 

Diagrams such as the one in Figure 3-2 may be used to draw electronic configurations (see Figure 3-3). Arrows pointing up are used to represent electrons with one given spin, and arrows pointing down are used to represent electrons with the opposite spin. In atoms with partially filled p, d, or/subshells, the electrons stay unpaired as much as possible. This effect is called Hund s rule of maximum multiplicity. 

The superscripts denote the number of electrons in each atomic orbital. Electrons must be paired (i.e., of equal and opposite spin) in atomic orbitals containing two electrons. Paired electrons do not contribute to the atomic or molecular spin angular momentum. Hund s rule of maximum multiplicity states that in the lowest energy configuration, the electrons must be spread over as many available orbitals of equal energy as possible, in order to maximize the spin multiplicity. Since three 2p orbitals are available in which 4 electrons must be distributed, the lowest electronic state therefore has two unpaired electrons in each of two 2p orbitals. Each unpaired electron contributes to the spin angular momentum. Thus 2S + 1 = 3 for the oxygen atom, and the term symbol is 3P. 

It is a general rule that if a group of n or less electrons occupies a set of n degenerate orbitals, they will spread themselves among the orbitals and give n unpaired spins. This is Hund s first rule, or the rule of maximum multiplicity. It means that pairing of electrons is an unfavorable process energy must be expended in order to make it occur. If two electrons are not only to... 

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