Maximum multiplicity

In Fig. 1 there is indicated the division of the nine outer orbitals into these two classes. It is assumed that electrons occupying orbitals of the first class (weak interatomic interactions) in an atom tend to remain unpaired (Hund s rule of maximum multiplicity), and that electrons occupying orbitals of the second class pair with similar electrons of adjacent atoms. Let us call these orbitals atomic orbitals and bond orbitals, respectively. In copper all of the atomic orbitals are occupied by pairs. In nickel, with ou = 0.61, there are 0.61 unpaired electrons in atomic orbitals, and in cobalt 1.71. (The deviation from unity of the difference between the values for cobalt and nickel may be the result of experimental error in the cobalt value, which is uncertain because of the magnetic hardness of this element.) This indicates that the energy diagram of Fig. 1 does not change very much from metal to metal. Substantiation of this is provided by the values of cra for copper-nickel alloys,12 which decrease linearly with mole fraction of copper from mole fraction 0.6 of copper, and by the related values for zinc-nickel and other alloys.13 The value a a = 2.61 would accordingly be expected for iron, if there were 2.61 or more d orbitals in the atomic orbital class. We conclude from the observed value [Pg.347]

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. Thus the configuration of the nitrogen and oxygen atoms are as follows ... 

In accord with the first rule, the electrons remain unpaired as long as possible when filling a set of orbitals because that is how the maximum multiplicity is achieved. With regard to the third rule, if a state is exactly half filled, the sum of the m values that gives the L vector is 0 and L + S and L — S are identical so only one / value is possible. 

Hund s rules tell us that the ground state of the ion has (a) the maximum multiplicity and (b) the maximum values of L consistent with maximum multiplicity. The ground states for the various dn configurations are as follows ... 

Hund s rule of maximum multiplicity predicts that the two electrons entering the -n level will occupy two different orbitals, so the electronic configuration can be written more explicitly as... 

Magnetic quantum number. 19 Magnetic susceptibility mass. 460-463 molar, 461 volume, 460 Maim. J. O.. 70 Map of twist angles, 490 Marcus theory, 571 Mass spectrometry. 239 Maximum multiplicity, 26-27 Mechanisms inner sphere, 565-567 outer sphere. 558-561 of redox reactions. 557-572 of substitution reactions. 545-547. 551-553 Medicinal chemistry, 954-960 Meissner effect, 285 Melting points, and chemical forces. 307-310... 

The non-dimensionalization used in this work is perhaps the simplest, but it suffers from the defect that important physical bifurcation parameters are not isolated. The simple cuspoid diagrams are probably not those that would be obtained from experiments, where the residence time is a convenient parameter. Balakotaiah and Luss (1983) considered such a formulation for two parallel or simultaneous reactions the diagrams for the case of sequential reactions are similar, at least when the activation energies are equal. The maximum multiplicity question, however, is independent of the formulation and we conjecture that diagrams with seven steady states could be found in a small region of parameter space, though we have not looked for them. 

The simplest example is bis-cyclopentadienylco-balt(II), where we add one electron. This may go either into one of the 4p orbitals or into the relatively unstable kag orbital. In either of these cases, of course, it lias one unpaired electron (i.e., it is in a doublet state). For bis-cyclopentadienylnickel-(II),1 on the other hand, two electrons must go into these orbitals. Whether they go, one into kag and the other into some 4p level, or both into the 4p levels, is in many ways immaterial. The proximity of the kag orbital energy to that of the 4p orbitals will ensure that we shall be left with two singly occupied orbitals whose electrons are in a triplet state with their spins parallel (Hund s principle of maximum multiplicity). In bis-eyclopentadienylchromium-(II) two electrons arc removed. If the hag orbital is appreciably more stable than the de2g orbitals, both will come from the latter level, leaving one... 

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... 

In table I, the systems of regularities now known for arc and spark spectra of ten elements in the fourth period are represented, the numbers, 1,2,3, 4, etc., indicating the maximum multiplicities in the spectral terms or atomic energy levels. 

The maximum multiplicity (number of lines, L) in a given NMR signal is determined by the number (n) of neighboring coupled nuclei according the Eq. (8.3), L... 

But the ribbons can be (and, for our purposes, must be) classified differently, taking into account the population density and pseudosymmetries of the highest occupied MOs (HOMO) and the lowest unoccupied MOs (LUMO). Then all polyene ribbons get subdivided into four groups (see the upper part of Fig. 25). To avoid the tiresome drawing of the MO layouts given above, we encode each layout by a certain number. Goldstein and Hofimann advised to do it as follows to each ribbon we ascribe the number (n — z) mod 4, where the arithmetic operation mod 4 stands for subtraction from (n — z) of the maximum multiple of four, i.e. 4g (g = 0, 1, 2,... ). In other words,... 

Hund s rule of maximum multiplicity when electrons partially fill a subshell, they remain as unpaired as possible. 

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