Orbitals spin pairing

This type of diagram shows the Is and 2s electrons spin-paired, but the p electrons occupy different orbitals and are not paired. The diagram only illustrates the state of electron spins in each orbital, and does not indicate the relationship between energy levels. The next element, oxygen, will have one of the p orbitals spin-paired, with two p orbitals singly occupied ... 

This is an example of a Mobius reaction system—a node along the reaction coordinate is introduced by the placement of a phase inverting orbital. As in the H - - H2 system, a single spin-pair exchange takes place. Thus, the reaction is phase preserving. Mobius reaction systems are quite common when p orbitals (or hybrid orbitals containing p orbitals) participate in the reaction, as further discussed in Section ni.B.2. 

The half-electron method can also apply to triplet states. For this calciilatioit. IlyperCheni populates selected molecular orbitals with pairs of half electron s. The final energy is computed by assigning the proper spins. 

A UHF wave function may also be a necessary description when the effects of spin polarization are required. As discussed in Differences Between INDO and UNDO, a Restricted Hartree-Fock description will not properly describe a situation such as the methyl radical. The unpaired electron in this molecule occupies a p-orbital with a node in the plane of the molecule. When an RHF description is used (all the s orbitals have paired electrons), then no spin density exists anywhere in the s system. With a UHF description, however, the spin-up electron in the p-orbital interacts differently with spin-up and spin-down electrons in the s system and the s-orbitals become spatially separate for spin-up and spin-down electrons with resultant spin density in the s system. 

We can now build a closed shell wavefunction by defining n/2 molecular orbitals for a system with n electrons, and then assigning electrons to these orbitals in pairs of opposite spin ... 

Draw a Lewis structure for singlet methylene, CH2 (all the electrons in singlet methylene are spin-paired). Ho many electrons remain after all bonds have been formei Where are the extra electrons located, in the plane the molecule or perpendicular to the plane Examine t highest-occupied molecular orbital (HOMO) of methyle to tell. 

Divalent carbon species called carbenes are capable of fleeting existence. For example, methylene, CH2, is the simplest carbene. The two unshared electrons in methylene can be either spin-paired in a single orbital or unpaired in different orbitals. Predict the type of hybridization you expect carbon to adopt in singlet (spin-paired) methylene and triplet (spin-unpaired) methylene. Draw a picture of each, and identify the valence orbitals on carbon. 

When drawing a box diagram, show the electrons in different orbitals of the same subshell with parallel spins electrons sharing an orbital have paired spins. 

C atom has one unpaired electron in each of its four sp hybrid orbitals and can therefore form four cr-bonds that point toward the corners of a regular tetrahedron. The C—C bond is formed by spin-pairing of the electrons in one sp hybrid orbital of each C atom. We label this bond hybrid orbital composed of 2s- and 2/t-orbitals on a carbon atom, and the parentheses show which orbitals on each atom overlap (Fig. 3.15). Each C—H bond is formed by spin-pairing of an electron in one of the remaining sp hybrid orbitals with an electron in a 1 s-orbital of an H atom (denoted His). These bonds are denoted cr(C2s/ Hls). 

Lewis s theory of the chemical bond was brilliant, but it was little more than guesswork inspired by insight. Lewis had no way of knowing why an electron pair was so important for the formation of covalent bonds. Valence-bond theory explained the importance of the electron pair in terms of spin-pairing but it could not explain the properties of some molecules. Molecular orbital theory, which is also based on quantum mechanics and was introduced in the late 1920s by Mul-liken and Hund, has proved to be the most successful theory of the chemical bond it overcomes all the deficiencies of Lewis s theory and is easier to use in calculations than valence-bond theory. 

First, note that there is a parallel relationship between high-spin tetrahedral and spin-paired planar d, as compared with the octahedral and planar situations just described. Analogous to Fig. 7-4, we have Fig. 7-5. Do not be confused about the reversed labelling of the xy and orbitals at the extremes of Fig. 7-4 and... 

Figure 2 Orbital splitting illustrating the reduced tendency for spin pairing in planar ds species with...

In the former, electrons are assigned to orbitals in pairs, the total spin is zero, so the multiplicity is 1. In this case, the restricted Hartree-Fock method (RHF) can be applied. For radicals with doublet or triplet states, the unrestricted Hartree-Fock (UHF) has to be applied. In this method, a and, 3 electrons (spin up and spin down) are assigned to different spatial orbitals, so there are two distinct sets I and FJf... 

The bonding n molecular orbital of the allyl cation contains two spin-paired electrons. 

Two of the 7i molecular orbitals of 1,3-butadiene are bonding molecular orbitals, i) In the ground state these orbitals hold the four tz electrons with two spin-paired... 

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