Molecular-orbitals orbital unpairing

For systems with unpaired electrons, it is not possible to use the RHF method as is. Often, an unrestricted SCF calculation (UHF) is performed. In an unrestricted calculation, there are two complete sets of orbitals one for the alpha electrons and one for the beta electrons. These two sets of orbitals use the same set of basis functions but different molecular orbital coefficients. 

Iron carries half the charge of a whole electron. The calculation produces a set of molecular orbitals appropriate for this pseudowave function. HyperChem then assigns the unpaired electron its proper spin (alpha), substitutes this electron in the orbital formerly occupied by the half electrons, and calculates energy and other properties. 

Aromatic Radical Anions. Many aromatic hydrocarbons react with alkaU metals in polar aprotic solvents to form stable solutions of the corresponding radical anions as shown in equation 8 (3,20). These solutions can be analyzed by uv-visible spectroscopy and stored for further use. The unpaired electron is added to the lowest unoccupied molecular orbital of the aromatic hydrocarbon and a... 

So far, we have considered only the restricted Hartree-Fock method. For open shell systems, an unrestricted method, capable of treating unpaired electrons, is needed. For this case, the alpha and beta electrons are in different orbitals, resulting in two sets of molecular orbital expansion coefficients ... 

The molecular orbital description of the bonding in NO is similar to that in N2 or CO (p. 927) but with an extra electron in one of the tt antibonding orbitals. This effectively reduces the bond order from 3 to 2.5 and accounts for the fact that the interatomic N 0 distance (115 pm) is intermediate between that in the triple-bonded NO+ (106 pm) and values typical of double-bonded NO species ( 120 pm). It also interprets the very low ionization energy of the molecule (9.25 eV, compared with 15.6 eV for N2, 14.0 eV for CO, and 12.1 eV for O2). Similarly, the notable reluctance of NO to dimerize can be related both to the geometrical distribution of the unpaired electron over the entire molecule and to the fact that dimerization to 0=N—N=0 leaves the total bond order unchanged (2 x 2.5 = 5). When NO condenses to a liquid, partial dimerization occurs, the cis-form being more stable than the trans-. The pure liquid is colourless, not blue as sometimes stated blue samples owe their colour to traces of the intensely coloured N2O3.6O ) Crystalline nitric oxide is also colourless (not blue) when pure, ° and X-ray diffraction data are best interpreted in terms of weak association into... 

This could account for the paramagnetism, but esr evidence shows that the 2 cobalt atoms are actually equivalent, and X-ray evidence shows the central Co-O-O-Co group to be planar with an 0-0 distance of l3l pm, which is very close to the 128 pm of the superoxide, 02, ion. A more satisfactory formulation therefore is that of 2 Co atoms joined by a superoxide bridge. Molecular orbital theory predicts that the unpaired electron is situated in a rr orbital extending over all 4 atoms. If this is the case, then the jr orbital is evidently concentrated very largely on the bridging oxygen atoms. 

In molecular orbital terms, the stability of the allyl radical is due to the fact that the unpaired electron is delocalized, or spread out, over an extended 7T orbital network rather than localized at only one site, as shown by the computer-generated MO in Fig 10.3. This delocalization is particularly apparent in the so-called spin density surface in Figure 10.4, which shows the calculated location, of the unpaired electron. The two terminal carbons share the unpaired electron equally. 

Our treatment of O2 shows that the extra complexity of the molecular orbital approach explains features that a simpler description of bonding cannot explain. The Lewis structure of O2 does not reveal its two unpaired electrons, but an MO approach does. The simple (t-tt description of the double bond in O2 does not predict that the bond in 2 is stronger than that in O2, but an MO approach does. As we show in the following sections, the molecular orbital model has even greater advantages in explaining bonding when Lewis structures show the presence of resonance. 

As all interatomic distances in the ligands remain unaffected, the oxidation occurs locally in the CuS and Br2CuS2 moieties, respectively. This is in accord with MO calculations (vide infra), which showed that the unpaired electron in Cu(R2t/tc)2 is in a molecular orbital of predominant metal character. 

Molecules with two or more unpaired electrons may be divided into two classes by far the most common examples are molecules where the unpaired electrons are contained in a set of degenerate atomic or molecular orbitals with qualitatively similar spatial distributions, e.g., an octahedral Cr(m) (4A2g) or Ni(n) (3A2g) complex, a ground state triplet molecule like 02, or the excited triplet states of naphthalene or benzophenone. 

Here, the directions are defined in Fig. 6. In natural N02 the 170 content is quite small so the only observable hyperfine structure will be due to HN, which has a nuclear spin of one. Recent experiments, however, have been carried out using N02 enriched in 170 (34-) Molecular orbital calculations indicate that c2 is reasonably large, i.e., the unpaired electron is expected to have considerable nitrogen p2 character. 

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