Singly Occupied MO

In PMD radicals, the bond orders are the same as those in the polymethines with the closed electron shell, insofar as the single occupied MO with its modes near atoms does not contribute to the bond orders. Also, an unpaired electron leads the electron density distribution to equalize. PMD radicals are characterized by a considerable alternation of spin density, which is confirmed by epr spectroscopy data (3,19,20). 

Polymethine Radicals. Two transitions occur with low energy involving the single occupied MO (SOMO) in the PMD radical (/) the electron transition from the highest double occupied MO to the SOMO and (2) the transition from the SOMO to the LUMO. 

The biradical resonance structure for ozone requires two singly occupied MOs, and it is clear that an RHF type wave function, which requires all orbitals to be doubly occupied, cannot describe this. A UHF type wave function, however, allows the a and /3 orbitals to be spatially different, and can to a certain extent incorporate both resonance structures. Systems with biradical character will often have a (singlet) UHF wave function different from an RHF. 

A common feature of all of the systems considered is the presence of an open shell, i.e., a singly occupied MO hence, they are all called open-shell systems. The radicals can be electroneutral (radicals in a narrow sense), electropositive (radical cations), or electronegative (radical anions). Radical di-ions and tri-ions are less frequent. 

The existing SCF procedures are of two types in restricted methods, the MO s, except for the hipest (singly) occupied MO, are filled by two electrons with antiparallel spin, while in unrestricted methods, the variation procedure is performed with individual spin orbitals. In the latter, a total wave function is not an eigenvalue of the spin operator S, which is disadvantageous in many applications because of a necessary annihilation of higher multiplets by the projection operator. Since in practical applications the unrestricted methods have not proved to be remarkably superior, we shall call our attention in this review mainly to the restricted methods. 

As has been mentioned in Chap. 5, the singly occupied MO in odd-electron molecules and radicals plays the role of HO or LU or both MO s according to the orbital energy relationship and the orbital overlapping situation. The importance of SO distribution is easily understood... 

In the reactions mentioned in the preceding sections, several "stereoselective processes have been involved. Various examples have verified that the extension of singly-occupied MO determines the favorable spatial direction of interaction with other species. If there are two such nonequivalent directions in the molecule, the reaction will become stereoselective. Two or more hydrogen atoms attached to the same carbon atom are in some cases nonequivalent. Such a nonequivalence becomes a cause of stereoselectivity and has been explained theoretically. Also several cases have been mentioned in which some nucleophiles selectively attack the molecule from a certain spatial direction. 

The interaction of a singly occupied MO, 0j, with a singly occupied degenerate MO, 0j, leads to two electron stabilization given by the following equation ... 

Radiation-induced electron transfer to nitroso compounds has also been studied. This technique, using electron expulsion from trichlorofluoromethane, provided data that the radical cation 54 is formed from nitrosobenzene at 77 K. Analysis of the EPR spectrum indicates that the singly occupied MO lies in the plane of the benzene ring and has high 2s character74. Irradiation of the dimer 55 under the same conditions shows that a trace of the monomeric radical cation 56 is produced74. 

Both theory and experiment point to an almost perpendicular orientation of the two butadiene H2C=C(t-Bu)— moieties see Scheme 3-47. On passing from the neutral molecule to its anion radical, this orthogonal orientation should flatten, because the LUMO of 1,3-butadiene is bonding between C(2) and C(3). So this bond should be considerably strengthened after formation of the anion-radical. The anion radical will acquire a cisoidal conformation. This conformation places two bulky tert-butyl substituents on one side of the molecule, so the alkali metal counterion (M+) can closely approach the anion radical from the other side. In this case, the cation will detain spin density in the localized part of the molecular skeleton. A direct transfer of the spin population from the singly occupied MO of the anion radical into the alkali cation has been proven (Gerson et al. 1998). 

For drug-sized molecules, an MO calculation is more practical than post-HF methods. Such a calculation will give you a set of filled MOs and a set of unoccupied (so-called virtual) MOs (and, in the case of radicals, one or more singly occupied MOs). Simplistically, electronic excitations can be thought of as promoting an electron from one of the occupied MOs to an unfilled one. In reality, of course, the MOs would adjust to the excitation so that the ground state MOs are only an approximation to the excited state MOs. 

In contrast to closed shell molecules, free radicals are species which have an odd number of electrons. Simply speaking, all electrons in free radical species are considered to be paired up, except for one orbital which contains the single electron. The molecular orbital which describes the distribution of this odd electron is called the SOMO (singly occupied MO). In the ground state of the radical, the SOMO is also the HOMO. In a carbon-based free radical the SOMO is generally strongly localized to a trigonal carbon atom. 

Method. Assume that (1) the reaction is controlled by the interaction between the radical SOMO (singly occupied MO) and the frontier orbitals of the substrates (2) the radical adds preferentially to the unsubstituted carbon of the vinyl acetate. 

However, it is wise to be careful. If the SOMO (singly occupied MO) lies close in energy to other orbitals, the radical must be described as a combination of several electronic configurations (by configuration interaction57). Thus, the ground state (a) may be affected by mixing with excited states, such as ... 

In the open-shell (os) case [48] one partitions the CBO matrix into contributions originating from the closed-shell (doubly occupied) MO open-shell (singly occupied) MO cs, os) ... 

Electrons must be in singly occupied MOs to conduct a current. 

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