Closed-shell molecules

Closed-shell molecules have a multiplicity of one (a singlet). Arad-ical, with one unpaired electron, has a spin multiplicity of two (a doublet). Amolecular system with two unpaired electrons (usually... 

In most cases of closed-shell molecules Koopmans theorem is a reasonable approximation but N2 (see Section 8.1.3.2b) is a notable exception. For open-shell molecules, such as O2 and NO, the theorem does not apply. 

Because of the general validity of Koopmans theorem for closed-shell molecules ionization energies and, as we shall see, the associated vibrational sttucture represent a vivid illustration of the validity of quite simple-minded MO theory of valence electrons. 

A few free radicals are indefinitely stable. Entries 1, 4, and 6 in Scheme 12.1 are examples. These molecules are just as stable under ordinary conditions of temperature and atmosphere as typical closed-shell molecules. Entry 2 is somewhat less stable to oxygen, although it can exist indefinitely in the absence of oxygen. The structures shown in entries 1, 2, and 4 all permit extensive delocalization of the unpaired electron into aromatic rings. These highly delocalized radicals show no tendency toward dimerization or disproportionation. Radicals that have long lifetimes and are resistant to dimerization or other routes for bimolecular self-annihilation are called stable free radicals. The term inert free radical has been suggested for species such as entry 4, which is unreactive under ordinary conditions and is thermally stable even at 300°C. ... 

Although not strictly part of a model chemistry, there is a third component to every Gaussian calculation involving how electron spin is handled whether it is performed using an open shell model or a closed shell model the two options are also referred to as unrestricted and restricted calculations, respectively. For closed shell molecules, having an even number of electrons divided into pairs of opposite spin, a spin restricted model is the default. In other words, closed shell calculations use doubly occupied orbitals, each containing two electrons of opposite spin. 

Electron propagator theory generates a one-electron picture of electronic structure that includes electron correlation. One-electron energies may be obtained reliably for closed-shell molecules with the P3 method and more complex correlation effects can be treated with renormalized reference states and orbitals. To each electron binding energy, there corresponds a Dyson orbital that is a correlated generalization of a canonical molecular orbital. Electron propagator theory enables interpretation of precise ab initio calculations in terms of one-electron concepts. 

A radical has a singly occupied molecular orbital (SOMO). This is the frontier orbital. The SOMO interacts with HOMO and the LUMO of closed-shell molecules to stabilize the transition state (Scheme 27). The radical can be a donor toward a monomer with low LUMO or an acceptor toward one with high HOMO. 

Experimental data on aliphatic radicals are more abundant. Unfortunately, the standard CNDO/2 method is not even appropriate to estimate heats of formation of closed-shell molecules (71). Among the UNDO modifications suggested, the most successful is that of Fischer and Kollmar (81), who have... 

Even the photoelectron spectroscopy of closed-shell molecules is valuable for the physical chemistry of radicals because a difference between the nth and the first adiabatic ionization potentials determines the excitation energy in a radical cation for a transition from the ground doublet state to the (n — 1) excited doublet state. 

In radical chemistry, one often needs to estimate a priori a value of the disproportionation constant. Before attempting to do this, let us start with the following consideration. In general, each closed-shell molecule can be converted to radical ions by a removal or an uptake of an odd number of electrons, and to polyions by a removal or an uptake of an even number of electrons. This statement can be expressed schematically as... 

C. A., Van Dorn, L.O. and Wilkinson, C.C. (2002) Most easily-ionized, closed-shell molecules known easier than the cesium atom. Science, 298, 1971-1974 ... 

Modern reviews of BDEs in closed-shell molecules measured by using mass spec-trometric methods have been provided by Ellison and co-workers. ° Additional evaluations have been provided by Ervin and DeTuri. A list of important fundamental hydrocarbon BDEs is given in Table 5.2. 

Furthermore, large amplitude vibrational motions are characterized by fundamental changes in the nature of the electronic structure of the system. Dissociation of many closed shell molecules, for example HC1, transforms two atoms cohabitating in a fashion that repels electrons into a non-interacting pair of electron-attractors . c This picture suggests that molecules subjected to the rigors of large amplitude vibrational motion... 

The OVGF function method provides a quantitative account of ionisation phenomena when the independent-particle picture of ionisation holds and as such is most applicable in the treatment of outer-valence orbitals. It provides an average absolute error for vertical ionisation energies below 20 eV of 0.25 eV for closed shell molecules. The TDA and ADC(3) methods allow for the breakdown of one particle picture of ionisation and so enable the calculation of the shake up spectra. The ADC(3) is correct up to 3rd order, is size consistent and includes correlation effects in both the initial and final states. 

The next approximation is to assume that exactly the same CMOs j of the radical cation M+, by simply removing one of the two electrons occupying the CMO [Pg.198]

FIGURE 3. Graphical representation of the electron configuration o of a closed-shell molecule M and of the configurations 20 of its radical cation M+ as approximations to the states and 2j (J = 1,2,3). The arrows in the representations of 22 and 23 indicate that these configurations correspond to electronic excitations of M+, relative to its ground-state configuration 2 i... 

V. REGIOSELECTIVITY IN REACTIONS OF POLYENYL RADICALS A. Trapping with Closed-shell Molecules... 

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