Shell molecule

IXDCf is faster than MINDO/3, MNDO, AMI, and PM3 and, unlike C XDO, can deal with spin effects. It is a particularly appealing choice for UHF calculations on open-shell molecules. It is also available for mixed mode calculations (see the previous section ). IXDO shares the speed and storage advantages of C XDO and is also more accurate. Although it is preferred for numerical results, it loses some of the simplicity and inierpretability of C XDO. 

Another way of constructing wave functions for open-shell molecules is the restricted open shell Hartree-Fock method (ROHF). In this method, the paired electrons share the same spatial orbital thus, there is no spin contamination. The ROHF technique is more difficult to implement than UHF and may require slightly more CPU time to execute. ROHF is primarily used for cases where spin contamination is large using UHF. 

Cl results can vary a little bit from one software program to another for open-shell molecules. This is because of the HF reference state being used. Some programs, such as Gaussian, use a UHF reference state. Other programs, such as MOLPRO and MOLCAS, use a ROHF reference state. The difference in results is generally fairly small and becomes smaller with higher-order calculations. In the limit of a full Cl, there is no difference. 

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... 

Berthier, G., Self-Consistent Field Methods for Open-Shell Molecules, in Molecular Orbitals in Chemistry, Physics, and Biology, P. O. Lbwdin and B. Pullman, Eds., Academic Press, New York, 1964, pp. 57-82. 

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 ... 

It is possible to construct a HF method for open-shell molecules that does maintain the proper spin symmetry. It is known as the restricted open-shell HF (ROHF) method. Rather than dividing the electrons into spin-up and spin-down classes, the ROHF method partitions the electrons into closed- and open-shell. In the easiest case of the high-spin wavefunction ( op = — electrons in op... 

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... 

---