Molecular semi-occupied

The strong electronic absorption of alkane radical cations is readily understood in molecular orbital terms. Extending down from the highest occupied molecular orbital (HOMO) is a rather closely packed set of valence molecular orbitals, that are clearly displayed in the photoelectron spectra (PES) of neutral alkanes. The electronic absorption of alkane radical cations is due to transitions (induced by photon absorption) of electrons from such lower-lying molecular orbitals to the semi-occupied molecular orbital (SOMO), which is the highest-occupied molecular orbital in the ground-state ion. By illumination within the (broad and largely unstructured) absorption band of alkane radical cations, electronically excited states of alkane radical cations can thus be created in a quite convenient way. 

Spin densities (p) are theoretical quantities, defined as the sum of the squared atomic orbital coefficients in the nonbonding semi-occupied molecular orbital (SOMO) of the radical species (Hiickel theory). For monoradical species, the spin density is connected to the experimental EPR hyperfine coupling constant a through the McConnell equation [38]. This relation provides the opportunity to test the spin density dependence of the D parameter [Eq. (8)] for the cyclopentane-1,3-diyl triplet diradicals 10 by comparing them with the known experimental hyperfine coupling constants (ap) of the corresponding substituted cumyl radicals 14 [39]. The good semiquadratic correlation (Fig. 9) between these two EPR spectral quantities demonstrates unequivocally that the localized triplet 1,3-diradicals 9-11 constitute an excellent model system to assess electronic substituent effects on the spin density in cumyl-type monoradicals. 

Early four-component numerical calculations of parity-violating effects in diatomic molecules which contain only one heavy nucleus and which possess a Si/2 ground state have been performed by Kozlov in 1985 [149] within a semi-empirical framework. This approach takes advantage of the similarity between the matrix elements of the parity violating spin-dependent term e-nuci,2) equation (114)) and the matrix elements of the hyperfine interaction operator. Kozlov assumed the molecular orbital occupied by the unpaired electron to be essentially determined by the si/2, P1/2 and P3/2 spinor of the heavy nucleus and he employed the matrix elements of e-nuci,2) nSi/2 and n Pi/2 spinors, for which an analytical expres-... 

The free radicals we shall discuss in this article have in common the basic structure of their semi-occupied orbitals. In its simplest form this semi-occupied molecular orbital is the linear combination F(2p) -M(ns) - F(2p), in which the fluorine 2p orbitals point towards the central atom (M) and are antibonding with respect to the M(ns) contribution (Fig. 3, top left). Also illustrated in Figure 3 are the prototypes of some of the fluorine-containing free radicals we shall be discussing. These examples illustrate the different ways linear F-M-F arrays can be combined to form molecular orbitals of various symmetries. In the case of the radicals SF3 and PF4 a single F-M-F array is used, but their low symmetries permit central-atom 3pg and apical fluorine Zp orbitals (z is the two-fold axis) also to be incorporated. 

This effect is probably due to an increased sulfur 3p contribution to the semi-occupied molecular orbital as the electronegativity of RO increases. An increased sulfur Sp contribution will cause increased polari zation of the S-F bond, resulting in a decrease in the F hyperfine interaction. It is not clear, however, why the effect is transmitted to the trans fluorine nucleus only, and it is a pity that no data are yet available on the 33s hyperfine interaction and hence on changes in the sulphur 3s contribution to the semi-occupied molecular orbital. 

Even with the minimal basis set of atomic orbitals used in most semi-empirical calculations, the number of molecular orbitals resulting from an SCFcalculation exceeds the number of occupied molecular orbitals by a factor of about two. The number of virtual orbitals in an ab initio calculation depends on the basis set used in this calculation. 

Eor transition metals the splitting of the d orbitals in a ligand field is most readily done using EHT. In all other semi-empirical methods, the orbital energies depend on the electron occupation. HyperChem s molecular orbital calculations give orbital energy spacings that differ from simple crystal field theory predictions. The total molecular wavefunction is an antisymmetrized product of the occupied molecular orbitals. The virtual set of orbitals are the residue of SCE calculations, in that they are deemed least suitable to describe the molecular wavefunction. 

Fig. 2.2 Self-Consistent Reaction Field (SCRF) model for the inclusion of solvent effects in semi-empirical calculations. The solvent is represented as an isotropic, polarizable continuum of macroscopic dielectric e. The solute occupies a spherical cavity of radius ru, and has a dipole moment of p,o. The molecular dipole induces an opposing dipole in the solvent medium, the magnitude of which is dependent on e.

AMI semi-empirical and B3LYP/6-31G(d)/AMl density functional theory (DFT) computational studies were performed with the purpose of determining which variously substituted 1,3,4-oxadiazoles would participate in Diels-Alder reactions as dienes and under what conditions. Also, bond orders for 1,3,4-oxadiazole and its 2,5-diacetyl, 2,5-dimethyl, 2,5-di(trifluoromethyl), and 2,5-di(methoxycarbonyl) derivatives were calculated <1998JMT153>. The AMI method was also used to evaluate the electronic properties of 2,5-bis[5-(4,5,6,7-tetrahydrobenzo[A thien-2-yl)thien-2-yl]-l,3,4-oxadiazole 8. The experimentally determined redox potentials were compared with the calculated highest occupied molecular orbital/lowest unoccupied molecular orbital (HOMO/LUMO) energies. The performance of the available parameters from AMI was verified with other semi-empirical calculations (PM3, MNDO) as well as by ab initio methods <1998CEJ2211>. 

The simple orbital basis expansion method which is used in the implementation of most models of molecular electronic structure consists of expanding each R as a linear combination of determinants of a set of (usually) atom-centred functions of one or two standard forms. In particular most qualitative and semi-quantitative theories restrict the terms in this expansion to consist of the (approximate) occupied atomic orbitals of the constituent atoms of the molecule. There are two types of symmetry constraint implicit in this technique. 

Some authors have described the time evolution of the system by more general methods than time-dependent perturbation theory. For example, War-shel and co-workers have attempted to calculate the evolution of the function /(r, Q, t) defined by Eq. (3) by a semi-classical method [44, 96] the probability for the system to occupy state v]/, is obtained by considering the fluctuations of the energy gap between and 11, which are induced by the trajectories of all the atoms of the system. These trajectories are generated through molecular dynamics models based on classical equations of motion. This method was in particular applied to simulate the kinetics of the primary electron transfer process in the bacterial reaction center [97]. Mikkelsen and Ratner have recently proposed a very different approach to the electron transfer problem, in which the time evolution of the system is described by a time-dependent statistical density operator [98, 99]. 

Unpaired electronic density can be delocalized onto the various nuclei of the complex via through-bond scalar hyperfine interactions involving occupied orbitals containing s-character (direct interaction or polarization according to the Fermi mechanism, Wertz and Bolton (1986)). Random electron relaxation thus produces a flip-flop mechanism which affects the nuclear spin and increases nuclear relaxation processes (Bertini and Luchinat, 1996). Since these interactions are isotropic, they do not depend on molecular tumbling and re is the only relevant correlation time for non-exchanging semi-rigid complexes. Moreover, only electronic spin can be delocalized via hyperfine interactions (no orbital contribution) and the contact re-... 

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