Frontier orbital approximation

Predictions obtained by using the frontier orbital approximation were unsuccessful, apparently due to inadequacies in these MO calculations mostly involving the energy gap between HO of the dipole and LU of the dipolarophile. 

Differentiating this expression with respect to the number of electrons gives a frontier orbital approximation in Equation 18.13 plus a correct due to orbital relaxation [17,18],... 

We start with Salem s treatment of the Walden inversion Frontier orbital approximation is assumed the major interaction is supposed to be that between the nucleophile s HOMO and the substrate s LUMO. Now, according to ab initio calculations, the latter is essentially an out-of-phase combination of a carbon hybrid atomic orbital 0c with a leaving group hybrid atomic orbital 0x- In the first approximation, the LUMO wave function may be written as ... 

Frontier-orbital approximations. A consistently useful frontier-orbital approximation for nucleophilic displacement at silicon was ex-... 

NUCLEOPHILIC DISPLACEMENTS AT SILICON A RATIONALIZATION OF THE STEREOCHEMISTRY BY A FRONTIER-ORBITAL APPROXIMATION... 

Anh and Minot (6) reported a rationalization of the stereochemistry at silicon by an extension of Salem s treatment of the Walden inversion (6 ). The frontier-orbital approximation is assumed, i.e., the major interaction during the reaction occurs between the HOMO of the nucleophile and the LUMO of the substrate o-f j-x. The calculated structure of the latter is shown below, with the big lobes of the hydrid AOs pointing toward each other (Scheme 9). 

This frontier-orbital approximation does not give a complete picture of the influence of the leaving group on the stereochemistry. For instance, it does not account for the aptitude of the Si—X bond to be stretched under... 

The last step in this argument, the frontier orbital approximation , is evidently of doubtful validity, and it is not surprising that the frontier electron density is not a reliable reactivity index, though at least one example of its failure 76 >84 has been disputed85 as attributable to an unsuitable choice of parameters. Since neither author gave his parameters, it is difficult to judge the validity of the criticism. We shall, however, return to the question of the frontier orbital approximation later. 

We now consider a more realistic case where molecules A and B each have several MOs, nA and nB, respectively. As a first approximation, we assume that each MO on A (or B) is perturbed by all the orbitals of B (or A), which act independently of each other. This amounts to treating nAnB two-orbital problems. This number will be significantly reduced by employing the frontier orbital approximation (see below). 

PMO methods can be easily applied only if the system can be modeled as a hydrocarbon, and can be disconnected into two alternant radicals. It cannot be used to determine the site of electrophilic attack on azulene, for example. Such a problem can easily be solved using the frontier orbital approximation see p. 119. 

This problem illustrates some of the limitations of rule 2 and the frontier orbital approximation. We begin by describing the carbonyl group in terms of an interaction between an sp2-hybridized C atom and an sp oxygen. We will place the molecule in the xy plane and orient the CO bond along the x-axis ... 

The simplest approximate description of II corresponds to what is known as the frontier orbitals approximation, where only the highest occupied and lowest unoccupied MOs (HOMO and LUMO, respectively) are involved. Within it one gets ... 

Up to this point, our main concern was to reformulate the results of the LD ligand influence theory in the DMM form. Its main content was the symmetry-based analysis of the possible interplay between two types of perturbation substitution and deformation, controlled by the selection rules incorporated in the polarization propagator of the CLS. The mechanism of this interplay can be simply formulated as follows substitution produces perturbations of different symmetries which are supposed to induce transition densities of the same symmetries. In the frontier orbital approximation, only those densities among all possible ones can actually appear, which have the symmetry which enters into decomposition of the tensor product TH TL to the irreducible representations. These survived transition densities then induce the geometry deformations of the same symmetry. 

Thus it may produce the transitional densities of the alg, egc, and tluz symmetries. At this point selection rules pertinent to the frontier orbitals approximation enter for the 12-electron complexes the symmetries of the frontier orbitals are Th = eg and Tl = ai3, the tensor product Th <8> TL = eg aig = eg contains only the irreducible representation eg so that the selection rules allow only the density component of the egc symmetry to appear. In its turn this density induces additional deformation of the same symmetry. That means that in the frontier orbitals approximation, only the elastic constant for the vibration modes of the symmetry eg is renormalized. This result is to be understood in terms of individual nuclear shifts of the ligands in the trans- and cis-positions relative to the apical one. They, respectively, are ... 

This section focuses on the main factors controlling the stereochemistry of substitution a possible rationalization of the experimental data based on a frontier-orbital approximation is presented (99, J00). A more detailed analysis may be found in our two previous comprehensive reviews (10,11). 

The frontier orbital approximation recognizes the interaction between the HOMO and LUMO on both reactants as the crucial effect controlling the course of a... 

The largest contribution to the double summation over orbital pairs in the second term will arise when the denominator is smallest. This occurs when the energies of the highest occupied MO (HOMO) of the base and the lowest unoccupied MO (LUMO) of the acid become closer. By considering only this contribution in the double summation (the so-called frontier orbitals approximation). Equation 1.38 simplifies to... 

---