Maximum overlap, principle

This reflects the maximum overlapping principle between HO and LU. 

For the catalytic reaction, it was assumed that adsorbed acrolein reacts on free dihydrop)T an, as suggested by the thermodynamical results. In fact, the complexation of acrolein with a Lewis acid reduces the LUMO-HOMO gap to 6.9 eV and thus stabilizes the transition state of the reaction. The acrolein protonation lowers again the orbital level of the diene and in this case the gap is lowered to 2.2 eV. In all three cases (uncatalyzed, Lewis and Bronsted acid-catalyzed) the major orbital interaction leading to the transition state occurs between the LUMO of acrolein and the HOMO of dihydropyran. Moreover the maximum overlap principle predicts the same major regioisomer, in agreement with experimental results. 

It is apparent that Corey s rule requires modification when strong steric opposition to axial attack exists. In an attempt to unify the conflicting views, Valls has suggested that Corey s principle of preferred axial attack, which ensures maximum overlap, be extended. 

It is thus evident that the reaction path is controlled by the frontier-orbital interaction. The position of reaction will be determined by the rule of maximum overlapping of frontier orbitals, that is, HO and LU MO s of the two reacting molecules. Sometimes SO takes the place of HO or LU in radicals or excited molecules. Hence, the general orientation principle would be as follows ... 

Localized bonding orbitals are then constructed from a linear combination of the orbital on each of the paired atoms. To do this we use the principle of maximum overlap, which states... 

Six-Membered Ring (endo-Cyclic). All the previous discussion of stereo-attack is based on steric hindrance, but in the case of a six-membered ring (endo-cyclic) enolate, the direction is affected simultaneously by stereo-electronic effects (Scheme 2-4).10 In the transition state, the attacking electrophiles must obey the principle of maximum overlap of participating orbitals by perpendicularly approaching the plane of atoms that constitute the enolate functional group. Electrophile attacks take place on the two diastereotopic... 

Due to the simplicity and the ability to explain the spectroscopic and excited state properties, the MO theory in addition to easy adaptability for modern computers has gained tremendous popularity among chemists. The concept of directed valence, based on the principle of maximum overlap and valence shell electron pair repulsion theory (VSEPR), has successfully explained the molecular geometries and bonding in polyatomic molecules. 

As we have pointed out many times previously, the columns of the standard tableaux functions are antisymmetrized, and the orbitals in a column may be replaced by any linear combination of them with no more than a change of an unimportant overall constant. In this case, consider a linear combination that has two hybrid orbitals that point directly at the H atoms in accord with Pauling s principle of maximum overlap. Using the parameter

[Pg.180]

This effect has been reproduced in ab initio calculations40 and rationalized.41 The principle of maximum overlap states that the preferred trajectory corresponds to the best molecular overlap between the reaction partners (rule 4). If the nucleophile adopts a perpendicular trajectory, the atomic overlap with the carbon will be maximized. However, a competing out-of-phase overlap between the nucleophile HOMO and the carbonyl LUMO (shown by the wavy line) reduces the overall frontier orbital interaction. If the nucleophile is displaced laterally (arrow), the small diminution in the overlap with C is outweighed by the reduction in the antibonding interaction with O. This increase in the overall overlap explains the preference for attack from an obtuse angle... 

The main factors that determine the steric coordination of molecules and crystal lattices (accepting that the positions of chemical bonds between atoms in lattice obey the same laws of electron density distribution that are actual for molecules) is the direction and the principle of maximum overlapping. The strongest chemical bonds are formed in the direction of maximum overlapping between the orbitals ofbinding electrons. 

If the wave function is the exact wave function, we obtain for E the exact (nonrelativistic) energy. If is an approximate wave function, the variational principle (Levine, 1983) tells us that the lower the E the more closely il> resembles the exact wave function, so long as it satisfies certain conditions, the most important being the Pauli exclusion principle. If i ( contains parameters, then that choice of parameters giving the lowest E will give the best wave function in the sense of maximum overlap with the true wave function. 

The principle of maximum overlap, first stated in 1931 by Linus Pauling (at the California Institute of Technology), has been ranked only slightly below the exclusion principle in importance to the understanding of molecular structure. 

For maximum charge-transfer interaction the relative orientations of the two molecules must provide maximum overlap of the filled donor orbital and the vacant acceptor orbital. This is known as Mulliken s Overlap and Orientation principle [94]. 

The structure in space of polyatomic molecules depends on the stereochemistry of their chemical bonds through the principle of maximum overlap (Magnasco, 2005). 

Neglecting hybridization, as we did so far, the angle between p and pi is 26 = 90°, so that the resulting O—H bonds will be bent outwards, since the experimentally observed valence angle is about 26 = 105° (Herzberg, 1956). This is contrary to the principle of maximum overlap... 

The hybridization parameter < >, arbitrary so far, is best chosen so as the bond hybrids bi and b2 point in the direction of the two O—H bonds, giving in this way strongest bonding with His orbitals and satisfying the principle of maximum overlap. According to Equation (2.214), 26 = 105° gives o)Ki 40°, and we obtain the set (Figure 2.21) ... 

This is what we expect in absence of hybridization, the resulting N—H bonds being strongly bent outwards, and so very far from the principle of maximum overlap. 

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