Molecular orbitals interactions

Unlike quantum mechanics, molecular mechanics does not treat electrons explicitly. Molecular mechanics calculations cannot describe bond formation, bond breaking, or systems in which electronic delocalization or molecular orbital interaction splay a major role in determining geometry or properties. 

Frontier-molecular-orbital Interactions for Carbo-Diels-Alder Reactions... 

The molecular orbital interactions are almost independent of the conformation of the sandwich complex with respect to rotation of the Cp rings. Both the staggered (Dsd) as well as the eclipsed conformation (Dsh) possess similar binding energies... 

As a consequence of the molecular orbital interactions, ferrocene adopts an axially symmetrical sandwich structure with two parallel Cp ligands with a distance of 3.32 A (eclipsed conformation) and ten identical Fe-C distances of 2.06 A as well as ten identical C-C distances of 1.43 A [12]. Deviation of the parallel Cp arrangement results in a loss of binding energy owing to a less efficient orbital overlap [8]. All ten C-H bonds are slightly tilted toward the Fe center, as judged from neutron-diffraction studies [13]. 

CHART 3. Molecular orbital interaction diagram between the two [W(calix)] fragments in 22. 

In diastereomeric bi- and tricyclic ring systems containing three-membered rings, the 13C chemical shifts can vary considerably due to molecular orbital interactions with the cyclopropane electrons (see review s on this topic430,431). 

Further examination of the results indicated that by invocation of Pearson s Hard-Soft Acid-Base (HSAB) theory (57), the results are consistent with experimental observation. According to Pearson s theory, which has been generalized to include nucleophiles (bases) and electrophiles (acids), interactions between hard reactants are proposed to be dependent on coulombic attraction. The combination of soft reactants, however, is thought to be due to overlap of the lowest unoccupied molecular orbital (LUMO) of the electrophile and the highest occupied molecular orbital (HOMO) of the nucleophile, the so-called frontier molecular orbitals. It was found that, compared to all other positions in the quinone methide, the alpha carbon had the greatest LUMO electron density. It appears, therefore, that the frontier molecular orbital interactions are overriding the unfavorable coulombic conditions. This interpretation also supports the preferential reaction of the sulfhydryl ion over the hydroxide ion in kraft pulping. In comparison to the hydroxide ion, the sulfhydryl is relatively soft, and in Pearson s theory, soft reactants will bond preferentially to soft reactants, while hard acids will favorably combine with hard bases. Since the alpha position is the softest in the entire molecule, as evidenced by the LUMO density, the softer sulfhydryl ion would be more likely to attack this position than the hydroxide. 

When an atom or molecule is adsorbed on a surface new electronic states are formed due to the bonding to the surface. The nature of the surface chemical bond will determine the properties and reactivity of the adsorbed molecule. In the case of physisorption, the bond is rather weak, of the order of 0.3 eV. The overlap of the wave functions of the molecule and the substrate is rather small and no major change in the electronic structure is usually observed. On the contrary, when the interaction energy is substantially higher, there are rearrangements of the valence levels of the molecule, a process often denoted chemisorption. The discrete molecular orbitals interact with the substrate to produce a new set of electronic levels, which are usually broadened and shifted with respect to the gas phase species. In some cases completely new electronic levels emerge which have no resemblance to the original orbitals of the free molecule. 

In a solid the atomic or molecular orbitals interact strongly to form broad energy bands (Figure 3.43) which are known as the valence band (VB) and the conduction band (CB). The valence band results from the interaction of filled bonding or non-bonding orbitals, while the conduction band results from the interaction of normally vacant antibonding orbitals. As their names imply, electrons are strongly bound to nuclei in the VB, but they can move freely in the CB over the whole solid lattice. 

Figure 3.43 In a solid the atomic or molecular orbitals interact to form broad energy bands known as the valence band, VB, and the conduction band, CB. The smallest energy between these bands is the band gap energy...

Fig. 20.2 Schematic view of molecular orbital interaction between the caboxylic group of Dye 1 and surface Ti or Sn sites of metal oxide semiconductors.

Tada, T., Nozaki, D., Kondo, M., Yoshizawa, K., Molecular orbital interactions in the nanostar dendrimer. J. Phys. Chem. B 2003,107, 14204-14210. 

The pronounced difference in the relative stability can be understood as a manifestation of molecular orbital interactions. The SOMO of the cyclobutene ion has high orbital coefficients on the internal sp2 hybridized carbons (—CH=), whereas the butadiene SOMO has the highest coefficients in the terminal ( = CH2) carbons. Accordingly, substituents in the l-(and 2-) position will stabilize the closed ion. On the other hand, substituents in the 3-(and 4-) position will favor the ring opened ion and lower the barrier to ring opening. 

The interaction of C-M bonding orbitals with heteroatom lone-pair orbitals is a two-center-four-electron interaction. This is destabilizing and raises the energy of the HOMO relative to the unperturbed orbitals, and hence lowers the ionization potential of the heteroatom lone-pair electrons. The interaction is qualitatively represented by the molecular orbital interaction diagram shown in Figure 11. The strength of the interactions depends on a number of factors but most importantly on the orientation of the C-M bond with respect to the lone-pair orbital and on the... 

Earlier theoretical treatments based on molecular orbital interactions revealed that very polar intermediates or transition states are involved in both reactions, but these studies could not differentiate between the two cycloaddition modes [13]. However, a more recent treatment suggests that a common unpolar biradical intermediate exists [14]. The distinction between the ortho and the meta mode than occurs by dynamic effects mainly influenced by the substituents. 

The regioselectivity of the 1,3-dipolar cycloadditions of azides to alkenes is usually difficult to predict due to the similar energies for the transition states which involve either the HOMO (dipole) or the LUMO (dipole). The results of a study which utilized 5-alkoxy-3-pyrrolin-2-ones as dipolar-ophiles in reactions with a variety of aryl azides seemed to reflect this problem the results suggested that the low regioselectivity observed was due to the frontier molecular orbital interactions between dipole and dipolarophile, and not any steric hindrance offered by the 5-alkoxy function <84H(22)2363>. 

As pointed out in Section I, there are several ways to depict the bonding situation in Fig. 2 in valence bond terms, all of them having drawbacks for the sake of simplification. A more precise description can only be given by molecular orbital interaction diagrams. 

Fio. 3. Frontier molecular orbital interaction diagram for Cp(OC)2Mn(H)SiH3. [Reproduced from RabaS et al. (3b) with permission of Elsevier Science Publishers, Amsterdam.)... 

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