Orbital overlap and energy

For a reaction that can give rise to more than one product, the amount of each of the different products can depend on the reaction temperature. This is because, although all reactions are reversible, it can be difficult to reach equilibrium and a non-equilibrium ratio of products can be obtained. 

At low temperatures, reactions are more likely to be irreversible and equilibrium is less likely to be reached. Under these conditions, the product that is formed at the fastest rate predominates. This is kinetic control. The kinetic product is therefore formed at the fastest rate (i.e. this product has the lowest activation energy barrier). 

The outcomes of reactions under kinetic control are determined by the relative energies of the transition states leading to various different products 

Two atomic orbitals can combine to give two molecular orbitals - one bonding molecular orbital (lower in energy than the atomic orbitals) and one antibonding molecular orbital (higher in energy than the atomic orbitals) (see Section 1.4). Orbitals that combine in-phase form a bonding molecular orbital, and for the best orbital overlap, the orbitals should be of the same size. 

The orbitals can overlap end-on (as for o-bonds) or side-on (as for re-bonds). The empty orbital of an electrophile (which accepts electrons) and the filled orbital of a nucleophile (which donates electrons) will point in certain directions in space. For the two to react, the filled and empty orbital must be correctly ahgned for end-on overlap, the filled orbital should point directly at the empty orbital. 

The two electrons enter a lower energy molecular orbital. There is therefore a gain in energy and a new bond is formed. The further apart the HOMO and LUMO, the lower the gain in energy 

For maximum orbital overlap attack at 90° is required. However, attack at -107° is observed because of the greater electron density on the carbonyl oxygen atom, which repels the lone pair on H2O 

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If many atoms are bound together, for example in a crystal, their atomic orbitals overlap and form energy bands with a high density of states. Different bands may be separated by gaps of forbidden energy for electrons. The calculation of electron levels in the periodic potential of a crystal is a many-electron problem and requires several approximations for a successful solution. 

This reactivity pattern is certainly unexpected. Why should low-valent complexes react as electrophiles and highly oxidized complexes be nucleophilic Numerous calculations on model compounds have provided possible explanations for the observed chemical behavior of both Fischer-type [3-8] and Schrock-type [9-17] carbene complexes. In simplified terms, a rationalization of the reactivity of carbene complexes could be as follows. The reactivity of non-heteroatom-stabilized carbene complexes is mainly frontier-orbital-controlled. The energies of the HOMO and LUMO of carbene complexes, which are critical for the reactivity of a given complex, are determined by the amount of orbital overlap and by the energy-difference between the empty carbene 2p orbital and a d orbital (of suitable symmetry) of the group L M. 

Another important point deals with selectivity in the abstraction of -protons on equally substituted carbons. In a iyw-periplanar transition state as described above, the minimization of energy concept implies proton abstraction with a maximum of orbital overlap and a minimum of molecular deformation. Consequently, conformations possessing the more acute dihedral angles for bonds H —C—C—O wiU be favored (Scheme 2l/. 

Bond energy increases as bond length decreases the shorter bond length makes for greater orbital overlap and a stronger bond. 

The rearrangement occurs at least partially with antarafacial allylie participation and was estimated to be concerted in the sense of orbital-symmetry conservation control. Transition-structures appropriate to concerted pathways were judged likely to have exorbitantly high energies as a result of poor orbital overlap and unfavorable steric interactions. 

For example, the well known Walsh rules 52 for molecular geometries were first based on simple molecular orbital arguments depending on orbital overlap and the difference between s and p atomic energies. Pearson 51 re-interpreted them from a symmetry point of view as the following example will show. 

We shall explore how the orbital symmetries and energies of these small molecular fragments contribute to the observed properties of these compounds by using semiempirical electronic structure calculations. Our tools for analysis include an arsenal of computational indices, e.g. overlap populations and Mulliken populations.4 The remainder of this introduction... 

Simple algebra (see Exercise 3.3) shows that in both cases, the overlap between the two interacting VB structures is equal to S (the (a b) orbital overlap) and that resonance energy follows Equation 3.48 ... 

In the Forster mechanism, energy transfer occurs through dipolar interactions. This process is not coupled through bond interactions, and therefore orbital overlap and inter-component electronic coupling are unimportant. Dipole-dipole interactions may occur efficiently in systems where the donor and acceptor species are over 100 A apart, whereas Dexter energy transfer is typically efficient only up to distances of approximately 10 A. 

The orbital overlaps and relative energies are illustrated in Fig. 13.4.3. Note that i/q, if2, and if3 are bonding, nonbonding, and antibonding molecular orbitals, respectively. For the 3c-2e BHB bond, only [Pg.471]

Somewhat different is the case of the induction and dispersion energies. For these the expansion in inverse powers of r is only valid in the limit of vanishing orbital overlap, and in this case the expansions of equations (38), (39) are shown to overestimate the true value of the energy when such orbital overlap is taken into account. Indeed, studies carried out for small systems68-77 show that the values of the induction and dispersion coefficients decrease with decreasing r. Formally, it is possible to account for this effect by introducing the so-called damping functions as follows ... 

In contrast with the EHF energy, which can generally be estimated by ab initio methods for many systems of practical interest (see ref. 140 for a semiempirical treatment), the interatomic correlation energy is most conveniently approximated from the dispersion energy by accounting semiempiri-cally for orbital overlap and electron exchange effects. Thus the following... 

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