Frontier orbital calculations

The oxidative degradations of binuclear azaarenes (quinoline, isoquinoline, and benzodrazines) by hydroxyl and sulfate radicals and halogen radicals have been studied under both photochemical and dark-reaction conditions. A shift from oxidation of the benzene moiety to the pyridine moiety was observed in the quinoline and isoquinoline systems upon changing the reaction from the dark to photochemical conditions. The results were interpreted using frontier-orbital calculations. The reaction of OH with the dye 3,3,6,6-tetramethyl-3,4,6,7,9,10-hexahydro-(l,8)(2//,5//)-acridinedione has been studied, and the transient absorption bands assigned in neutral solution.The redox potential (and also the pA a of the transient species) was determined. Hydroxyl radicals have been found to react with thioanisole via both electron transfer to give radical cations (73%) and OH-adduct formation (23%). The bimolec-ular rate constant was determined (3.5 x lO lmoU s ). " ... 

There have been discussions whether the amide addition at C-6 is charge-controlled or orbital-controlled. Charge density calculations in 4-phenylpyrimidine (MNDO method) predict that the addition of the amide ion would preferably take place at position 2 (95UP1) this, however, does not agree with the experimental results. Therefore, the conclusion seems justified that the addition is not charge-controlled. Frontier orbital calculations, using the SCF-PPP method, show that the frontier orbital densities in the LUMO of pyrimidine are zero at C-2 and C-5, making these positions... 

It would be pointless anyhow to make approximate frontier orbital calculations, when the transition state is already known. 

During the reaction of cyclopentadiene with methylacrylate, higher temperatures in combination with longer reaction times lead to a shift in the endoiexo ratio from 1 1 to 3 1. This is contradictory to frontier orbital calculations predicting a loss of mdo exo selectivity in supercritical water because of the loss of the hydrophobic effect [48]. 

A rich cycloaddition chemistry with phosphaalkynes 9 may be expected from cross-conjugated carbocyclic compounds of the heptafulvene type (in the present case, tropone (41)). Thermal [rtf - and [jt a ]-cycloadditions are allowed by symmetry. Thus, the thermal reaction of tropone (41) with an excess of the phosphaalkynes 9 a, 9 e (without a solvent) furnishes the diphosphatetracyclic products 43a,b [45]. The initiating Diels-Alder reaction to 42 (there are P-NMR spectroscopic indications for its intermediate formation) is accordingly followed by a [2 -t- 2 + 2]-cycloaddition (ashomo-Diels-Alder reaction) with a second equivalent of the phosphaalkyne to yield 43 (Scheme 6-9). The observed peri- and regioselectivities of the two reaction steps can be confirmed by frontier orbital calculations [43],... 

The descriptors are based on the similarity of the frontier orbitals of the molecule in question to those of benzene and involves an analytical least squares fitting of the molecules frontier orbitals, calculated by any semiempirical or ab initio method to those carefully calculated for unsubstituted benzene. Both the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) of benzene are degenerate, and each consists of two components that may be mixed in any proportion with normalization to form an infinity of equally acceptable frontier orbitals. In benzene itself, each of these mixtures is equivalent. When the benzene is substituted, the degeneracy is lifted, and each of the resulting separate orbitals may be considered as being approximately derived from one particular linear combination of the original two components. 

HOMO and LLMO, also known as Frontier orbitals, are important in in tcrprcLitig results of a calculation (see Frontier Molecular Orbitals on page 141). You can use these m olecular orbiLals to comptiLe the lowest excited electronic singlet state of molecules and the ground states of radicals. 

Extended Huckel provides the approximate shape and energy ordering of molecular orbitals. It also yields the approximate form of an electron density map. This is the only requirement for many qualitative applications of quantum mechanics calculations, such as Frontier Orbital estimates of chemical reactivity (see Frontier Molecular Orbitals on page 141). 

You can use the information obtained from semi-empirical calculations to investigate many thermodynamic and kinetic aspects of chemical processes. Energies and geometries of molecules have clear relation ships to chemical ph en om ena. 0ther quan tities, like atomic charges and Frontier Orbitals, are less defined but provide useful qualitative results. 

Frontier Orbital theory supplies an additional assumption to this calculation. It considers only the interactions between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO). These orbitals have the smallest energy separation, leading to a small denominator in the Klopman-Salem equation. The Frontier orbitals are generally diffuse, so the numerator in the equation has large terms. 

Frontier Orbital theory is qualitative, so there is no need for great accuracy in the calculation as long as it produces the approximate form of the orbitals. 

This example uses AMI for optimization and orbital calculations. For more examples of Frontier Orbital theory, see Fleming sbook. ... 

Calculations at several levels of theory (AMI, 6-31G, and MP2/6-31G ) find lower activation energies for the transition state leading to the observed product. The transition-state calculations presumably reflect the same structural features as the frontier orbital approach. The greatest transition-state stabilization should arise from the most favorable orbital interactions. As discussed earlier for Diels-Alder reactions, the-HSAB theory can also be applied to interpretation of the regiochemistry of 1,3-dipolar cycloaddi-... 

Tile basic chromophors of indigo and of some tetraazafulvalenes are very similar and therefore the frontier orbitals are comparable (90JPC949). PPP calculations on the 1,3,5,7-tetraazafulvalene 90 (R = Me) showed a good agreement with its UV/VIS spectrum. Tlie substitution of both methyl-sulfanyl groups in 90 by diethylamino/piperidino moieties led to a hypso-chromic shift of about 45 nm. 

Predictions obtained by using the frontier orbital approximation213 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. 

Naphthalene undergoes electrophihc substitutions at the a rather than p position. The Hueckel molecular orbital calculations show that all the carbons have the same jt electron density 1.0. This is not in agreement with the theory of organic reactions based on the Coulombic interaction that electrophilic attack occurs on the most negatively charged atom. Fukui [7] proposed the frontier orbital theory for the discrepancy between the theory and the experimental observation. The importance of... 

According to the calculations at high levels of theory, the [4+2] cycloaddition reactions of dienes with the singlet ( A oxygen follow stepwise pathways [37, 38], These results, which were unexpected from the Woodward-Hoffmann rule and the frontier orbital theory, suggest that the [4+2] cycloadditions of the singlet ( A oxygen could be the reactions in the pseudoexcitation band. 

---