Molecular orbital substitution

Equation A.6 results because only the terms in (A.5) that survive when (A.5) is substituted into <0 2 / A> are those for which7 =kg and7 = / (where / designates any SCF molecular orbital). Substituting for kQ> from (A.1) yields... 

A is a parameter that can be varied to give the correct amount of ionic character. Another way to view the valence bond picture is that the incorporation of ionic character corrects the overemphasis that the valence bond treatment places on electron correlation. The molecular orbital wavefimction underestimates electron correlation and requires methods such as configuration interaction to correct for it. Although the presence of ionic structures in species such as H2 appears coimterintuitive to many chemists, such species are widely used to explain certain other phenomena such as the ortho/para or meta directing properties of substituted benzene compounds imder electrophilic attack. Moverover, it has been shown that the ionic structures correspond to the deformation of the atomic orbitals when daey are involved in chemical bonds. 

Having the Slater atomic orbitals, the linear combination approximation to molecular orbitals, and the SCF method as applied to the Fock matrix, we are in a position to calculate properties of atoms and molecules ab initio, at the Hartree-Fock level of accuracy. Before doing that, however, we shall continue in the spirit of semiempirical calculations by postponing the ab initio method to Chapter 10 and invoking a rather sophisticated set of approximations and empirical substitutions... 

For this class of thiazoles most of the chemical and physicochemical studies are centered around the protomeric equilibrium and its consequences. The position of this equilibrium may be determined by spectroscopic and titrimetric methods, as seen in each section. A simple HMO (Hiickel Molecular Orbitals) treatment of 2-substituted compounds however, may, exemplify general trends. This treatment considers only protomeric forms 1 and 2 evidence for the presence of form 3 has never been found. The formation energy reported in Table 1 is the energy difference in f3 units. 

Sandstrom et al. (65) evaluated the Kj value for 4,5-dimethyl-A-4-thiazoline-2-thione (46) in water (Scheme 19) K-j= 10. A-4-Thiazoline-2-thiones are less basic in the first excited state (61) than in the ground state, so application of Forster s cycle suggests that the thione form is even more favored in the first excited state. Huckel molecular orbital (HMO) calculations suggest that electronic effects due to substitution in... 

High level molecular orbital calculations of cyclobutadiene itself and experimen tally measured bond distances of a stable highly substituted derivative both reveal a pat tern of alternating short and long bonds characteristic of a rectangular rather than square geometry... 

Iron carries half the charge of a whole electron. The calculation produces a set of molecular orbitals appropriate for this pseudowave function. HyperChem then assigns the unpaired electron its proper spin (alpha), substitutes this electron in the orbital formerly occupied by the half electrons, and calculates energy and other properties. 

Now that you know the mathematical form, you can solve the independent-electron Schrodinger equation for the molecular orbitals. First substitute the LCAO form above into equation (47) on page 193, multiply on the left by and integrate to represent... 

Electrophilic Aromatic Substitution. The Tt-excessive character of the pyrrole ring makes the indole ring susceptible to electrophilic attack. The reactivity is greater at the 3-position than at the 2-position. This reactivity pattern is suggested both by electron density distributions calculated by molecular orbital methods and by the relative energies of the intermediates for electrophilic substitution, as represented by the protonated stmctures (7a) and (7b). Stmcture (7b) is more favorable than (7a) because it retains the ben2enoid character of the carbocycHc ring (12). 

The problems associated with predicting regioselectivity in quinone Diels-Alder chemistry have been studied, and a mechanistic model based on frontier molecular orbital theory proposed (85). In certain cases of poor regioselectivity, eg, 2-methoxy-5-methyl-l,4-ben2oquinone with alkyl-substituted dienes, the use of Lewis acid catalysts is effective (86). 

Vertical Ionization Energies (eV) of ttj and ir2 Molecular Orbitals of 2-Substituted Heterocycles... 

The TT-electron density refers to the electron density at a given carbon atom obtained by summing the contributions from all the filled molecular orbitals. Electrophilic attack occurs where this density is highest, and nucleophilic attack where it is lowest tt-electron densities are not dominant in determining the orientation of homolytic substitution. 

Perfluoroalkyl groups adjacent to multiple bond systems lower the frontier molecular orbitals (FMOs) Therefore, cycloaddition reactions preferentially occur with electron-rich multiple-bond systems The preference of bis(trifluoromethyl)-substituted hetero-l,3-dienes for polar reacuons makes them excellent model compounds for developing new types of diene reactions deviating from the well documented Diels-Alder scheme (pathway 1) A systematic study of the reactions of diene (1 =2-3=4)-dienophile (5=6) combinations reveals new synthetic possibilities that have not yet been fully exploited as tools for preparative organic cherrustry (equation 25)... 

Selective ether cleavage comes about during the substitution step, which obeys an Sn2 mechanism. Therefore, selective cleavage requires selective attack by Y on one of the electrophilic carbons in the protonated ether. Determine if selective attack is likely by examining the shape of the lowest-unoccupied molecular orbital (LUMO) in protonated ethyl propyl ether. Is this orbital larger near one carbon than the other If so, what product combination will result What other atom(s) contribute to the LUMO What would happen if 1 attacked this atom(s) ... 

One way to anticipate the favored product is to consider the shape of naphthalene s best electron-donor orbital, the highest-occupied molecular orbital (HOMO). Display the HOMO in naphthalene and identify the sites most suitable for electrophilic attack. Which substitution product is predicted by an orbital-control mechanism Ts this the experimental result ... 

Examine pyrrole s highest-occupied molecular orbital (HOMO) to see if your can predict the most favorable protonation site. Which of the pyrrole s conjugate acids (N protonated, C2 proto noted, C3 proto noted pyrrole) is lowest in energy Examine electrostatic potential maps to see if the lowest-energy form is also that in which the positive charged is best delocalized. Rationalize your result using resonance arguments. What should be the favored substitution product ... 

In addition to electrophilic attack on the pyrrole ring in indole, there is the possibility for additions to the fused benzene ring. First examine the highest-occupied molecular orbital (HOMO) of indole. Which atoms contribute the most What should be the favored position for electrophilic attack Next, compare the energies of the various protonated forms of indole (C protonated only). These serve as models for adducts formed upon electrophilic addition. Which carbon on the pyrrole ring (C2 or C3) is favored for protonation Is this the same as the preference in pyrrole itself (see Chapter 15, Problem 2)1 If not, try to explain why not. Which of the carbons on the benzene ring is most susceptible to protonation Rationalize your result based on what you know about the reactivity of substituted benzenes toward electrophiles. Are any of the benzene carbons as reactive as the most reactive pyrrole carbon Explain. 

Radicaloid substitution has not been extensively studied in the thiophene series. Molecular orbital calculations indicate that substitution should occur in the a-position. This has been found to be the case in the Gomberg-Bachmann coupling of diazohydroxides with thiophenes which has been used for the preparation of 2-(o-nitro-phenyl) thiophene, 2-(p-toluyl) thiophene, " " and 2-(p-chloro-phenyl)thiophene. " Coupling in the /8-position has been used for the preparation of 1,3-dimethyl-4,5-benzisothionaphthene (148) from 2-amino-tt-(2,5-dimethyl-3-thienyl)cinnamic acid (149). A recent investigation describes the homolytic phenylation of 2- and 3-phenyl-... 

Molecular orbital calculations have been used to estimate equilibrium constants, although up to the present these attempts have not met with much success. Using calculations of this type, 2- and 4-hydroxypyridine 1-oxide were predicted to be more stable than 1-hydroxypyrid-2- and -4-one by ca. 20 kcal/mole, which corresponds to a ratio of ca. 10 between the forms. It was later shown experimentally that, at least in the series of 4-substituted compounds, there is very little energy difference between the forms and that the ratio between them is about unity. Molecular orbital calculations for... 

Two independent molecular orbital calculations (HMO method) of delocalization energies for isoindole and isoindolenine tautomers agree that the isoindole form should possess the more resonance stabilization. The actual difference calculated for isoindole-isoindolenine is about 8 kcal/mole, but increases in favor of the isoindole with phenyl substitution at position 1 (Table VI).Since isoindole and isoindolenine tautomers have roughly comparable thermodynamic stabilities, the tautomeric proce.ss is readily obser-... 

Le Fevre, both by degradation and by synthesis. The eourse of the substitutions described abo e was accounted for by molecular orbital calculations. ... 

To explain tlie stereodieniistiy of tlie allylic substitution reaction, a simple stereoelectronic model based on frontier molecular orbital considerations bas been proposed fl55. Fig. G.2). Organocopper reagents, unlike C-nudeopbiles, possess filled d-orbitals fd - configuration), wbidi can interact botli witli tlie 7t -fC=C) orbital at tlie y-carbon and to a minor extent witli tlie cr -fC X) orbital, as depicted... 

Most electrophilic substitutions in benzimidazole (31 R = H) occur primarily in the 5-position. In multiple bromination the order followed, 5 > 7 > 6,4 > 2, parallels molecular orbital calculations. In benzimidazole itself the 4(7)- and 5(6)-positions are tautomerically equivalent. Fusion of a benzene ring deactivates C-2 to electrophilic attack to such an extent that it is around 5000 times less reactive than the 2-position of imidazole. Strong electron donors at C-5 direct halogenation to the 4-position, whereas electron-withdrawing groups favor C-4 or C-6 substitution (84MI21). 

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