Orbitals relative energies

The energies of these hydrogenie orbitals, relative to an eleetron infinitely far from the nueleus and with zero kinetie energy, are... 

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). 

Although the Hiickel method has now been supplanted by more complete treatments for theoretical analysis of organic reactions, the pictures of the n orbitals of both linear and cyclic conjugated polyene systems that it provides are correct as to symmetry and the relative energy of the orbitals. In many reactions where the n system is the primary site of reactivity, these orbitals correctly describe the behavior of the systems. For that reason, the reader should develop a familiarity with the qualitative description of the n orbitals of typical linear polyenes and conjugated cyclic hydrocarbons. These orbitals will be the basis for further discussion in Chapters 9 and 11. 

Fig. 11.13. Coefficients and relative energies of dienophile and diene molecular orbitals. [From K.. N. Houk, J. Am. Chem. Soc. 95 4092 (1973).]...

The geometries and relative energies of the different conformations of model chalcogen diimides E(NR)2 (E = S, Se R = H, Me, Bu and SiMe3) have been investigated by using ab initio and DET molecular orbital methods.The cis,trans conformation is predicted to be most stable with the exception of the parent molecules E(NH)2 and the unsymmetrical systems RNSNH, for which the cis,cis conformation is slightly more stable than the cis, trans isomer. 

Figure 6.13 Formation of a bonding, central 3-centre bond and schematic representation of the relative energies of the 3 molecular orbitals xj/i, j/2 and...

No completely general and quantitative theory of the stereochemical activity of the lone-pair of electrons in complex halides of tervalent As, Sb and Bi has been developed but certain trends are discernible. The lone-pair becomes less decisive in modifying the stereochemistry (a) with increase in the coordination number of the central atom from 4 through 5 to 6, (b) with increase in the atomic weight of the central atom (As > Sb > Bi), and (c) with increa.se in the atomic weight of the halogen (F > Cl > Br > 1). The relative energies of the various valence-Ievel orbitals may also be an important factor the F(a) orbital of F lies well below both the s and the p valence... 

The CNDO method has been modified by substitution of semiempirical Coulomb integrals similar to those used in the Pariser-Parr-Pople method, and by the introduction of a new empirical parameter to differentiate resonance integrals between a orbitals and tt orbitals. The CNDO method with this change in parameterization is extended to the calculation of electronic spectra and applied to the isoelectronic compounds benzene, pyridine, pyri-dazine, pyrimidine and pyrazine. The results obtained were refined by a limited Cl calculation, and compared with the best available experimental data. It was found that the agreement was quite satisfactory for both the n TT and n tt singlet transitions. The relative energies of the tt and the lone pair orbitals in pyridine and the diazines are compared and an explanation proposed for the observed orders. Also, the nature of the lone pairs in these compounds is discussed. 

Most reactions discussed can be classified into two types of [n s+iAs cycloadditions, the normal and inverse electron-demand cycloaddition reactions, based on the relative energies of the frontier molecular orbitals of the diene and the dieno-phile (Scheme 4.2) [4]. 

Problem 15.10 I Show the relative energy levels of the seven 77 molecular orbitals of the cvclohepta-trienyl system. Tel) which of the seven orbitals are filled in the cation, radical, and anion, and account for the aromaticity of the cycloheptatrienyl cation. 

In this chapter, we focus on electron arrangements in atoms, paying particular attention to the relative energies of different electrons (energy levels) and their spatial locations (orbitals). Specifically, we consider the nature of the energy levels and orbitals available to—... 

The Schrodinger equation can be solved approximately for atoms with two or more electrons. There are many solutions for the wave function, ij/, each associated with a set of numbers called quantum numbers. Three such numbers are given the symbols n, , and mi. A wave function corresponding to a particular set of three quantum numbers (e.g., n = 2, = 1, mi = 0) is associated with an electron occupying an atomic orbital. From the expression for ij/y we can deduce the relative energy of that orbital, its shape, and its orientation in space. 

The molecular orbitals are arranged in order of increasing energy. The relative energies of these orbitals are ordinarily deduced from experiment Spectra and magnetic properties of molecules are used. 

Relative energies, so far as filling order is concerned, for the molecular orbitals formed by combining 2s and 2p atomic orbitals. 

The relative energies of the molecular orbitals available for occupancy by the valence electrons of the second period elements are shown in Figure 3. This order applies at least through N2- ... 

In a similar vein the in-phase combination of the 7r ,f3 localized pairs, which is CH antibonding but CC bonding, is possibly the lowest unoccupied orbital it lies very close to the [Pg.19]

At the start, the relative energies of the four orbitals are represented in Fig. 33. The correct procedure requires that we first interact the degenerate orbitals nj and n2, and then mix the resulting combinations with orcc and significantly different energies. This is true even though the overlap between n and n2 is extremely small, because n, and n2 are symmetry-equivalent orbitals. The... 

Figure 2.38 The effect of varying the relative energies of the metal and ligand orbitals upon the final molecular orbital scheme for a dimeric rhodium carboxylate. (Reprinted from Coord. Chem. Rev., 50, 109, 1983, with kind permission from Elsevier Science S.A., P.O. Box 564,...

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