It* orbital

Conservation of orbital symmetry is a general principle that requires orbitals of the same phase (sign) to match up in a chemical reaction. For example, if terminal orbitals are to combine with one another in a cyclixation reaction as in pattern. A, they must rotate in the same dii ection (conrotatory ovei lap). but if they combine according to pattern H. they must rotate in opposite directions (disrotatory). In each case, rotation takes place so that overlap is between lobes of the it orbitals that are of the same sign. 

FIGURE 10 5 (a) Isolated double bonds are separated from one another by one or more sp hybridized carbons and cannot overlap to give an extended it orbital (b) In a conjugated di ene overlap of two it orbitals gives an extended it system encompassing four carbon atoms... 

You can use the semi-empirical and ab initio Orbitals dialog box in HyperChem to request a contour plot of any molecular orbital. When requested, the orbital is contoured for a plane that is parallel to the screen and which is specified by a subset selection and a plane offset, as described above. The index of the orbital and its orbital energy (in electron volts, eV) appears in the status line. 

Each electron in an atom has two possible kinds of angular momenta, one due to its orbital motion and the other to its spin motion. The magnitude of the orbital angular momentum vector for a single electron is given, as in Equation (1.44), by... 

A second approximation neglects coupling between the spin of an electron and its orbital momentum but assumes that coupling between orbital momenta is strong and that between spin momenta relatively weak but appreciable. This represents the opposite extreme to the 77-coupling approximation. It is known as the Russell-Saunders coupling approximation and serves as a useful basis for describing most states of most atoms and is the only one we shall consider in detail. 

The reason for the slow hydrolysis compared to that of structurally similar compounds like nitrones or 0,lV-acetals might be the following (b-67MI50800) in the protonated species (77) assistance of the lone pair of electrons at nitrogen is sterically hindered due to the large angle of its orbital to the plane of the ring. 

There are probably several factors which contribute to determining the endo exo ratio in any specific case. These include steric effects, dipole-dipole interactions, and London dispersion forces. MO interpretations emphasize secondary orbital interactions between the It orbitals on the dienophile substituent(s) and the developing 7t bond between C-2 and C-3 of the diene. There are quite a few exceptions to the Alder rule, and in most cases the preference for the endo isomer is relatively modest. For example, whereas cyclopentadiene reacts with methyl acrylate in decalin solution to give mainly the endo adduct (75%), the ratio is solvent-sensitive and ranges up to 90% endo in methanol. When a methyl substituent is added to the dienophile (methyl methacrylate), the exo product predominates. ... 

The arrangement of electrons in an atom is described by means of four quantum numbers which determine the spatial distribution, energy, and other properties, see Appendix 1 (p. 1285). The principal quantum number n defines the general energy level or shell to which the electron belongs. Electrons with n = 1.2, 3, 4., are sometimes referred to as K, L, M, N,. .., electrons. The orbital quantum number / defines both the shape of the electron charge distribution and its orbital angular... 

Draw three resonance forms for the pentadienyl radical. A radical is a substance that contains a single, unpaired electron in one of its orbitals, denoted by a dot ( )-... 

What kind of hybridization must the central carbon have Sketch the bonding it orbitals in allene. What shape do you predict for allene ... 

What s so special about periplanar geometry Because the sp3 a orbitals in the reactant C-H and C-X bonds must overlap and become p it orbitals in the alkene product, there must also be some overlap in the transition state. This can occur most easily if all the orbitals are in the same plane to begin with—that is, if they re periplanar (Figure 11.181. 

Note that both suprafacial and antarafacial cycloadditions are symmetry-allowed. Geometric constraints often make antarafacial reactions difficult, however, because there must be a twisting of the it orbital system in one of the reactants. Thus, suprafacial cycloadditions are the most common for small tt systems. 

SOLUTION Recall from Example 6.6 that the electron configuration of sulfur is ls22s22p63s23p4. Its orbital diagram is... 

Assuming confirmation by further work, these compounds are the first Pu compounds to show Pu-ethylenic bonding. The nature of this bonding is unknown, but participation of 5f orbitals with it orbitals of the ethylene double bond, though unlikely, should be considered. The large and easily polarizable iodide ions could be the key factor in stabilizing the proposed Pu+3-ethylene bonds. 

An important aspect of a imdciulc in addition to ( gewn-trical shape and (tic energies of its orbit lb is the distri-... 

A.26 Mars orbits the Sun at 25 km-s. A spaceship attempting to land on Mars must match its orbital speed. If the mass of the spaceship is 2.5 X 1(T kg, what is its kinetic energy when its speed has matched that of Mars ... 

Heisenberg, Z. Physik, 33, 879 (1925). Bom and Jordan, ibid., 34, 858 (1925). Born, Heisenberg and Jordan, ibid., 35, 557 (1926) etc. Heisenberg based his theory on the thesis that it should not contain reference to quantities which are in principle unobservable. It is of interest that G. N. Lewis, in 1923, suggested this idea, writing. "we should look for no effects which depend upon the momentary position of any electron in its orbit ("Valence and the Structure of Atoms and Molecules, Chemical Catalog Co., New York, 1923, p. 52). 

Now many physical properties depend mainly on the behaviour of the electron in the outer part of its orbit. As an example we may mention the mole refraction or polarizability of an atom, which arises from deformation of the orbit in an external field. This deformation is greatest where the ratio of external field strength to atomic field strength is greatest that is, in the outer part of the orbit. Let us consider such a property which for hydrogen-like atoms is found to vary with nrZ t. Then a screening constant for this property would be such that... 

In this picture of ethylene, the two orbitals that make up the double bond are not equivalent. The ct orbital is ellipsoidal and symmetrical about the C—C axis. The it orbital is in the shape of two ellipsoids, one above the plane and one below. The plane itself represents a node for the it orbital. In order for the p orbitals to maintain... 

Scheme 3b). The it orbital of ethene has a low-lying bonding orbital mix out of phase, and the low-lying n orbital mix out of phase with (7, . The relations are placed where the strongest interactions occur, or between (7, and the p orbital on the closer carbon (C ) in rand 7t. The phase relation of tt with ris uniquely determined. The signs of p orbitals in n and r are the same on and opposite on Cj. Thep amplitnde increases on and decreases on Cj. It follows that the LUMO of propene has large amplitude on C. ...

---