Orbital characteristics

This discrepancy between experiment and theory (and many others) can be explained in terms of an alternative model of covalent bonding, the molecular orbital (MO) approach. Molecular orbital theory treats bonds in terms of orbitals characteristic of the molecule as a whole. To apply this approach, we carry out three basic operations. 

The atomic orbitals of atoms are combined to give a new set of molecular orbitals characteristic of the molecule as a whole. The number of molecular orbitals formed is equal to the number of atomic orbitals combined. When two H atoms combine to form H two s orbitals, one from each atom, yield two molecular orbitals. In another case, six p orbitals, three from each atom, give a total of six molecular orbitals. 

Pop I stars subsequently formed, inheriting their orbital characteristics from the disk gas. 

Fig. 4.10. Angle dependence of photoelectrons from different states. The polar-angle dependence of the photoelectrons reflects the orbital characteristics of the wavefunctions at surfaces, (a) <7. peak on M0S2. (b) / . peak on GaSe. (c) An. v like state on M0S2. (Reproduced from Cardona and Ley, 1978, with permission.)...

For example, for an s state, the angular distribution should be a constant for a Pi state, the dependence should like cos 0 and for a state, a dependence of (3 cos 0-1)2 should be observed. This model has been verified by experiments (Smith, 1978). Figure 4.10 shows the polar-angle dependence of certain peaks in the spectra, which match what is expected from the knowledge of the orbital characteristics of the wavefunctions at these surfaces. 

When asteroid collisions are especially violent, sufficient kinetic energy may be imparted to launch fragments at greater than escape velocities. In that case, separate asteroids are formed. These fragments share similar orbital characteristics and are referred to as families. The members of most asteroid families share the same spectral characteristics, further linking them together. Families composed of fragments of differentiated asteroids can potentially provide important information on their internal compositions. 

Pericyclic reactions are unimolecular, concerted, uncatalyzed transformations. They take place in a highly stereoselective manner governed by symmetry proper-ties of interacting orbitals. - Characteristic of all these rearrangements is that they are reversible and may be effected thermally or photochemically. The compounds in equilibrium are usually interconverted through a cyclic transition state,224 although biradical mechanisms may also be operative. A few characteristic examples of pericyclic rearrangements relevant to hydrocarbon isomerizations are presented here. 

Intramolecular dynamics and chemical reactions have been studied for a long time in terms of classical models. However, many of the early studies were restricted by the complexities resulting from classical chaos, Tlie application of the new dynamical systems theory to classical models of reactions has very recently revealed the existence of general bifurcation scenarios at the origin of chaos. Moreover, it can be shown that the infinite number of classical periodic orbits characteristic of chaos are topological combinations of a finite number of fundamental periodic orbits as determined by a symbolic dynamics. These properties appear to be very general and characteristic of typical classical reaction dynamics. 

It has not proved mathematically feasible to calculate the electron-electron repulsion that causes this change in orbital-energies for many-electron molecules. It is even difficult to rationalize the qualitative changes in sequence on the basis of the shapes of the 11orbitals. Greater success has been achieved by an approximate method which begins with orbitals characteristic of the isolated atoms present in the molecule, and assumes that molecular orbital wave functions can be obtained by taking linear combinations of atomic orbital wave functions (abbreviated L.C.A.O.). For... 

Knowing the symmetries of the operators we can now construct coupled quantities with well defined spin and orbital characteristics. As an example two-particle states with total quantum numbers S and L can be formed as follows ... 

To see how the concept of hybrid orbitals helps us understand bonding, let s go back to the example of BeH2 that we mentioned on Page 37. Instead of assuming that the two bonding electrons occupy s- and p orbitals characteristic of the isolated atoms, we place them in sp hybrid orbitals of identical character which arise from in- and out-of-phase combinations of the atomic orbitals as described above. 

Another demonstration of the validity of these calculations is provided by BEDT-TTF-based salts. The calculated Fermi surface of these materials exhibit closed orbits characteristic of two-dimensional electronic interactions and this has been confirmed experimentally. For example, in the case of (BEDT-TTF)2I3, the calculated surface of these orbits (Fig. 21) [61] agrees well with the one measured by magnetic experiments [161]. However, the overall good agreement between calculation and experiment must not hide the fact that some qualitative discrepancies may arise in some cases. For example, (TMTTF)2X salts exhibit a resistivity minimum at a temperature at which no structural transition has yet been observed. The resistivity minimum is not explained by the one-electron band structure, and to account for this progressive electron localization, it is necessary to include in the calculations the effect of the electronic correlations [162]. Another difficulty has been met in the case of the semiconducting materials a -(BEDT-TTF)2X, for which the calculated band structure exhibits the characteristic features of a metal [93,97,100] and it is not yet understood... 

In Chapter 1 we saw that in moving from homonuclear to heteronuclear diatomics a new factor enters - the atom characters are distributed differently over the filled and unfilled MOs. As only the filled orbitals contribute to the atomic charges, the Mulliken charge distribution reflects the polarity of the molecule. Similar information for the HOMO and FUMO permitted us to discuss properties such as Lewis acidity and basicity in terms of frontier-orbital characteristics. As we were able to unravel the DOS of the metal chain in terms of AO type, we can also interrogate the DOS of a heteroatomic system for information on the distribution of atomic character over the total DOS. That is, we can reveal the contributions or character of a chosen atom to the DOS. We can begin to appreciate the power of this tool by... 

The "native" 2s and three 2p atomic orbitals characteristic of a free carbon atom are combined to form a new set of four sp3 orbitals. The small lobes of the orbitals are usually omitted from diagrams for clarity. 

By electron injection into an antibonding orbital or electron removal from a bonding orbital characteristic bonds are weakened as a consequence a plethora of bond cleavage processes is typical for both radical anions and cations. 

Conservation of Orbital Symmetry. This approach relies on a detailed analysis of the symmetry properties of the molecular orbitals of starting materials and products. Orbital correlation diagrams link the orbital characteristics of starting materials and products. 

ORBITAL CHARACTERISTICS OF THE MOLECULAR ORBITALS OF COFj, IN ORDER OF INCREASING STABILITY [1857aa]... 

Ab initio calculations on COBtj 2 symmetry) and the asymmetrically substituted carbonyl halides COCIF, COBrF and COBrCl (which have only C, symmetry) have shown that when a bromine atom is present in the molecule, the highest occupied molecular orbital has bromine lone-pair character [1857aa]. In contrast to this, the HOMO of COCIF has mixed chlorine and oxygen character. The principal orbital characteristics for the most chemically significant orbitals of these molecules are given in Tables 17.3 and 17.4 it must be remembered that the low symmetry means that there is little bar to extensive mixing of the molecular orbitals. 

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