P-type atomic orbital

For each atom there are a maximum of five one-center two-electron integrals, that is (ssiss), (ssipp), (spisp), (ppipp), and (ppip p ), where p and p are two different p-type atomic orbitals. It has been shown that the extra one-center two-electron integral, (pp Ipp ), is related to two of other integrals by... 

The simplest basis sets are those used in the simple Hiickel and the extended Hiickel methods (SHM and EHM, Chapter 4). As applied to conjugated organic compounds (its usual domain), the simple Hiickel basis set consists of just p atomic orbitals (or geometrically p-type atomic orbitals, like a lone-pair orbital which can be considered not to interact with the er framework). The extended Hiickel basis set consists of only the atomic valence orbitals. In the SHM we don t worry about the mathematical form of the basis functions, reducing the interactions between them to 0 or —1 in the SHM Fock matrix (e.g. Eqs. 4.64 and 4.65). In the EHM the valence atomic orbitals are represented as Slater functions (Sections 4.4.1.2 and 4.4.2). 

To do a CASSCF calculation, one must first choose the active space, that is, the relevant MOs. Which MOs are relevant depends on the purpose of the calculation, and on how complete one wants the active space to be. The unattainable limit of course would be full Cl. This will be illustrated with a few examples. Consider the diradicals 1,3-propanediyl and 1,4-butanediyl. Intuitively, it seems that we should consider at least these two MOs the MO that resembles a bonding linear combination (Section 5.2.3.6) of the two p-type atomic orbitals on the end carbons and the... 

A nonempirical molecular orbital calculation reported recently for COS by dementi" has indicated, however, that the first excited state is a 7T—IT type. Only s and p type atomic orbitals were used in these calculations. To examine the effect of the 3d orbitals of the sulfur atom on the molecular orbital energy values, an extended Hiickel molecular orbital calculation has also been carried out with and without the inclusion of the 3d orbitals. The resulting energy level diagram for the ground and excited molecular orbitals, in comparison with the atomic... 

A theoretical study of the effects of structure and substituents on reactivity in allylboration has recently been completed [116]. Electron delocalization from the oxygen of an attacking aldehyde to the boron p-type atomic orbital is crucial in the allylboration reaction. The ab initio molecular orbital study indicates that the complex between the allylic borane and the aldehyde is weak. The relative elec-trophilicity of the boron atom in allylboron reagents is estimated by projecting out the unoccupied reactive orbital having the maximum amplitude onto the boron p-type atomic orbital. Two factors which are considered to be of importance in the reaction include the electron accepting level of the reactive unoccupied orbital and the efficiency of localization of the orbital in the unoccupied MO space. 

Basis effects energy and kinetic energy (in hartree) for H-(-C=C-)-jH. A (ij/klm) basis set means that each contributing H atom contributes i s-type atomic orbitals and j p-type atomic orbitals and each contributing C atom contributes k s-type atomic orbitals, 1 p-type atomic orbitals, and m d-type atomic orbitals. 

It is not possible to place two singlet paired electrons in overlapping p-type atomic orbitals without creating a bond. 

Indeed, it has only recently become clear that the planar, closed, overlapping set (or ring) of what look like occupied p-type atomic orbitals could be experimentally probed. As already discussed in Chapter 2, the Ti-electron system of benzene (CeHe) can be treated as a circular loop, in which an induced current results in dia-... 

Fig. 19.18. Representation of a typical B—A—B bond angle formed by overlap of two s-p-type atomic orbitals of A, each with a p orbital of atom B. Dashed line indicates the bond axis.)...

Fig. 6A. (a) Two n molecular orbitals from p-type atomic orbitals, (b) A stack of parallel ethylene molecules, represented by the double bond. The diagram shows the qualitative trends in the band structure horizontal lines are the energies of the orbitals of an isolated molecule. For clarity the a manifold is represented by a single E k) curve. The a bands are high above the Ti one. 

In the case of ketones, the lone pair orbital from which excitation occurs is essentially a p-type atomic orbital on oxygen. The associated n,re transition has no electric transition dipole moment (only quadrupole, see Scheme 3.1) and is therefore forbidden. In addition, orbital overlap is poor such that typical extinction coefficients (e) as low as ca. 10 M cm for aliphatic ketones and ca. 200 M" cm for aromatic ketones result. 

These functions are called circular or trigonometric functions. Note that Equations (2-25) are just the transformation Equations (1-4) with r = 1. It is interesting to compare the graphs of functions, such as sin 0 and cos 0, in linear coordinates (coordinates in which 0 is plotted along one axis) to those in plane polar coordinates. Consider, for example, the equation r = A cos 0y where A is a constant. Such an equation can be used to describe the wave properties of p-type atomic orbitals in two dimensions. The functional dependence of r upon 0 can be seen in Table 2-1. 

---