Hybrid orbitals orbital regions

Orient the coordinate axes so that each atom has a hybrid orbital region pointing at the other atom. Make the bonding factor with one of the hybrid orbitals on each atom and nse the other three for lone pairs. Denote the hybrids involved in the bond as 2sp )K and 25/ (l)B. We omit the spin factors. Use the D and the other 2sp orbitals as nonbonding orbitals. Without complete antisymmetrization, the wave function is... 

The structure of ethylene and the orbital hybridization model for its double bond were presented m Section 2 20 and are briefly reviewed m Figure 5 1 Ethylene is planar each carbon is sp hybridized and the double bond is considered to have a a component and a TT component The ct component arises from overlap of sp hybrid orbitals along a line connecting the two carbons the tt component via a side by side overlap of two p orbitals Regions of high electron density attributed to the tt electrons appear above and below the plane of the molecule and are clearly evident m the electrostatic potential map Most of the reactions of ethylene and other alkenes involve these electrons... 

FIGURE 14 3 (a) The unshared electron pair occupies an sp hybridized orbital in dichlorocarbene There are no electrons in the unhybridized p orbital (b) An electrostatic potential map of dichlorocarbene shows negative charge is concentrated in the region of the unshared pair and positive charge above and below the carbon... 

According to the orbital hybridization model, benzene has six tt electrons, which are shared by all six 5/r -hybridized car bons. Regions of high TT electron density are located above and below the plane of the ring. 

The vinyl H2C=CH radical can be produced by cleavage of a C-H bond in ethene, and has been studied in the gas phase. The unpaired electron clearly occupies a carbon sp hybrid orbital, to lapse into the language of descriptive organic chemistry, but there are regions of space where the, 6-spin electrons have... 

Molecular orbital (MO) theory describes covalent bond formation as arising from a mathematical combination of atomic orbitals (wave functions) on different atoms to form molecular orbitals, so called because they belong to the entire molecule rather than to an individual atom. Just as an atomic orbital, whether un hybridized or hybridized, describes a region of space around an atom where an electron is likely to be found, so a molecular orbital describes a region of space in a molecule where electrons are most likely to be found. 

Orbital Region of space in which there is a high probability of finding an electron within an atom, 141 band theory and, 654—655 hybrid, 186,187 relation to ligand, 418... 

To circumvent problems associated with the link atoms different approaches have been developed in which localized orbitals are added to model the bond between the QM and MM regions. Warshel and Levitt [17] were the first to suggest the use of localized orbitals in QM/MM studies. In the local self-consistent field (LSCF) method the QM/MM frontier bond is described with a strictly localized orbital, also called a frozen orbital [43]. These frozen orbitals are parameterized by use of small model molecules and are kept constant in the SCF calculation. The frozen orbitals, and the localized orbital methods in general, must be parameterized for each quantum mechanical model (i.e. energy-calculation method and basis set) to achieve reliable treatment of the boundary [34]. This restriction is partly circumvented in the generalized hybrid orbital (GHO) method [44], In this method, which is an extension of the LSCF method, the boundary MM atom is described by four hybrid orbitals. The three hybrid orbitals that would be attached to other MM atoms are fixed. The remaining hybrid orbital, which represents the bond to a QM atom, participates in the SCF calculation of the QM part. In contrast with LSCF approach the added flexibility of the optimized hybrid orbital means that no specific parameterization of this orbital is needed for each new system. 

Figure 4.7 The formation of the two sp hybrid orbitals of the carbon atom used in the production of molecular orbitals in the CO molecule. h1 is directed towards the oxygen atom, h2 is directed diametrically opposite to the CO bonding region...

It is clear that if the repulsive fields are operative in those regions where hae is small, namely, in the areas labeled F in the diagrams, then hae may be considerably more stable than kag and, indeed, more stable than either of the original orbitals, sae and dag. Regarding the field as a perturbation, we see that the effect of the field on the dag and sag orbitals is to mix them in such a way as to produce one orbital, haR, which is more stable than either and another, kag, which is more highly excited. If there are two electrons of ag type, therefore, these will be most firmly bound in the hybrid orbital hag, and not in either sag or dag. (The precise values of the coefficients determining the amount of hybridiza-... 

In order to obtain correct expressions for hybrid orbitals, we first need to describe more precisely than has been done in Section 1.2 some properties of orbitals. Recall that orbital function, gives the probability of finding the electron in each region of space. If we were to add up the values of this function over all points, we would have the total probability of finding the electron, which should equal unity. Orbitals are ordinarily constructed so as to satisfy this requirement when they are, they are said to be normalized. The normalization condition is Equation Al.l, where dr signifies integration over all coordinates. 

---