Geometry of orbitals

Three is the maximum number of bonds that can be formed between two atoms. This limitation is caused by the geometry of orbitals used in bonding and will be discussed later. 

Geometry of orbitals. S-orbitals are spherical, p-orbitals are shaped like a dumbbell... 

The geometry of orbitals involved in the reactions requires that the migration proceeds to the cis position. This phenomenon has been proven for many reactions (Figure 13.2b). However, external addition to alkene of a nucleophilic group which is not present in the coordination sphere may take place. In this case, the product possessing trans structure is formed (Figure 13.2c). 

Jahn-TeHer effect The Jahn-Teller theorem states that, when any degenerate electronic slate contains a number of electrons such that the degenerate orbitals are not completely filled, the geometry of the species will change so as to produce non-degenerate orbitals. Particularly applied to transition metal compounds where the state is Cu(II)... 

A variation on MNDO is MNDO/d. This is an equivalent formulation including d orbitals. This improves predicted geometry of hypervalent molecules. This method is sometimes used for modeling transition metal systems, but its accuracy is highly dependent on the individual system being studied. There is also a MNDOC method that includes electron correlation. 

Orbital-based methods can be used to compute transition structures. When a negative frequency is computed, it indicates that the geometry of the molecule corresponds to a maximum of potential energy with respect to the positions of the nuclei. The transition state of a reaction is characterized by having one negative frequency. Structures with two negative frequencies are called second-order saddle points. These structures have little relevance to chemistry since it is extremely unlikely that the molecule will be found with that structure. 

Acetylene is linear and alkynes have a linear geometry of their X—C=C—Y units The carbon-carbon triple bond m alkynes is com posed of a CT and two tt components The triply bonded carbons are sp hybridized The ct component of the triple bond contains two electrons m an orbital generated by the overlap of sp hybndized orbitals on adja cent carbons Each of these carbons also has two 2p orbitals which over lap m parrs so as to give two tt orbitals each of which contains two electrons... 

Structural studies show allene to be nonplanar As Figure 10 7 illustrates the plane of one HCH unit is perpendicular to the plane of the other Figure 10 7 also portrays the reason for the molecular geometry of allene The 2p orbital of each of the terminal car bons overlaps with a different 2p orbital of the central carbon Because the 2p orbitals of the central carbon are perpendicular to each other the perpendicular nature of the two HCH units follows naturally... 

You can use the information obtained from semi-empirical calculations to investigate many thermodynamic and kinetic aspects of chemical processes. Energies and geometries of molecules have clear relation ships to chemical ph en om ena. 0ther quan tities, like atomic charges and Frontier Orbitals, are less defined but provide useful qualitative results. 

This stereoelectronic requirement would lead to a large distortion of the normal geometry of a five-membered ring and introduce strain. It is this distortion and strain that disfavor the 5-endo-trig cyclization. In contrast, 5-endo-dig cychzation is feasible because the acetylenic system provides an orbital that is available for a nearly planar mode of approach. 

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