Orbital occupation

For Woodward-Hoffm an allowed thermal reactions (such as the con rotatory ring opening of cyclobulan e), orbital symmetry is conserved and there is no change in orbital occupancy. Hven though bonds are made and broken, you can use the RHFwave fun etion. 

The UHF option allows only the lowest state of a given multiplicity to be requested. Thus, for example, you could explore the lowest Triplet excited state of benzene with the UHF option, but could not ask for calculations on an excited singlet state. This is because the UHF option in HyperChem does not allow arbitrary orbital occupations (possibly leading to an excited single determinant of different spatial symmetry than the lowest determinant of the same multiplicity), nor does it perform a Configuration Interaction (Cl) calculation that allows a multitude of states to be described. 

Specific electronic states may also be specified using the Gue s=Alter keyword, which allows you to explicitly designate orbital occupancies. See the Gaussian User s Reference for details. 

Table 4.4 Natural orbital occupation numbers for the distorted acetylene model in Figure 4.11. Only the occupation numbers for the six central orbitals are shown...

The orbital occupation numbers n, (eigenvalues of the density matrix) will be between 0 and 1, corresponding to the number of electrons in the orbital. Note that the representation of the exact density normally will require an infinite number of natural orbitals. The first N occupation numbers N being the total number of electrons in the system) will noraially be close to 1, and tire remaining close to 0. 

The ionization energy, electron affinity, and orbital occupancy determine the chemical behavior, or reactivity, of the elements. The uppermost (high-est-energy) occupied orbitals are called the valence orbitals the electrons occupying them are the valence electrons. An element s ionization energy, the energy required to remove an electron from a neutral atom, is related to its reactivity A low ionization energy means that the valence electron is readily removed, and the element is likely to become involved in... 

Figure 16-3D shows the simplified representation of the interaction of two helium atoms. This time each helium atom is crosshatched before the two atoms approach. This is to indicate there are already two electrons in the Is orbital. Our rule of orbital occupancy tells us that the Is orbital can contain only two electrons. Consequently, when the second helium atom approaches, its valence orbitals cannot overlap significantly. The helium atom valence electrons fill its valence orbitals, preventing it from approaching a second atom close enough to share electrons. The helium atom forms no chemical bonds. ... 

A fluorine atom has the orbital occupancy shown below ... 

The experimental quantities shown in (14) and (15) indicate that the F ion is more stable than a fluorine atom and an electron. Energetically, a fluorine atom wants" another electron. It is profitable to express reaction (12) in terms of orbital occupancy ... 

Remember the spatial arrangement of the p or- atom has partially filled valence orbitals. Elec-bitals Each one protrudes along one of the tron sharing can occur, placing electrons close three cartesian axes (as shown in Figure 15-9). to two nuclei simultaneously. Hence a stable If the electrons have the orbital occupancy of bond can occur. This is shown in representations 20), then two electrons occupy the p orbital (22) and (23). 

There are a number of orbital occupancies that we might consider for the carbon atom ... 

In fact, both CH2 and CF2 are considered to be stable but extremely reactive molecules. Though there is reaction mechanism evidence verifying the existence of each species, it is not possible to prepare either substance pure. This great reactivity shows that energy considerations favor the use of all four of the valence orbitals if possible. This argument leads us to consider a third orbital occupancy ... 

The boron atom presents the same sort of option in orbital occupancy as does carbon ... 

Aluminum, silicon, and sulfur are close together in the same row of the periodic table, yet their electrical conductivities are widely different. Aluminum is a metal silicon has much lower conductivity and is called a semiconductor sulfur has such low conductivity it is called an insulator. Explain these differences in terms of valence orbital occupancy. 

Discuss the conduction of heat by copper (a metal) and by glass (a network solid) in terms of the valence orbital occupancy and electron mobility. 

Draw on one line a set of orbitals from Is through 4d. Under this give the orbital occupancy for Al, Sc, and Y. Account for the fact that yttrium is much more like scandium than is aluminum. 

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