Orbitals in diatomic molecules

Combining two Is orbitals in this manner, then, seems a good first approximation to describe bonding using this theory. 

Will the electron in H2+ occupy the orbital (1 sA + lsB) rather than a Is orbital on one H atom Yes it will, because an electron in (lsA + lsB) is more likely to be attracted to both nuclei than one in a 1 s orbital. This means that the electron is more strongly bound and its energy is lower. An electron in (lsA + lsB) is therefore of lower energy than one in a Is orbital. Orbitals such as (lsA + lsB) are called bonding orbitals. 

H2+ is easy to deal with because it has only one electron, but it is not a very common molecule. Can we use the idea of combining atomic orbitals when we come to study molecules with more than one electron Let us start with H2, dihydrogen, a more familiar molecule. 

H2 has two electrons and we can use a building-up process similar to that used to determine electronic configuration for atoms. The orbital (lsA + lsB) can take two electrons of opposite spin. If we draw a molecular orbital diagram for H2, we put 

We should point out here that the bonding orbital (1 sA + lsB) will not be exactly the same for H2+ and H2. As with atoms, when we have more than one electron we have to allow for the other electron(s) when we calculate an orbital. 

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Wallis, R. F., and Hulburt, H. M., J. Chem. Phys. 22, 1774, "Approximation of molecular orbitals in diatomic molecules by diatomic orbitals."... 

The Tormation of bonding and antibonding combinations of atomic orbitals in diatomic molecules, and the corresponding energy-level diagrams. 

In Chapters 4 and 6 we have distinguished between a molecular orbitals and 7T molecular orbitals in diatomic molecules on the basis of the symmetry of the m.o.s with respect to rotation around the intemuclear axis whereas a a orbital has cylindrical symmetry, a tt orbital changes sign upon a rotation of 180°. In Chapters 7 and 8 we have extended the notion of a orbitals to polyatomic molecules by referring to the local symmetry with respect to each X-Y intemuclear axis. We will now study systems of tt m.o.s in polyatomic species. 

These new orbitals look like bent bonds and are rather close to Van t Hoff s 39> original description of a double bond. The density diagrams of the various types of orbitals in diatomic molecules can be seen in 1 and 4, namely delocalized (canonical) MO s on Fig. 1 and localized (equivalent) MO s on Fig. 4. 

They could overlap to form a bonding orbital similar to the n orbitals in diatomic molecules. 

O. Goscinski Bonding Character of Inner-Shell Orbitals in Diatomic Molecules (Quantum Science - Methods and Structure, Eds. J.-L. Calais et al.. Plenum Press 1976, p. 427). 

Elliptical-type basis functions can provide a very accurate representation of orbitals in diatomic molecules. In Table III, we compare the results of calculations employing basis sets of elliptical-type functions with fully numerical studies. It can be seen that the two approaches yield results of comparable accuracy. It should be emphasized that the basis set approach, in contrast to the fully numerical technique, affords a compact representation of the wavefunction. 

In Section 10.8, we shall see the need to include d orbitals in the description of bonding between d-metal ions, such as Fe +, and proteins, such as hemoglobin. To get a sense of how molecular orbitals can be built from d orbitals, show how they can contribute to the formation of a and n orbitals in diatomic molecules. 

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