Orbital Interactions in Chemistry
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A: MO Theory: Orbital Interactions - Chemistry LibreTexts
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ISBN 13: 9780471080398
Binding has minimal wear. The majority of pages are undamaged with minimal creasing or tearing, minimal pencil underlining of text, no highlighting of text, no writing in margins. No missing pages. All readers will discoverthe underlying structure that unites all disciplines inchemistry. SloanResearch Fellow. He has been interested in exploring reactiondynamics in organometallic chemistry. Sloan Foundation. Orbital Interactions in Chemistry Thomas A.
avermale.gq This qualitative approach to molecular orbital theory is part of the start of modern quantum chemistry. Linear combinations of atomic orbitals LCAO can be used to estimate the molecular orbitals that are formed upon bonding between the molecule's constituent atoms. For simple diatomic molecules, the wavefunctions obtained are represented mathematically by the equations. These coefficients can be positive or negative, depending on the energies and symmetries of the individual atomic orbitals. As the two atoms become closer together, their atomic orbitals overlap to produce areas of high electron density, and, as a consequence, molecular orbitals are formed between the two atoms.
The atoms are held together by the electrostatic attraction between the positively charged nuclei and the negatively charged electrons occupying bonding molecular orbitals. When atomic orbitals interact, the resulting molecular orbital can be of three types: bonding, antibonding, or nonbonding. Antibonding MOs :. These are the Greek letters corresponding to the atomic orbitals s, p, d, f and g respectively. This means that rotation of the MO about the internuclear axis does not result in a phase change.
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This means that rotation of the MO about the internuclear axis will result in a phase change. There is one nodal plane containing the internuclear axis, if real orbitals are considered. Because these molecular orbitals involve low-energy d atomic orbitals, they are seen in transition-metal complexes. Theoretical chemists have conjectured that higher-order bonds, such as phi bonds corresponding to overlap of f atomic orbitals, are possible. For molecules that possess a center of inversion centrosymmetric molecules there are additional labels of symmetry that can be applied to molecular orbitals.
Centrosymmetric molecules include:.
If inversion through the center of symmetry in a molecule results in the same phases for the molecular orbital, then the MO is said to have gerade g symmetry, from the German word for even. If inversion through the center of symmetry in a molecule results in a phase change for the molecular orbital, then the MO is said to have ungerade u symmetry, from the German word for odd.
- Orbital Interaction Theory.
- Orbital Interactions in Chemistry, 2nd Edition by Thomas A. Albright, – Dattani Book Agency!
The qualitative approach of MO analysis uses a molecular orbital diagram to visualize bonding interactions in a molecule. In this type of diagram, the molecular orbitals are represented by horizontal lines; the higher a line the higher the energy of the orbital, and degenerate orbitals are placed on the same level with a space between them. Then, the electrons to be placed in the molecular orbitals are slotted in one by one, keeping in mind the Pauli exclusion principle and Hund's rule of maximum multiplicity only 2 electrons, having opposite spins, per orbital; place as many unpaired electrons on one energy level as possible before starting to pair them.
For more complicated molecules, the wave mechanics approach loses utility in a qualitative understanding of bonding although is still necessary for a quantitative approach. Some properties:. The general procedure for constructing a molecular orbital diagram for a reasonably simple molecule can be summarized as follows:. Estimate the relative energies of the molecular orbitals from considerations of overlap and relative energies of the parent orbitals, and draw the levels on a molecular orbital energy level diagram showing the origin of the orbitals.
Confirm, correct, and revise this qualitative order by carrying out a molecular orbital calculation by using commercial software. Molecular orbitals are said to be degenerate if they have the same energy. For example, in the homonuclear diatomic molecules of the first ten elements, the molecular orbitals derived from the p x and the p y atomic orbitals result in two degenerate bonding orbitals of low energy and two degenerate antibonding orbitals of high energy.
When the energy difference between the atomic orbitals of two atoms is quite large, one atom's orbitals contribute almost entirely to the bonding orbitals, and the other atom's orbitals contribute almost entirely to the antibonding orbitals. Thus, the situation is effectively that one or more electrons have been transferred from one atom to the other. This is called an mostly ionic bond. The bond order, or number of bonds, of a molecule can be determined by combining the number of electrons in bonding and antibonding molecular orbitals. A pair of electrons in a bonding orbital creates a bond, whereas a pair of electrons in an antibonding orbital negates a bond.
For example, N 2 , with eight electrons in bonding orbitals and two electrons in antibonding orbitals, has a bond order of three, which constitutes a triple bond.
Bond strength is proportional to bond order—a greater amount of bonding produces a more stable bond—and bond length is inversely proportional to it—a stronger bond is shorter. There are rare exceptions to the requirement of molecule having a positive bond order. This notion is often the matter of confusion in literature and should be considered with caution. Its value is usually located between the fundamental gap difference between ionization potential and electron affinity and the optical gap. Homonuclear diatomic MOs contain equal contributions from each atomic orbital in the basis set. This is shown in the homonuclear diatomic MO diagrams for H 2 , He 2 , and Li 2 , all of which containing symmetric orbitals.
As a simple MO example, consider the electrons in a hydrogen molecule, H 2 see molecular orbital diagram , with the two atoms labelled H' and H". The lowest-energy atomic orbitals, 1s' and 1s", do not transform according to the symmetries of the molecule. However, the following symmetry adapted atomic orbitals do:. The symmetric combination called a bonding orbital is lower in energy than the basis orbitals, and the antisymmetric combination called an antibonding orbital is higher. Because the H 2 molecule has two electrons, they can both go in the bonding orbital, making the system lower in energy hence more stable than two free hydrogen atoms.
This is called a covalent bond. The bond order is equal to the number of bonding electrons minus the number of antibonding electrons, divided by 2. In this example, there are 2 electrons in the bonding orbital and none in the antibonding orbital; the bond order is 1, and there is a single bond between the two hydrogen atoms. On the other hand, consider the hypothetical molecule of He 2 with the atoms labeled He' and He".
As with H 2 , the lowest energy atomic orbitals are the 1s' and 1s", and do not transform according to the symmetries of the molecule, while the symmetry adapted atomic orbitals do. The symmetric combination—the bonding orbital—is lower in energy than the basis orbitals, and the antisymmetric combination—the antibonding orbital—is higher.