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Molecular orbital diagram of dinitrogen. With nitrogen, we see the two molecular orbitals mixing and the energy repulsion. This is the reasoning for the rearrangement from a more familiar diagram. The σ from the 2p is more non-bonding due to mixing, and same with the 2s σ. This also causes a large jump in energy in the 2p σ* orbital.
For the simplest AH 2 molecular system, Walsh produced the first angular correlation diagram by plotting the ab initio orbital energy curves for the canonical molecular orbitals while changing the bond angle from 90° to 180°. As the bond angle is distorted, the energy for each of the orbitals can be followed along the lines, allowing a quick ...
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). [13]
The d xy, d xz and d yz orbitals remain non-bonding orbitals. Some weak bonding (and anti-bonding) interactions with the s and p orbitals of the metal also occur, to make a total of 6 bonding (and 6 anti-bonding) molecular orbitals [7] Ligand-Field scheme summarizing σ-bonding in the octahedral complex [Ti(H 2 O) 6] 3+.
Molecular orbital theory revolutionized the study of chemical bonding by approximating the states of bonded electrons – the molecular orbitals – as linear combinations of atomic orbitals (LCAO). These approximations are made by applying the density functional theory (DFT) or Hartree–Fock (HF) models to the Schrödinger equation .
An initial assumption is that the number of molecular orbitals is equal to the number of atomic orbitals included in the linear expansion. In a sense, n atomic orbitals combine to form n molecular orbitals, which can be numbered i = 1 to n and which may not all be the same. The expression (linear expansion) for the i th molecular orbital would be:
Localized molecular orbitals are molecular orbitals which are concentrated in a limited spatial region of a molecule, such as a specific bond or lone pair on a specific atom. They can be used to relate molecular orbital calculations to simple bonding theories, and also to speed up post-Hartree–Fock electronic structure calculations by taking ...
Some orbitals (e.g. p x and p y orbitals from the fluorine in ) may not have any other orbitals to combine with and become non-bonding molecular orbitals. In the example, the p x and p y orbitals remain p x and p y orbitals in shape but when viewed as molecular orbitals are thought of as non-bonding. The energy of the orbital does not depend on ...