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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 metal also has six valence orbitals that span these irreducible representations - the s orbital is labeled a 1g, a set of three p-orbitals is labeled t 1u, and the d z 2 and d x 2 −y 2 orbitals are labeled e g. The six σ-bonding molecular orbitals result from the combinations of ligand SALCs with metal orbitals of the same symmetry. [8]
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 .
The highest occupied orbital energy level of dioxygen is a pair of antibonding π* orbitals. In the ground state of dioxygen, this energy level is occupied by two electrons of the same spin, as shown in the molecular orbital diagram. The molecule, therefore, has two unpaired electrons and is in a triplet state.
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:
Molecular orbital theory predicts the electronic ground state denoted by the molecular term symbol 3 Σ – g, and two low-lying excited singlet states with term symbols 1 Δ g and 1 Σ + g. These three electronic states differ only in the spin and the occupancy of oxygen's two antibonding π g-orbitals, which are degenerate (equal in energy).