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Octahedral crystal field stabilization energy. Degenerate atomic d-orbitals of a free metal ion (left), destabilization of d-orbitals within a spherical negative electric field (center), and loss of degeneracy relative to the spherical field when ligands are treated as point charges in an octahedral geometry.
The oxygen atomic orbitals are labeled according to their symmetry as a 1 for the 2s orbital and b 1 (2p x), b 2 (2p y) and a 1 (2p z) for the three 2p orbitals. The two hydrogen 1s orbitals are premixed to form a 1 (σ) and b 2 (σ*) MO. Mixing takes place between same-symmetry orbitals of comparable energy resulting a new set of MO's for water:
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]
Diradicals are usually triplets.The phrases singlet and triplet are derived from the multiplicity of states of diradicals in electron spin resonance: a singlet diradical has one state (S=0, M s =2*0+1=1, m s =0) and exhibits no signal in EPR and a triplet diradical has 3 states (S=1, M s =2*1+1=3, m s =-1; 0; 1) and shows in EPR 2 peaks (if no hyperfine splitting).
In quantum mechanics, an energy level is degenerate if it corresponds to two or more different measurable states of a quantum system.Conversely, two or more different states of a quantum mechanical system are said to be degenerate if they give the same value of energy upon measurement.
Chemist Linus Pauling first developed the hybridisation theory in 1931 to explain the structure of simple molecules such as methane (CH 4) using atomic orbitals. [2] Pauling pointed out that a carbon atom forms four bonds by using one s and three p orbitals, so that "it might be inferred" that a carbon atom would form three bonds at right angles (using p orbitals) and a fourth weaker bond ...
The method predicts how many energy levels exist for a given molecule, which levels are degenerate and it expresses the molecular orbital energies in terms of two parameters, called α, the energy of an electron in a 2p orbital, and β, the interaction energy between two 2p orbitals (the extent to which an electron is stabilized by allowing it ...
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.