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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 ...
In the case of water, with its 104.5° HOH angle, the OH bonding orbitals are constructed from O(~sp 4.0) orbitals (~20% s, ~80% p), while the lone pairs consist of O(~sp 2.3) orbitals (~30% s, ~70% p). As discussed in the justification above, the lone pairs behave as very electropositive substituents and have excess s character.
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When the atoms are far apart (right side of graph) the eigenstates are the atomic orbitals of carbon. When the atoms come close enough (left side) that the orbitals begin to overlap, they hybridize into molecular orbitals with different energies. Since there are many atoms, the orbitals are very close in energy, and form continuous bands.
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 ...
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:
In the usual analysis, the p-orbitals of the metal are used for σ bonding (and have the wrong symmetry to overlap with the ligand p or π or π * orbitals anyway), so the π interactions take place with the appropriate metal d-orbitals, i.e. d xy, d xz and d yz. These are the orbitals that are non-bonding when only σ bonding takes place.
When phosphines bond to electron-rich metal atoms, backbonding would be expected to lengthen P–C bonds as P–C σ* orbitals become populated by electrons. The expected lengthening of the P–C distance is often hidden by an opposing effect: as the phosphorus lone pair is donated to the metal, P(lone pair)–R(bonding pair) repulsions ...
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