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2 O, the 2s orbital of oxygen is mixed with the premixed hydrogen orbitals, forming a new bonding (2a 1) and antibonding orbital (4a 1). Similarly, the 2p orbital (b 1) and the other premixed hydrogen 1s orbitals (b 1) are mixed to make bonding orbital 1b 1 and antibonding orbital 2b 1. The two remaining 2p orbitals are unmixed.
The p-orbitals oriented in the z-direction (p z) can overlap end-on forming a bonding (symmetrical) σ orbital and an antibonding σ* molecular orbital. In contrast to the sigma 1s MO's, the σ 2p has some non-bonding electron density at either side of the nuclei and the σ* 2p has some electron density between the nuclei.
[12] [27] Namely the atomic s and p orbital(s) are combined to give four sp i 3 = 1 ⁄ √ 4 (s + √ 3 p i) orbitals, three sp i 2 = 1 ⁄ √ 3 (s + √ 2 p i) orbitals, or two sp i = 1 ⁄ √ 2 (s + p i) orbitals. These combinations are chosen to satisfy two conditions. First, the total amount of s and p orbital contributions must be ...
Added orbital diagrams for molecular orbitals. 16:49, 21 May 2015: 2,020 × 1,070 (138 KB) Officer781: 2pz MO in wrong orientation relative to the other orbitals per the LCAO notation. 16:40, 21 May 2015: 2,020 × 1,070 (138 KB) Officer781: Moved 2s orbital higher in energy as that MO has more hydrogen admixture.
A molecular orbital (MO) can be used to represent the regions in a molecule where an electron occupying that orbital is likely to be found. Molecular orbitals are approximate solutions to the Schrödinger equation for the electrons in the electric field of the molecule's atomic nuclei.
In the water molecule for example, ab initio calculations show bonding character primarily in two molecular orbitals, each with electron density equally distributed among the two O-H bonds. The localized orbital corresponding to one O-H bond is the sum of these two delocalized orbitals, and the localized orbital for the other O-H bond is their ...
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:
For N 2 in contrast, the order of orbital energies is not identical to the order of ionization energies. Near-Hartree–Fock calculations with a large basis set indicate that the 1π u bonding orbital is the HOMO. However the lowest ionization energy corresponds to removal of an electron from the 3σ g bonding orbital. In this case the ...