화학15. MO

(1) Sketch an MO energy diagram showing only the molecular orvitals and electiron distribution in CO. Label the energy levels according to the type of orbitals from which they are made, whether they are sigma- or pi-orbitals.

 

(2) Sketch the MO boundary surface of the CO highest energy occupied MO(HOMO) and lowest energy unoccupid MO(LUMO).

 

 

 

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Molecular Orbitals

 

Bonding in Inorganic Compounds

• Valence Bond Theory (VBT)
• Crystal Field Theory (CFT)
• Molecular Orbital Theory (MOT)

 

15.1. Valence Bond Theory (VBT)

• 1916 electron pairing model by Lewis
• 1927 Q. M. method by W. Heitler & F. London
• 1930s valence bond approach by L. Pauling & J. C. Slater

Resonance : minimize E_b

 

15.2. Molecular Orbital Theory (MOT)

 

Electrons are not assigned to individual bonds between atoms, but are treated as moving under the influence of the nuclei in the whole molecule. (HundMulliken theory)

 

The Delocalized Approach to Bonding: Molecular Orbital Theory

The localized models for bonding we have examined (Lewis and VBT) assume that all electrons are restricted to specific bonds between atoms or in “lone pairs”. In contrast, the delocalized approach to bonding places the electrons in Molecular Orbitals (MO’s) - orbitals that encompass the entire molecule and are not associated with any particular bond between two atoms. In most cases, MO theory provides us with a more accurate picture of the electronic structure of molecules and it gives us more information about their chemistry (reactivity).

Molecular orbitals are constructed from the available atomic orbitals in a molecule. This is done in a manner similar to the way we made hybrid orbitals from atomic orbitals in VBT. That is, we will make the MO’s for a molecule from Linear Combinations of Atomic Orbitals (LCAO). In contrast to VBT, in MO theory the atomic orbitals will come from several or all of the atoms in the molecule. Once we have constructed the MO’s, we can build an MO diagram (an energy level diagram) for the molecule and fill the MO’s with electrons using the Aufbau principle.

 

15.3. Fundamental Rules for MO

(Schrödinger orbital that includes several nuclei)

 

• Linear Combination of Atomic Orbitals (LCAO)(The molecular orbital wave function may be written as a simple weighted sum of the constituent atomic orbitals. And the coefficients may be determined numerically by substitution of this equation into the Schrödinger equation and application of the variational principle.)
• Only Valence electrons can participate in chemical bonding and form M.O.
• Conservation of Orbital in Bonding(no. of total A.O. = no. of M.O.)
• M.O. follows Hund’s rule and Pauli’s exclusion principle.
• Only A.O. with identical symmetry property can interact.
• To combine, the atomic orbitals must be of similar energy.
• Each MO must be normal and must be orthogonal to every other MO.
• Types of MO :(Bonding MO: the electron(s) in the orbital have a higher probability of being between nuclei than elsewhere. Antibonding MO: the electrons tend to be present in a molecular orbital in which they spend more time elsewhere than between the nuclei)
• In M.O., there are Highest Occupied Molecular Orbital (HOMO) and Lowest Unoccupied Molecular Orbital (LUMO)
• Bond Order: (# of e in Bonding M.O. - # of e in Antibonding M.O.) / 2

 

15.4. Diatomic molecules: The bonding in He2

He also has only 1s AO, so the MO diagram for the molecule He2 can be formed in an identical way, except that there are two electrons in the 1s AO on He.

The bond order in He2 is (2-2)/2 = 0, so the molecule will not exist.

However the cation [He2 ] + , in which one of the electrons in the sigma_u * MO is removed, would have a bond order of (2-1)/2 = ½ , so such a cation might be predicted to exist. The electron configuration for this cation can be written in the same way as we write those for atoms except with the MO labels replacing the AO labels:

Molecular Orbital theory is powerful because it allows us to predict whether molecules should exist or not and it gives us a clear picture of the of the electronic structure of any hypothetical molecule that we can imagine.

 

15.5. Diatomic molecules: Homonuclear Molecules of the Second Period

Li has both 1s and 2s AO’s, so the MO diagram for the molecule Li2 can be formed in a similar way to the ones for H2 and He2 . The 2s AO’s are not close enough in energy to interact with the 1s orbitals, so each set can be considered independently.

 

The bond order in Li2 is (4-2)/2 = 1, so the molecule could exists. In fact, a bond energy of 105 kJ/mol has been measured for this molecule. Notice that now the labels for the MO’s have numbers in front of them - this is to differentiate between the molecular orbitals that have the same symmetry.

 

Be also has both 1s and 2s AO’s, so the MO’s for the MO diagram of Be2 are identical to those of Li2 . As in the case of He2 , the electrons from Be fill all of the bonding and antibonding MO’s so the molecule will not exist. The bond order in Be2 is (4-4)/2 = 0, so the molecule can not exist. The shells below the valence shell will always contain an equal number of bonding and antibonding MO’s so you only have to consider the MO’s formed by the valence orbitals when you want to determine the bond order in a molecule!

 

MO diagram for F2

Another key feature of such diagrams is that the pi-type MO’s formed by the combinations of the px and py orbitals make degenerate sets (i.e. they are identical in energy). The highest occupied molecular orbitals (HOMOs) are the 1pi_g * pair - these correspond to some of the “lone pair” orbitals in the molecule and this is where F2 will react as an electron donor. The lowest unoccupied molecular orbital (LUMO) is the 3sigma_u * orbital - this is where F2 will react as an electron acceptor.

15.6. Orbital Mixing

• s, p orbital overlap
• s, p orbital energy gap