Lecture 27 - Diatomic molecules.pdf

Lecture 27 - Diatomic molecules.pdf - Lecture 27 Diatomic...

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Lecture 27 –Diatomic molecules Lecture 27: Diatomic Molecules TTT 2017 Lecture 27/ 2 H 2 Molecule square4 We can treat H 2 using LCAO-MO theory simply by installing the bonding wavefunction ψ b ≡ψ bond = ψ + in a Slater determinant : square4 The spatial and spin parts of the wave function separate for two electron system. square4 The two electrons have opposite spins, as expected. ( ) - = = ) 2 ( ) 1 ( ) 2 ( ) 1 ( 2 1 ) 2 ( ) 1 ( ) 2 ( ) 2 ( ) 1 ( ) 1 ( 2 1 α β β α ψ ψ β ψ α ψ β ψ α ψ ψ b b b b b b TTT 2017 Lecture 27/ 3 H 2 Molecule square4 ψ MO is a product of molecular orbitals , which in turn are linear combinations of atomic orbitals . square4 The spin function has no effect on the energy barb2right Ground- state energy of H 2 can be calculated: [ ][ ] ( ) [ ][ ] spin MO spin B A B A B A B A s s s s S s s s s S ψ ψ ψ α β β α ψ = + + + = - + + + = ) 2 ( 1 ) 2 ( 1 ) 1 ( 1 ) 1 ( 1 2 2 1 ) 2 ( ) 1 ( ) 2 ( ) 1 ( 2 1 ) 2 ( 1 ) 2 ( 1 ) 1 ( 1 ) 1 ( 1 2 2 1 2) (1, ˆ ) 2 1, ( * 2 1 MO MO MO H dr dr E ψ ψ = TTT 2017 Lecture 27/ 4 Diatomic Molecules Number of electrons 5 10 15 20 TTT 2017 Lecture 27/ 5 LCAO-MO square4 Orbitals can be made by guesswork, by Hartree-Fock calculations , or by Density Functional calculations . For small diatomics, results agree. square4 Orbitals must match symmetry of molecule automatic for H-F or other calculations square4 Orbitals are made by combining atomic orbitals of similar energy square4 Orbitals are filled from lowest to highest energy square4 Hund’s rule for spin applies if degenerate orbitals are available: unpaired spin is lower in energy TTT 2017 Lecture 27/ 6 Orbitals Must Match Symmetry of Molecule G- G+ U+ U+ U- depends on which plane G (German gerade, even) and U (ungerade, odd) apply to changing the sign of the wavefunction on changing x,y,z to -x,-y,-z, that is, looking opposite a center of symmetry. Only molecules with such a center have this designation. + or - refers to reflection across a plane passing through the symmetry axis. An orbital with two paired spin electrons is always G+. Only an orbital with only one electron can be otherwise.
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