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Unformatted text preview: Chem 120A Polyatomic molecules: Molecular geometry and Hartree- Fock theory 05/03/06 Spring 2006 Lecture 40 READING: Engel (QCS): Ch. 16.3 McQuarrie and Simon: Ch. 10 (Walsh Diagrams) Using LCAO theory to predict molecular shape As you have probably seen in general chemistry and organic chemistry, hybrid orbitals can be used to predict molecular geometry. Here we examine the basis of the theory of hybridization. Let’s consider the methane molecule, CH 4 , which has tetrahedral geometry. The carbon atom is located at the center of the tetrahedron and each of the hydrogen atoms is at a vertex of the tetrahedron. The electron configuration of carbon is 1 s 2 2 s 2 2 p 2 . We can use the 2 s and the 2 p orbitals to form linear combinations that have the appropriate geometry: ψ c = c 1 ψ 2 s + c 2 ψ 2 p x + c 3 ψ 2 p y + c 4 ψ 2 p z . (1) Because there are initially 4 orbitals available (one 2 s and 3 2 p orbitals), we can find 4 hybridized orbitals using the linear combination. The orbitals are sp 3 hybridized, and the angle between the orbitals is 109.5 o . The molecular orbitals in the methane molecule are then formed from a linear combination of each of these hybrid orbitals with the 1 s orbital of a hydrogen atom, which gives σ and σ ∗ orbitals. Another example is SF 6 , which is octahedral. The electron configuration of the central sulfur atom is [Ne]3 s 2 3 p 4 . In order to form this molecule, the sulfur atom needs to have 6 hybridized orbitals. The electron configuration we have written shows that there are only 4 orbitals in sulfur’s valence shell. The key point here is that the 3 d orbitals are close in energy to the 3 s and 3 p orbitals, so the d orbitals can be used in the linear combination. Taking a linear combination of the one 3 s , three 3 p , and two 3 d orbitals, we obtain a total of 6 sp 3 d 2 hybridized orbitals. Each of these hybridized atomic orbitals can then be used in a linear combination with a 2 p orbital of fluorine, which again yields σ and σ ∗ orbitals....
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