A Simple Quantum Mechanical Theory of Chemical Bonding · 2020. 12. 10. · Valence Bond Theory...

EXPLAINING MOLECULAR GEOMETRY

Valence Bond TheoryA Simple Quantum Mechanical Theory

of Chemical Bonding

• Atoms must be close to each other

• Orbitals must overlap with each other

• Other orbitals shouldn't get in the way

• The greater the overlap, the stronger the bond.

• Orbitals with similar energy can overlap more effectively than orbitals of dramatically different energy.

Formation of a Covalent Bond

Orbitals on different atoms must overlap to form a bond.

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Formation of Covalent Bonds in H2 and HCl

• Atomic orbitals on two different atoms overlap and form a bond

• There's plenty of room – other atomic orbitals aren't in the way

• Angles between different p orbitals are 90o

• Angles between most d orbitals are 90o

• p orbitals stick out in two directions but can make bond in one

direction only and block the other direction from forming a bond

• Central atom needs to make bonds at 90o, 120o, 180o

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Problem: Atomic orbitals don't point in the right directions to describe chemical bonds and molecular geometry in molecules with more than two atoms.

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Valence Bond Theory

• A simple but mathematically rigorous theory• Originated from quantum mechanics• Explains the directions of covalent bonds• Explains single, double, triple bonds

• Uses the idea of hybrid orbitals• Create n hybrid orbitals using n atomic orbitals

– 2 atomic orbitals form 2 hybrid orbitals– 4 atomic orbitals form 4 hybrid orbitals, etc.

• Hybrid orbitals take the name of the atomic orbitals fromwhich they were made– sp hybrid orbitals from s+p, sp2 orbitals from s+p+p, etc.

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Combining atomic orbitals is allowed by the mathematics of quantum mechanics.

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orbitals-which-of-the-p-orbitals-do-you-think-contribute

• Each atomic orbital is described by a complex mathematical function that can be drawn in three dimensions

• Atomic orbitals can be added/subtracted to form new orbitals pointing in different directions

• Combining 1 s orbital with 3 p orbitals in different ways creates 4 new sp3 orbitals that point towards the corners of a tetrahedron

• The tiny parts of the new orbitals are ignored

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orbitals-which-of-the-p-orbitals-do-you-think-contribute

• Adding orbitals together is just like adding vectorstogether: the resulting vector is pointing in a new direction.

Valence bond theory uses math - calculus and analytic geometry - to create orbitals pointing in the

correct directions.

Formation of sp3 Hybrid Orbitals

• Use one s and three p atomic orbitals to make four sp3

orbitals• Use the sp3 orbitals for form covalent bonds

4 4

Energy level diagrams can be used to represent theformation of sp3 hybrid orbitals.

• The energy of the final hybrid orbitals is intermediate between the energies of the atomic orbitals

• The "promote" step doesn't actually happen – it's just a way torepresent the hybridization process when teaching valence bond theory.

Bonding of nitrogen and oxygen can also be represented with sp3 hybrid orbitals.

• Nitrogen forms bonds with three of its sp3 orbitals. The fourth one has a lone pair of electrons.

• Oxygen has two lone pairs in twosp3 orbitals and forms chemical bonds with the other two.

Energy

Compounds that contain double bonds require sp2

hybrid orbitals.• sp2 orbitals are made from one s and two p orbitals

• both atoms must undergo sp2

hybridization• the sp2 hybrid orbitals on both

atoms form one bond

• the single leftover p atomicorbitals on each atom form a second bond

Energy

• sp orbitals are made from one sand one p orbitals

• both atoms must undergo sphybridization

• the sp hybrid orbitals on both atoms form one bond

• the two remaining p atomicorbitals on each atom form two more bonds

Triple bonds require sp hybrid orbitals.

The carbon atom in CO2 is sp hybridized and forms two double bonds.

• sp orbitals are made from one sand one p orbitals

• carbon dioxide forms a linear structure, so it must have sphybridization

• the oxygen atoms require sp2

hybrid orbitals to accommodate their two lone pairs and keep one p orbital free to form the double bond

Valence bond theory does not work well when d orbitals are included.

• In some older textbooks, d orbitals are used with s and p orbitals to produce hybrid orbitals to explain trigonal bipyramidal (dsp3) and octahedral (d2sp3) geometry

• Hybridization schemes involving d orbitals do not show significant agreement withexperimental results, so we don't use them anymore

Valence Bond Theory

One hybrid orbital is required for each bond (whether a single or a multiple bond) and for each lone pair.

A multiple bond can form by the overlapping of more than one orbital from each bonding atom.

A s bond (sigma) It is formed either when two s orbitals overlap or with directional orbitals (p or hybrid), when they overlap along their axis. It has a cylindrical shape about the bond axis.

A p bond (pi) has an electron distribution above and below the bond axis. It is formed by the sideways overlap of two parallel p orbitals. These form only after s bonds have formed.

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Valence Bond Theory