atomic and molecular orbitals

John E. McMurry

www.cengage.com/chemistry/mcmurry

Paul D. Adams • University of Arkansas

Atomic and Molecular Orbitals

Structure and Properties of Organic Molecules

Electrons act as both particles and waves (duality) An orbital can be described as a 3D standing

wave To understand this, we can look at wave

properties of guitar strings

http://www.rollingstone.com/music/lists/100-greatest-guitarists-of-all-time-19691231/jimi-hendrix-19691231; Wade, Organic Chemistry, 2013

Wave Harmonics with Dr. Jimi

Wade, Organic Chemistry, 2013

Wave properties of electron in s orbitals


Wave properties of electron in p orbitals

Atomic orbitals combine and overlap to produce more complex standing waves

Any wave overlap can be constructive or destructive.

Wade, Organic Chemistry, 2013; http://animals.howstuffworks.com/insects/butterfly-colors1.htm

Linear Combination of Atomic Orbitals

When orbitals on different atoms interact (think of covalent bonds), they produce molecular orbitals that lead to bonding or antibonding interactions.


Electrostatic potential map of H2

• There is an optimal distance between these nuclei where charge attraction and repulsion are balanced.

• This leads to a somewhat consistently fixed bond length.

• The stability of covalent bond results from increased electron density in the bonding region (i.e., the space between the 2 nuclei where orbitals overlap).

Linear Combination of Atomic Orbitals


• Formation of cylindrically symmetrical sigma (σ) bond as a result of constructive addition • e- density in bonding region increases• Forms bonding MO

Sigma Bonding in Hydrogen Molecules


• The 2 out of phase 1s hydrogen orbitals overlap destructively to cancel out part of the wave, producing a node

• Forms antibonding MO with (σ*) bond


A molecular orbital (MO): where electrons are most likely to be found (specific energy and general shape) in a molecule

Additive combination (bonding) MO is lower in energy Subtractive combination (antibonding) MO is higher energy

Describing Chemical Bonds: Molecular Orbital Theory

The bonding MO is from combining p orbital lobes with the same algebraic sign

The antibonding MO is from combining lobes with opposite signs

Only bonding MO is occupied

Molecular Orbitals in Ethylene

Destructive interference of orbitals

Constructive interference of orbitals


Formation of MO’s


Formation of the bonding MO requires less E to maintain, i.e., it is more stable



Sigma Bonding between p and s orbitals

Pi (π) bonds formed by overlap of 2 parallel p orbitals. Not cylindrically symmetrical like σ bond Not as strong as σ bond Important for chemical reactions

Pi bonds form double and triple bonds.


Pi (π) Bonds

When orbitals on the same atom interact, they produce hybrid atomic orbitals that define bond geometry.

Consider the problem with carbon in the energy diagram below:


2p2s1s

EnergyEnergy

Valence Valence shell shell

electronelectronss

C1

2

How does carbon form 4 bonds?

1s22s22p2

Orbital Hybridization

Carbon has 4 valence electrons (2s2 2p2) In CH4, all C–H bonds are identical (tetrahedral) sp3 hybrid orbitals: s orbital and three p orbitals

combine to form four equivalent, unsymmetrical, tetrahedral orbitals (sppp = sp3), Pauling (1931)


EnergyEnergy

2p2s1s

Valence shell

electrons

1s

4 x sp3

An sp3 orbital has a two-lobed shape, similar to the shape of a p orbital but with different-sized lobes.

Each carbon-hydrogen bond in methane arises from an overlap of a C (sp3) and an H (1s) orbital.

The sharing of two electrons in this overlap region creates a sigma (σ) bond.

Seager SL, Slabaugh MR, Chemistry for Today: General, Organic and Biochemistry, 7th Edition, 2011


Two C’s bond to each other by overlap of an sp3 orbital from each

Three sp3 orbitals on each C overlap with H 1s orbitals to form six C–H bonds

C–H bond strength in ethane 421 kJ/mol C–C bond is 154 pm long and strength is 377 kJ/mol All bond angles of ethane are tetrahedral

sp3 Orbitals and the Structure of Ethane

The tetrahedral geometry can be explained by Valence Shell Electron Pair Repulsion (VSEPR) Theory

(VSEPR) Theory: Electron pairs repulse each other in such a way so that they are as far apart from each other as possible.

The bond angles observed in organic compounds can (currently) only be explained by this repulsion of hybridized orbitals.


trigonaltetrahedral linear geometry

VSEPR Theory

In C=C bonds, sp2 hybrid orbitals are formed by the carbon atoms, with one electron left in a 2p orbital. A representation of sp2 hybridization of carbon.

During hybridization, two of the 2p orbitals mix with the single 2s orbital to produce three sp2 hybrid orbitals. One 2p orbital is not hybridized and remains unchanged.

2p2s1s

Energy

2p3 sp2

1s

The Geometry of Alkenes

1. One bond (sigma, σ) is formed by overlap of two sp2 hybrids.

2. The second bond (pi, π) is formed by connecting the unhybridized p orbitals.

2p2s1s

Energy

2p3 sp2

1s



The planar geometry of the sp2 hybrid orbitals and the ability of the 2p electron to form a “pi bond” bridge locks the C=C bond firmly in place.



Because there is no free rotation about the C=C bond, geometric isomerism is possible.

cis- isomers have two similar or identical groups on the same side of the double bond.

trans- isomers have two similar or identical groups on opposite sides of the double bond.



Geometric isomers have different physical properties.



2p2s1s

Energy

2p2 sp1s

• Insoluble in water

• Less dense than water

• Low MP, BP


Hybridization/Geometry of Alkynes

Summary of Hybridizations

Adjacent Double Bonds

Comparison of C–C and C–H Bonds

Elements other than C can have hybridized orbitals H–N–H bond angle in ammonia (NH3) 107.3°

C-N-H bond angle is 110.3 ° N’s orbitals (sppp) hybridize to form four sp3 orbitals One sp3 orbital is occupied by two nonbonding

electrons, and three sp3 orbitals have one electron each, forming bonds to H and CH3.

Hybridization of Nitrogen and Oxygen

atomic and molecular orbitals

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organic chemistry

bondsigma bonding

stablesigma bonding

opposite signsonly bonding

s hydrogen orbitals

occupiedmolecular orbitals

wave properties of electron

p orbitalsatomic orbitals