Graphical Models• We will examine a number of useful graphical models including

- molecular orbitals- electron densities- spin densities- electrostatic potentials- local ionization potentials

• Spartan makes generation of such graphical models straightforward (via the “Surfaces” menu).

Molecular Orbitals• MO’s () are written as linear combinations of basis functions () which themselves are centered on the nuclei (c are the expansion coefficients).

• MO’s (whether occupied by electrons or not) can offer important insight into the properties of molecules.

• The MO’s with the most significance in chemistry are the HOMO (highest occupied MO) and the LUMO (lowest unoccupied MO).

• Computational chemistry allows easy calculation and graphical display of any MO.

φcμii functions

basis

Spartan calculation of surfaces

Calculation of MO’s requires selection of the MO from the Surface menu

Calculation of a property map requires you first to select a size surface (usually an electron density surface) and then you choose the property to be mapped onto this surface. Typical properties include LUMO, potential or ionization.

Anti-bonding MO’s

Bonding MO’s1

2

3

4

1

2

3

4

(0 nodes)

HOMO (1 node)

LUMO (2 nodes)

(3 nodes)

1 2 3 4

Hückel treatment of the -electrons of benzene

Increasing energy

MO calculation of benzene yields orbitals consistent with Hückel theory

1

2 3

4

Molecular orbitals of H2O

O HH

HOMO -4 (s orbital on

O atom)

O HH

HOMO -3

O HH

HOMO -1

O HH

HOMO (lone pair on O atom

in pz orbital)

H

O

H

x

y

O HH

H

O

H

HOMO -2

1

2

3

4

5

Antibonding MO’s of H2O

Based on our calculated MO’s, since orbitals 6 and 7 are antibonding in nature, we would predict that excitation of an electron from the HOMO (5) into either orbital 6 or orbital 7 will result in an “unstable” species – that is the O-H bonds will break once electrons are placed into the antibonding orbitals and the H2O is therefore predicted to dissociate into H and OH. This is indeed what is seen experimentally.

H

O

H

LUMO

H

O

H

LUMO +16 7

NH H

H

HOMO of NH3

Clearly shows the lone pair on the nitrogen atom

MO’s of acetylene

• Note that even in simple cases the MO’s do not correspond one-to-one with chemical bonds. The -orbital on the left consists of both CC and CH components. This is due to the fact that MO’s are generated as linear combination of nucleus-centered basis functions, and hence will tend to be delocalized over the entire nuclear framework of the molecule.

Use of MO’s in predicting reactivity

cis-1,3-butadiene + ethylene → cyclohexene (FAVORABLE)

LUMO (ethylene)

HOMO (cis-1,3-butadiene)

+

Use of MO’s in predicting reactivity

ethylene + ethylene → cyclobutane (NOT FAVORABLE)

LUMO (ethylene)

HOMO (ethylene)

+

CN

HOMO of cyanide anion (CN―)

Note that the HOMO is concentrated more on the carbon atom than on the nitrogen. This suggests it will act more as a carbon nucleophile (which indeed is what is observed experimentally).

Planar Perpendicular

LUMO Benzyl cations

The LUMO is the energetically most accessible unfilled orbital and so electrons (from an nucleophile) will go into these orbitals.

The LUMO in the planar form is delocalized away from the formal cation center and onto the ortho and para ring carbons, in line with classical resonance structures (see later). The perpendicular form has its LUMO localized primarily on the benzylic carbon and is less stable due to the lack of delocalization.

Methyl iodide LUMO

Donation of an electron pair into this MOwill cause weakening and eventual breakage of the C―I bond.

Antibonding MO between C & I