Heisenberg Uncertainty Principle states that it is impossible to define what time and where an electron is and where is it going next. This makes it impossible to know exactly where an electron is traveling in an atom.
Since it is impossible to know where an electron is at a certain time, a series of calculations are used to approximate the volume and time in which the electron can be located. These regions are called Atomic Orbitals. These are also known as the quantum states of the electrons.
Only two electrons can occupy one orbital and they must have different spin states, ½ spin and – ½ spin (easily visualized as opposite spin states).
S subshell: (Spherical shape) There is one S orbital in an s subshell. The electrons can be located anywhere within the sphere centered at the atom’s nucleus.
P Orbitals: (Shaped like two balloons tied together) There are 3 orbitals in a p subshell that are denoted as p x , p y , and p z orbitals. These are higher in energy than the corresponding s orbitals.
When atoms share electrons to form a bond, their atomic orbitals mix to form molecular bonds. In order for these orbitals to mix they must:
Have similar energy levels.
Be close together .
This is and example of orbital mixing. The two atoms share one electron each from there outer shell. In this case both 1s orbitals overlap and share their valence electrons. http://library.thinkquest.org/27819/ch2_2.shtml
Energy Diagram of Sigma Bond Formation by Orbital Overlap
In the case of diatomic molecules, the interactions are easy to see and may be thought of as arising from the constructive interference of the electron waves (orbitals) on two different atoms, producing a bonding molecular orbital, and the destructive interference of the electron waves, producing an antibonding molecular orbital
A Little Math is need to understand Only a Little I promise!
This Approach is called LCAO-MO
(Linear Combination of Atomic Orbitals to Produce Molecular Orbitals)
Molecular Orbital Diagram (HF) http://www.ch.ic.ac.uk/vchemlib/course/mo_theory/main.html
Valence MOs 1s F H HF 2s 2p Energy Levels in HF This diagram shows the allowed energy levels of Isolated H (1s 1 ) and F (1s 2 2s 2 2p 5 ) atoms and, between them, the HF molecule. Note: 1. F 1s is at much lower energy than H 1s (because of the higher nuclear charge) 2. F 1s 2 electrons are core electrons. Their energy does not change when HF is formed. 3. H 1s and F 2p valence electrons go into molecular orbitals with new energies.
1s F H HF 2s 2p Molecular Orbitals in HF This core orbital is almost unchanged from the F 1s orbital. The electrons are bound tightly to the F nucleus. This non-bonding molecular orbital ( n ) has an almost spherical lobe showing only slight delocalisation between the two nuclei. Non-bonding orbitals look only slightly different to atomic orbitals, and have almost the same energy. H F n n
Molecular Orbitals in HF These two degenerate (filled) HOMO’s are centred on the F atom, like 2p x and 2p y orbitals. This MO, which is is like a 2p z orbital, is lower in energy in the molecule (a bonding orbital), and one lobe is delocalised around the H atom. This ( empty ) LUMO is an antibonding orbital with a node on the interatomic axis between H and F. Electrons in these two orbitals are not shared (much) by the fluorine nucleus. They behave like the 2p orbitals and are also non-bonding (n) . 1s F H HF 2p n n n n
The second set of combinations with symmetry (orthogonal to the first set): This produces an MO over the molecule with a node on the bond between the F atoms. This is thus a bonding MO of u symmetry. Molecular Orbital Theory Diatomic molecules: The bonding in F 2 2p xA + This produces an MO around both F atoms that has two nodes: one on the bond axis and one perpendicular to the bond. This is thus an antibonding MO of g symmetry. u = 0.5 (2p xA + 2p xB ) 2p xB - g * = 0.5 (2p xA - 2p xB ) 2p xA 2p xB
F Energy F F 2 2s 2s 2 g 2 u * 2p 2p 3 g 3 u * 1 u 1 g * Molecular Orbital Theory MO diagram for F 2 (p x ,p y ) p z You will typically see the diagrams drawn in this way. The diagram is only showing the MO’s derived from the valence electrons because the pair of MO’s from the 1s orbitals are much lower in energy and can be ignored. Although the atomic 2p orbitals are drawn like this: they are actually all the same energy and could be drawn like this: at least for two non-interacting F atoms. Notice that there is no mixing of AO’s of the same symmetry from a single F atom because there is a sufficient difference in energy between the 2s and 2p orbitals in F. Also notice that the more nodes an orbital of a given symmetry has, the higher the energy. Note: The the sake of simplicity, electrons are not shown in the atomic orbitals.
F Energy F F 2 2s 2s 2 g 2 u * 2p 2p 3 g 3 u * 1 u 1 g * Molecular Orbital Theory MO diagram for F 2 (p x ,p y ) p z Another key feature of such diagrams is that the -type MO’s formed by the combinations of the p x and p y orbitals make degenerate sets (i.e. they are identical in energy). The highest occupied molecular orbitals (HOMOs) are the 1 g * pair - these correspond to some of the “lone pair” orbitals in the molecule and this is where F 2 will react as an electron donor. The lowest unoccupied molecular orbital (LUMO) is the 3 u * orbital - this is where F 2 will react as an electron acceptor. HOMO LUMO
B Energy B B 2 2s 2s 2 g 2 u * 2p 2p 3 g 3 u * 1 u 1 g * Molecular Orbital Theory MO diagram for B 2 ( p x ,p y ) p z In the MO diagram for B 2 , there several differences from that of F 2 . Most importantly, the ordering of the orbitals is changed because of mixing between the 2s and 2p z orbitals. From Quantum mechanics: the closer in energy a given set of orbitals of the same symmetry, the larger the amount of mixing that will happen between them. This mixing changes the energies of the MO’s that are produced. The highest occupied molecular orbitals (HOMOs) are the 1 u pair. Because the pair of orbitals is degenerate and there are only two electrons to fill, them, each MO is filled by only one electron - remember Hund’s rule. Sometimes orbitals that are only half-filled are called “singly-occupied molecular orbtials” (SOMOs). Since there are two unpaired electrons, B 2 is a paramagnetic (triplet) molecule. HOMO LUMO
Remember that the separation between the n s and n p orbitals increases with increasing atomic number. This means that as we go across the 2nd row of the periodic table, the amount of mixing decreases until there is no longer enough mixing to affect the ordering; this happens at O 2 . At O 2 the ordering of the 3 g and the 1 u MO’s changes. As we go to increasing atomic number, the effective nuclear charge (and electronegativity) of the atoms increases. This is why the energies of the analogous orbitals decrease from Li 2 to F 2 . The trends in bond lengths and energies can be understood from the size of each atom, the bond order and by examining the orbitals that are filled. Diatomic molecules: MO diagrams for Li 2 to F 2 Molecular Orbital Theory In this diagram, the labels are for the valence shell only - they ignore the 1s shell. They should really start at 2 g and 2 u *. 2s-2p z mixing Molecule Li 2 Be 2 B 2 C 2 N 2 O 2 F 2 Ne 2 Bond Order 1 0 1 2 3 2 1 0 Bond Length (Å) 2.67 n/a 1.59 1.24 1.01 1.21 1.42 n/a Bond Energy (kJ/mol) 105 n/a 289 609 941 494 155 n/a Diamagnetic (d)/ Paramagnetic (p) d n/a p d d p d n/a