Molecular Structure Both atoms and molecules are quantum systems

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1 Molecular Structure Both atoms and molecules are quantum systems We need a method of describing molecules in a quantum mechanical way so that we can predict structure and properties The method we use is the Linear Combination of Atomic Orbitals where we can use the properties of atoms to predict the properties of molecules. Molecular Structure We combine atoms to form molecules by considering the phase of the atomic orbitals we are using We represent the phase via the shading we give the orbital. The phase represents the sign of the wavefunction Molecular Structure We combine atoms to form molecules by considering the phase of the atomic orbitals we are using The phase represents the sign of the wavefunction We represent the phase via the shading we give the orbital.

2 Molecular Structure For an s orbital, the orbital has the same phase everywhere: 1s orbital, n = 1, l = 0 For a p orbital, there is a change in the sign of the wavefunction across the nodal plane: 2p orbital, n = 2, l = 1, m l = -1 Molecular Structure Consider two H atoms (1s 1 ) coming together from infinite separation. There are two possibilities: 1 The wavefunctions are in phase 2 The wavefunctions are not in phase Molecular Structure Case 1: The wavefunctions are in phase The atoms move together and the electron waves overlap with the same phase, producing constructive interference and a build up of electron density between the nuclei The energy of the system drops and we form a bond

3 r = 8 Å r = 3 Å r = 7 Å r = 2 Å r = 6 Å r = 1 Å r = 5 Å r = 0.75 Å Molecular Structure Case 2: The wavefunctions are out of phase The atoms move together and the electron waves have opposite phase. The electron waves overlap producing destructive interference and electron density between the nuclei is reduced. The energy of the system rises and we have an antibonding situation r = 8 Å r = 3 Å r = 7 Å r = 2 Å r = 5 Å r = 1 Å r = 4 Å r = 0.75 Å

4 Two atoms with wavefunctions in phase overlap with constructive interference. Electron density increases between the nuclei and the overall energy decreases. Bonding When the wavefunctions are of opposite phase, the electron density between the nuclei decreases due to destructive interference. The energy of the system rises and we have an antibonding situation Antibonding Bonding Here we see 2 2s orbitals in the bonding and antibonding regimes In the antibonding regime, there is no build-up of density between the nuclei at any separation. How do we represent this energetically? Antibonding Energies and phase Antibonding Bonding Bond length at the minimum energy

5 Energies and phase For the antibonding interaction, there is no minimum in energy at any distance Antibonding Bonding Bond length at the minimum energy For the bonding interaction, there is a minimum. The distance is the bond length and the energy is the bond energy σ bonds are in general stronger than π bonds and can be formed from either s or p orbitals: σ bonds have no nodal plane that contains the two nuclei. The σ* antibonding orbital has a nodal plane between the two nuclei

6 π bonds have a nodal plane that contains both nuclei, The π* antibonding orbital also has a plane between the nuclei These σ, π bonding orbitals and σ*, π* antibonding orbitals are the orbitals that are used to bind all simple organic molecules together. We can also describe the bonding in diatomic molecules important models for larger organic systems To describe the bonding in the diatomic molecules such as O 2, N 2 and X 2 (X = F, Cl, Br and I), we use both the s orbitals and the p orbitals on the two atoms as a basis set - the palette of atomic orbitals from which we will build the molecular orbitals. The energies of the two different l states, s and p, are slightly different in polyelectronic atoms.

7 The s orbitals and the p orbitals appear as follows We arrange the atoms along one of the axes for convenience and so the first pair of orbitals we construct are the sσ and sσ* orbitals from the s orbitals on the atoms. σ bonds and π bonds We now us the higher energy p orbitals to construct pσ and pπ orbitals

8 The complete molecular orbital diagram for all the diatomic molecules from Li 2 to N 2 The complete molecular orbital diagram for all the diatomic molecules from Li 2 to N 2 As each molecule has a different number of electrons, Li 2 2 Be 2 4 B 2 6 C 2 8 N 2 10 O 2 12 F 2 14 Ne 2 16 Li 2 2 Be 2 4 B 2 6 C 2 8 N 2 10 O 2 12 F 2 14 Ne 2 16 We can write the electronic structure of each molecule by placing electron pairs into the orbitals.

9 Li 2 2 Be 2 4 B 2 6 C 2 8 N 2 10 O 2 12 F 2 14 Ne 2 16 Something peculiar happens after N 2 Recall that as the charge on the nucleus increases, the orbitals become more stabilized and the electrons become more strongly bound. Li 2 2 Be 2 4 B 2 6 C 2 8 N 2 10 O 2 12 F 2 14 Ne 2 16 This happens by different amounts, depending on the orbital. After N 2 (10 e - ), the ordering of the orbitals derived from p change their order in the molecule For N 2 (10 e - ), the ordering is this For O 2 (12 e - ), the ordering is this

10 This is an example of configurational interaction Each electron moves in the field of the other electrons. If the energies of the two molecular orbitals are sufficiently close and the nodal properties are correct, molecular orbitals will interact and shuffle their energies in the molecule. This causes the σ orbitals to change their energetic ordering but only when the nuclear charge is high enough to force the electrons close in energy. Configurational interaction Each electron moves in the field of the other electrons. If the energies of the two molecular orbitals are sufficiently close and the nodal properties are correct, molecular orbitals will interact and shuffle their energies in the molecule. This causes the σ orbitals to change their energetic ordering but only when the nuclear charge is high enough to force the electrons close in energy.