Molecular Structure

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.

2. 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

3. 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.

4. Molecular Structure For an s orbital, the orbital has the same phase everywhere: For a p orbital, there is a change in the sign of the wavefunction across the nodal plane: 1s orbital, n = 1, l = 0 2p orbital, n = 2, l = 1, ml = -1

5. Molecular Structure • Consider two H atoms (1s1) coming together from infinite separation. • There are two possibilities: • The wavefunctions are in phase • The wavefunctions are not in phase

6. 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

7. 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

8. 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

9. r = 8 Å r = 3 Å r = 2 Å r = 7 Å r = 5 Å r = 1 Å r = 4 Å r = 0.75 Å

10. Two atoms with wavefunctions in phase overlap with constructive interference. Electron density increases between the nuclei and the overall energy decreases. • 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 Bonding Antibonding

11. 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

12. Energies and phase Antibonding Bonding Bond length at the minimum energy

13. Energies and phase • For the antibonding interaction, there is no minimum in energy at any distance • For the bonding interaction, there is a minimum. The distance is the bond length and the energy is the bond energy Antibonding Bonding Bond length at the minimum energy

14. Organic Structure and Bonding s bonds and p bonds s bonds are in general stronger than p bonds and can be formed from either s or p orbitals:

15. Organic Structure and Bonding s bonds and p bonds s bonds have no nodal plane that contains the two nuclei. The s* antibonding orbital has a nodal plane between the two nuclei

16. Organic Structure and Bonding s bonds and p bonds p bonds have a nodal plane that contains both nuclei, The p* antibonding orbital also has a plane between the nuclei

17. Organic Structure and Bonding s bonds and p bonds These s, p bonding orbitals and s*, p* 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

18. Organic Structure and Bonding s bonds and p bonds To describe the bonding in the diatomic molecules such as O2, N2 and X2 (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.

19. Organic Structure and Bonding s bonds and p bonds The s orbitals and the p orbitals appear as follows

20. Organic Structure and Bonding s bonds and p bonds We arrange the atoms along one of the axes for convenience and so the first pair of orbitals we construct are the ss and ss* orbitals from the s orbitals on the atoms.

21. Organic Structure and Bonding s bonds and p bonds We now us the higher energy p orbitals to construct ps and pp orbitals

22. Organic Structure and Bonding s bonds and p bonds The complete molecular orbital diagram for all the diatomic molecules from Li2 to N2

23. Organic Structure and Bonding s bonds and p bonds The complete molecular orbital diagram for all the diatomic molecules from Li2 to N2 As each molecule has a different number of electrons, Li2 2 Be2 4 B2 6 C2 8 N2 10 O2 12 F2 14 Ne2 16

24. Organic Structure and Bonding s bonds and p bonds Li2 2 Be2 4 B2 6 C2 8 N2 10 O2 12 F2 14 Ne2 16 We can write the electronic structure of each molecule by placing electron pairs into the orbitals.

25. Organic Structure and Bonding s bonds and p bonds Li2 2 Be2 4 B2 6 C2 8 N2 10 O2 12 F2 14 Ne2 16 Something peculiar happens after N2 Recall that as the charge on the nucleus increases, the orbitals become more stabilized and the electrons become more strongly bound.

26. Organic Structure and Bonding s bonds and p bonds Li2 2 Be2 4 B2 6 C2 8 N2 10 O2 12 F2 14 Ne2 16 This happens by different amounts, depending on the orbital. After N2 (10 e-), the ordering of the orbitals derived from p change their order in the molecule

27. Organic Structure and Bonding s bonds and p bonds For N2 (10 e-), the ordering is this For O2 (12 e-), the ordering is this

28. Organic Structure and Bonding s bonds and p bonds 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 s orbitals to change their energetic ordering but only when the nuclear charge is high enough to force the electrons close in energy.

29. Organic Structure and Bonding s bonds and p bonds 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 s orbitals to change their energetic ordering but only when the nuclear charge is high enough to force the electrons close in energy.