Molecular Orbitals

CHAPTER 4 Density Functional Theory

4.6 Results and Discussion

4.6.3 Molecular Orbitals

Also determined from the computations were the four frontier molecular orbitals (FMOs) for each of the metal complexes. Although these orbitals may be useful in the qualitative understanding of some molecules, they are merely mathematical functions that represent solutions to the Hartree-Fock equations for that molecule. It is possible for other orbitals

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to exist, which look quite different, yet produce the same energy and properties. There is no physical reality that can be connected with these images; individual orbitals are mathematical not physical constructs.³³¹

Here, we are mainly interested in determining to what degree the different bridging groups and metals may or may not perturb the frontier MOs of the complex. GaussView 3.09³⁹⁶ was used to compute the surfaces for the four frontier molecular orbitals of the thirty-six metal complexes. These four frontier molecular orbitals include the highest and second-highest occupied molecular orbitals and the lowest and second-lowest unoccupied molecular orbitals. These are denoted HOMO, HOMO-1, LUMO, LUMO+1, respectively. Given that the frontier molecular orbitals for each range of metal complexes are all rather similar, for brevity we shall present the discussion for the metal complexes of one ligand from each group. The wavefunctions for the molecular orbitals of platinum and palladium complexes of L2, L2m and L2b are shown pictorially in Figures 4.8, 4.9 and 4.10, respectively.

Molecular orbitals can be useful in identifying the orbitals involved in electronic excitations. The frontier molecular orbitals play an important role in electric, optical and spectroscopic properties, as well as chemical reactivity. These orbitals have been generated using an isovalue for the surfaces of 0.02 (smaller isosurface values produce larger orbitals). The red and green colours of the orbitals represent different phases of the wavefunction. Sometimes molecular orbitals are consistent with our ideas of bonding and anti-bonding, sometimes they are delocalised.

There is impressive similarity observed for the corresponding molecular orbitals for the platinum and palladium complexes of L2, as seen in Figure 4.8. This is also the case for the equivalent MOs of the platinum and palladium complexes of L2m and L2b. Each of the two HOMO and each of the two LUMO orbitals for all three sets of ligands look almost identical. The HOMO and LUMO levels have π symmetry, with opposite phases below and above the molecular plane.

LUMO1

LUMO

HOMO

HOMO–1

Figure 4.8: LUMOs (top) and HOMOs (bottom) calculated for PtL2 (left images) and PdL2

Pt Pd

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LUMO1

LUMO

HOMO

HOMO–1

Figure 4.9: LUMOs (top) and HOMOs (bottom) calculated for PtL2m (left images) and PdL2m (right images) with GaussView.³⁹⁶

Pt Pd

LUMO1

LUMO

HOMO

HOMO–1

Figure 4.10: LUMOs (top) and HOMOs calculated for PtL2b (left images) and PdL2b (right images) with GaussView.³⁹⁶

Pt Pd

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For all six of the complexes they are localised mainly on the central metal and imine/

pridine ligand structure, with little or no contribution from the bridging groups, depending on the particular complex and orbital. The HOMO-1 orbitals generated for the metal complexes of L2 and L2m seem to be localised metallic orbitals (Pt(II) or Pd(II) dz² orbitals); while the HOMOs are π molecular orbitals of mainly pyridine and imine character mixed with a dyz metal-based orbital. The HOMO-1 is therefore mainly the dz² orbital that has only partial mixing with the ligand causing them to be close to pure metal atomic orbitals. The HOMO is metal dyz orbital mixed with ligand π-orbital with its main components on the pyridine rings and imine double bonds.

The LUMO and LUMO+1 are mainly composed of the metal centre, pyridine rings and imine, with almost negligible contribution from the bridging fragments. The LUMO is near degenerate with the LUMO+1; this trend is evident for these frontier orbitals for the other complexes as well. There is an interesting inverse symmetry observed for the LUMO+1 and delocalised orbitals across the metal for the LUMOs. The LUMO is essentially a pure ligand π* molecular orbital, while the LUMO+1 is the metal dxz orbital mixed with the ligand π* MO.

The LUMOs and LUMO+1 molecular orbitals for the platinum and palladium complexes of L2b are quite similar to those of L2 and L2m. They also show negligible contribution from the bridging fragments, as well as from the phenyl groups. Inverse symmetry is also present for the delocalised orbitals across the metal for the LUMOs. The HOMO and HOMO-1 orbitals are very different to those of the L2 and L2m complexes. They are based predominantly on the phenyl substituents with little or no contribution from the rest of the structure. These molecular orbitals are near-degenerate.

The energies of the four frontier molecular orbitals of all thirty-six complexes are given in Table C2.2 in Appendix C. Orbital energy level diagrams with structures showing the calculated energy levels of the HOMO-1, HOMO, LUMO, and LUMO+1 orbitals of the complexes are shown in Figures 4.11, 4.12 and 4.13. From the figures, it is clear that the bridge structure affects the HOMO-LUMO gap and energies and that similar trends exist for the Pt(II) and Pd(II) chelates. The HOMO and LUMO energies systematically increase in a similar manner as we move to the bulkier ligands; however, the magnitudes are clearly metal dependent.

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Figure 4.12: The frontier molecular orbitals for the metal complexes of the methyl-substituted ligands: L1m – L6m.

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For the complexes of the original ligands (Figure 4.11) there is a general increase in MO energy with increasing bridge length and/or complexity for both metals. The difference in energy between HOMO-1 and HOMO, as well as the difference between LUMO and LUMO+1, for each metal complex is relatively similar. However, the energies for the LUMOs for the complexes of L6 are almost identical. This is also seen for the metal complexes of L6m (Figure 4.12). The other methyl-substituted ligand complexes (L1m–

L5m) show a slightly less defined increase with steric bulk; however, there is a definite increase in energies in comparison to Figure 4.11. This may be accounted for by the addition of the electron-donating methyl group. The energies for the metal complexes of the phenyl-substituted ligands increase even further (Figure 4.13). These frontier molecular orbitals are all very similar to each other; the exception once again is for the complexes with the aromatic ring bridging group (L6b). The HOMO and HOMO-1 energies are almost identical for each of these metal complexes.

The energy gaps between the HOMO and the LUMO orbitals for each complex are depicted in Table 4.7. The energy of the LUMO is directly related to the electron affinity and the energy of the HOMO is directly related to the ionisation potential. Thus the energy difference between HOMO and LUMO orbitals, the so-called HOMO-LUMO gap, is important with regards to the stability of structures.³⁹⁷ The magnitude of this HOMO–

LUMO energy gap could then indicate the reactivity pattern of the molecule. According to molecular orbital theory, HOMOs and LUMOs have an important influence on bioactivity.³⁹⁷ The interaction between the receptor of the cancer cell and the complex may be dominated by π–π or hydrophobic interaction amid these frontier molecular orbitals. The positive charges located on the atoms will most likely interact with the negative part of the receptor. In contrast, the most negatively charged parts will interact quite easily with the positively charged part of the receptor. These interactions will subsequently be part of the molecular mechanism of action that may inhibit the growth of cancer cells.

The larger the HOMO-LUMO gap, the higher the kinetic stability as it is energetically unfavourable to extract electrons from a low-lying HOMO or to add them to a high-lying LUMO.³⁹⁸ There is an obvious increase in the HOMO–LUMO gap from the platinum complexes to the palladium complexes. The Pd(II) complexes are harder in Pearson's classification of hard and soft metal ions;³⁹⁹ they are less polarisable than the Pt(II) complexes. The largest HOMO–LUMO energy gap is calculated for PdL1m and the

smallest for PtL3b. An increase in the metal-ligand interaction energy is noted when the electron donating methyl group is present on the imine carbon and a decrease when this is exchanged for a conjugating phenyl ring.²⁸⁷ This is expected as the energy levels of the occupied orbitals will clearly change due to electrostatic effects caused by these groups.

Table 4.7: The energy difference between the HOMO and the LUMO orbitals for each complex.