Molecular Modeling of (Z)-Ligustilide
Derivatives

by Nausheena Baig

Introduction
The herb Oshá is used to treat many illnesses, such as the common cold, anemia, headaches, and menstrual irregularities (1). Oshá can be found in the southwestern United States and South America. It has been found that the bioactive component in Oshá is (Z)-ligustilide (2). The specific site of reactivity in (Z)-ligustilide, Compound 1, is C-8 (Figure 1).

Figure 1

Molecular orbital theory suggests if an elecrophile is not stable then it is more susceptible to an attack by a nucleophile (3). By making the LUMO at C-8 larger, the atom becomes more susceptible to an attack; therefore the molecule should be made more bioactive. The LUMO at C-8 is varied in size by replacing the propyl group at C-8 with an aromatic ring containing a functional group (Figure 2). The 4,5 dihydro portion is modified to the aromatic phthalide for synthetic reasons. The dihydro molecule will be studied in subsequent investigations.

1

Figure 2

Hypothetically, a change in functional group at the benzylic ring should result in a change in LUMO size at C-8. Relative to ligustilide, if the functional group is an EWG (compounds 2- 8), the LUMO at C-8 should increase in size. The EWGs draw electron density away from the molecule, either inductively or via resonance out of the aromatic ring, destabilizing the partial positive charge at C-8 and making it more reactive. Figure 3 illustrates the case of an EWG destabilizing C-8 via resonance. Conversely, for the EDGs on compounds 9- 11, the LUMO at C-8 should decrease in size. This is due to the fact that an EDG adds electron density to C-8, therefore making it less reactive (see Figure 3 for an example). The addition of electron density to the molecule makes it less reactive because it becomes electron- rich.

Figure 3

Figure 4

The LUMOs of (Z)-Ligustilide and the corresponding analogs were studied using the molecular modeling program Spartan '02 with an isovalue of 0.002 e/au3 (4). The LUMO map was plotted onto the electron density map, so a quantitative and qualitative value of the LUMO could be obtained.

Results & Discussion
Appendix A shows the LUMO value of every atom, excluding hydrogens, for all the derivatives studied. Along with these LUMO values, the electron density/LUMO map was also taken into consideration. The atoms of interest are positions that have a blue area around them indicating a large LUMO value. The red areas indicate atoms with a small LUMO value. The electron density/LUMO map of 1 (Figure 5) shows that C-8 does not have the largest LUMO, even though it has been found to be the site that has reactivity. Both C-7a and C-3a had LUMOs larger than that of C-8, (0.029, 0.026, and 0.022, respectively). As seen in the electron density map, there are blue areas around C-3a, C-7a, and C-8. The darker blue area is around C-7a, indicating that C-7a has the larger LUMO, which is supported quantitatively.

Figure 5

Compound 2 also does not have C-8 with the largest LUMO, but it does have the second largest LUMO at 0.021. C-1 has the largest LUMO at 0.022. There is not a significant enough difference to say that C-1 does have the largest LUMO, so it can be safely concluded that 1 could have reactivity at C-8, thus supporting experimental evidence.

The results of 3 also do not give C-8 the largest LUMO. It was expected that the EWG nitro group would give C-8 the largest LUMO of all the derivatives due to its resonance as demonstrated in Figure 3. However, the results indicate that C-3 and C-3a have the largest LUMO (0.018 and 0.020 respectively), and C-8 has the fifth largest LUMO with 0.014. We can hypothesize that C-8 could still be the reactive site on the molecule, because it did not have the largest LUMO in ligustilide either, but we can also hypothesize that the nitro group was too destabilizing to the molecule. We can hypothesize that 3 will not be more bioactive than ligustilide because of the decrease in the size of the LUMO compared to the ligustilide. This remains to be evaluated both experimentally and by molecular modeling of the dihydro derivatives.

Compound 4 indicates that the LUMO size of C-8 does not change, but the LUMOs of other significant atoms in the molecule decrease in size making C-8 the largest LUMO. C-3a and C-7a had the largest LUMOs in 1 followed by C-8. In 4, the LUMO of C-8 is 0.021, and the LUMOs of C-3a and C-7a are 0.015 and 0.018, respectively. It can be concluded that since the LUMO of C-8 is now the largest, C-3a and C-7a are no longer hindering any nucleophilic attack at C-8. This indicates that C-8 is more susceptible to nucleophilic attack, therefore making it more bioactive than 1.

The same trend that was observed in 4 can also be observed in compounds 5-8. The LUMO at C-8 is the same general size as 1. LUMOs for C-3a and C-7a decreased in size allowing for C-8 to be the largest LUMO and thus, more susceptible to nucleophilic attack.

Compound 9 was expected to have a smaller LUMO at C-8, but the results of the Spartan Program show the LUMO of C-8 remaining the same size it was with 1: 0.022. Despite the LUMO of C-8 remaining the same, it can be concluded that the bioactivity will be the same as or less than that of ligustilide, since C-8 did not have the largest LUMO in Compound 9. C-3a of 9 had a slightly larger LUMO than did C-8 at 0.023. This indicates that the LUMO of C-3a possibly hinders the reactivity at C-8, therefore making it less bioactive.

Compound 10 shows that once again the LUMO at C-8 does not change in size. The LUMO at C-8 for 10 is the largest in the molecule, similar to what was observed in the EWGs, but the difference is that C-3a, 0.020, is large enough to hinder the reactivity at C-8 and make the molecule less bioactive. The conjecture has yet to be supported by experimental evidence.

Compound 11 is expected to decrease the reactivity at C-8 the most because of the electron density that is added to the molecule from the hydrogen through resonance. The calculations of 11 indicate that this will be the result. The size of the LUMO at C-8 decreases in size compared to 1, (0.017 and 0.022 respectively). The LUMO at C-3a is the largest in the molecule, 0.020. This indicates that the reactivity, thus bioactivity, at C-8 will be reduced.

Conclusion  
The calculations of the derivatives of ligustilide indicate that an EWG will increase the molecule's reactivity and bioactivity. It has also been indicated that if an EWG pulls too much electron density away from the molecule, it can be too destabilizing and result in a decrease in bioactivity. The indicated decrease in reactivity from the EDGs supports the theory that the EWGs were the reason for increased reactivity at C-8 and overall bioactivity.

Experimental
The calculations were performed on a Dell, Pentium III processor, with 256 MB SDRAM. The program used was Spartan '02. The molecule was minimized and maps were submitted for calculations. The map submitted was an electron density surface and LUMO property. The calculation submitted was Hartree-Fock with a basis set of 6-31 G*. The numbers were obtained by right-clicking on the optimum position of each atom. The values were viewed in the property dialog box. The numbers indicate the absolute value of the LUMO at that position.

Appendix A

References

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