In order to maximize the binding interaction between a host and guest, the host structure must be organized to bind the guest. In an ideal situation the binding sites in the host will match the binding sites on the guest (host is complementary) and the lowest energy conformation of the host is (1) the one that binds the guest and (2) is rigid (host is preorganized). Molecular mechanics calculations can be used to analyze the degree of complementarity and preorganization.
The degree of complementarity can be measured as the difference in energy between the bound form of the ligand and the binding form of the ligand. This energy difference is computed by first optimizing the host-guest complex, second removing the guest and computing a single point energy (Ebound), third optimizing the bound form of the ligand to get the energy of the binding form (Ebind), and fourth
∆E1 = Ebound – Ebind.
The lower the ∆E1, the more complementary the ligand structure.
One measure of the degree of preorganization is the difference in energy between the lowest energy form of the host and the binding form of the host. This energy difference is computed by first conformer searching the host to get the energy of the lowest energy form and second
∆E2 = Ebind – Elow.
The lower the ∆E2, the more preorganized the host structure.
The overall degree of host organization is the sum of the two energy differences,
∆Etot = ∆E1 + ∆E2.
Note that one can compute this value without consideration of the binding conformer,
∆Etot = Ebound – Elow.
By computing ∆Etot over a series of metal ions, for example, over the lanthanide series, by plotting Etot as a function of metal ionic radius, it is possible to determine whether the ligand exhibits a steric preference for a specific size metal and how strong this preference is. Although the calculation of ∆Etot is straight forward, these calculations become tedious when doing an entire series of metal ions. For this reason, the utility code named scanme was created (see insert link to scanme for how to make and install this code).
When scanme is run, it prompts the user for input twice. The first prompt asks for the name of the PCModel input file containing the metal-ligand structure. The second prompt asks whether the user wants to conformer search the ligand. The reason for this second question is that although some ligands are not searchable due to excessive freedom, it is still possible to evaluate the complementarity of the host binding conformer. If the user chooses not to search the free ligand, searchme will report only ∆E1 for each metal and if the user chooses to search the free ligand, searchme will report ∆Etot for each metal. Note that if the binding form is the same over the entire metal size range, then these two methods will give the same shaped energy versus radius plots, where the ∆E1 plot is offset from the ∆Etot plot by a constant ∆E2 value.
To provide an example of how to use scanme, six example PCModel input files are provided as Supporting Information (in directory size_scan). The first training assignment is to determine and compare intrinsic metal size preferences in bis-amine and bis-ether chelates when the connecting link between the donor groups is varied over 1,2-ethane, cis-1,2-cyclohexane, and trans-1,2-cyclohexane links. To do this run scanme for each of the input structures doing conformer searches for each case and graph the ∆Etot values vs. metal ion radii for all six ligands on the same plot.
Bear in mind that because the data set involves variation of the host donor atoms and the guest metal ion, the ∆Etot values do not reflect relative ∆G or log K values. They only show steric preferences as a function of the size of the metal and represent the intrinsic size selectivity associated with the ligand binding conformation.
A second training assignment is to attempt to reproduce one of the ∆Etot values reported by scanme. Here is the process:
Note, when using mengine, specify the MM3 model and a dielectric = 4.0. An example conpcm file would look like this:
mode opt
infile en_amine.pcm
outfile opt.pcm
forcefield mm3
dielec 4.0
The reason for using this dielectric constant is that it is believed to better represent experimental behavior in condensed phases. For this reason, a dielectric constant of 4.0 was used when fitting MM3 parameters to x-ray data to develop the automated parameter assignment algorithms for metal complexes.
Up to this point attention has focused on comparison of ∆Etot values. It can be argued that for a series of ligands containing the same set of donor groups with the same metal ion, the ∆Etot values can be transformed into relative ∆G values by adding a term to account for entropic contributions associated with restricted bond rotation. This magnitude of this term is
0.31 x Nrot kcal/mol,
where Nrot is the number of rotatable single bonds that become non-rotatable when the ligand complexes the metal ion. Because HostDesigner always builds a series of host candidates with the same set of donor groups that interact with the same guest, molecular mechanics post-processing methods in HostDesigner are based on such ∆Grel values.
Note that with the data set under consideration in this section, the ∆Grel values would be expected to correlate with experimental data only when comparing results for a single metal ion with either the three bis-ether ligands or the three bis-amine ligands.