3.4 Summary and perspective
4.3.2 Internal self-consistency test
4.3.2.1 Aim and setup
The first test with the nineteen inhibitor molecules was aimed at providing a reference for the upper limit of quality for invariom point charge transfer and at helping to identify problems with the automated procedure. Therefore, point charges fitted to the molecular ESP of one specific molecule were merged if they contained the same invariom name (as discussed in Section 4.3.2.2). Subsequent charge reassignment via invarioms, ESP calculation and RRMS evaluation were carried out for several basis sets and different ways of classifying hydrogen atoms. The assessment concerned A) individual point-charge comparisons for two molecules and B) ESP evaluation for the complete test set of nineteen angiogenesis inhibitors described in Section 4.1.2.
4.3.2.2 A: Results and discussion of point charge differences
Correct implementation of all steps involved in point charge transfer was tested by setting up a special charge database which contained only charges of one angiogenesis inhibitor at a time. Next, those charges were ’transferred’ back to the exact inhibitor they came from. Compared to the original charges fitted for every atom against the ESP of the whole molecule (realMK), difference should only appear for atoms with invariom names that occur more than once within a molecule. The charges of atoms with the same invariom name are averaged before reassignment. Therefore the differences show how well charges of the same invariom name agree. The results of this internal self-consistency test are reported here for imatinib and cediranib.
Indeed, differences between these specially merged charges and those for the whole molecule appeared as expected only for those charges of invarioms that were found more than once in a molecule. Average differences between the realMK and the charges merged according to invariom name are given in Table 4.2 for imatinib and cediranib.
imatinib cediranib
C H H C H H
invname old new old new
av. diff. (merged) 0.090 0.035 0.020 0.083 0.020 0.018
Table 4.2: Average difference of point charges from a fit to B3LYP/6-31G(d) ESP and point charges merged within the molecule according to invariom classification for the compounds imatinib and cediranib separately. The unit ise (elementary charge) for all charges and differences.
15 of 37 non-hydrogen atoms of imatinib had invariom names that occurred more than once; for cediranib 10 out of 33 did. This was the expected result, so the charge procedures had been implemented correctly.
The average difference between the averaged point charges for the eight carbon atoms of imatinib was 0.090e and 0.083e for cediranib. Hydrogen atoms with the same invariom name were more frequent, and more of them belonged to the same name. The average of absolute differences for hydrogen atoms in imatinib is 0.035 e, which was significantly more than the 0.020e for cediranib. A closer look at imitinib revealed that most of the hydrogen
atoms were attached to an aromatic ring and thus classified as H@6c. Consequently, improvement of transferability seemed possible for those hydrogen atoms.
Inclusion of next nearest neighbor atoms in invariom classification for hydrogen atoms at aromatic rings should improve charge transferability. In the end an even more extensive classification by elongating the invariom name of hydrogen atoms by that of the atoms they are bonded to (see Section 4.2.1.3) was applied. This way the model compound for the directly bonded parent atom also supplies the property for the hydrogen atom, leading to a higher degree of classification by getting the most out of the model compounds already in the database. Application of this new nomenclature as classification decreased differences between the charges merged from 0.035 e to 0.020 e for imatinib. Although the decrease in difference of the merged charges is smaller for cediranib (0.020 e to 0.018 e) the new hydrogen atom treatment was beneficial in this case, too.
Hence the performance in reproducing molecular ESP is also expected to improve upon this more differentiated treatment of hydrogen atoms.
4.3.2.3 B: Results and discussion of ESP evaluation
How averaging of charges with the same invariom name within each agniogenesis inhibitor molecule affected the ESP was investigated by comparing the RRMS of the resulting ESP with respect to the ESP calculated from the MK charges fitted to the ESP of the whole molecule (realMK). The basis set for computation of the ESP against which the charges were fitted was computed by three different basis sets: 6-31g(d), TZVP and def2TZVP.
Thus the influence of different basis sets could be evaluated in addition to loss of information upon merging of charges according to invariom classification.
When the point charges were averaged for the original invariom names[81] the resulting ESP had an averaged RRMS of 0.55. The new hydrogen invariom names improved the RRMS to an average of 0.34. This demonstrated how sensitive the RRMS is towards choices in atom classification. Thus the RRMS is a suitable criterion for evaluating transferability.
Out of all the molecules studied axitinib turned out to be the most problematic molecule in this internal test (Figure 4.8). Its functional groups are a thioether, a carbon carbon double bond and annulated six- and five-membered rings. This specific variety led to several disagreements, but the largest differences were observed for carbon and hydrogen atoms of six-membered aromatic systems; one such ring contains a nitrogen atom, and the other one is linked via a sulfur atom to the rest of the molecule. The high RRMS for this molecule could be due to averaging, or it could be an extremely unlikely but possible statistical coincidence. Later on it was found that one of the charges was an outlier compared to the charges of all the atoms of the same invariom within the whole invariom database.
Such outliers will have a small influence after averaging the charges of an invariom for the complete charge database, but since here one of the outliers is part of the reference the RRMS is unusually high. Hence , invariom point charges derived from the complete database can, like in this case, perform even better than expected from this internal test.
Also noteworthy was vandetanib. It had an especially low RRMS throughout, because the absolute potential values were in general higher than for the other molecules. Thus the RMS of the ESP was 20 times as much as for the average molecule, but the RMS of the potential differences was about the same as those of the other molecules. The cause
Figure 4.8: Detailed RRMS results for the internal test of all investigated angiogenesis inhibitors with respect to the ’whole molecule’ ESP from 6-31g. Old and new hydrogen invariom names are compared and a different basis set was included to get an estimate of the error upon basis set change. creprinted with permission of Wiley.
for the higher potential and its RMS was the bromine substituent, which was only present in vandetanib. Bromine has a high van-der-Waals radius, which led to a larger number of potential points in the sum for the RMS. Simultaneously bromine had a high charge and thereby additionally created high ESP values.
Basis set influence The same procedure was applied to investigate differences between basis sets 6-31g(d), TZVP and def2TZVP. So different sets of charges fitted to the ESP derived from a wave function of the whole molecule (no invariom averaging at all, further referred to as realMK) were studied for the different basis sets as well as transferred from model compounds that were treated with different basis sets.
The RRMS for simply changing the basis was approximately 0.09 (Figure 4.9). Figure 4.8 shows that mainly two molecules have especially different charges from fits to different basis sets: semaxanib and cabozantinib. The most deviating charges in cabozantinib are found for atoms in condensed rings and those in close non-bonding interactions (with other parts of the molecule). Additional diffuse basis functions could be the cause for the differences between the basis sets, since they could influence the ESP and thus yield different charges in interacting regions. Those different charges then reproduced the deviating ESP which led to higher RRMS numbers. This hypothesis was in agreement with the low RRMS for the test with TZVP, where the same functional groups were averaged for different non-boning interactions. In semaxanib an intramolecular hydrogen bond was formed, but the charge differences were concentrated at the condensed five-membered ring attached to an oxygen atom. So this particular region might be especially sensitive to the choice of basis set.
In general, however, differences due to changing the basis set were minor. Therefore, employing def2TZVP instead of the frequently used 6-31G(d) basis set for deriving point charges from invariom model compounds was no problem. The basis set influence was smaller than the approximation of look-up point charges instead of molecule specific ones.
Figure 4.9 also shows that charges fitted to an ESP from a def2TZVP wave function are not as transferable as those from TZVP. This tendency was also observed for charges from
Figure 4.9:RRMS results from the internal invariom averaging tests, averaged for 19 angiogenesis inhibitors. Old and new hydrogen invariom names are compared. Moreover, a different basis set was tested to get an estimate of the error upon basis set change. realMK shows the RRMS upon basis set change without invariom averaging. On the upper chart the reference is the realMK with 6-31g(d) basis set while on the lower one realMK with def2TZVP is the reference. creprinted with permission of Wiley.
the invariom database. This could originate in the higher capability of the larger basis set, def2TZVP, to describe individual molecular features better and would yield a wider spread of charges to be averaged. Therefore, the following tests rely on TZVP invariom point charges.