A Computational Route to Hansen Solubility Parameters of Nitrated (Chapter 4)

CHAPTER IV DISCUSSION QSAR1 As one might expect, the dipole moment is significant for the determination of the polar solubility parameter. The  charge variable was also significant for this parameter. The  charge variable appears to also be significant for determining the hydrogenbonding parameter, see Figure 4. Correlation of the predicted dispersion parameters to the dispersion parameters in the training set appears to be exceptionally poor (R2 = 0.4737), however this is an effect of the predicted dispersion parameter’s variability over a relatively small range. Nearly all tabulated dispersion parameters exist somewhere between 15 and 30 MPa1/2. Most of the dispersion parameters in the training sets of this work exist between 15 and 20 MPa1/2. The variability of the predicted values when compared to the training set values over this small range exhibit the small R-squared value seen in Figure 7. In actuality it appears as though most of the dispersion values between 15 and 20 MPa1/2 are predicted to within 2 MPa1/2. This is good considering that it has been shown that the very literature values the predictions are based on and compared to are possibly erroneous (REF). The only major outliers appear to be species with literature values of approximately 10 and 13 MPa1/2 which are predicted to be around 15 MPa1/2. This model’s prediction of the polar solubility parameter is also poor. In this case the variability is over a wider range so the previous explanation of poor correlation does not apply. Here the prediction is actually the problem. As evidenced in Figure 8, there are few species which are correctly predicted by the model (R2=0.6472). Many are predicted between 3 and 8 MPa1/2 off of their target value. There appears to be no trend which can be noted in this figure. The model does not predict one sub-set of chemical species better than any other, nor does it err in any consistent fashion. The reason for this is likely due to the amount of variability in the dipole moment when calculated with the B3LYP/6-31g(d) model chemistry. A species can be optimized three times at this model chemistry to the same geometry and the resulting dipole moment calculation can vary by as much as a Debye or more. A variation of 1 Debye in the QSAR1 model will result in a 2.51 MPa1/2 change in P. For this reason, any calculation which is based on these dipole moments can be compromised. The solution for this is to calculate all species at a more computationally expensive model chemistry which will remove some of this variability. Because of the high computational cost, this change will likely have to be addressed in a later work. Hydrogen-bonding parameter predictions from QSAR1 show considerable promise (R2=0.7594). Many of the species with literature values between 0 and 20 MPa1/2 are modeled to within 3 MPa1/2. The correlation drops off above 20 MPa1/2; the notable outlier is water (dH = 42.3) which is predicted at 20 MPa1/2. If water is removed from the model and the correlation is quantified the R-squared value is greater than 0.8. As with the polar parameter predictions from this model there is no discernable trend which can be noted about the predictions. No chemical group is predicted any better or worse than the others. The only trend appears to be that the hydrogen-bonding parameter becomes harder to predict the larger it becomes. This is problematic for the prediction of unknowns in that there can be no confidence in values predicted at 20 MPa1/2 or higher. This means that this model with likely have trouble predicting the nitramine species discussed in Chapter 1. Based on their structure, these species are suspected of having large hydrogen-bonding contributions to their total cohesive energy. If these observations are applied to the predictions of the explosive unknowns then the reliability of these predictions (Table 4) can be evaluated. First, the dispersion values are predicted largely between 20 and 30 MPa1/2. This is outside of the normal range of dispersion parameters; however, the size of these species is not to be underestimated. It is likely that the presence of two, three, or sometimes four nitro groups in these species serves to swell the electron cloud and increase the size of the molecule and also the value of the dispersion parameter. This might also help explain why these molecules exhibit such poor solubility in many common solvents which have dispersion parameters between 15 and 20 MPa1/2. It may be wise to discount the polar parameter predictions from this model because of the poor correlation which was achieved in that model. The hydrogen-bonding parameter predictions should prove reliable up to 20 MPa1/2 as noted earlier. Unfortunately, this caveat discredits the values for nitramine species such as tetranitrocarbazole, picramide, TATB, and DATB. QSAR2 As with the first model, the polar parameter depends heavily on dipole moment and  charge structure variables. The hydrogen-bonding parameter in this model depends largely upon  charge (d), polarizability (), and HOMO energy (I) terms as was expected. It is interesting to note that the coefficient which is calculated for the /Vm1/2 term (37.4) is the same as the coefficient in Hansen and Beerbower’s simplified Böttcher equation. This tells more about the way in which most of the P parameters were calculated in the first place and not necessarily a validation of the model. What this also means is that Gaussian® calculated dipole moments may be applied to the simplified Böttcher equation to calculate P. Correlation of the dispersion parameter predictions from this model (Figure 10) looks very similar to that of the first model. The correlation is slightly improved (R2= 0.5806) however this nominally poor correlation is subject to the same explanation as the other dispersion parameter predictions. The polar parameter is predicted better by this model. The overall correlation is better (R2 = 0.7381). More of the species are predicted accurately by the expanded variable set this model uses, however there still are some major outliers. Some species are predicted as much as 10 MPa1/2 off of their literature values. In these extreme cases it is likely that the literature value was not determined in the same way as the rest of values. The hydrogen-bonding parameter is also predicted better by this model. A ten percent increase in correlation with the training set values (R2 = 0.8771) is accompanied by the ability to predict even the highest hydrogen-bonding parameter (water, H = 42.3 MPa1/2) with a degree of confidence. One thing that can be noted from Figure 12 is that a large number of the species which are calculated to be higher than the literature values are primary amines. In fact, nearly all of these species are calculated as having a hydrogen-bonding parameter 6-8 MPa1/2 larger than the literature value. The reason for this is unknown. It is possible that the ability of primary amine to form two hydrogenbonds is somehow involved in this error. If more primary amines are investigated with this model it may be possible to institute some subtractive term for a primary amine which can be applied after the transformation matrix to correct for this effect. In practice however this may prove difficult as there is no easy way to determine from a Gaussian® result file if the geometry present is a primary amine or not. As with the first model, the observations about the correlations may help evaluate the prediction of the explosive unknowns. The predictions of these species from the QSAR2 model are shown in Table 5. Dispersion parameters are very similar to those calculated by QSAR1. They range from the low twenties to the low thirties and are consistent with the approximate size of those species. The polar parameters calculated by QSAR2 can now be accepted a little more than in QSAR1. It should be noted that the polar parameters are the least reliable numbers compared to the dispersion and hydrogenbonding parameters of this model. This is owing to the variability of the dipole moment calculations and also the varied methods with which the training set polar parameters were calculated. The hydrogen-bonding parameter predictions fall within the normal range of values, however, species with large expected hydrogen-bonding parameters (H>20 MPa1/2) such as DATB and picramide were not predicted to be so. They were indeed larger than their companion explosive unknowns; however, this fact coupled with the primary amine discrepancy leaves some doubt with these numbers. QSAR3 In general, the correlation of this model’s prediction of the training set values appears to be increased. This is due to the smaller training set and so any comparison of correlation with QSAR1 or QSAR2 would be erroneous. There are some important features to notice in this model that may serve to interpret the predictions of the explosive unknowns later on. The dispersion parameter predictions of the training set species in this model are very accurate. The overall correlation is great for the variability over the small range of dispersion parameters (R2 = 0.8132). A look at Figure 13 shows that most species are predicted to within 1 MPa1/2 of the literature values. The deviation that is present likely results from the variability in the computational route to the structure variables. A higher basis set such as 6-311G(d,p) could possibly tighten these values up; however, they are accurate enough for use with other solubility parameters in their current state. Polar parameter predictions of training set species are accurate as well. Figure 14 shows a good overall correlation (R2 = 0.9008). There are a few species which are predicted to be 4 -5 MPa1/2 from their target values, most notably on the high side. The majority of species are predicted within 3 MPa1/2 and 44.4% are calculated to within 1 MPa1/2. The major outliers are not exclusively of one chemical group or another. Two are oxygen containing ringed systems (1,4-dioxacyclohexane and 4-methyl-1,3-dioxolan2-one). The rest are species which contain nitro-groups (nitrobenzene, 4-nitrotoluene, and 3,5-dinitrophenol). This is not to say that all species with nitro-groups were predicted poorly. In fact, several species of this category were very accurately predicted. 3-nitroaniline, 2,4-dinitrotoluene, and the nitropropanes were some of the best. QSAR3 consistently predicts hydrogen-bonding parameters to within 5 MPa1/2 or less. This is not ideal; however the high correlation which is achieved suggests that the model may be on the right track. One thing that may tighten these values up may be achieved with an increase the computational effort. Figure 6 shows that the model for the hydrogen-bonding parameter in QSAR3 is extremely simple. One variable is the /Vm1/2 term. An increase in the computational effort as discussed earlier may determine this /Vm1/2 term more accurately and lead to a better prediction of the hydrogen-bonding parameter. Dispersion parameter predictions of the explosive unknowns are much lower than the other models. It has been noted that this model seems to predict dispersion parameters as much as 5 MPa1/2 below the actual value of the parameter. This suggests that the real dispersion parameters of these species may lie between 20 and 26 MPa1/2 instead of between 15 and 21 MPa1/2 as shown in Table 6. Predictions of the polar parameters for the explosive unknowns must be taken with a grain of salt. QSAR3 predicts polar parameters between 8 and 22 MPa1/2. According to the training set correlation these predictions should be lower than actual; however these predictions are higher than the previous two models. The hydrogen-bonding parameters may be off by as much as 5 MPa1/2. CHAPTER V CONCLUSION In conclusion, the author has demonstrated a fast, unambiguous tool for the determination of the solubility parameters of nitrated materials. There is good evidence to suggest that the explosive unknowns presented in this work have dispersion parameters in the high teens to around 20 MPa1/2. Polar parameters were determined but users should be cautious of values which were calculated by QSAR models 1 and 2 because many values were calculated to be as much as 5 MPa1/2 off of their target values. However, the polar parameters predicted by QSAR3 appear to be very reliable. The most interesting findings in this work may be the hydrogen-bonding parameters. The precision with which the hydrogen-bonding parameter can be calculated by QSARs 2 and 3 suggests that this work is well on its way to the reliable determination of hydrogenbonding parameters. Recent work in the area of solute precipitation has indicated that the hydrogen-bonding character of a solvent may influence the crystal morphology of the precipitate (22). This is exciting for explosives manufacturers because certain crystal morphologies have been linked to desirable detonation properties. This information may be enough for the estimation of where to begin probing blended solvents for the solubility of nitrated species. Table 7 shows recently obtained experimental data from the Pantex facility (23). Ra is a value that represents the “distance” between two solubility parameters in the (D,P,H) Cartesian space. Clearly a small Ra would indicate a prediction is close to accuracy. This column shows that QSAR3 predicts the HSPs of HMX, RDX, PETN, and HNS better than either group contribution method. Table 7. A comparison of group contribution methods and QSAR3 HSP predictions of HMX, RDX, PETN, and HNS with experimentally determined HSPs Cutoff Method g/100mL D /MPa1/2 exp 0.10 17.7 GCa 22.5 GCb 23.5 QSAR3 15.3 RDX exp 1.40 17.3 GCa 18.5 22.0 GCb QSAR3 15.5 PETN exp 1.50 16.7 GCa 21.4 GCb 18.8 QSAR3 16.8 HNS exp 0.15 18.9 GCa 21.0 GCb 28.0 QSAR3 20.7 a VanKrevelen method, bStefanis method HE HMX P /MPa1/2 H /MPa1/2 11.6 22.9 45.2 13.4 12.4 18.8 35.8 11.1 12.0 21.2 50.4 17.8 13.9 13.3 33.0 17.1 13.7 6.9 7.3 5.6 9.1 5.7 7.5 6.5 8.4 9.5 3.0 6.4 6.1 8.6 1.9 5.6 R0 / MPa1/2 12.1 FIT 1.00 Ra Exp/ MPa1/2 16.4 36.1 8.6 8.4 1.00 7.7 25.3 3.4 7.8 1.00 13.1 39.0 6.1 6.0 0.98 4.9 26.7 3.7 Another exciting aspect of this work is that the methodology can be applied to predict the solubility parameters of any chemical group. Indeed, it may be possible to expand this work to predict the Hansen solubility parameters of species that are important to other disciplines such as ink pigments, polymer additives, surfactants, etc.