A Computational Route to Hansen Solubility Parameters of Nitrated (Chapter 2)

CHAPTER II EXPERIMENTAL Species which were used for training QSAR matrices 1 and 2 were selected from a single reference (16). The species in this reference were originally the only source of solubility parameters the author had access to. As the author acquired references with more comprehensive tables of solubility parameters (4, 20) QSAR3 was able to more effectively target the nitrated functionality. Computational Chemistry All electronic structure calculations were made using the Gaussian® ‘03W (17) and GaussView computational package. Calculations were run on either one of two systems: 1) a Dell™ Optiplex745 desktop PC running Microsoft Windows XP™ with a dual-core central processing unit speed of 3.4 GHz and 2 Gb of random access memory, or 2) a Dell™ Precision690 running Linux with two quad-core processors at a speed of 2.66 GHz and 32 Gb of memory. A parallel processing version of the Gaussian software package was used on the eight core machine so that as many as eight calculations could be performed simultaneously. This was also helpful in assigning multiple processors to one job to increase the computational power for difficult or long calculations. Each molecule’s geometry optimization and subsequent frequency calculation was made using the B3LYP hybrid density functional (18, 19) and a 6-31G(d) basis set. The majority of the calculations were performed by the author however acknowledgement is given to Derek Blaylock and Katie Rothlisberger who did perform some calculations under the direction of the author and Dr. Darren Williams. All calculations were optimized to a minimum with no observed negative frequencies. Structure variables were then extracted from the result files. The result file was opened and checked for proper optimization by verifying the absence of negative harmonic frequencies. The dipole moment , electronic spatial extent ese,  charge d, polarizability , and molar volume Vm were extracted for use in the first structure activity relationship. The dipole moment is reported explicitly in the Gaussian® result file in units of Debye. The electronic spatial extent is also reported explicitly in the Gaussian® result file and has units of Å2. The  charge value is calculated from the difference in Mulliken charge of the most negative heteroatom (not carbon or hydrogen) and the most positive hydrogen atom. For species in which there are no heteroatoms or in which the heteroatoms were all positive the Mulliken charge for the most negative heteroatom was assigned the value of zero. The charge of the most positive hydrogen atom was assigned a value of zero for species in which there were no hydrogen atoms present. The polarizability was calculated as the square root of the sum of the squares of the six exact polarizability tensors reported in the result file and has units of Å3. The molar volume is calculated in a rather roundabout way. The reason for this is that the electronic structure calculation does a poor job of estimating the molar volume. Hansen solubility parameters are typically reported along with a molar volume so one could look the experimental value up if one so chooses, however, it is the goal of this project to provide all the information necessary to calculate the HSPs of a nitrated species from a computational result file. To calculate the molar volume a regression was performed on all of the training set species’ experimental molar volumes with respect to the molecular formula which is an explicit output of the Gaussian® result file. For the second and third structure activity relationships the energy of the highest occupied molecular orbital (HOMO) I, was extracted from the result files as well. This was done to approximate the first ionization energy of the species which was was reported to have some correlation with the dispersion properties (20). Structure Activity Relationship Training Once structure variables have been calculated the relationship matrix must be optimized or “trained” to the activities of the calculated species. These species are termed the “training set.” The activities of interest are the three Hansen solubility parameters. To accomplish this, a step-wise regression technique was employed. The training set structure variables and activities were imported to Minitab® 15 (21) and the program’s step-wise regression application was used. The step-wise regression of each HSP was performed individually so that for a given training set there were three regression matrices, one for each HSP. The criteria for inclusion and exclusion was set at a p-value of 0.2. This is analogous to a minimum %80 confidence that the coefficient is not due to random noise. The size of the training set as well as the structure variables selected as potential predictors are what set the various QSAR models apart. Structure variable predictors for this model were: dipole moment µ, electronic spatial extent ese, ∆ charge d, polarizability α, and molar volume Vm. The matrix resulting from this first model is termed “QSAR1.” The second model which is termed “QSAR2” shares the same 183 chemical species as QSAR1 but with a larger structure variable set. In this model the set of structure variables is expanded by using mathematical transforms of the original five structure variables and the energy of the HOMO, I. The square, square-root, inverse, natural logarithm, and exponential of each variable was included in the model with the exception of electronic spatial extent. In addition to these simple mathematical transforms, some of the original structure variables were combined by multiplication/division. These combinations include a µ (Vm)-0.5 term, a d αterm, an I αterm, and an (I 1−)αterm. These combination terms were included after studying equations put forth in Barton’s Handbook of Solubility Parameters (20) as well as Hansen’s own handbook (4). The third model, “QSAR3” has a shortened list of chemical species in the training set. Unfortunately the accepted values for HSPs cannot be regarded as canon due to the many ways in which they can be calculated. The list of 183 chemical species was narrowed down to 39 species which were believed to be calculated from experiment based on their cost and ubiquity. Added to this list, however, are 15 more species which have similarity to the functionality depicted in Figure 1. This was done in an effort to further enhance the predictive power of the third model toward nitrated species. Because this new functionality was included, a new regression to calculate molar volume was also performed (Table 3, and Figure 3). In addition to the structure variables used in QSAR2, stoichiometry was also included. It was postulated that if activities such as molar volume could be approximated using the molecular formula then they might also be useful for the approximation of HSPs. Calculation of Previously Unknown HSPs Finally, the models were put to use by calculating the HSPs for various energetic materials. Each species was calculated by Gaussian ‘03W at the same level of theory and basis set as the training set species. The appropriate structure variables were extracted from the result files and were operated on by the three QSAR matricies. The result is three models of HSPs for these energetic materials. The strengths and weaknesses of these models will be discussed later. CHAPTER III RESULTS Molar Volumes Molar volumes were calculated using the method described in Chapter 2. QSAR1 and QSAR2 were calculated using the molar volume regression shown in Table 2 and Figure 2. Figures 2 and 3 show an equation for the correlation trendline. This is not to indicate how the correlation applies to the variable “x” but rather to show the slope of the trendline. As the correlation improves the slope will approach a value of one. Table 2. Regression coefficients of stoichiometry modeling molar volume (N=183) Variable Intercept #C #H #N #O #S #P #F #Cl #Br Coefficient 15.51199403 9.023012684 3.807253279 1.36510039 5.16678748 15.97578012 14.78730787 14.34459346 16.50292516 19.0710091 Standard Error 1.656059157 0.32021995 0.178497756 1.139692896 0.729221579 3.555444864 8.866345126 1.588282536 1.016481139 1.768516926 500 Calculated molar volume (cm3) 450 y = 0.9825x + 2.1839 R² = 0.9825 400 350 300 250 200 150 100 50 0 0 50 100 150 200 250 300 350 400 450 Experimental molar volume (cm3) Figure 2. Correlation chart of regression calculated molar volume to experimental molar volume. (N=183) The molar volumes for QSAR3 were calculated using a different regression because the number and identity of species in the training set changed. This training set includes some species which are also in the training set of QSAR1 and QSAR2 as well as several new nitrated species to enhance the predictive power of QSAR 3 toward the target nitrated species. Results of this regression are shown in Table 3 and Figure 3. Note that in this training set there were no phosphorous or fluorine containing species. Table 3. Regression coefficients of stoichiometry modeling molar volume (N=54) Variable Intercept #C #H #N #O #S #P #F #Cl #Br Coefficient 9.84325433 6.852084724 4.910317572 7.217614235 6.484731548 19.68305223 0 0 20.2641589 27.96045898 Standard Error 4.236976949 0.56839236 0.569191206 1.773869329 0.926807038 3.801321124 0 0 1.721525705 5.510054368 160 y = 0.9187x + 7.2756 R² = 0.9187 Calculated molar volume (cm3) 140 120 100 80 60 40 20 0 0 20 40 60 80 100 120 140 160 Experimental molar volume (cm3) Figure 3. Correlation chart of regression calculated molar volume to experimental molar volume. (N=54) QSAR Matrices Once the QSAR matrices were generated they were then used to calculate the HSPs of the training set to look for predictive trends. Figures 4 through 6 depict the transformation matrices and how they are used to generate HSPs. 18.07 0.073 0.111 · .00006 0.68 0.0632 1 3.8558 0.0513 2.51 0.00008 1.86 0.0233 6.148 0.0677 0.0 0.00013 11.85 0.0255 Figure 4. QSAR1 transformation matrix 1 . … . . 12.39 0.0712 0 0 0.0172 13.2 3.7 … 0 · 5.3 0 0.53 0 0 0.0155 0 47.2 0.2602 0.034 37.4 5 0 6.5 12.7 0 0 0 0 0 0 0.132 12.8 0 0.452 0.0283 0 0 0 0 18.9 29 18.69 0.0202 0 . 00003 3.83 0 91 0 Figure 5. QSAR2 transformation matrix. Here the ellipses do not indicate a sparse matrix. They indicate the continuation of the 1 by 16 input matrix. . . . . . . . . … # # # . … . # # · . . . . . . . . . . Figure 6. QSAR3 transformation matrix. Here the ellipses do not indicate a sparse matrix. They indicate the continuation of the 1 by 15 input matrix.