Rapid QSPR model development technique for prediction of vapor pressure of. organic compounds

Transcription

1 Rapid QSPR model development technique for prediction of vapor pressure of organic compounds Alan R. Katritzky a, Svetoslav H. Slavov a,c, Dimitar A. Dobchev a,b, Mati Karelson b,c a Center for Heterocyclic Compounds, Department of Chemistry, University of Florida, Gainesville, Florida 32611, USA b Department of Chemistry, University of Tartu, 2 Jakobi Street, Tartu 51014, Estonia c Department of Chemistry, Tallinn University of Technology, Ehitajate tee 5, Tallinn 19086, Estonia Abstract A novel QSPR development technique is proposed with the aim to combine the advantages of the two methods most frequently applied. A quantitative structure-property relationship (QSPR) is developed using this technique to relate the molecular structures of 645 diverse organic compounds to their vapor pressures at 25 C expressed as logvp. The compounds are encoded with topological, electronic, geometrical, and hybrid type descriptors calculated by CODESSA PRO software. The best QSPR model involves 4 descriptors and has R 2 = 0.937, F = and s = Keywords: Vapor pressure, QSPR, BLMR, CODESSA Pro Corresponding author: Phone: (352) , Fax: (352) , katritzky@chem.ufl.edu 1

2 1. Introduction Vapor pressure (VP) is an important factor for the study of the environmental fate, transport, and distribution of the compounds in water, air, and soil. For environmental pollutants, their VP determines their distribution between the atmosphere and the soil. The VP of toxic chemicals can be used to estimate the rate of evaporation after a spill. VP data are also used in the estimation of liquid viscosity, enthalpy of vaporization, air-water partition coefficient, and some other important physico-chemical properties of the compounds. As one of the important chemical-engineering properties vapor pressure plays significant role for fire and explosion prevention, gas separation, design and optimization of the processes (process engineering) and process control (Lawson, 1980; Redeker, 1997; Sandler et al., 2002; Stoll, 2005). Recently, many molecular modeling methods based on widely spread quantitative structureproperty/activity relationships (QSPR/QSAR) techniques found their place as an important tool for the chemical engineers (Liu et al., 2003; Sandler et al., 2002; Stoll, 2005). Lack of resources and facilities rends the laboratory determination of the vapor pressure of all of the ever increasing number of chemicals impractical. Hence, QSPR relating vapor pressure to theoretical descriptors without requiring experimental data, are of significant value. Most of the methods for the prediction of vapor pressure are based on multilinear or neural networks approaches including only molecular orbital/dynamics theory descriptors or a combination between them and/or a set of topological descriptors (Beck et al., 2000; Burkhard et al., 1983; Chalk et al., 2001; Chen et al., 2003; Goll & Jurs 1999; Liang & Gallagher, 1998; McClelland & Jurs, 2000; Prem, 2005). 2

3 Further methods employed linear correlations with MCI and the molecular topological indices of Kier and Hall (Kier & Hall, 1986) or were based on the Clapeyron-Clausius equation, the group-contribution method, or Gibbs free energy of vaporization and hierarchical approach (Subhash & Mills, 2001). Considering the technological importance of the vapor pressure, more rapid methods for its estimation are searched for. The aim of the present article is to propose and validate a novel, more rapid approach for the development of robust QSPR models for vapor pressure as based on the large space of theoretically calculated molecular descriptors. 2. Experimental data Experimental data of logarithm of the vapor pressure at 25 o C for 645 unique compounds (see the supplementary material) were taken from articles containing 411 (Katritzky et al., 1998) and 420 structures (McClelland & Jurs, 2000), respectively (with 186 common to both). The structures included saturated, unsaturated and halogenated hydrocarbons, and compounds containing alcoholic and phenolic hydroxyl, amino, cyano, nitro, thio, ester, ether, carboxyl, sulfide, and sulfoxide groups, ketones, aldehydes, furans, pyrans, biphenyls, naphthalenes, pyridines, pyrazines, and multifunctional compounds. The data set includes compounds which are gases, liquids, and solids at 25 o C/760mmHg. The supplementary material table shows the compounds and their corresponding experimental vapor pressures indicated as logvp. 3. QSPR analysis Methodology for a general QSAR/QSPR approach has been developed and coded as the CODESSA PRO software package. CODESSA PRO enables the calculation of numerous 3

4 quantitative descriptors solely on the basis of molecular structural information (Hansch-type approach) (Katritzky et al., 1995; Katritzky et al., 1997). Research using CODESSA PRO has successfully correlated and predicted various physical and biological properties reported by Basak and Mills (2005), Karelson et al. (1999), Katritzky et al. (2004), Katritzky et al. (2005), Katritzky, Dobchev et al. (2005), Katritzky et al. (2006) and Thakur (2005) including gas chromatographic properties, melting and boiling points, solvent scales, refractive indexes, human breast milk and antimalarial activity. In the present study we used CODESSA PRO software for the prediction of vapor pressure; we believe the modules integrated in this software package provide an optimum way to high quality results. QSPR modeling, by multilinear regression utilized in the CODESSA PRO program which applies up to 800 different constitutional, geometrical, topological, electrostatic, quantum chemical, and thermodynamic molecular descriptors. Topological descriptors contain information about the number, type, and connectivity of atoms in the molecule. Such descriptors include atom, bond, and path counts. Information about the electronic aspects of the structures is encoded by electronic descriptors. Examples of such descriptors include the dipole moment and the sum of the negative charges in the molecule. Geometric descriptors are used to encode information about the three-dimensional structure of a compound. One such descriptor is the molecular volume. Finally, hybrid descriptors such as charged partial surface area (CPSA) descriptors combine information about both the geometric and electronic aspects of a molecule. In our treatment all descriptors used were derived solely from molecular structure and do not require experimental data. 4

5 4. Molecular modeling Three-dimensional conversions and pre-optimization were performed using the molecular mechanics (MM+) implemented in the HyperChem 7.5 package ( Final geometry optimization of the molecules was carried out by using the semi-empirical quantum-mechanical AM1 parameterization (Dewar et al., 1985). The optimized geometries were loaded into CODESSA PRO software ( Overall, more than 800 theoretical descriptors were calculated. 5. Multilinear regression modeling An important stage of the multilinear regression QSAR methodology is the search for the best multilinear equation among a given descriptor set. In other words, the aim is to find the best correlation of the vapor pressure (A) with a certain number, n, of molecular descriptors(d i ) weighted by the regression coefficients b i, as defined by eq. 1: n A = b 0 + i= 1 b i D i (1) The Best Multilinear Regression method (BMLR) described in Katritzky et al. (1996) and Karelson (2000) and encoded in CODESSA PRO software was used to select significant descriptors for building multilinear QSAR models. The treatment started with the reduction of the number of molecular descriptors. If two descriptors were highly correlated, then only one descriptor was selected; the descriptors with insignificant variance were also rejected. This helps 5

6 to speed up the descriptor selection and reduces the probability of including unrelated descriptors by chance. Therefore, to develop physically meaningful multilinear QSAR equations containing a limited number of adjustable parameters from the very large pool of descriptors, a workable combination of the multilinear regression and forward selection procedures was employed as described in Karelson (2000). 6. QSPR procedure In this work a modified approach for QSPR modeling is proposed, with the aim to combine the advantages of the two QSPR methods most frequently applied, i.e. (i) use of all data points to build the model and to apply as validation method only the internal crossvalidation procedures for validation or (ii) to use only a part of the available data for building the model, keeping the remaining data points for external validation. The following procedure was used to build a QSPR model: 1. All data points were ordered in the ascending order of logvp values. 2. The series was separated into three subsets (conditionally denoted as A, B and C) by selection of every third point from the original dataset in order to obtain a similar distribution of the investigated property values for the whole set. 3. Three new datasets were constructed using all combinations of the binary sums: A+B, A+C and B+C. 4. The standard QSPR modeling procedure including Best Multiple Linear Regression Method (BMLR) was applied to those three datasets obtained in step 3. 6

7 5. The complimentary parts to each of these three datasets (respectively C, B and A) were used as external validation datasets, by considering their consistency. 6. All the descriptors that appeared in the obtained models of step 4 were tested to obtain a general model including all the existing compounds. 7. The general model was again validated using classical internal crossvalidation procedures: leave-one-out and leave-many-out. 7. Results The procedure described above was applied to the complete data set of 645 points. Three subsets were constructed each containing 430 compounds. In each case, the remaining 215 compounds were used as external validation datasets. The distributions of the A+B, A+C and B+C data sets were also explored, and are given in the histograms of Figure 1. Figure 1. Data distribution histograms for the LogVP values in the obtained subsets. The histograms in Figure 1 show that all three datasets have almost the same statistical parameters (mean, standard deviation see top of the figures). By applying the BLMR method, the best QSPR models for each subset were derived. Although application of the braking rule did not provide an unambiguous break point (Katritzky et al., 7

8 2005), inspection of the equation suggests the four descriptor linear models * for A+B, A+C and B+C subsets, which are shown below (see Tables 1-3; the descriptors are explained in Table 6). In Tables 1-4 R 2 cvoo denotes the square of the leave-one-out cross-validated correlation coefficient; R 2 cvmo is the square of the leave-many-out cross-validated correlation coefficient; RMSPEOO and RMSPEMO are calculated root mean square predictive errors in the case of leave-one-out and leave-many-out procedure, respectively as described by Karelson (2000). A detailed description of all statistical parameters used is given in Table 6. Table 1. Set A+B # B s t IC Name of descriptor Intercept Gravitation index (all bonds) Number of F atoms HA dependent HDCA-1 (Zefirov PC) FNSA-2 Fractional PNSA (PNSA-2/TMSA) (MOPAC PC) R 2 = 0.932; F = ; s = 0.380; N = 4; n = 430 R 2 cvoo = 0.929; R 2 cvmo = 0.930; RMSPEOO = 0.390; RMSPEMO = 0.390; Ranges: Observed (-1.338; ) Predicted (-1.328; ) External test set C: R 2 ext. = Table 2. Set A+C # B s t IC Name of descriptor Intercept Gravitation index (all bonds) HA dependent HDCA-2 (Zefirov PC) Number of F atoms WNSA-1 Weighted PNSA (PNSA1*TMSA/1000) (MOPAC PC) * Also the 5 parameters model was obtained but it did not show significant improvement of the statistical parameters over the 4 parameter model. 8

9 R 2 = 0.938; F = ; s = 0.361; N = 4; n = 430 R 2 cvoo = 0.936; R 2 cvmo = 0.935; RMSPEOO = 0.370; RMSPEMO = Ranges: Observed (-1.338; ) Predicted (-1.166; ) External test set B: R 2 ext. = Table 3. Set B+C # B s T IC Name of descriptor Intercept Gravitation index (all bonds) Number of F atoms HA dependent HDCA-1 (Zefirov PC) FNSA-2 Fractional PNSA (PNSA-2/TMSA) (MOPAC PC) R 2 = 0.943; F = ; s = 0.350; N = 4; n = 430 R 2 cvoo = 0.941; R 2 cvmo = 0.940; RMSPEOO = 0.350; RMSPEMO = Ranges: Observed (-0.810;-7.910) Predicted (-0.804; ) External test set A: R 2 ext. = The linear dependences between the predicted and observed logvp values for all three subsets are illustrated by plots in Figure 2. 9

10 Figure 2. Scatter plots of the calculated versus experimental LogVP values at 25 o C for each subset. The descriptors appearing in Tables 1, 2 and 3 for the submodels of datasets A+B, A+C and B+C are quite similar, with small differences due to the procedure applied for the descriptor selection in the BLMR method. Namely, only one of a pair or a set of highly intercorrelated descriptors is used in the further model development. Depending on the data set, different but physically similar and highly intercorrelated descriptors may therefore appear in different models. In the next step of the modeling process, only those descriptors contained in these submodels were treated further to build a general model for all 645 compounds. The calculated statistical parameters that define the quality of the final model and its predictive power are shown below. Table 4. General model for all 645 compounds # B s t IC Name of descriptor Intercept Gravitation index (all bonds) Number of F atoms HA dependent HDCA-1 (Zefirov PC) WNSA-1 Weighted PNSA (PNSA1*TMSA/1000) (MOPAC PC) 10

11 R2 = 0.937; F = ; s = 0.366; N = 4; n = 645 R2cvOO = 0.935; R2cvMO = 0.936; RMSPEOO = 0.370; RMSPEMO = Ranges: Observed (-1.338; ) Predicted (-1.232; ) [Figure 3. Scatter plot of the calculated vs. experimental log(vp) values at 25oC for 645 compounds. 11

12 Figure 4. Scatter plots of the observed and predicted values vs. residuals. For our general four-descriptor model, the cross-validated correlation coefficient R 2 cv = 0.935, as compared to the correlation coefficient R 2 = 0.937, indicates the high stability of the regression equation. The scatter plot of the logarithm of vapor pressure calculated using the model of Table 4 versus experimental logvp is presented in Figure 3. In order to investigate the error distribution we present the plots of the observed and predicted values vs. residuals as shown in Figure 4. As can be seen from these figures the residuals show random character with respect to the predicted and observed logvp values. Therefore, no systematic in the errors, which is in agreement with the general multilinear theory (Johnson & Wichern, 2000). 12

13 8. Discussion and Interpretation Physicochemical background Using a logarithmic function, the Clausius-Clapeyron equation can be written as follows: H ln p = vap + C (2) RT At constant temperature, all quantities on the RHS of Eq. 2 except H vap are constants. We therefore consider how H vap depends on molecular structure. The enthalpy of vaporization according to physicochemical laws depends on intermolecular forces, which can be described by taking into account the following interactions: a) Nonspecific or Van der Waals attractions between all molecules, even paraffin hydrocarbons. b) Unevenly distributed electron densities giving rise to bond-size dipoles which are attractive to other dipoles or which induce electron redistribution in neighboring molecules and thereby establish dipole: induced dipole attractions. c) Hydrogen atoms bonded to oxygen or nitrogen attracted by the nonbonded electrons of electronegative electrondonor atoms thus establishing hydrogen bonds. Interpretation The descriptors involved in the model of Table 4 are: (i) gravitational index, (ii) hydrogen acceptor dependent HDCA-1 (HA dependent HDCA-1 descriptor is based on Zefirov charges), (iii) weighted partial negative charged surface area as a part of Total molecular surface area (WNSA-1) and (iv) number of F atoms. 13

14 The gravitational index reflects the effective mass distribution in the molecule and describes the molecular dispersion forces in the bulk liquid media. This descriptor partially corresponds to the point a given above in the explanation of the H function. The second descriptor (HA dependent HDCA-1) used is connected with the hydrogen-bonding ability of compounds, described in point c. WNSA-1 can be related to the point b treated above, concerning charge distribution, which induces electron redistribution in neighbor molecules and thereby established dipole: induced dipole attractions. The last descriptor used is the number of F atoms (the most electronegative element) in the compounds and possibly it reflects the polarity of the molecules. Another possible explanation was given previously in Katritzky et al. (1998): The inclusion of these three further descriptors (see Table 5) in the model shows that the G i and HDCA do not describe adequately the intermolecular interactions with solute molecules containing fluorine, chlorine, or nitrogen atoms, possibly because of the deficiency in AM1 calculation of partial charges in those atoms or because of the requirement of corrected effective atomic masses in the formulation of the gravitation index. The combination of these four descriptors evidently represents the forces of intermolecular attraction adequately as would be expected from the nature of the vapor pressure phenomena. Our model suggests that the order of overall significance in the present set of molecules for the vapor pressure of these three types of interactions is: nonspecific or Van der Waals attractions > hydrogen bonding > dipole dipole attractions. Katritzky et al. (1998) previously screened 800 potential descriptors for a data set of 411 compounds to obtain a five-descriptor equation for vapor pressure with R 2 = with the gravitational index and hydrogen bonding donor charged surface area (HDCA) as the most important descriptors adequately representing the forces of intermolecular attraction. The best model then reported is in Table 5. 14

15 Table 5. The best 5 parameter model obtained by the authors of [xiv-98jcics720]. n descriptor X + X t-test R 2 R cv 2 0 intercept 2.30 (± 0.06) GI (± ) HDCA(2) (±0.10) SA-2(F) (±0.006) MNAC(Cl) 6.02 (±0.574) SA(N) (±0.0017) R 2 = 0.949, F = , s = 0.331, R cv 2 = Table 6. Description of the statistical parameters and molecular descriptors used. F n N R 2 s F B t IC R 2 cvoo Notation R 2 cvmo RMSPEOO RMSPEMO FNSA-2 Fractional PNSA (PNSA-2/TMSA) (MOPAC PC) WNSA-1 Weighted PNSA (PNSA1*TMSA/1000) (MOPAC PC) Gravitation index (all bonds) Description number of the compounds used number of the descriptors used in the model square of the correlation coefficient standard deviation Fisher criterion linear regression coefficients Student's criterion partial intercorrelation coefficient square of the leave-one-out cross-validated correlation coefficient square of the leave-many-out cross-validated correlation coefficient root mean square predictive error in the case of leave-one-out procedure used root mean square predictive error in the case of leave-many-out procedure used Fractional partial negatively charged surface area (PNSA-2 / Total molecular surface area) Weighted partial negatively charged surface area (PNSA1* Total molecular surface area /1000) m i, m j - atomic masses of atoms i and j r ij - interatomic distance of atoms i and j N a - number of atoms in the molecule N b - number of chemical bonds in the molecule HA dependent HDCA-1 (Zefirov PC) Number of F atoms Hydrogen acceptor dependent hydrogen donors charged surface area Number of fluorine atoms 15

16 The models of Tables 4 and 5 are similar in physico-chemical meaning. However, the statistical parameters indicate that the model in Table 4 is significantly better than that in Table 5 for the following reasons: (i) lower number of descriptors used, (ii) reduction from 3 to 1 of descriptors connected with a specific atom type, (iii) significantly higher Fisher criterion and (iv) larger number of compounds in the set. Hence it can be concluded that the new proposed QSPR model is more robust and with increased predictive power. We now compare our model with those previously reported by other groups. Liang and Gallagher (1998) tested several multilinear regressions and artificial neural network analyses with a range of topological and quantum mechanical descriptors derived solely by computations from the molecular structures of a set of 479 compounds. They reported a seven descriptor linear regression with R 2 = Goll et al. (1999) related the vapor pressures at 25 C of 352 hydrocarbons and halo-hydrocarbons to their molecular structures by a seven descriptor model with R 2 = Compared with the report of Liang and Gallagher (1998) our model: (i) includes more compounds; (ii) uses less descriptors; (iii) avoids topological descriptors. Compared with the Goll et al. (1999) model ours uses: (i) a dataset consisting of diverse classes of compounds; (ii) more datapoints; (iii) less descriptors in the equation. Comparison of our model with the model reported from Beck et al. (2000) based on a neural net interpretation of descriptors derived from semiempirical quantum mechanical calculations is more difficult because of the significant difference of the methods used. Our results fully support the conclusion of McClelland and Jurs (2000) who found that the vapor pressures of diverse organic compounds were correlated better by models including semiempirical molecular orbital theory descriptors, than models based on topological descriptors alone. Chalk et al. (2001) have presented a temperature-dependent model for vapor pressure based on a feed-forward neural net and descriptors calculated using AM1 semiempirical MO theory, based on a set of

17 measurements at various temperatures performed on 2349 molecules. Chen et al. (2003) developed QSPR models for subcooled liquid vapor pressures (pl) of polybrominated diphenyl ether (PBDE) congeners based on quantum chemical descriptors by the use of partial leastsquares regression. Burkhard et al. (1983) developed QSPR models for n-alkanes, biphenyls, and numerous polychlorinated biphenyl (PCB) congeners with new variables obtained from a principal component analysis of molecular connectivity indices (MCI), variables which have a similar meaning for all the compounds and reflect the physical characteristics of the molecules. We also cannot compare our model with the last three models due to the difference of methodology and datasets used: (i) our model is not temperature dependent; (ii) it is not applied to subcooled polybrominated diphenyl ether (PBDE) congener liquids and (iii) it is not comparable with the models obtained only for dataset consisting of narrow classes of compounds (congeneric series). 9. Conclusions A modified QSPR approach combining the advantages of the two QSPR methods most frequently used was applied successfully to a series of 645 compounds with measured vapor pressure values at 25 o C. QSPR equations with four theoretical molecular descriptors were obtained for the constructed subsets. A general model for all the compounds was proposed based on the results derived from the subsets. The descriptors involved are calculated solely from the chemical structures of the compounds and have definite physical meaning corresponding to the intermolecular interactions. Our work fully supports the results obtained earlier by. In addition, an explanation based on the physicochemical nature of the vapor pressure phenomena was given 17

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