Internet Electronic Journal of Molecular Design

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1 ISSN Internet Electronic Journal of Molecular Design July 2003, Volume 2, Number 7, Pages Editor: Ovidiu Ivanciuc Special issue dedicated to Professor Nenad Trinajsti on the occasion of the 65 th birthday Part 1 Guest Editors: Douglas J. Klein and Sonja Nikoli QSPR with TAU Indices: Water Solubility of Diverse Functional Acyclic Compounds Kunal Roy 1 and Achintya Saha 2 1 Drug Theoretics and Cheminformatics Lab, Division of Medicinal and Pharmaceutical Chemistry, Department of Pharmaceutical Technology, Jadavpur University, Calcutta , India 2 Department of Chemical Technology, University of Calcutta, 92 A P C Road, Calcutta , India Received: April 7, 2003; Revised: April 28, 2003; Accepted: May 12, 2003; Published: July 31, 2003 Citation of the article: K. Roy and A. Saha, QSPR with TAU Indices: Water Solubility of Diverse Functional Acyclic Compounds, Internet Electron. J. Mol. Des. 2003, 2, ,. Copyright 2003

2 K. Roy and A. Saha Internet Electronic Journal of Molecular Design QSPR with TAU Indices: Water Solubility of Diverse Functional Acyclic Compounds # Kunal Roy 1, * and Achintya Saha 2 1 Drug Theoretics and Cheminformatics Lab, Division of Medicinal and Pharmaceutical Chemistry, Department of Pharmaceutical Technology, Jadavpur University, Calcutta , India 2 Department of Chemical Technology, University of Calcutta, 92 A P C Road, Calcutta , India Received: April 7, 2003; Revised: April 28, 2003; Accepted: May 12, 2003; Published: July 31, 2003 Internet Electron. J. Mol. Des. 2003, 2 (7), Abstract Motivation. The topochemically arrived unique (TAU) scheme, developed in valence electron mobile (VEM) environment, is unique in that it unravels specific contributions of functionality, branching, shape and size factors to the physicochemical property or biological activity while most other indices give mainly a global contribution of the molecule. QSPR/QSAR studies with TAU indices on different physicochemical properties/biological activities of diverse functional compounds will explore the usefulness of TAU indices in modeling studies. Method. The present communication attempts to correlate water solubility, ln S, of 193 diverse functional acyclic compounds with different TAU indices, namely T, T R, F, B, N V, N P, N I, N X, and N Y. Sometimes, TAU relations have been improved further upon inclusion of suitable indicator or integer variables. The statistical quality of the QSPR model has been judged by statistical parameters such as predicted variance Q 2, explained variance R 2 a, correlation coefficient R, and variance ratio F. Results. This study shows that TAU indices, along with appropriate indicator variables, can predict up to 91.4% and explain 91.9% of the variance of water solubility. The relations can unravel specific contributions of molecular bulk (size), functionality, branching and shape parameters to the water solubility of diverse functional compounds. In general, water solubility increases with increase in functionality and branching, and decreases with increase in molecular bulk. Further, halocarbons and hydrocarbons specifically show reduced water solubility. Some of the hydrocarbons and halogen compounds act as outliers. Conclusions. The TAU index is an important tool in exploring structure property relationships in view of its potential to unravel specific contributions of different structural parameters like molecular bulk, shape factors, branching, functionality and carbon skeletal structure. Keywords. Quantitative structure property relationships; QSPR; topochemically arrived unique (TAU) scheme; water solubility; valence electron mobile (VEM) environment; topological indices; structural descriptor. # Dedicated to Professor Nenad Trinajsti on the occasion of the 65 th birthday. * Correspondence author; phone: (O), (R); E mail: kunalroy_in@yahoo.com, URL: 475

3 QSPR with TAU Indices: Water Solubility of Diverse Functional Acyclic Compounds 1 INTRODUCTION Exploring quantitative structure property relationships (QSPR) of physico chemical properties of organic compounds using topological indices is a fertile field of research in theoretical chemistry. Structural attributes responsible for contributing to the physico chemical properties are identified by various structural descriptors. These indices encode structural information such as atomic connectivity, size, shape, branching, cyclicity, presence of hetero atoms and unsaturation in numerical form purporting for correlation of chemical structure with various physical properties, chemical reactivity or biological activity [1 7]. Usually, the numerical basis of topological indices is either the adjacency matrix or the topological distance matrix [8]. Often a variety of descriptors are required to generate a satisfactory model as different structural aspects are revealed from different indices. A large number of such descriptors have been described in the last three decades and their usefulness in quantitative structure activity relationship (QSAR) and quantitative structure property relationship (QSPR) studies has been extensively studied [4]. Among these, some of the most commonly used indices are the Wiener path number [9], the molecular connectivity indices [8,10,11], the Balaban indices [12], the kappa shape indices [13], the electrotopological state atom index [14,15], the Basak indices [3], etc. Very recently, a few more novel indices have been introduced by different groups of workers and their usefulness in QSAR/QSPR studies are being investigated [16 20]. A database of different descriptors may also help in the classification of chemical compounds for a target property or activity [21 23]. Similarly with the lipid water partition coefficient [24 30], water solubility is a very important physico chemical parameter that can account for many properties of organic chemicals including biopharmaceutical behavior of drugs [31]. Many attempts have been made to model water solubility using different indices, e.g., the Wiener and connectivity indices [32], PI index [33], quantum chemical descriptors [34,35], dipole moment, surface area, volume, molecular weight, number of hydrogen bond acceptor/donor(s) and number of rotable bonds [36], etc., and different statistical and QSAR methods, e.g., genetic algorithm and partial least squares [37], principal component analysis [38], comparative molecular field analysis [39], artificial neural network [40], etc. In the late eighties, the topochemically arrived unique (TAU) scheme was described by Pal et al. [41,42] in valence electron mobile (VEM) environment and this index was claimed to have the power to decode chemical information unraveling specific contributions of functionality, branching, shape and size factors to the physicochemical property or biological activity. We have recently explored comparative QSAR and QSPR studies with TAU indices along with different topological parameters [43 46]. In the present communication, we report the modeling of water solubility of diverse functional acyclic compounds with TAU indices to unravel the diagnostic feature of TAU indices. Though mostly straight chain aliphatic compounds have been considered in the present study, the subsets of alcohols and hydrocarbons contain a few alicyclic compounds also. In some 476

4 K. Roy and A. Saha cases, attempt has been made to improve TAU relations with appropriate indicator parameters or integer variables. 2 MATERIALS AND METHODS The physicochemical parameter (ln S) values were taken from the literature [8,47]. TAU [41,42,48,49] are Topochemically Arrived Unique indices developed in VEM (valence electron, mobile) environment as an extension of the connectivity concept [8]. The first order composite topochemical index, T, is defined as: T i j E ij i j ( VV ) where E ij is the VEM edge weight of the edge between i th and j th vertices, V i represents the VEM vertex weight of the i th vertex, which may be calculated as the ratio of core count of the i th vertex, i, to VEM count of the i th vertex ( i ). i may be calculated as (Z Z v )/Z v whereas i may be calculated as 8 (2h n). When unsaturation is present, i should be calculated as The notations, n and represent the numbers of sigma bonds (other than hydrogen), nonbonding electrons and bonds associated with the atom in that order. Z, Z V and h represent the atomic number, number of valence electrons and number of hydrogens attached respectively. The values of core count, VEM count and VEM vertex weight of different atoms in different hybridization states and skeletal arrangements are shown in Table 1. i j 0.5 Table 1. Core count, VEM count and VEM vertex weight for different sets of isovertices Atom Feature Core Count ( i ) VEM Count ( i ) VEM Vertex Weight (V i ) CH CH =CH >CH =CH CH >C< =C= =C< C OH O =O NH NH =NH >N =N N F Cl Br

5 QSPR with TAU Indices: Water Solubility of Diverse Functional Acyclic Compounds Table 1. (Continued) Atom Feature Core Count ( i ) VEM Count ( i ) VEM Vertex Weight (V i ) I SH S >S >S< =S In the case of a heteroatom, the VEM edge weight of an edge incident upon the heteroatom is assigned a negative value (i.e., multiplied by 1). The composite index T can further be divided into two components: the skeletal index T R and the functionality F. The skeletal index T R is the topochemical index of the reference alkane that may be obtained by replacing a heteroatom with carbon and removing the multiple bonds that may be present. The derived index F can be easily calculated as T R T. T R may further be factored as the branching parameter B and the constitutional parameter vertex count N V. B is calculated as T N T R where T N is the topochemical index of the corresponding normal alkane (for acyclic molecules). N V for the reference alkane may further be partitioned into N P (number of methyl carbons), N I (number of methylene carbons), and N B (number of branched carbons). N B is composed of N Y (number of tertiary carbons) and N X (number of quaternary carbons). Obviously, the value of N V is equal to sum of N P, N I, N X and N Y. The vertex count N V of a hydrogen suppressed molecular graph is purely a constitutional parameter because it may be obtained directly from the molecular formula. Even the structural formula is not needed for obtaining the value of N V. Obviously, any index showing better correlation with physicochemical or biological activity than that shown by N V will have significance in the context of QSPR/QSAR studies. The first order VEM skeletal index T R is considered as the index for intrinsic lipophilicity while N B, N P, N X and N Y represent shape parameters. The functionality contribution and bulk parameter are represented by F and N V, respectively [41,42,48,49]. All TAU indices are basically derived by sequentially partitioning the composite index T into different factors. During the development of QSAR equations with TAU parameters, the above hierarchical relations were followed. For obvious reasons, B and N B, or N P and N B, or N V and N I [49] were not used in the same equation. The calculations of different TAU parameters are illustrated in Table 2 taking as example 2 methyl 4 hexen 3 ol. Multiple linear regression analyses were done using a software program RRR98 developed by one of the authors [50]. The statistical quality of the equations [51] was judged by examining the parameters like Q 2 (crossvalidation R 2 or predicted variance), R 2 a (adjusted R 2, i.e., explained variance), r or R (correlation coefficient), F (variance ratio) with df (degree of freedom), s (standard error of estimate), AVRES (average of absolute values of residuals) and SDEP (standard deviation 478

6 K. Roy and A. Saha of error of predictions). The significance of the regression coefficients was judged by the t test. In case that the intercept of an equation was statistically insignificant and omission of the same did not affect the quality of the equation, the exclusion of the intercept gave statistically more acceptable equation. A compound was considered as an outlier for a particular equation when the residual exceeded twice the standard error of estimate of the equation. PRESS statistics were calculated by the leave one out (LOO) technique [52] using the programs KRPRES1 and KRPRES2 [50]. Finally, the leave many out cross validation was applied on the final equation of the composite set. 6 e Table 2. Calculation of TAU parameters: example of 2 methyl 4 hexen 3 ol 7 7 f f d 3 a 6 c d c 3 a 8 g 7 4 g b 2 1 e 4 b 2 1 f 5 5 g OH 8 8 e 5 c 3 6 d 4 b 2 a 1 2-Methyl-4-hexen-3-ol Reference alkane Normal alkane Compound Vertex Count Edge Count a b c d e f g 2 Methyl 4 hexen 3 ol 1 1/3 1/3 1/6 1/ / Reference alkane 1 1/3 1/3 1/2 1/ Normal alkane 1 1/2 1/2 1/2 1/2 1 1/ T = T R = T N = F = B = N V = 8 N B = 2 N X = 0 N Y = 2 N I = 2 N P = 4 3 RESULTS AND DISCUSSION The calculated topological indices of 193 compounds consisting of 60 alcohols (1 60), 43 esters (61 103), 16 ethers ( ), 20 ethers ( ), 41 hydrocarbons ( ) and 13 ketones ( ) are given in Table 3. Tables 4 through 10 show relations of water solubility with different topochemical indices. All regression coefficients and variance ratios of the reported equations are significant at 95% and 99% levels respectively unless otherwise stated. Table 3 shows the literature water solubility values of the compounds [8,47] and also the calculated values according to the best equations of individual series and the composite set (vide footnote of Table 3). 479

7 QSPR with TAU Indices: Water Solubility of Diverse Functional Acyclic Compounds Table 3. Topological indices and observed and calculated water solubility (ln S) of diverse functional aliphatic compounds No Compound Name Descriptors ln S T T R T N Obs a Calc Res Calc h Res h 1 n Butanol b b Methylpropanol b b Butanol b b n Pentanol b b Methylbutanol b b Methylbutanol b b Pentanol b b Pentanol b b Methyl 2 butanol b b Methyl 2 butanol b b n Hexanol b b Hexanol b b Hexanol b b Methyl 3 pentanol b b Methyl 2 pentanol b b Methyl 3 pentanol b b Methyl 2 pentanol b b ,3 Dimethyl 2 butanol b b ,3 Dimethylbutanol b b ,3 Dimethyl 2 butanol b b Methylpentanol b b Methyl 2 pentanol b b Ethylbutanol b b Cyclohexanol b b n Heptanol b b Methyl 2 hexanol b b Methyl 3 hexanol b b Ethyl 3 pentanol b b ,3 Dimethyl 2 pentanol b b ,3 Dimethyl 3 pentanol b b ,4 Dimethyl 2 pentanol b b ,4 Dimethyl 3 pentanol b b ,2 Dimethyl 3 pentanol b b Heptanol b b Heptanol b b n Octanol b b ,2,3 Trimethyl 3 pentanol b b Octanol b b Ethylhexanol b b n Nonanol b b Nonanol b b Nonanol b b Nonanol b b Nonanol b b ,6 Dimethyl 3 heptanol b b ,5 Dimethyl 4 heptanol b b ,1 Diethylpentanol b b Methyloctanol b b ,5,5 Trimethylhexanol b b n Decanol b b n Tetradecanol b b n Pentadecanol b b n Hexadecanol b b

8 K. Roy and A. Saha Table 3. (Continued) No Compound Name Descriptors ln S T T R T N Obs a Calc Res Calc h Res h 54 2,2 Dimethyl propanol b b Penten 1 ol b b Penten 2 ol b b Penten 3 ol b b Hexen 3 ol b b Hexen 4 ol b b Methyl 4 penten 3 ol b b Methyl formate c c Ethyl formate c c Ethyl formate c c Propyl formate c c Propyl formate c c Butyl formate c c Butyl formate c c Pentyl formate c c Methyl acetate c c Methyl acetate c c Ethyl acetate c c Ethyl acetate c c Isopropyl acetate c c Isopropyl acetate c c Propyl acetate c c Propyl acetate c c Isobutyl acetate c c Butyl acetate c c Isopentyl acetate c c Pentyl acetate c c Hexyl acetate c c Methyl propionate c c Methyl propionate c c Ethyl propionate c c Ethyl propionate c c Isopropyl propionate c c Propyl propionate c c Propyl propionate c c Butyl propionate c c Isopentyl propionate c c Pentyl propionate c c Methyl butyrate c c Methyl butyrate c c Ethyl butyrate c c Isopropyl butyrate c c Propyl butyrate c c Propyl butyrate c c Ethyl heptanoate c c Ethyl valerate c c Ethyl hexanoate c c Ethyl octanoate c c Ethyl nonanoate c c Ethyl decanoate c c Dimethyl ether d d Isopropyl methyl ether d d Isopropyl methyl ether d d Diethyl ether d d Diethyl ether d d

9 QSPR with TAU Indices: Water Solubility of Diverse Functional Acyclic Compounds Table 3. (Continued) No Compound Name Descriptors ln S T T R T N Obs a Calc Res Calc h Res h 109 Methyl propyl ether d d Methyl propyl ether d d Ethyl isopropyl ether d d Methyl isobutyl ether d d Methyl sec butyl ether d d Butyl methyl ether d d Isopropyl propyl ether d d Dipropyl ether d d Dibutyl ether d d Methyl t butyl ether d d Ethyl propyl ether d d Chloroethane e e Chloropropane e e Chloropropane e e Chlorobutane e e Isobutyl chloride e e ,3 Dichloropropane e e Chloroform e e Bromoethane e e Bromopropane e e Bromopropane e e Bromobutane e e Isobutyl bromide e e Isoamyl bromide e e ,3 Dibromopropane e e Iodomethane e e Iodoethane e e Iodopropane e e Iodobutane e e Diiodomethane e e Dichloroethsulfide e e n Butane f f Isobutane f f n Pentane f f Methyl butane f f ,2 Dimethyl propane f f ,2 Dimethyl butane f f ,4 Dimethyl pentane f f ,2,4 Trimethyl pentane f f ,2,5 Trimethyl hexane f f Cyclohexane f f Methylcyclohexane f f ,2 Dimethylcyclohexane f f Cycloheptane f f Cyclooctane f f n Hexane f f n Heptane f f n Octane f f Methyl pentane f f Methyl pentane f f ,2 Dimethylpentane f f Cyclopentane f f Methylcyclopentane f f Pentyne f f

10 K. Roy and A. Saha Table 3. (Continued) No Compound Name Descriptors ln S T T R T N Obs a Calc Res Calc h Res h Hexyne f f Heptyne f f Octyne f f Nonyne f f ,8 Nonadiyne f f ,6 Heptadiyne f f Pentene f f Pentene f f Hexene f f Heptene f f Octene f f Methyl 1 pentene f f ,6 Heptadiene f f ,5 Hexadiene f f ,4 Pentdiene f f Cyclopentene f f Cyclohexene f f Cycloheptene f f Butanone g g Pentanone g g Pentanone g g Methyl 2 butanone g g Hexanone g g Hexanone g g Methyl 2 pentanone g g Methyl 2 pentanone g g Methyl 3 pentanone g g Heptanone g g Heptanone g g ,4 Dimethyl 3 pentanone g g Nonanone g g Obs = Observed; Cal = Calculated; Res = Residual a Refs. [8] and [47]; b From Eq. (6); c From Eq. (10); d From Eq. (17); e From Eq. (20); f From Eq. (26); g From Eq. (29); h From Eq. (36). 3.1 QSPR for Alochols (n = 60) Table 4 shows QSPR models for the water solubility of alcohols with topochemical indices. The first order VEM composite topochemical index T explains 93.5% and predicts 93.2% of the variance while the skeletal index T R has 97.2% explained variance and 97.1% predicted variance. When T R was split into the branching parameter B and the vertex count N V, the resultant equation showed 97.3% explained variance and 97.1% predicted variance. Similar relations were obtained by using shape parameters (N P, or N B, or N X and N Y ) along with vertex count. Positive coefficients of B and various shape parameters indicate that water solubility increases with increase in branching. Negative coefficients of N V and T R are indicative of negative contributions of bulk and skeletal index to water solubility. The calculated water solubility values according to Eq. (6) are given in Table 3. 3,3 Dimethylbutanol (19), cyclohexanol (24) and 2 hexen 4 ol (59) act as outliers (but not excluded) for Eq. (6). 483

11 QSPR with TAU Indices: Water Solubility of Diverse Functional Acyclic Compounds Table 4. Relations of water solubility (ln S) of alcohols with topochemical indices. Model equation, ln S = i x i + Eq Regression coefficient(s) and constant # Statistics Q 2 2 R a s AVRES se se se se (SDEP) (rorr) (F (df)) (n) T (0.834) (0.968) (8.51x10 2 (1, 58)) (60) T R (0.551) (0.986) (2.06x10 3 (1, 58)) (60) B N V (0.549) (0.987) (1.05x10 3 (2, 57)) (60) N V N B (0.616) (0.983) (8.33x10 2 (2, 57)) (60) N V N P (0.584) (0.985) (9.57x10 2 (2, 57)) (60) N V N X N Y (0.533) (0.988) (7.61x10 2 (3, 56)) (60) se = standard error; F values are significant at 99% level [df = np, n np i, np = no. of predictor variables; i = 1 if intercept is present; i = 0, otherwise] # t values of the regression coefficients and constants are significant at 95% level [df = n np i] 3.2 QSPR for Esters (n = 43) The QSPR models for the water solubility of esters with different topochemical indices are shown in Eqs. (7) (11) (Table 5). The variation of water solubility of the esters can be explained to the extent of 97.4% (predicted variance 97.2%) by the first order composite topochemical index T while it was 98.2% for first order skeletal index T R (predicted variance 98.0%). When T was split into different components, the resultant relations Eqs. (9) (11) were similar in quality to that of the skeletal index. However, these relations show specific contributions of branching, shape factors and bulk. From the sign of the regression coefficients Eqs. (9) (10), it is evident that water solubility of esters increase with increase in branching and decrease with increase of bulk. In Eq. (11), N B shows negative coefficient as it is a component of N V which has negative contribution to water solubility. The effects of branching or shape parameters will be evident in equations containing N V term. The calculated solubility values according to Eq. (10) are given in Table 3. Isopropyl butyrate 95 acts as outlier (but not excluded) for Eq. (10). Table 5. Relations of water solubility (ln S) of esters with topochemical indices. Model equation, ln S = i x i + Eq Regression coefficient(s) and constant # Statistics 1 2 Q 2 2 R a s AVRES se se se (SDEP) (rorr) (F (df)) (n) T (0.410) (0.987) (1.57x10 3 (1, 41)) (43) T R (0.345) (0.991) (2.31x10 3 (1, 41)) (43) B N V (0.354) (0.991) (1.14x10 3 (2, 40)) (43) N V N B (0.354) (0.991) (1.14x10 3 (2, 40)) (43) N I N B (0.354) (0.991) (1.14x10 3 (2, 40)) (43) 484

12 K. Roy and A. Saha 3.3 QSPR for Ethers (n =16) Table 6 shows the QSPR models for the water solubility of ethers with different topochemical indices, Eqs. (12) (17). The first order composite topochemical index T can explain 86.0% variance (predicted variance 81.8%) of the water solubility of ethers. On splitting of T into skeletal index T R and functionality F, considerable rise in statistical quality (explained variance 98.6% and predicted variance 98.3%) was obtained. When T R was further split into different shape and size terms, the resultant relations could explain up to 99.1% of the variance Eq. (17). However, due to insufficient occurrence of quaternary type vertex (N X ), leave one out could not be applied for Eq. (17). The relations showed positive impact of branching and shape factors and negative impact of functionality and bulk. Eq. (17) shows that the effect of quaternary type of vertex is more pronounced than that of the tertiary type (regression coefficient for N X vs for N Y ). The calculated water solubility values according to Eq. (17) are shown in Table 3, which shows that all ether compounds fitted well in this equation. Table 6. Relations of water solubility (ln S) of ethers with topochemical indices. Model equation, ln S = i x i + Eq Regression coefficient(s) and constant # Statistics Q 2 2 R a s AVRES se se se se se (SDEP) (rorr) (F (df)) (n) T (0.746) (0.927) (1.63x10 2 (1, 15)) (16) T R F (0.226) (0.994) (5.45 x10 2 (2, 13)) (16) F B N V (0.283) (0.994) (3.52x10 2 (3, 12)) (16) F N V N B (0.371) (0.985) (1.29x10 2 (3, 12)) (16) F N V N P (0.316) (0.992) (2.63x10 2 (3, 12)) (16) F N V N X N Y (0.997) (4.17x10 2 (4, 11)) (16) + LOO could not be applied because of insufficient occurrence of N X type vertex. 3.4 QSPR for Halocarbons (n = 20) Eqs. (18) (20) describing QSPR for water solubility of halocarbons with topochemical indices are given in Table 7, showing that only 45.0% of the variance could be explained by the first order skeletal index (predicted variance 38.1%). The composite topochemical index gave further inferior relation. However, by incorporating two indicator variables I Br and I I (indicating the presence or absence of Br and I, respectively) along with integer variables, statistically acceptable relation (explained variance 78.4%, predicted variance 66.8%) was obtained. The regression coefficients of I Br and I I suggest that presence of Br and I decreases water solubility. Further, increase in branching (as shown by the coefficient of N P ) also reduces water solubility. All compounds fitted well in Eq. (20). The calculated water solubility values according to Eq. (20) are shown in Table

13 QSPR with TAU Indices: Water Solubility of Diverse Functional Acyclic Compounds Table 7. Relations of water solubility ln S of halocarbons with topochemical indices. Model equation, ln S = i x i + Eq Regression coefficient(s) and constant # Statistics Q 2 2 R a s AVRES se se se se se (SDEP) (rorr) (F (df)) (n) T R (1.084) (0.671) (3.52x10 2 (1, 19)) (20) N P N I (1.134) (0.688) (1.75x10 2 (2, 18)) (20) N P N I I Br I I (0.794) (0.911) ( (4, 15)) (20) I Br and I I denote presence or absence of bromine and iodine respectively. 3.5 QSPR for Hydrocarbons (n = 41) Table 8 shows that variance of water solubility of hydrocarbons is explained to the extent of 75.2% (predicted variance 73.0%) by the composite topochemical index. When the composite index was split into T R and F, there was a slight reduction in quality. In the case of hydrocarbons, F signifies the presence of multiple bonds (electron richness). The relation involving F and N V explained to the extent of 78.4% (predicted variance 75.7%). On introduction of the indicator variable I cyclo (indicating the presence or absence of cyclicity) and integer variables N trip and N doub (indicating the number of triple and double bonds, respectively), the QSPR quality increases up to 96.1% of explained variance, Eq. (26). These relations show that the water solubility of hydrocarbons increases with branching, cyclicity and presence of multiple bonds while it decreases with an increase in bulk. The effect of triple bond is more pronounced than that of double bond (regression coefficient for triple bond vs for double bond in Eq. (26)). 2,2,4 Trimethylpentane (147) and 2,2 dimethylpentane (159) act as outliers (but not excluded) for Eq. (26). The calculated solubility values according to Eq. (26) are given in Table 3. Table 8. Relations of water solubility (ln S) of hydrocarbons with topochemical indices. Equation ln S = i x i + Eq Regression coefficient(s) and constant # Statistics Q 2 2 R a s AVRES se se se se se se (SDEP) (rorr) (F (df)) (n) T (1.006) (0.871) (1.22x10 2 (1, 39)) (41) T R F (1.030) (0.871) ( (2, 38)) (41) F N V (0.954) (0.892) ( (2, 38)) (41) F N V I Cyclo (0.841) (0.920) ( (3, 37)) (41) N V N P I Cyclo N trip N doub (0.425) (0.981) (1.78x10 2 (5, 35)) (41) B N V I Cyclo N trip N doub (0.425) (0.983) (2.00x10 2 (5, 35)) (41) I cyclo denotes presence or absence of cyclicity. N doub and N trip denote number of double and triple bonds respectively 486

14 K. Roy and A. Saha 3.6 QSPR for Ketones (n = 13) The equations Eqs. (27) (30) relating water solubility of ketones with topochemical indices are shown in Table 9. The first order composite topochemical index can explain 98.5% of the variance (predicted variance 97.1%) while the first order skeletal index explained 98.1% of the variance (predicted variance 96.5%). With integer variables (N I and N P or N B ), relations explaining 98.9% of variance (predicted variance 97.9%) were obtained. The calculated solubility values according to Eq. (29) are shown in Table 3. 2 Butanone (181) behaves as an outlier (but not excluded) for Eq. (29). Table 9. Relations of water solubility (ln S) of ketones with topochemical indices. Model equation, ln S = i x i + Eq Regression coefficient(s) and constant # Statistics 1 2 Q 2 2 R a s AVRES se se se (SDEP) (rorr) (F (df)) (n) T (0.299) (0.993) (7.71 x10 2 (1, 11)) (13) T R (0.331) (0.991) (6.20x10 2 (1, 11)) (13) N I N B (0.257) (0.995) (5.44x10 2 (2, 10)) (13) N I N P (0.257) (0.995) (5.44x10 2 (2, 10)) (13) 3.7 QSPR for All Compounds (n = 193) Table 10 lists the relations of water solubility values of all compounds (composite set) with topochemical indices. Table 10. Relations of water solubility (ln S) of the composite set with topochemical indices. Equation ln S = i x i + Eq Regression coefficient(s) and constant # Statistics Q 2 2 R a s AVRES se se se se se se (SDEP) (rorr) (F (df)) (n) T (2.727) (0.556) ( (1, 191)) (193) T R F (2.684) (0.573) (2.61x10 2 (2, 191)) (193) F N V N X N Y (2.506) (0.659) ( (4, 188)) (193) F N V N P (2.480) (0.663) ( (3, 189)) (193) F N V N B (2.496) (0.657) ( (3, 189)) (193) F N V N X N Y I HC X (0.943) (0.960) (4.38x10 2 (5, 187)) (193) F N V N X N Y I HC X (0.750) (0.974) (6.59x10 2 (5, 181)) (187) I HC X denotes hydrocarbon or halacorbon compounds The composite topochemical index T singularly explained only 30.5% of the variance (predicted variance 28.0%). When T was partitioned into T R and F, the relation could explain 32.5% of the variance (predicted variance 30.2%). On further partitioning of T R, different relations, Eqs. (33) 487

15 QSPR with TAU Indices: Water Solubility of Diverse Functional Acyclic Compounds (35), showing about 42% explained variance (about 40% predicted variance) were obtained. When an indicator variable I HC X (denoting hydrocarbon or halocarbon compounds) was included, there was considerable rise in the statistical quality: both explained variance and predicted variances increased by 50 units. Table 11. Results of leave many out cross validation applied on Eq. (36). Model equation, ln S = i x i + Type of cross validation Number of cycles Average regression coefficients (standard deviations) Q 2 Leave 10% out 10 a (0.036) F (0.009) N V (0.068) N X (0.030) N Y (0.056) I HC X (0.106) Leave 25% out 4 b (0.067) F (0.018) N V (0.096) N X (0.036) N Y (0.124) I HC X (0.198) Q 2 denotes cross validated R 2. Average Pres means average of absolute values of predicted residuals a Compounds were deleted in 10 cycles in the following manner: (1, 11, 21,...191), (2, 12, 22,...192),..., (10, 20, 30,...190) b Compounds were deleted in 4 cycles in the following manner: (1, 5, 9,...193), (2, 6, 10,...190),..., (4, 8, 12,...192) (Av. Pres) (0.664) (0.665) The calculated water solubility values according to the Eq. (36) are given in Table 3. Leave many out cross validation (leave 10% out and leave 25% out) has been applied on Eq. (36) and the results are given in Table 11, which shows the robustness of Eq. (36). The scatter plot of observed vs. calculated, Eq. (36), water solubility values are shown in Figure 1. Diidomethane 138, 2,4 dimethylpentane 146, n octane 156, 1 pentyne 162, 1,8 nonadiyne 167 and 1,6 heptadiyne 168 act as outliers (but not excluded) for Eq. (36). When these outliers were excluded, a much better QSPR (explained variance 94.6% and predicted variance 94.4%) was obtained. The relations show that water solubility increases with functionality and branching (as evidenced from the coefficients of F and shape factors) while it decreases with an increase in bulk. Further, water solubility is specifically smaller for hydrocarbons and halocarbon compounds (as evidenced from large negative coefficient of I HC X ). 5 ln S (Obs.) ln S (Calc.) -20 Figure 1. Scatter plot of observed vs. calculated values Eq. (36) of water solubility. 488

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