Solvation Parameters. Part 4: What is the Impact of Recent Chromatographic Data Update?

Accurate solvation parameters have been established using solely gas/liquid partition data by gas/chromatography from the Kováts group (Laffort et al. J. Chromatog. A, 2005, 1100, 90-107). Because these chromatographic data have been recently updated (Kováts and Kresz, J. Chromatog. A, 2006, 1113, 206-219), the solvation parameters of the involved solutes and stationary phases have been entirely computed on again. It appears from this enquiry that the solute paramers values (127 compounds) are almost identical, whereas solvent parameters (11 stationary phases) have been slightly improved. A simple method of stationary phases classification is derived from these results, as well as a method for further determination of solute parameters. INTRODUCTION The conceptual definition of solvation parameters or descriptors can be expressed as follows: if a matrix of a given solubility property can be expressed as a product of matrices A*B, then A and B are respectively matrices of solute and solvent solvation parameters. Because infinite number of matrices A and B can provide such product, some rules and procedures have been developed in order, among others, to get parameters mutually as independent as possible (i.e. faintly correlated), and clearly reflecting understandable physicochemical properties [1-3]. In addition to these rules and procedures, the second tool needed to rightly characterize the solvation parameters of solutes is a reliable experimental database of solubility properties. Recently, Laffort et al. [1] used an accurate matrix of retention indices in gas-liquid chromatography (GLC) for 133 solutes and 10 stationary phases. Eight of these phases, of polar nature, were established by Kováts and co-authors [4-7], and the other two non polar phases were published by Laffort et al. [1]. However, one year later, Kováts and Kresz [8] published updated values of most of the GLC retention indices previously published in the references [4-7]. This update has raised two questions, the first one should be firstly solved before getting an answer to the second one: • Have the remaining GLC values published by Laffort et al. [1], and principally those on apolar phases, to be similarly updated? • Have these updated results on polar and apolar phases, an impact on the definitions of solvation parameters of solutes and solvents? The aim of the present study is to answer these two points and, if needed, specify some consequences. *Address correspondence to this author at the CNRS, Centre des Sciences du Goût UMR 5170, 15 rue Hugues Picardet, F.21000 Dijon, France; E-mail: [email protected] CHECKING THE REMAINING GLC VALUES The Original Database According to [1] This experimental data matrix of GLC retention indices RI (133 solutes x 10 stationary phases) is reported in Supplementary Information (Table SI-1), exactly as it was published in [1]. It includes RI values on two families of branched stationary phases, with respectively four and six branches, as reported in Fig. (1) (we call these two families of phases 4B and 6B). The eight polar phases, synthesized by Cloux et al. [9], are all of 4B type. The RI values reported are exactly in agreement with the references [4-7]. The nature of these phases is summarized in Table 1. The two apolar phases from which the experimental RI values are reported in Table SI-1 are hydrocarbons of 6B type (C67 and C103). This hydrocarbon family was firstly explored by Riedo et al. [10] and later developed by Défayes et al. [11]. The advantage of the alkane phases of 6B type over the 4B type is, for a given molecular weight, a lower melting point together with a similar shape. Strictly speaking, the 6B alkane family only concerns compounds with odd number of carbon atoms. However, RI values on a hypothetical C78 hydrocarbon phase of the same series were interpolated, using the following equation: RIC78-6B = 0.4035 RIC103-6B + 0.5965 RIC67-6B (1) Similarly, RI values on a hypothetical alkane of infinite molecular weight were extrapolated using the following equation: RIC -6B = 2.8611 RIC103-6B 1.8611 RIC67-6B (2) These two equations are based on the fact, every thing else being equal, that the GLC retention indices are linearly proportional to the inverse of the molecular weight of the stationary phases [11-13]. The Corrected Database According to [8] As already mentioned, the overlapping of the two databases in [1] and [8] is not complete: the most important Solvation Parameters. Part 4 The Open Applied Informatics Journal, 2009, Volume 3 13 difference concerns the absence of GLC retention indices for an alkane phase of infinite molecular weight, in the publication by Kováts and Kresz [8]. RI values for the primary bromo phase are also missing in this cited article. Otherwise, are included RI values for a secondary alcohol of the 4B family, established by Dallos et al. [14]. Finally, the RI values for C78, present in both databases, are from the 4B family in one case, and from the 6B family in the other case. Table 1. Structural Details of the Polar Phases Studied in [1]. See X and Y Meaning in Fig. (1, Left Side) Polar Interacting Group(s) X Y PCI Primary chloro CH2CI CH2CH3 PBr Primary bromo CH2Br CH2CH3 MTF Monotrifluoromethyl CH2CF3 CH2CH3 TTF Tetrakistrifluoromethyl CH2CF3 CH2CF3 TMO Tetramethoxy OCH3 OCH3 PCN Primary cyano CH2CN CH2CH3 PSH Primary thiol CH2SH CH2CH3 POH Primary alcohol CH20H CH2CH3 Structure of polar phases C67 : n = 13 C103 : n = 22 Structure of alkane phases 4B (4 branches) 6B (6 branches) Fig. (1). Schematic representation of the two types of stationary phases synthesized and used by the Kováts group, and applied by Laffort et al. [1]. Experimental retention indices of 133 solutes on 10 of these phases are reported in Table SI-1. The corrected database as reported in Table SI-2 (Supplementary Information) is exactly in agreement with Kováts and Kresz [8], with the unique exception of the 2Methyl-2-hexanol on Tetrakistrifluoromethyl phase (TTF). Indeed, a minimal transcription error from the references [5] to [8] has been observed in this case. Comparison of the Two Databases The differences of RI values in Tables SI-1 and SI-2 are reported in Table 2, for the eight phases present in both tables (including the C78 phase in its two types 4B and 6B). It is observed in 99% of cases (i.e. 1054 out of 1064) that the corrective increments characteristic of the solutes are constant for the eight phases. The exceptions are highlighted in Table 2. Among the polar phases, only one minimal exception is observed. Therefore, these corrective increments must also be applied to the primary bromo phase. In spite of the different molecular structure of the two C78 phases, their comparison only reveals nine non zero differences, from which eight are equal or less than 1 index unit, which can be considered as faint. The ninth value, equal to 4 index units, concerns the tetramethylsilane. This difference can not be considered as negligible, but it concerns one of the five solutes out of the 133 under study which presents RI values smaller than 500 (i.e. less than for pentane). It is well known that at this level, the experimental accuracy of chromatographic measurements is lower. In the same way as in our last publication on this topic [3], we have therefore decided to discard these five solutes from the final experimental data matrix. The results about the two C78 phases reported in Table 2 are very interesting, in the sense that C78-6B being established from C67 and C103 (eq. 1), the same corrections must be applied to these latter phases, and therefore also to a hypothetical alkane of infinite molecular weight (eq. 2). Taking into account these facts, Table SI-3 (Supplementary Information) includes the updated matrix of experimental retention indices as follows: • The data of Table SI-1 have been corrected using the not highlighted corrective increments of Table 2. • The data concerning the secondary alcohol phase SOH have been added, as it appears in Table SI-2. Because data on SOH are missing for the 1,1,1trifluorooctane, this solute has been discarded. • The data concerning the five solutes with RI values smaller than 500 have been also discarded, as we saw. The names of these five solutes have been highlighted in Table SI-1. The C78-6B values have been preferred to the C78-4B ones, in order to maintain a closer consistency between the C78 and Cinf phases. Finally, the experimental matrix reported in Table SI-3 concerns 127 solutes and 11 stationary phases. IMPACT ON THE SOLVATION PARAMETERS The tool applied for checking a possible impact of the updated GLC retention indices above reported, on the characterization of solvation parameters, is the algorithm named MMA (as Multiplicative Matrix Analysis), already applied in [1]. This algorithm was firstly presented in 1976 [15] and detailed in [1]). It is a tool to test theories on the basis of experimental data, whenever products of matrices are involved. The Fig. (2) summarizes how the program works in a particular application of gas-liquid-chromatography (GLC), where the experimental matrix R is a product of the matrix A of parameters of solutes and a matrix B of parameters of solvents. For a given matrix of experimental data R, a theoretical matrix A is placed in INPUT. The program runs using successive iterations, until the reconstruction of the experimental matrix in OUTPUT is optimal. The quality of this reconstruction (R compared to A * B) only depends on the number of input parameters A, not on their nature. By contrast, the output parameters A resemble to the input parameters A only when the latter are involved in the phenomenon under study. 14 The Open Applied Informatics Journal, 2009, Volume 3 Laffort and Héricourt Table 2. Differences of GLC Retention Indices According to [1] and [8] (Tables SI-1 and SI-2 in the Present Study), for 133 Solutes and the Eight Stationary Phases Present in Both Tables ID [1] ID [8] Solutes C78 POH TTF MTF PCL TMO PSH PCN 1 76 1-Butanol 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9 2 84 2-Methyl-2-propanol 2.9 2.9 2.9 2.9 2.9 2.9 2.9 2.9 3 77 1-Pentanol 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 4 85 2-Methyl-2-butanol 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 5 78 1-Hexanol 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 6 131 Cyclohexanol 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 7 86 2-Methyl-2-pentanol 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 8 79 1-Heptanol 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 9 87 2-Methyl-2-hexanol -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 10 80 2-Butanol 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 11 81 2-Pentanol 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 12 82 2-Hexanol -0.2 -0.2 -0.2 -0.2 -0.2 -0.2 -0.2 -0.2 13 83 2-Heptanol -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 14 159 2-Phenylethanol 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 15 158 Benzyl alcool 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 16 96 Pentanal 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 17 97 Hexanal 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 18 91 2-Butanone 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 19 92 2-Pentanone 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 20 129 Cyclopentanone 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 21 93 2-Hexanone 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 22 130 Cyclohexanone 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 23 94 2-Heptanone -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 24 99 Dipropylether 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 25 100 Dibutylether 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 26 126 Tetrahydrofuran 0.3 0.3 0.3 0.3 0.4 0.3 0.3 0.3 27 127 1,4-Dioxane 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 28 160 Methyl phenyl ether (Anisole) 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 29 161 Phenetole 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 30 69 Nitroethane 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 31 70 1-Nitropropane -0.4 -0.4 -0.4 -0.4 -0.4 -0.4 -0.4 -0.4 32 71 1-Nitrobutane -0.6 -0.6 -0.6 -0.6 -0.6 -0.6 -0.6 -0.6 33 72 1-Nitropentane -0.3 -0.3 -0.3 -0.3 -0.3 -0.3 -0.3 -0.3 34 157 1-Nitrobenzene 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 35 65 1-Cyanoethane 6.3 6.3 6.3 6.3 6.3 6.3 6.3 6.3 36 66 1-Cyanopropane (Butyronitrile) 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 37 67 1-Cyanobutane (Valeronitrile) 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 38 68 1-Cyanopentane 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 39 116 Pyridine 2.2 2.2 2.2 2.2 2.2 2.2 2.2 2.2 40 117 2-Picoline 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 41 118 3-Picoline 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 42 119 4-Picoline 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 43 143 2,3-Lutidine 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 Solvation Parameters. Part 4 The Open Applied Informatics Journal, 2009, Volume 3 15 (Table 2) contd..... ID [1] ID [8] Solutes C78 POH TTF MTF PCL TMO PSH PCN 44 144 2,4-Lutidine 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 45 145 2,5-Lutidine 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 46 146 2,6-Lutidine 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 47 147 3,4-Lutidine 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 48 148 3,5-Lutidine 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 49 120 3-Chloropyridine 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 50 73 1-Acetoxypropane 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 51 74 1-Acetoxybutane (Butylacetate) 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 52 75 1-Acetoxypentane (Pentyl acetate) 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 53 57 1,1,1-Trifluorooctane -2.3 -2.3 -2.3 -2.3 -2.3 -2.3 -2.3 -2.3 54 111 Fluorobenzene -0.7 -0.7 -0.7 -0.7 -0.7 -0.7 -0.7 -0.7 55 112 Hexafluorobenzene -2.9 -2.9 -2.9 -2.9 -2.9 -2.9 -2.9 -2.9 56 113 Trifluoromethylbenzene -1.0 -1.0 -1.0 -1.0 -1.0 -1.0 -1.0 -1.0 57 107 Dichloromethane 5.9 5.9 5.9 5.9 5.9 5.9 5.9 5.9 58 108 Trichloromethane 3.6 3.6 3.6 3.6 3.6 3.6 3.6 3.6 59 109 Tetrachloromethane 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 60 59 1-Chlorobutane -0.7 -0.7 -0.7 -0.7 -0.7 -0.7 -0.7 -0.7 61 60 1-Chloropentane 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 62 61 1-Chlorohexane 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 63 114 Chlorobenzene 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 64 62 1-Bromopropane -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 65 63 1-Bromobutane -0.3 -0.3 -0.3 -0.3 -0.3 -0.3 -0.3 -0.3 66 64 1-Bromopentane -0.2 -0.2 -0.2 -0.2 -0.2 -0.2 -0.2 -0.2 67 115 Bromobenzene 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 68 88 1-Butanethiol 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 69 89 1-Pentanethiol 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 70 90 n-Hexanethiol 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 71 128 Thiophene 2.2 2.2 2.2 2.2 2.2 2.2 2.2 2.2 72 24 1-Hexene 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 73 47 Cyclohexene -0.2 -0.2 -0.2 -0.2 -0.2 -0.2 -0.2 -0.2 74 49 1,4 Cyclohexadiene 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 75 48 1,3 Cyclohexadiene 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 76 25 1-Heptene 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 77 26 1-Octene 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 78 27 1-Nonene 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 79 28 1-Decene 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 80 29 1-Pentyne 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 81 30 1-Hexyne -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 82 35 2-Hexyne -1.1 -1.1 -1.1 -1.1 -1.1 -1.1 -1.1 -1.1 83 36 3-Hexyne -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 84 31 1-Heptyne -0.8 -0.8 -0.8 -0.8 -0.8 -0.8 -0.8 -0.8 85 32 1-Octyne -0.3 -0.3 -0.3 -0.3 -0.3 -0.3 -0.3 -0.3 86 37 4-Octyne -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 87 33 1-Nonyne -0.2 -0.2 -0.2 -0.2 -0.2 -0.2 -0.2 -0.2 88 34 1-Decyne -0.2 -0.2 -0.2 -0.2 -0.2 -0.2 -0.2 -0.2 16 The Open Applied Informatics Journal, 2009, Volume 3 Laffort and Héricourt (Table 2) contd..... ID [1] ID [8] Solutes C78 POH TTF MTF PCL TMO PSH PCN 89 50 Benzene 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 90 51 Toluene 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 91 52 Ethylbenzene 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 92 141 Naphthalene 0.7 0.0 0.0 0.0 0.0 0.0 0.0 0.0 93 142 Azulene 0.2 0.0 0.0 0.0 0.0 0.0 0.0 0.0 94 1 Pentane 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 95 38 Cyclopentane -0.4 -0.4 -0.4 -0.4 -0.4 -0.4 -0.4 -0.4 96 11 2,2-Dimethylbutane -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 97 12 2,3-Dimethylbutane 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 98 2 Hexane 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 99 39 Cyclohexane -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 -0.1 100 13 2,2-Dimethylpentane -0.4 -0.4 -0.4 -0.4 -0.4 -0.4 -0.4 -0.4 101 14 2,3-Dimethylpentane 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 102 15 2,4-Dimethylpentane 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 103 20 2,2,3-Trimethylbutane 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 104 3 Heptane 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 105 40 Cycloheptane 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 106 42 Methylcyclohexane 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 107 17 2,3-Dimethylhexane 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 108 18 2,4-Dimetylhexane 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 109 19 3,4-Dimetylhexane 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 110 21 2,2,4-Trimethylpentane -0.7 -0.7 -0.7 -0.7 -0.7 -0.7 -0.7 -0.7 111 22 2,3,4-Trimethylpentane -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 -0.5 112 43 cis 1,2-Dimethylcyclohexane 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 113 44 trans 1,2 Dimethylcyclohexane 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 114 45 cis 1,4-Dimethylcyclohexane 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 115 46 trans 1,4 Dimethylcyclohexane 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 116 4 Octane 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 117 41 Cyclooctane 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 118 5 Nonane 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 119 6 Decane 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 120 135 Cyclodecane -1.1 0.0 0.0 0.0 0.0 0.0 0.0 0.0 121 136 cis-Hydrindane 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 122 137 trans-Hydrindane 0.5 0.0 0.0 0.0 0.0 0.0 0.0 0.0 123 138 cis-Decalin -0.6 0.0 0.0 0.0 0.0 0.0 0.0 0.0 124 139 trans-Decalin 0.6 0.0 0.0 0.0 0.0 0.0 0.0 0.0 125 140 Adamantane 0.4 0.0 0.0 0.0 0.0 0.0 0.0 0.0 126 7 Undecane 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 127 8 Dodecane 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 128 9 Tridecane 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 129 10 Tetradecane 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 130 121 Tetramethylsilane 4.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 131 122 Hexamethyldisilane 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 132 123 Hexamethyldisiloxane 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 133 125 Tetramethylthin 2.8 2.8 2.8 2.8 2.8 2.8 2.8 2.8 Solvation Parameters. Part 4 The Open Applied Informatics Journal, 2009, Volume 3 17 Fig. (2). Diagram of the INPUT/OUTPUT of the Multiplicative Matrix Analysis (MMA), according to Laffort et al. [1] (see text). In practice, the program starts with a classical multilinear regression, with R as independent variables and A as dependent variables. A first matrix B of solvent parameters is obtained, which in turn is considered as fixed. A first comparison between R and the product A * B is made. In a second step, a multi-linear regression is applied to B and R and a second value of matrix A of solute parameters is obtained. Further similar steps are used until two successive cycles do not provide an improvement in reconstruction of matrix R (it is experimentally observed that the system is convergent). A revised version of the MMA programme in MATLAB language, previously published in [1], can be seen in Appendix A. Otherwise, an updated MMA applet is freely available in the web site: http://paul.laffort.free.fr Solute Parameters The MMA algorithm has been applied to the experimental R matrix of GLC data, as reported in Table SI3 (127 x 11). Two input matrices A (127 x 5) have been tested: i ) the solubility parameters according to [1], and ii ) a randomized data matrix. The results are summarized in Table 3, in which , , , and respectively stand for the solute parameters of dispersion, orientation, induction /polarizability, acidity and basicity. Table 3. Comparisons of Input and Output Solute Parameters Using the MMA Algorithm Applied to the Table SI-3, with Two Input Options (r and b Respectively Stand for Correlation Coefficient and for Multiplicative Coefficient)