Masoud Shariati-Rad Masoumeh Hasani

Transcription

1 J IRAN CHEM SOC (2013) 10: DOI /s x ORIGINAL PAPER Linear and nonlinear quantitative structure property relationships modeling of charge transfer complex formation of organic donors with iodine and iodine monochloride using partial least squares and radial basis function partial least squares Masoud Shariati-Rad Masoumeh Hasani Received: 8 April 2013 / Accepted: 12 April 2013 / Published online: 23 April 2013 Ó Iranian Chemical Society 2013 Abstract Using the formation constants of 74 charge transfer complexes in which iodine and iodine monochloride act as acceptors, quantitative structure property relationships models were developed for predicting these constants for the first time. The procedure was based on reducing a large number of the descriptors based on the variable importance in projection and subsequent selection by stepwise regression and genetic algorithm. The most important variables influencing the charge transfer interactions were identified and interpreted. Models were obtained by linear methods of multiple linear regression and partial least squares regression and the nonlinear method of radial basis function partial least squares. The best predictions were obtained with the Gaussian radial basis function with r = 0.9 and LV = 10. The obtained results confirm the capability of the proposed approach to give predictive models for K CT. Keywords Charge transfer complex Descriptors Quantitative structure property relationships Radial basis function partial least squares Introduction The quantitative structure activity/property relationships (QSAR/QSPR) studies are considered to be one of the most M. Shariati-Rad (&) Department of Analytical Chemistry, Faculty of Chemistry, Razi University, Kermanshah, Iran mshariati_rad@yahoo.com M. Hasani Faculty of Chemistry, Bu-Ali Sina University, Hamedan, Iran effective computational approaches for the estimation of different types of properties and constants [1 9]. QSPR uses chemometrics methods to describe how a given physical or physicochemical property varies as a function of molecular descriptors describing the chemical structure of the molecule. Thus, it is possible to replace costly analytical or biological tests or experiments of a given physical or physicochemical property (especially when involving hazardous and toxically risky materials and solvents or unstable compounds) with calculated descriptors, which can in turn be used to predict the responses of the interest for new compounds. The primary event in the action of many drugs is often a reversible association between a drug molecule and a receptor to form a complex. In such reactions, some drugs can behave as electron donors, forming charge transfer complexes by electron transfer from an occupied orbital to an empty orbital of an acceptor molecule [10]. A precise knowledge about the structural properties of the molecular compounds affecting their charge transfer complex formations is of crucial significance for the understanding of mechanisms of action of drugs. In addition, charge transfer interactions affect drug absorption, bioavailability, hydrophobic drug receptor interactions, metabolism of molecules, as well as their toxicity. The ability of an organic compound to form a stable charge transfer complex is stated to be dependent on the Ip, EA, the presence of N or O atoms and etc [11, 12]. However, a more precise consideration about the effect of different structural features has not been yet performed. Moreover, the development of theoretical methods for prediction of formation constants is needed and interesting. The advantages of this approach lie in the fact that it requires only the knowledge of chemical structure and is not dependent on any experiment properties.

2 1248 J IRAN CHEM SOC (2013) 10: Despite numerous QSPR studies on different physical properties and constants, it can be seen rare cases about charge transfer formation constants [13]. Recently, we studied charge transfer complex formation constants of 46 organic donors with p-chloranil in carbon tetrachloride [13]. Now, we report here the results obtained in the prediction K CT values of a wider set of donors with two acceptors. In the present work, we use descriptors of the donors and the two acceptors simultaneously. Owing to the presence of nonlinearity, nonlinear models based on the radial basis function partial least squares (RBF PLS) were developed. Radial basis function partial least squares (RBF PLS) and the model validation The purpose of the PLS is to build a linear model enabling the prediction of chemical/physical characteristics e.g. K CT (involved in y) from measured variables e.g. descriptors (involved in X) [14 16]. For m objects and n variables, dimensionality of X is m 9 n. Vector y describing the property of m objects with the dimensionality of m 9 1 contains the values of the studied property. There is a linear model y = Xb in matrix notation where b contains the regression coefficients that are determined during the calibration step. The F statistic was used to make the significance determination of the number of LVs and to avoid over-fitting [17]. In RBF PLS [18, 19], instead of applying PLS to the X and y containing the initial data, it can be applied to the matrices A and y, where A is the so-called activation matrix. The elements of A are defined as: a ij ¼ exp jjc j x i jj 2 =r 2 j for i; j ¼ 1; 2;...; m ð1þ where x i is a vector containing the values of the variables taken from the ith object, a ij is the element of A at ith row and jth column, jj jj is the norm which denotes here the Euclidean distance, c j and r j are the center and width of the jth RBF hidden unit, respectively which are presented as: c j ¼ x j for j ¼ 1; 2;...; m ð2þ r j1 ¼ r j2 ¼ e m X m i¼1 jjx i x j jj ð3þ where e is a assigned positive number. Thus, the resulting symmetrical matrix A has ones on its diagonal. Then, the PLS procedure will be applied to the matrices A and y in a similar way as linear one. A and y are projected on the lowdimensional score matrix T, respectively: A ¼ TP T þ E Y ¼ UQ T þ F ð4þ ð5þ where the T, U are the matrices of the extracted scores, the matrix P and the matrix Q represent matrices of loadings and the matrix E and the matrix F are the matrices of residuals. In the case of having one independent variable, Y collapses to vector y so do F. T can be represented as the linear combination of A, so the linear PLS model is set up as: y ¼ Tb þ F f ¼ AWb þ f f ð6þ where b (m 9 l) represents the regression coefficient vector and W is the transformation matrix of A. Because of the fact that T is a linear combination of radial basis functions that will maximize the covariance between A and y, f plays an important role in the RBF PLS network. When f is determined, the RBF PLS network can be obtained and used for prediction or other purposes. Therefore, by combining PLS algorithm with RBF network, the nonlinear relation between A and y is transformed to problem in linear algebra. After training, the RBF PLS network can be used to make predictions on new observations y unk ¼ A unk Wb ð7þ where A unk is the activation matrix of X unk which is used for prediction, y unk is the resulting dependent matrix. The complexity of the RBF PLS and partial least squares regression (PLSR) models was estimated based on the leave-one-out cross-validation (LOOCV) procedure [20]. In LOOCV one repeats the calibration m times (m is the number of the objects in training set), each time treating the ith left-out object as the prediction object. The dependent variable for each left-out object is calculated based on the model with one, two, three, etc factors. The root mean squares errors of cross-validation (RMSECV) for the model with specific number of latent variables is defined as RMSECV ¼ sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi KCT iobsþ2 P m i¼1 ðkipred CT m 1 ð8þ where obs denotes the assayed value, pred denotes the predicted value of the dependent variable, and i refers to the object index, which ranges from 1 to m. Model with k factors, for which RMSECV reaches a minimum, is considered as an optimal one. The quality of external predictions was measured by the root mean squares errors of prediction (RMSEP) and crossvalidated R 2 test (Q2 test )[20]:

3 J IRAN CHEM SOC (2013) 10: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi P m0 i¼1 RMSEP ¼ ð^k CT i Ki CT Þ2 m 0 1 ð9þ P m0 Q 2 test ¼ 1 i¼1 ðki CT ^K CT i P Þ2 m 0 i¼1 ðki CT K CT Þ 2 ð10þ where ^K CT i is the predicted Ki CT, K CT is the mean of the K CT in the test set, and i refers to the object index in the test set, which ranges from 1 to m (m is the number of the objects in test set). Materials and methods Softwares The RBF PLS, GA-PLSR, and SR-MLR (multiple linear regression) procedures were programmed within the MATLAB environment (MATLAB 6.5) [21]. For the calculation of molecular descriptors, HyperChem 7.5 [22] and DRAGON software version 3.0 [23] were used. The chemical structures of the molecules were drawn and optimized by HyperChem software and entered to DRA- GON software. Dataset The K CT of 74 organic compounds taken from [24 27] were used as a data-set. These data are charge transfer complex formation constants of I 2 and ICl with the mentioned donors in carbon tetrachloride at 25 C. The list of molecules of the data-set, including hydrocarbons, alkylhalides, alcohols, ethers, amides, acetanilides, ketones, halobenzenes, polycyclic aromatic hydrocarbons, heterocyclic compounds, and benzene derivatives is given in Table 1. The formation constants fall in the range between 0.07 and 7.6 values for methyl iodide with I 2 and dibenzyl ether with ICl, respectively. Molecular descriptors The chemical structures of all 74 pure components were drawn in HyperChem software [22] and pre-optimized using MM? molecular mechanics force field. A more precise optimization was done using semi-empirical AM1 in HyperChem. Using these minimum energy conformations, we computed 1,497 molecular descriptors using the software DRAGON 3.0 software [23], including descriptors of all types, such as Constitutional, Topological, Geometrical, Charge, Geometry, Topology and Atoms-Weighted AssemblY (GETAWAY), Weighted Table 1 Donors and their K CT contained in data-set No. Name Acceptor K CT 1 1,1-Dimethoxy ethane I ,2,3,5-Tetramethyl benzene I ,2,3-Trimethyl benzene I ,2,4-Trimethyl benzene I ,2-Dimethoxy benzene a I ,2-Dimethoxy benzene ICl ,2-Dimethoxy ethane I ,3,5-Trioxane a I ,3,5-Trioxane ICl ,3-Dimethoxy benzene I ,4-Benzodioxane I ,4-Benzodioxane a ICl ,4-Dimethoxy benzene a I ,4-Dimethoxy benzene ICl ,4-Dioxane I Chloro-N-methyl acetamide I Methyl-N-methyl acetamide I c4 I c5 I c6 I Anisole I Anisole a ICl Benzene a I Benzene ICl Benzyl methyl ether I Bibenzyl I Bibenzyl a ICl Bromobenzene a I Bromobenzene ICl Cycloheptene I Cyclohexene I Cyclooctene I Cyclopentene I Dibenzyl ether a I Dibenzyl ether ICl Diethylene glycol dimethyl ether I Di-n-butyl ether I Diphenyl ether a I Diphenyl ether ICl Durene a I Durene ICl Ethyl benzene ICl Ethyl iodide I Hexaethyl benzene a I Hexaethyl benzene ICl Hexamethyl benzene I Isopropenyl benzene ICl Mesitylene a I

4 1250 J IRAN CHEM SOC (2013) 10: Table 1 continued No. Name Acceptor K CT 49 Mesitylene ICl Methyl iodide I m-xylene I m-xylene a ICl N,N-dimethyl benzamide I Naphtalene a I Naphtalene ICl N-ethyl acetanilide I N-methyl acetanilide I o-xylene a I o-xylene ICl p-chloro-n,n-dimethyl benzamide I Pentamethyl benzene a I Pentamethyl benzene ICl Phenanthrene I Phenetole a I Phenetole a ICl p-xylene a I p-xylene a ICl Stilbene I Styrene I t-butyl benzene ICl THF a I Toluene I Toluene a ICl Trimethyl orthoformate I a Donors in external test set Holistic Invariant Molecular descriptors (WHIM), 3D- Molecular Representation of Structure based on Electron diffraction (3D-MoRSE), Molecular Walk Counts, BCUT descriptors, 2D-Autocorrelations, Aromaticity Indices, Randic Molecular Profiles, Radial Distribution Functions, Functional Groups, Atom-centered fragments, Empirical and Properties. Furthermore, molecular features such as the number of H donors (D), the number of H acceptors (A) and the number of heteroatoms (H) present in the molecular structure were added to the group of the descriptors. Hydrophobicity, dipole moment, polarity, charge-related properties, the highest occupied molecular orbital energy (E HOMO ), the lowest unoccupied molecular orbital energy (E LUMO ), and thermodynamics properties as a group of well-known properties were computed for two acceptors and included in the matrix of the descriptors. In total, 16 descriptors were calculated for each acceptor. Results and discussion Pretreatment step To ensure that a derived model has good general ability, first, representative training and test sets needs to be selected. Ideally, the division of the data-set should be performed such that points representing both training and test set are distributed within the whole descriptor space that is occupied by the entire data-set. To obtain such training and test sets, the data-set was divided into two sets by Kennard Stone algorithm [28]: the training and external test sets consisting of 51 and 23 members, respectively. This dividing guarantees that the two subsets contain values in the two acceptors studied and with all the types of donors. The training and test sets were used to construct and evaluate the predictivity of the QSPR models, respectively. Before performing any variable selection method and model construction, the matrix of the descriptors was scaled (i.e. unit variance). The variable importance in projection (VIP) derived from PLSR weights were used to make the first reduction in the pool of descriptors with the compounds forming the training set [15]. This is a weighted sum of squares of the PLS weights (w). The weights are calculated from the amount of the variance of the independent variable vector of each PLS latent loading. Using this process, we can distinguish the important and information rich descriptors. Applying a threshold value of VIP, the initial pool of descriptors was reduced to 216. This procedure avoids selection of the descriptors by chance upon application of genetic algorithm (GA) [29, 30] and stepwise regression (SR) [31]. Afterwards, GA and SR were applied to this reduced collection to further reduce this collection and to find the best QSPR models. Interpretation of the selected descriptors Following variable reduction by VIP, two selection tools were employed: SR and GA. The top respective 17 and 30 selected descriptors by SR and GA have been reported in Table 2. In Table 2, the selected descriptors have been briefly defined. Surprisingly, the two selection methods gave almost completely different results. This is attributed to the different evaluation strategies for selection of variables. MAXDP, R4u, and ionization_potential are the only two donor related descriptors seen in the two groups. However, common acceptor related descriptors are more (like Se_a, l_a, g_a, and I_a,). Acceptor related descriptors have higher contribution in the GA selected descriptors.

5 J IRAN CHEM SOC (2013) 10: Table 2 Top 30 and 17 descriptors selected by GA and SR, respectively Selected descriptors by GA a Symbol Definition Sv_a Sum of atomic van der Waals volume Se_a Sum of atomic Sanderson electronegativities Mv_a Mean atomic van der Waals volume Mp_a Mean atomic polarizabilities l_a Dipole moment I_a Ionization energy EA_a Electron affinity V_a Volume SA_a Surface area LUMO_a Lowest unoccupied molecular orbital g_a Strength of acceptor (from I 2 -important) IAC Total information index of atomic composition (topological descriptor) MAXDP Maximal electrotopological positive variation(topological descriptor) S0K Kier symmetry index (topological descriptor) BEHp1 Highest eigen value n. 1 of Burden matrix/weighted by atomic polarizabilities qpmax Maximum positive charge (charge descriptors) qnmax Maximum negative charge (charge descriptors) SPP Submolecular polarity parameter RDF065p Radial distribution function - 6.5/weighted by atomic polarizabilities (RDF descriptor) Mor11u 3D-Morse-signal 11/unweighted Mor22u 3D-Morse-signal 22/unweighted Mor23u 3D-Morse-signal 23/unweighted Mor23e 3D-Morse-signal 23/weighted by atomic Sanderson electronegativities G1u 1st component symmetry directional WHIM index/ unweighted P2m 2nd component shape directional WHIM index/weighted by atomic masses G1p 1st component symmetry directional WHIM index/ weighted by atomic polarizabilities H3v H autocorrelation of lag 3/weighted by atomic van der Waals volumes (GETAWAY descriptor) H_bond_acceptor I Ionization_potential R4u R autocorrelation of lag 4/unweighted (GETAWAY descriptor) Selected descriptors by SR a Symbol MAXDP g_a R4u Definition Maximal electrotopological positive variation (topological descriptor) Strength of acceptor R autocorrelation of lag 4/unweighted (GETAWAY descriptor) Table 2 continued Selected descriptors by SR a Symbol R2u H3m I Mor21m RDF035m LUMO HD J3D MV Se_a l_a I_a HOMO TIE Definition R autocorrelation of lag 2/unweighted (GETAWAY descriptor) H autocorrelation of lag 3/weighted by atomic masses (GETAWAY) Ionization_potential 3D-MoRSE-signal 21/weighted by atomic masses Radial distribution function - 3.5/weighted by atomic masses (RDF descriptor) Lowest unoccupied molecular orbital Hansen_dispersion 3D Balaban index (geometrical) Molecular_volume Sum of atomic Sanderson electronegativities (constitutional) Dipole moment Ionization potential Highest occupied molecular orbital E_state (topological descriptor) a Descriptors tailing by _a are related to acceptors The developed QSPR model should not only have a comparative prediction capability for the studied properties, but also requires a postulate of the underlying physical phenomenon and identification of the key physical variables. By interpreting the selected descriptors, it is possible to gain some insight into factors that are likely to govern the K CT of the studied donor compounds with I 2 and ICl. An examination of the selected descriptors shows that these descriptors incorporate a diverse set of descriptors and different natures. From Table 2, it can be seen that these descriptors mainly encode information such as mass, electronic, polarizability, charge, topology, and etc. Three out of the four acceptor selected by SR are electronic (I_a, l_a, and Se_a). Influence of these descriptors in charge transfer processes is expected. These descriptors show the importance of the electronic characteristics on formation of the related complexes. The values of I_a, l_a, and Se_a exactly describe the strengths of the charge transfer complexes of I 2 and ICl. This means that for stronger complexes of ICl, all three descriptors are higher. These descriptors describe the electron acceptor capabilities of a compound. In addition, the strength of the acceptors (g_a) [32] has been included in the group of the acceptor related selected descriptors. As is expected for weaker acceptor like I 2, g_a is smaller. In overall, it can be concluded that electronic characteristics of the acceptors play an important role in the strength of the related charge transfer complexes. In the group of GA selected descriptors,

6 1252 J IRAN CHEM SOC (2013) 10: most of the acceptor selected descriptors are volume related ones. This means on the other hand, polarizability plays an important part in the electron donor acceptor complexes. Apparently, descriptors of acceptor, such as l, I_a, EA_a, LUMO_a, and g_a have influences on their charge transfer complex formation properties. These descriptors describe the electron acceptor capabilities of a compound. It must be mentioned that g_a is the most important descriptor of the acceptors which take a parts in the most of the models. WHIM descriptors have been selected by GA. WHIM descriptors [33, 34] are based on the statistical indices calculated on the projections of atoms along principal axes. Directional WHIM descriptors are molecular descriptors calculated as univariate statistical indices on the scores of each individual principal component. Symmetry directional WHIM descriptors such as G1u and G1p are the eigen values of the weighted covariance matrix of the atomic coordinates and account for the molecular symmetry along the principal axes. In particular, G1u and G1p describe the extent of the donors in the first spatial axes which is weighted by atomic polarizabilities. P2m is a WHIM descriptor of electrotopological state type. The Electro topological State Si of the ith atom in a molecule, also called the E-state index gives information related to the electronic and topological state of the atom in the molecule. The group contributions, also known as fragmental constants, are numerical quantities associated with substructures of the molecule, such as single atoms, atom pairs, atom-centered substructures, molecular fragments, functional groups, etc. For example, atom contribution models exhibit an one-to-one correspondence between atoms and property contributions, i.e. the molecular property is a function of all the single atomic properties. Therefore, selection of G1u and G1p further confirms the interaction through single points in the donors especially in the N and O atom containing donors. GETAWAY descriptors have a high contribution in the selected descriptors by SR (R4u, R2u, and H3m). The most proximity of the selected descriptors by SR and GA occurs by this group (R4u and H3v have been selected by GA). The GETAWAY descriptors [35, 36] are recently proposed molecular descriptors derived from a new representation of molecular structure, the molecular influence matrix (MIM). Each off-diagonal element of MIM (h ij ) represents the degree of accessibility of the jth atom to interact with the ith atom or, in other words, the attitude of the two considered atoms to interact themselves. A positive sign for the off-diagonal elements means that the two atoms occupy similar molecular regions with respect to the center. Hence the degree of their interaction should be high. For the lag 3 (topological distance), this contribution has been selected (H3v and H3m). These descriptors can be attributed to the interaction of O atom with the benzene ring in aromatic ethers and N atom with carbonyl group in amide and acetamide donors studied. R4u and R2u, which are unweighted represent R index of maximal contribution to the autocorrelation in lags 4 and 2 (topological distance), respectively. These descriptors are expected to have a lower dependence on conformational changes since it encodes information on pairs of atoms very near each other. For this reason, we can say that the charge transfer complex formation constants for the studied database have slighter dependence on the conformational changes. It also can be concluded that a small group of atoms or functional groups in the donors can participate in charge transfer complex formation as the donation sites. These descriptors are unweighted, which implies that R4u and R2u can describe strong interactions via single atoms (like N and O atoms) or functional groups (amide, keto, and carbon carbon double bond). This is because properties, such as volume, mass, and electronegativity describe weak interactions through polarizabilities. On the other hand, H3m and H3v that are weighted by masses and volume, respectively, can describe interactions which polarizability favors them. These descriptors can explain the interaction of the donors containing benzene rings. Topological distances which selected GETAWAY descriptors show ranges between 2 and 4. This further confirms interaction of the donors through atoms and functional groups. The roles of atoms in a compound making it act as a strong donor is reflected in IAC. The total information content on atomic composition of the molecule is calculated from the complete molecular formula, hydrogen included. The topological charge indices were proposed to evaluate the charge transfer between pairs of atoms and therefore, the global charge transfer in the molecule. The most important descriptor relating to donors is topological one (MAXDP). It contributes in all of the constructed models along with g. MAXDP belongs to topological descriptors and is given by MAXDP ¼ if Ii [ 0 Ii is the field effect on the ith atom due to the perturbation of all other atoms in the molecule [37]. Generally, topological descriptors can be sensitive to one or more structural features of the molecule such as size, shape, symmetry, branching and cyclicity and can also encode chemical information concerning atom type and bond multiplicity. In the unsaturated cycloalkenes, this descriptor plays an important role in their interactions. MAXDP is mainly related to the topological distance between the ith and other atoms and the intrinsic state of the ith atom, i.e. the principal quantum number, the number of valence electrons (valence vertex degree) and the

7 J IRAN CHEM SOC (2013) 10: number of sigma electrons (vertex degree). Thus, MAXDP describes molecular polarity and electrophilicity, which affect positively to make a compound to act as a strong donor. As can be expected, descriptors reflecting the charge can potentially be important in the interaction between donor and acceptor. Descriptors belonging to this group have been selected only by GA. qpmax, qnmax, and SPP are three charge related descriptors selected among 14 ones with completely opposite character. These descriptors are related to the maximum charges on an atom in a molecule. It must be mentioned that there are charge descriptors among this 14 descriptors which describe total or mean charges in the molecule but, qpmax and qnmax have been selected. Hence, it can be inferred that interaction between donor and acceptor most probably occurs through single points in the molecule, i.e. atoms. SPP is an electronic descriptor defined as the maximum excess charge difference for a pair of atoms in the molecule [38], i.e. calculated from the difference between the atomic maximum positive charge and the atomic maximum negative charge in a molecule. These descriptors can be accounted for the relatively high values of K CT for N and O atom containing donors. The only 3D MoRSE descriptor selected is Mor21m which is weighted by mass. On the other hand, 3D MoRSE descriptors have a main contribution to the donors selected descriptors by GA that are unweighted and weighted by atomic Sanderson electronegativities (Mor11u, Mor22u, Mor23u, and Mor23e). These descriptors [39] are based on the idea of obtaining information from the 3D atomic coordinates by the transform used in electron diffraction studies for preparing theoretical scattering curves. Inspection of the selected 3D MoRSE descriptors reveals that sum of the properties calculated for the atoms at 11th, and 21 23th signal from the three-dimensional atomic coordinates of a molecule is decisive for explaining the charge transfer complex formation, i.e. single atoms or closely spaced ones forming functional groups. The RDF descriptors selected are RDF035m and RDF065p; descriptors weighted by atomic masses and polarizabilities, respectively. RDF descriptors were proposed based on a radial distribution function different from that commonly used to calculate molecular transforms I(s) [40]. Formally, the radial distribution function of an ensemble of A atoms can be interpreted as the probability distribution to find an atom in a spherical volume of radius R. These atomic properties enable the discrimination of the atoms of a molecule for almost any property that can be attributed to an atom. The selected 3D MoRSE and RDF descriptors show how importance of interactions influenced by polariazability (they are weighted by masses and polarizabilities). The energy of the lowest energy level containing no electrons (LUMO) and the highest energy level occupied by electrons (HOMO) in the molecule are two electronic descriptors related to donors which have been selected by SR. LUMO of acceptor has been selected by GA. Apparently, the studied complexes are charge transfer ones which electron transfers during their formation. This electron transfer occurs to some extent. Molecules with high HOMO energy values are more able to donate electrons than molecules with low HOMO energy values. Therefore, the E HOMO descriptor which is related to E LUMO, is a measure of the electrodonocity of a molecule and is important in the modelling of molecular properties and reactivity, in particular for charge transfer complex formation reactions. The above discussion demonstrates that in the weak studied charge transfer complexes interactions between the donor and acceptor is through electron-donor sites, functional groups, and dipole dipole interactions. The presence of topological and the polarizability-related descriptors in the selected descriptors verify this. These interactions are stronger in the N atom containing donors specially when accompanied by the presence of ether groups (O atoms) and are responsible for stronger complexes of these donors. Polarizability of the organic compounds increases by volume and mass. The 3D-Balaban Index is derived from the geometry distance matrix (hence, a 3D descriptor). The geometry matrix G is a square symmetric matrix where the ijth entry is the Euclidean distance between the ith and the jth atoms. The geometric distance degree is the ith row sum in the geometry matrix G for each i. Index 3 (in J3D) implies the importance of near atoms probably in a functional group for donation site. TIE denotes the E_state of the two atoms connected by a bond. This descriptor is higher in donors like amides and acetamides that contain N and O atoms adjacent to each other. These donors have the highest K CT values. Molecular_volume and Hansen_dispersion are two descriptors which explain weak dispersion interactions. These descriptors can encode polarizability and volume which are responsible for weak interactions of compounds without functional groups like benzene and its derivatives, ethyl iodide, and methyl iodide. Model development and evaluation In QSPR, it is desired to find a multivariate preferably linear relation with accuracy, in the prediction of the desired property. To obtain simple QSPR models, we decided to select among the 206 descriptors obtained from VIP by SR-MLR. Selected descriptors were used to construct both PLSR and MLR models. PLSR has been shown to be an efficient approach in monitoring many complex processes, reducing the high dimensional strongly crosscorrelated data to a much smaller and interpretable set of

8 1254 J IRAN CHEM SOC (2013) 10: principal factors or latent variables. The optimum number of latent variables in the PLSR modeling was found in most cases to be equal to the number of the descriptors in the models. Therefore, it can be concluded that the resulted PLSR models explain completely different sources of variation with the selected descriptors. The results are models with 2 12 descriptors that those with the best statistical characteristics have been collected in Table 3. The predictive ability of the modeling approaches was shown through statistical parameters, i.e. RMSECV, RMSEP, Q 2, and R 2 for both training and test sets in Table 4. It can be seen that the characteristic performances of the models especially for the external test prediction is not good. It must be mentioned that the results of the modeling by PLSR was exactly similar to those of obtained by MLR in the models. Therefore, only the results of PLSR modeling have been reported in Table 4. Even linear PLSR modeling by a 20 descriptors model selected by SR resulted in the statistical characteristics of RMSECV = 0.749, R 2 = 0.840, RMSEP = 1.808, R 2 test ¼ 0:432, Q 2 = Notwithstanding, the improvement of the performances like RMSECV, RMSEP, and R 2 values, the predictivity shown by Q 2 is not yet satisfactory. This may be due to the nonlinear relation between the selected descriptors and K CT. Apparently, the model obtained by 20 Table 4 Statistics of the QSPR models reported in Table 3 No. PLS modeling R 2 (cv) R 2 (test) Q 2 RMSECV RMSEP Table 3 QSPR models obtained by SR among the descriptors reported in Table 2 No. Descriptors in the model a 1 MAXDP g_a 2 MAXDP l_a 3 MAXDP I_a 4 MAXDP Se_a 5 MAXDP LUMO_a 6 MAXDP g_a R4u 7 MAXDP g_a Se_a 8 MAXDP g_a I_a 9 MAXDP g_a l_a 10 MAXDP g_a R4u Mor21m 11 MAXDP g_a R4u HOMO 12 MAXDP g_a R4u R2u 13 MAXDP g_a R4u Mor21m RDF035m 14 MAXDP g_a R4u Mor21m RDF035m R2u 15 MAXDP g_a R4u Mor21m RDF035m R2u LUMO 16 MAXDP g_a R4u Mor21m RDF035m R2u LUMO HD 17 MAXDP g_a R4u Mor21m RDF035m R2u LUMO HD H3m 18 MAXDP g_a R4u Mor21m RDF035m R2u LUMO HD H3m J3D 19 MAXDP g_a R4u Mor21m RDF035m R2u LUMO HD H3m J3D MV 20 MAXDP g_a R4u Mor21m RDF035m R2u LUMO HD H3m J3D MV a Descriptors tailing by _a are related to acceptors

9 J IRAN CHEM SOC (2013) 10: Number of LVs in consecutive RBF-PLS models RMSECV σ Fig. 2 Experimental versus predicted K CT values for calibration (circle) and test sets (triangle) obtained by a RBF PLS 30 descriptor model Fig. 1 Variation of RMSECV with number of LVs and r for optimization with 30 descriptors in RBF PLS modeling descriptors suffers from overfitting (relatively large R 2 for calibration set and low R 2 and Q 2 for test set). Therefore, in the next step, we construct nonlinear models using RBF PLS. Employing descriptors selected by GA, nonlinear models were constructed. First, the training set was selected as the input file for optimization. The lowest RMSECV of and using 23 and 30 descriptors were obtained by LV and r of 11, 0.9, 10, and 0.9, respectively. Figure 1 shows the variation of RMSECV with LV and r for optimization with 30 descriptors. The best statistics obtained for modeling by 23 and 30 descriptors. The models derived were used to predict the K CT in the external test set. The statistics of these two best models are shown in Table 5. Performance characteristics of these models are comparable. As can be inferred from the statistics, the predictivities of the models are good and there are no evidences of overfitting (large Q 2 and low RMSEP). The GA- RBF PLS developed models perform well with respect to both internal and external validation statistics. Figure 2 shows the plot of the predicted versus experimental value of K CT for training and test sets for 30 descriptor model. This plot illustrate that the RBF PLS is a powerful technique for prediction of K CT. The residuals of the RBF PLS calculated values of K CT are plotted against the experimental values in Fig. 3. The Fig. 3 Residuals of K CT prediction obtained by RBF PLS versus experimental K CT values propagation of residuals at both sides of the zero line indicates that no systematic error exists in the development of the RBF PLS model. Superiority of the results of modeling by RBF PLS over those by PLSR and MLR is obvious. From the results, it can be concluded that the nature of the relation between descriptors and K CT, i.e. linear or nonlinear character of the modeling method can be mentioned as the main reason for the great differences between the results of the linear models (MLR and PLSR) and RBF PLS. Therefore, a nonlinear modeling method like RBF PLS is more efficient to show the relation between the selected descriptors with K CT. As can be seen from Tables 3 and 4, the values of Q 2 for the RBF PLS models are and 0.708, which should be compared with corresponding values obtained by PLSR Table 5 Statistics of the two best nonlinear models obtained by RBF PLS Number of descriptors r #LV a R 2 (CV) R 2 (test) Q 2 RMSECV RMSEP a Number of latent variables

10 1256 J IRAN CHEM SOC (2013) 10: modeling reported in Table 4. Comparison of these values indicates that the obtained results by RBF PLS are much better than those obtained using the MLR and PLSR methods. This is believed to be due to the nonlinear capabilities of the RBF PLS. In a previous paper [13], we studied a set of 46 K CT values corresponding to 46 donors with a wide variety in the structure. Eight models with 2 4 descriptors were derived. There is no similarity between the descriptors contained in those models and the ones derived here. Atom or functional groups related descriptors had a major contribution in the models derived previously [13]. However, in the present work the data is comprises of K CT with I 2 and ICl as acceptors and therefore descriptors of these donors have been included in the data. Moreover, we can see descriptors in the present model which can be interpreted as properties of single atoms participating in the charge transfer interactions. Conclusions In this paper, charge transfer complex formation of a diverse set of donors, containing oxygen or nitrogen atoms and some aromatic ether was modeled successfully by MLR, PLSR, and RBF PLS in a QSPR approach. We investigated the parameters affecting the charge transfer complex formation systems through descriptor selection in a reduced population of descriptors by VIP. Descriptors finally incorporated in the models contain information about single atoms or groups of them in the donors. The results obtained reveal the superiority of RBF PLS over the MLR and PLS models. This is due to the ability of the RBF PLS to allow for flexible mapping of the selected features by manipulating their functional dependence implicitly unlike regression analysis. A general QSPR model based on RBF PLS approach was developed for K CT of a diverse set of organic donors using a 30 descriptor model. 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