DOI: 10.1002/minf.201100119

QSPR Study of Valproic Acid and Its Functionalized Derivatives Nieves C. Comelli,*[a] Pablo R. Duchowicz,[a] Rosana M. Lobayan,[b] Alicia H. Jubert,[c] and Eduardo A. Castro[a]

Abstract: This work establishes a Quantitative StructureProperty Relationships (QSPR) based analysis with the aim of interpreting both the structural and electronic properties of the polar region of valproic acid and its derivatives, in terms of stabilizing intramolecular interactions related to the involved substituents. We consider ten different calculated properties as dependent variables for the QSPR models: the bond lengths C8=O9, C8X10, and the percent-

age of s-character of the natural hybrids forming the bonding s orbitals of the O9=C8X10 region. The representative descriptors are the charges transferred during donor/acceptor interactions around this function calculated at the B3LYP/6-311 + + G**(6d,10f) level of theory, and/or hybrid descriptors derived therefrom. The models so established result simple, predictive, and have a quite direct physical meaning.

Keywords: Pauling’s Resonance Theory · QSPR Theory · Valproic Acid · Molecular Descriptors · Atoms in Molecules Theory

1 Introduction Given the remarkable value of valproic acid in the treatment of epilepsies, and its shortcomings in terms of adverse effects – such as weight gain, toxic effects on the liver, and teratogenicity – there is interest in the search for derivatives with improved pharmacokinetic or safety profiles .[1,2] The study carried out by Tasso et al.[3] on a group of amides and esters of valproic acid has demonstrated that such compounds have a pharmacological profile resembling the Phenytoin (PHE). Considering the origin of the biological activity of derivatives of Vpa and the factors that modulate it, from quantitative structure-activity relationship models (QSAR) using different molecular descriptors[4,5] it was stressed the importance of the electronic properties of the C=O group and adjacent atoms in controlling the anticonvulsant behavior. In fact, it is postulated that the manifestation of the activity of Vpa and its derivatives involves initial electrostatic interactions between the C=O group and the receptor active site. From the findings reported and based on the consideration that the receptor site perceives an approaching electronic distribution, as well as that molecules with similar biological activity share certain physicochemical characteristics, we have reported in recent papers[6,7] that the structural and electronic properties of the polar region of valproic acid (Vpa) and its derivatives: propyl valproate (Prvpa), isopentyl valproate (Ispvpa), benzyl valproate (Benvpa), 1-isobutanol valproate (Isbvpa), 1-secbutanol valproate (Secvpa), valpromide (Vpd), N-ethyl valpromide (Etvpd), N-ethylamine valpromide (Etavpd), N-isopropyl valpromide (Ipvpd), N-alphaphenethyl valpromide (Aphvpd), N-benzhydryl valproMol. Inf. 2012, 31, 181 – 188

mide (Bzvpd), N-cyclohexyl valpromide (Chvpd), 4-(valproylamido) benzenesulfonamide (Suvpd), N,N-dimethyl valpromide (Dmvpd) are not able to be rationalized in terms of the Pauling’s Resonance Theory. The molecular structure and nomenclature of the 15 selected compounds are depicted in Figure 1. About the results reported in the literature[6,7] obtained from conformational minima at the B3LYP/6-311 + + G**6d,10f level (Table 1), these predict an irregular change of the geometrical parameters describing the out-of-plane distortion of the O9=C8X10 with the percentage of changes of rC8=O9 and rC8X10. In fact, an increase of t is not accompanied by a regular increase of cC, cX, %DrC8X10 and a decrease of %DrC8=O9 respectively, and the molecules with the most planar carboxylate or amide backbone (Benvpa, t = 0.018 and Aphvpd, t = 0.38) does not show the shortest C8O10 [a] N. C. Comelli, P. R. Duchowicz, E. A. Castro INIFTA, Instituto de Investigaciones Fisicoqumicas Tericas y Aplicadas (CCT La Plata-CONICET) Diag. 113 y 64, C.C. 16, Sucursal 4, 1900 La Plata, Argentina tel.: (+ 54)(221)425-7430/(+54)(221)425-7291; fax: (+ 54) 221 425 4642 *e-mail: [email protected] [b] R. M. Lobayan Facultad de Ingeniera, Universidad de la Cuenca del Plata Lavalle 50, 3400 Corrientes, Argentina [c] A. H. Jubert CEQUINOR, Centro de Qumica Inorgnica, Universidad Nacional de la Plata CC 962, 1900 La Plata, Argentina Supporting Information for this article is available on the WWW under http://dx.doi.org/10.1002/minf.201100119.

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Figure 1. Molecular structure and nomenclature of Vpa and its functionalized derivatives.[1] The same atomic numbering is used for both the polar region of Vpa and the valproyl group appearing in all the drawn structures.

Table 1. Descriptors of the out-of-plane deformation in R1C8(=O9)X10R2R3 and %DrC8 X10 and %DrC8 ¼O9 calculated using as reference values the rC8 X10 and rC8 ¼O9 of molecules with the O9=C8X10 group less distorted in gas phase (angles in degree and distances in ). Data reported were obtained at B3LYP/6-311 + + G**(6d, 10f) level and presented in increasing order of t. Molecules

O9=C8O10 0.01 0.4 0.94 1.25 1.74 4.55 O9=C8N10 0.3 0.48 0.5 0.9 1.1 1.2 1.28 1.55 2.25

Benvpa Ispvpa Secvpa Prvpa Isbvpa Vpa Aphvpd Suvpd Bzvpd Etvpd Etavpd Dmvpd Chvpd Ipvpd Vpd

182

t (8)

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cC (8)

cX (8)

%DrC8 X10 ()

%DrC8 ¼O9 ()

0.01 0.2 1.06 2.08 1.76 0

0.02 1.8 4.73 2.02 5.15 9.1

0 0.1 0.75 0.02 0.38 0.62

0 0 0.66 0.04 0.5 0.21

0.1 0.04 0.6 0.7 0.7 0.3 1.43 1 2.2

5.9 0.19 15.9 6.7 5.9 3.1 0.92 5.7 4.5

0 1.32 0.44 0.22 0.32 0.89 0.01 0.07 0.18

0 0.54 0.18 0.36 0.12 0.19 0.01 0.03 0.66

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QSPR Study of Valproic Acid and Its Functionalized Derivatives

Figure 2. Stabilizing interactions between aliphatic chains and atoms of the polar region of Vpa and its derivatives. The atomic numbering in O9=C8X10 is the same for all the studied structures.

and largest C8=O9 bonds, and vice versa (i.e., the carboxylate or amide group with the less polarized p system does not correspond to the molecule with the most high value of t, cC, cX). In addition, a study on the spatial configuration of the functional groups C8=O9, :10 / > N:10 in relation to the C H/C bonds at the valproyl (R1) and acyl (R2) substituents [(CH/C)R1,R2] has revealed a three-dimensional arrangement of such units located at lower distances than the summation of their van der Waals radii, forming quasi-planar pseudo-rings having 4, 5, and 6 atoms (see Figure 2). From Natural Bonding Orbitals (NBO) calculations, Topological Analysis of the Electronic Localization Function (ELF) and the Atoms in Molecules Theory (AIM) in the literature[6,7] we have determined that in the [O/N/CH)R2…O9/ X10], [(CH)R1…HN10/O10] and [(CH)R1…(HC)R2] subspaces of Vpa and its derivatives there exist stabilizing intramolecular interactions. The existing linear correlation between the interchanged NBO charge in such regions and the structural and electronic properties of the O9=C8X10 region has been attributed to the fact that the observations in O9=C8X10 from Vpa and its derivatives are dependent upon the way the functional groups of valproyl (R1) and acyl (R2) substituents interact with the polar region. Therefore, from the interdependence between the properties of the polar region of Vpa and its derivatives with the interaction between the structural unit that is being modified in the series (acyl substituent) and the group that as a whole is being influenced (valproyl group), we understand that it is possible to quantify such relations through the proposal of Quantitative Structure-Property Relationships (QSPR).[8,9] The Quantitative Structure-Property Relationships (QSPR) are mathematical equations linking compositional, electronic, and steric attributes/descriptors of molecular systems to their biological activity, chemical reactivity and/or physicochemical properties. The QSPR enable to achieve quantitative predictions for the studied property, while the analysis of the information contained in such mathematical relationships enables elucidating the relevant factors affecting the property.[10,11] Mol. Inf. 2012, 31, 181 – 188

The first step during the design of a QSPR model is to find the most relevant molecular descriptor or more than one, that explain the variations of the predicted property. In particular, the electronic effects exhibited by a given substituent on the polarization of a functional group in the molecule can be tested through the quantification of its capacity to attract and retain electrons.[12] In this regard, a substituent can delocalize the electrons of a given functional group by resonance or hyperconjugation.[13] These electronic effects involve specific orbital interactions and have particular associated stereo-electronic requirements (i.e., the interacting orbitals have to be correctly aligned).[14] The electronic effects exerted by a substituent (X) on the properties of a molecular region (QX), this one having a constant electronic demand during the interaction with its environment, can be modeled with the biparametric model proposed by M. Charton.[15,16] QX ¼ Ls IX þ Ds dX þ h

ð1Þ

In Equation 1, sIX represents the inductive or field electronic effect of X, sdX describes the intrinsic resonance effects of X, L and D are adjustable coefficients and h is a generalized intersection point that in most cases measures the precision of the regression. The quantitative description of sIX and sdX can be achieved through any kind of experimental or theoretical observation that is a function of the electronic density of a chemical system.[17] In particular, the NBO method[18] of Quantum Chemistry is a methodology that may offer information on the inductive and resonance electronic effects of X. In a molecular system, the NBO representations enable to differentiate the core orbitals (CR) from: bonding orbitals of s and/or p symmetry; orbitals describing non-bonding electron pairs (n); antibonding orbitals of s and/or p symmetry (s*, p*); additional orbitals of the valence shell of atomic fragments (Rydberg orbitals, Ry*). The values of the off-diagonal elements of the Fock matrix that are associated to the donor/acceptor interaction energies s!s*, p!s*, n!p, p!p*, s!Ry*, etc, may

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be valuable for characterizing the electronic effects of the X substituent. In this work, we are interested in determining the way that the intrinsic electronic effects of R1 and R2 modulate the structural and electronic properties of O9=C8X10 and its derivatives. Therefore, we present QSPR models relating the interchanged charge values during donor/acceptor interactions around this function and ten different structural and electronic calculated properties at the B3LYP/6-311 + + G**(6d,10f) theory level.[19] The present work is organized as follows: in Section 2 we describe the methodological considerations. In Section 3 we analyze and discuss the general results derived from this study. Finally, in Section 4 we draw conclusions.

2 Methodological Considerations The electronic effects of R1 and R2 on O9=C8X10 are assumed to operate by delocalizing the electronic charge by means of some of the following types of orbital interaction: n!p*, p!p* (conjugation) or n!s*, s!s*, s!p*, s! Ry* (hyperconjugation). The quantitative description of these effects can be done from empirical values of properties such as acid dissociation constant (pKa), 13C NMR, values of infrared absorption frequencies, oxidation-reduction potential, dipole moments or capacity to form hydrogen bondig.[20] When the experimental data on a set of molecules is limited, the quantification of substituent effects can be made from information provided by Quantum Chemistry. From this perspective the NBO methodology[18] can provide useful information about the interaction between parts in a molecule. In particular, after obtaining the geometries describing minimum energy conformations in vacuum, we analyzed the electronic interchange between R1, R2 and O9=C8X10 with wavefunctions calculated at the B3LYP/6-311 + + G**(6d,10f) theory level using the program NBO version 3.1[21] implemented in Gaussian03.[22] The value of the charge transferred in each kind of donor/acceptor interaction is estimated using the expres2

sion

hi jF^j*j i Qi!j* ¼ 2 2 , ðe*j ei Þ

where fi and fj* are the elec(i)

tron donor and acceptor orbitals, respectively, ej* and ei their energy, and F^ is the Fock operator.[18] The total charge of O9=C8X10 that is delocalized over the antibonding and and Rydberg orbitals of R1 and R2 is designated as  QO¼CX R1  O¼CX QR 2 (the electron releasing role of O9=C8X10 group is and þ QO¼CX repreindicated with a minus sign). þ QRO¼CX R2 1 sent the charge that the bonding orbitals of R1 and R2 transfer to the orbitals s*, p* and Ry* of O9=C8X10 (the electron withdrawing role of O9=C8X10 group is indicated with a plus sign). þ QpnXO¼C is the conjugation of the non-bonding electron pair of X10 (nX) with the p*C=O orbital. 184

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In this work, ten computed properties are considered as the dependent variables of the QSPR models: the bond lengths rC8 X10 , rC8 ¼O9 and the percentage of s character of the natural hybrids (A) forming the bonding orbitals s (NBO) in O9=C8X10 sANBO , which lead to sCs4CC , sCs8CC , sCs8C¼O , 9 , sCs8CX , sXs10CX , sXs10XC=H , ssC=H . The quantities sANBO measure sOsC¼O XC=H the electronegativity of atoms in O9=C8X10 during their interaction with the nearest environment.[18] The independent variables considered as representative descriptors for the structural and the electronic properties of the O9=C8X10 region and the adjacent groups are the  QO¼CX ,  QO¼CX , R1 R2 þ O¼CX þ O¼CX þ pO¼C QR 1 , QR2 , QnX charges and/or hybrid descriptors derived therefrom. The hybrid descriptors are built as simple algebraic combinations between the charges in order to achieve physical meaning in the so resulting variable, and are included as part of the QSPR whenever these hybrids improve the correlation with the property being modeled. The quality of the established QSPR models is measured with standard statistical parameters: correlation coefficient (R), coefficient of determination (the square of the correlation coefficient, R2), standard deviation (S), and Fisher parameter (F).[8] We choose the models having the lowest S parameter subjected to the condition of a maximum of two regression variables, due to the limited number of data points treated. The search of the most relevant molecular descriptors, and their hybrids, is performed with the Replacement Method (RM),[23,24] a method whose linear regression results have been reported to be comparable to the ones achieved by using a combinatorial (exact) search of descriptors. Respect to the development procedure of QSPR model, we choose an optimal subset dm = {Xm1, Xm2, . . Xmd} of d descriptors from a large set D = {X1,X2, . . XD} of D ones (d < D) provided by some available commercial program, with a minimum standard deviation (S). Notice that S(dm) is a distribution on a discrete space of D!/d!(Dd)! disordered points dm. The full search (FS) that consists of calculating S(dm) on all those points always enables us to arrive at the global minimum, but it is computationally prohibitive if D is sufficiently large. From RM, the development procedure of QSPR model consists of the following steps:[25,26]

(ii)

We choose an initial set of descriptors dk at random, replace one of the descriptors, say Xki, with all the remaining Dd descriptors, one by one, and keep the set with the smallest value of S. This is one step of the procedure. In the resulting set, we choose the descriptor with the greatest standard deviation in its coefficient and substitute all the remaining Dd descriptors, one by one, for it. We repeat this procedure until the set remains unmodified. In each cycle we do not modify the descriptor optimized in the previous one. Thus, we obtain the candidate dm(i) that came from the so-con-

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QSPR Study of Valproic Acid and Its Functionalized Derivatives

structed path i. It is worth noting that if the replacement of the descriptor with the largest error by those in the pool does not decrease the value of S, then we do not change that descriptor. (iii) We carry out the process above for all the possible paths i = 1,2, . .,d and keep the point dm with the smallest standard deviation: min Sðd ðiÞ m Þ. i

The design of a QSPR model involves both calibration and validation stages. While from the calibration stage one usually finds a quantitative relationship for predicting the property, the validation reveals whether the model results meaningful, that is to say, it enables to check the predictive power. In our analysis, the best linear regressions are found through the RM by fitting the properties of 13 molecules composing the calibration set: Vpa, Vpd, Dmvpd, Ipvdp, Etavpd, Aphvpd, Bzvpd, Ispvpa, Benvpa, Isbvpa y Secbvpa, while the predictive power is measured on the test set

composed of Etvpd and Prvpa. We choose such test set molecules as their structural characteristics at the hydrophobic region are representative of most molecules under analysis. In addition, we validate our QSPR equations by means of the well-known Leave-One-Out (loo) Cross Validation technique.[27]

3 Results and Discussion We report in Table 2 the numerical values of total charge ,  QRO¼CX , transferred predicted in vacuum:  QO¼CX R1 2 þ O¼CX þ O¼CX þ pO¼C QR 1 , QR2 , QnX . The different types of donor/acceptor interactions found in Vpa and its derivatives appear summarized in Table 1S of Supporting Information. In Table 3 we present the correlation matrix for evaluating the interrelatedness degree between the different varia-

Table 2. Charges  QO¼CX ,  QO¼CX , þ QO¼CX , þ QO¼CX , þ QpnXO¼C obtained with wave functions calculated at the B3LYP/6-311 + + G**(6d,10f) R1 R2 R1 R2 theory level (in vacuum). Compound

Molecular descriptors 

Benvpa Ispvpa Secvpa Prvpa Isbvpa Vpa Aphvpd Suvpd Bzvpd Etvpd Etavpd Dmvpd Chvpd Ipvpd Vpd



QO¼CX R1

0.06014 0.06015 0.05783 0.06031 0.05784 0.06621 0.06671 0.06481 0.06733 0.06789 0.06713 0.06539 0.06701 0.06596 0.06931

þ

QO¼CX R2

0.03219 0.03400 0.04952 0.03331 0.04611 0.00299 0.03882 0.22612 0.04697 0.04121 0.03958 0.08485 0.03893 0.04180 0.00077

þ

QO¼CX R1

0.04519 0.04377 0.04486 0.04470 0.04721 0.04004 0.04084 0.03994 0.04092 0.03810 0.04038 0.03924 0.04103 0.04021 0.03803

þ

QO¼CX R2

0.00918 0.01114 0.00971 0.01121 0.00921 0.00942 0.01935 0.01970 0.02097 0.02421 0.01826 0.02659 0.02109 0.02217 0.00809

QpnXO¼C

0.22092 0.22484 0.24713 0.21702 0.21702 0.19755 0.28489 0.32000 0.29902 0.30420 0.36735 0.00852 0.34818 0.25383 0.25383

Table 3. Correlation matrix obtained with the different variables analyzed and calculated in vacuum. Variable





1 0.04 0.93 0.56 0.29 0.79 0.53 0.75 0.81 0.18 0.14 0.75 0.88 0.47 0.42

QRO¼CX 1 QRO¼CX 2 þ O¼CX QR1 þ O¼CX QR2 þ pO¼C QnX rC8 X10 rC8 ¼O9 4 sCsCC 8 sCsCC C8 ssC¼O 9 sOsC¼O 8 sCsCX sXs10CX sXs10CX=H sC=H sXC=H 

QO¼CX R1



QO¼CX R2

1 0.11 0.38 0.07 0.53 0.22 0.19 0.19 0.18 0.15 0.24 0.16 0.49 0.32

Mol. Inf. 2012, 31, 181 – 188

þ

QO¼CX R1

1 0.59 0.12 0.82 0.5 0.68 0.74 0.32 0.29 0.71 0.85 0.42 0.43

þ

QO¼CX R2

1 0.04 0.72 0.82 0.85 0.76 0.55 0.5 0.81 0.64 0.75 0.4

þ

QpnXO¼C

rC8 X10

rC8 ¼O9

sCs4CC

1 0.09 0.14 0.35 0.39 0.73 0.78 0.3 0.3 0.55 0.11

1 0.57 0.71 0.74 0.43 0.38 0.74 0.78 0.6 0.14

1 0.93 0.86 0.51 0.45 0.91 0.78 0.78 0.33

1 0.97 1 0.34 0.26 1 0.27 0.19 1 1 0.98 0.99 0.38 0.31 1 0.89 0.95 0.3 0.24 0.93 1 0.86 0.86 0.08 0.0046 0.86 0.71 1 0.21 0.08 0.11 0.07 0.16 0.18 0.49 1

8 sCsCC

sCs8C¼O

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9 sOsC¼O

sCs8CX

sXs10CX

sXs10XC=H

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sC=H sXC=H

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bles used in the linear regressions ( QO¼CX ,  QO¼CX , R1 R2 þ O¼CX þ O¼CX þ pO¼C C4 C8 9 QR 1 , QR2 , QnX , rC8 X10 , rC8 ¼O9 , ssCC , ssCC , sCs8C¼C , sOsC¼C , sCs8CX , sXs10CX , sXs10XC=H , ssC=H ). With exception to the XC=H  O¼CX QR 1  þ QO¼CX pair, which involves correlated variables R1 and (R = 0.93), the low linear correlation of  QRO¼CX 1 þ O¼CX QR 1 with  QO¼CX , þ QO¼CX and þ QpnXO¼C (R < 0.7, see R2 R2 Table 3) suggests that such kind of descriptors would result of value for the analysis. The correlation between the regressor variables and the ten molecular properties of Table 3, reveals a one-descriptor interdependence (R > 0.7) between the properties rC8 X10 , sCs4CC , sCs8CC , sCs8CX , sXs10CX and the and þ QO¼CX . We interpret that such redescriptors þ QRO¼CX R2 1 sults suggest the need to generate one-descriptor models or the proposal of hybrid descriptors for these properties. An interesting result extracted from Table 3 stands for the correlation values R < 0.7 between þ QpnXO¼C and rC8 X10 /rC8 ¼O9 . Such predictions reveal the reduced importance of using þ QpnXO¼C for the design of one-descriptor models for rC8 X10 and rC8 ¼O9 with a good significance level. This fact, that in other words indicates that the structural properties in O9=C8X10 are not correlated with the conjugation of nX in the p system, corroborates, once more, that the Pauling’s Resonance model is not sufficient for interpreting the structural changes at the polar region of Vpa and its derivatives. The regression equations for the theoretical properties rC8 X10 , rC8 ¼O9 , sCs4CC , sCs8CC , sCs8CX , sXs10CX , sXs10XC=H , ssC=H are presented XC=H in Table 4 (see Equations 1–4; 7–10). The values in parentheses indicate the absolute error of the regression coefficients; F is the Fisher test parameter; and Rloo2 and Sloo are the coefficient of determination and standard deviation as obtained from Leave-One-Out. Values of Rloo2 (and Sloo) close to R2 (and S) confirm the predictive character of the QSPR theoretical predictions. For the case of the mentioned properties, the statistical analysis demonstrates in Table 4 satisfactory correlations (R2  0.757, S < 1.917, F > 15.6), ob-

tained by using the charges  QO¼CX ,  QO¼CX , þ QRO¼CX , R1 R2 1 O¼CX QR 2 as regressor variables. The plots of predicted properties as function of actual values tend to follow a straight line trend throughout all the series of compounds, without the occurrence of outliers (molecules whose absolute residual exceed the value of two times of S). The residuals plots reveal that the descriptors used in the QSPR models of Table 4 lead to a random distribution. Table 5 includes the values for the ten observed properties, together with their QSPR predictions and residuals. The statistical quality obtained for the regression models given by Equations 1–4 and 7–10, and the fact that the ,  QO¼CX , þ QO¼CX describe in charge descriptors  QO¼CX R1 R2 R2 average a 90 % of the properties rC8 X10 , rC8 ¼O9 , sCs4CC , sCs8CC , ratify our corollary that the structural sCs8CX , sXs10CX , sXs10XC=H , ssC=H XC=H and electronic properties of Vpa and its derivatives are dependent upon the existing connectivity degree between the functional groups of valproyl and acyl substituents with the polar region. 9 properties, the definiFor the case of the sCs8C¼O and sOsC¼O tion of hybrid descriptors by using þ QO¼CO=N and þ QpnXC¼O reR2 sults very useful for the design of acceptable QSPR models (0.974  R2  0.986, 1.123  S  1.223; 426.4  F  747.0). According to Table 4, the þ QO¼CO=N =þ QpnXC¼O hybrid in EquaR2 tions 5–6 explains the s character of natural orbitals ob8 9 , sOsC¼O ). The absence of tained from the sC=O NBO (sCsC¼O Leave-One-Out parameters for such properties is due to the occurrence of linear dependencies during the removal of molecules through the application of this technique on such small dataset. However, this does not constitute a limitation, as the Cross Validation process is not considered as a real validation process but a condition that a model should fulfill whenever the size of the dataset enables the application of the loo procedure. Equations 5–6 reveal that the C=O bond polarization changes with the intrinsic ability of the bonding orbitals of þ

Table 4. QSPR models for the chemical and structural properties at the polar region in Vpa and its derivatives. Geometries are obtained in vacuum. R2

N8 QSPR equations h

i

h

i

þ 5:770ð0:6Þ  QO¼CX þ 1:227ð0:01Þ þ QO¼CX rC8 X10 ¼ 2:032ð0:2Þ  QO¼CX R1 R2 R2 h i h i þ O¼CX þ O¼CX 4 5  O¼CX  O¼CX 2 rC8 ¼O9 ¼ 1:550ð0:2Þ QR1 þ 1:9  10 ð5:1  10 Þ QR1 þ 1:135ð0:01Þ þ QR2 = QR2 h i h i C4  O¼CX þ pC¼O þ 1:345ð0:5Þ QnX þ 22:803ð0:2Þ 3 ssCC ¼ 47:011ð7:3Þ QR1 h i h i 4 sCs8CC ¼ 201:991ð65:8Þ  QO¼CX þ 101:419ð39:9Þ þ QO¼CX þ 52:319ð3:9Þ R1 R2 h i C8 þ O¼CX þ pC¼O = QnX þ 32:484ð0:4Þ 5 ssC¼O ¼ 8:575ð0:4Þ QR2 h i O9 þ O¼CX þ pC¼O = QnX þ 39:765ð0:3Þ 6 ssC¼O ¼ 10:421ð0:4Þ QR2 h i C8  O¼CX þ O¼CX þ 13:962ð2:6Þ þ QR2 7 ssCX ¼ 197:495ð32:9Þ QR1 h i h i  1:578ð0:1Þ  QO¼CX þ 41:492ð0:7Þ = QO¼CX =þ QO¼CX 8 sXs10CX ¼ 0:122ð0:01Þ  QO¼CX R1 R2 R1 R2 h i h i X10  O¼CX þ O¼CX þ O¼CX þ þ 11:571ð23:1Þ QR1 =1000 þ 16:487ð2:0Þ þ QnX  QO¼CX 9 ssXC=H ¼ 23:615ð5:2Þ QR2 R2 h i h i C=H þ O¼CX  O¼CX þ O¼CX þ 0:105ð0:01Þ QR1 þ 4:005ð0:4Þ = QR2 10 ssXC=H ¼ 73:818ð10:2Þ QR1 1

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Rloo2

S

Sloo

F

0.958 0.914 0.0025 0.004 120.5 0.826 0.642 0.0031 0.005

24.0

0.824 0.591 0.161

0.257

23.6

0.757 0.466 0.769

1.214

15.6

0.974

1.223

–

426.4

0.986

1.123

–

747.0

0.766 0.704 1.023

1.155

36.1

0.929 0.850 0.755

1.115

65.7

0.850 0.741 1.917

2.581

28.4

0.893 0.755 0.092

0.164

42.0

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QSPR Study of Valproic Acid and Its Functionalized Derivatives

ces[6,7] on the role of the additional hyperconjugative or polar effects of R1 and R2 on the polarization and structural properties of the O9=C8X10 function. Regarding the electronic effects on R1 according to the occurring ones at R2 (Equation 3 from Table 4), and the variable for the description of need to consider the þ QRO¼CX 2 the ssC=H property (Equation 10 from Table 4), it is possible XC=H to conclude that such equations also indicate the way the electronic effects of substituents are transmitted throughout the O9=C8X10 electronic system. In fact, the regression Equations 3 and 10 provide a statistical support to sCs4CC and þ O¼CX QR2 and þ QO¼CX respectively (0.824  sC=H s XC=H based on R1 2 R  0.893). We understand that such relationships reveal that the electronic effects of the valproyloxy and/or valproylamido group is dependent of the electronic effects of R2 which are manifested according to the electronic demand of the molecular environment that this group connects. This last interpretation enables to justify another anticipated conclusion from our previous study:[6,7] the activa-

R2 to donate electrons into the p system, apart from the nX delocalization into p*C=O. This last transfer, represented by nX !p*C=O, is in theory subjected to the condition of the hybridization degree of X10 atom in O9=C8X10 group. As in Table 3, 0.3  R  0.55 between sXs10CX , sXs10XC=H and þ QpnXC¼O and  þ QO¼CX , we unR > 0.6 between sXs10CX , sXs10XC=H and  QO¼CX R1 R2 derstand that the hybridization of the X10 atom and the nX !p*C=O conjugation depend of the intrinsic ability of the NBO of R1 and R2 substituents to act as electron donor or acceptor of the electronic density of O9=C8X10. This explicit dependence appears described by the models of Equations 8 and 9 (Table 4), which define sXs10CX and sXs10XC=H in ,  QO¼CX and þ QO¼CX . terms of  QO¼CX R1 R2 R2 With all the previous relationships for the electronic properties of the C8=O9 and C8X10 bonds which depend upon the intrinsic ability of the bonding orbitals of R2 to donate electrons into the O9=C8X10 electronic system and and  QO¼CX , we recognize the charges transferred  QRO¼CX R2 1 evidences that corroborate our assumptions in Referen-

9 Table 5. Observed values for rC8 X10 , rC8 ¼O9 , sCs4CC , sCs8CC , sCs8C¼O , sOsC¼O , sCs8CX , sXs10CX , sXs10XC=H , sC=H sXC=H for molecules calculated in vacuum, together with QSPR predictions.

Compound Benvpa Ispvpa Secvpa Prvpa Isbvpa Vpa Aphvpd Suvpd Bzvpd Etvpd Etavpd Dmvpd Chvpd Ipvpd Vpd Compound Benvpa Ispvpa Secvpa Prvpa Isbvpa Vpa Aphvpd Suvpd Bzvpd Etvpd Etavpd Dmvpd Chvpd Ipvpd Vpd

sCs4CC

rC8 ¼O9

rC8 X10

sCs8CC

sCs8C¼O

Obs.

Pred.

Dif.

Obs.

Pred.

Dif.

Obs.

Pred.

Dif.

Obs.

Pred.

Dif.

Obs.

Pred.

Dif.

1.3533 1.3520 1.3431 1.3530 1.3481 1.3616 1.3647 1.3827 1.3707 1.3676 1.3690 1.3768 1.3649 1.3657 1.3671

1.3508 1.3513 1.3471 1.3515 1.3468 1.3615 1.3667 1.3842 1.3693 1.3706 1.3674 1.3727 1.3677 1.3662 1.3677

0.0025 0.0007 0.0040 0.0014 0.0013 0.0001 0.0021 0.0016 0.0014 0.0029 0.0016 0.0041 0.0029 0.0006 0.0006

1.2167 1.2167 1.2247 1.2163 1.2228 1.2142 1.2323 1.2256 1.2301 1.2279 1.2308 1.2346 1.2321 1.2319 1.2242

1.2196 1.2204 1.2198 1.2220 1.2227 1.2159 1.2286 1.2275 1.2312 1.2319 1.2262 1.2372 1.2316 1.2320 1.2238

0.0029 0.0037 0.0049 0.0057 0.0001 0.0017 0.0036 0.0019 0.0011 0.0040 0.0046 0.0025 0.0005 0.0001 0.0004

23.45 23.49 23.56 23.45 23.49 23.38 24.22 23.95 24.14 24.16 24.24 24.12 24.27 24.22 23.90

23.53 23.63 23.59 23.62 23.53 23.51 24.10 24.16 24.19 24.35 24.16 24.06 24.26 24.19 23.52

0.08 0.14 0.03 0.17 0.04 0.13 0.12 0.21 0.05 0.19 0.08 0.06 0.01 0.03 0.38

39.38 39.29 39.14 39.28 39.45 39.91 36.53 37.11 36.55 36.48 36.62 37.16 36.36 36.49 36.55

39.24 39.04 39.65 39.00 39.70 37.99 36.88 37.23 36.59 36.15 36.91 36.41 36.64 36.75 37.50

0.14 0.25 0.51 0.28 0.25 1.92 0.35 0.12 0.04 0.33 0.29 0.75 0.28 0.26 0.95

33.33 33.35 32.62 33.34 32.32 34.03 30.44 32.36 31.44 30.86 32.21 5.77 31.66 29.48 30.96

32.13 32.06 32.15 32.04 32.12 32.08 31.90 31.96 31.88 31.80 32.06 5.73 31.96 31.74 32.21

1.20 1.29 0.47 1.30 0.20 1.95 1.46 0.40 0.44 0.94 0.15 0.04 0.30 2.26 1.25

9 sOsC¼O

sCs8CX

sXs10CX

sXs10XC=H

ssC=H O=NC=H

Obs.

Pred.

Dif.

Obs.

Pred.

Dif.

Obs.

Pred.

Dif.

Obs.

Pred.

Dif.

Obs.

Pred.

Dif.

40.40 40.37 39.67 40.06 39.02 39.99 37.84 40.23 38.96 38.53 40.06 7.28 39.32 36.59 37.94

39.33 39.25 39.36 39.23 39.32 39.27 39.06 39.12 39.03 38.94 39.25 7.25 39.13 38.86 39.43

1.07 1.12 0.31 0.83 0.30 0.72 1.22 1.11 0.07 0.41 0.81 0.03 0.19 2.27 1.49

27.41 27.47 27.98 27.39 27.63 26.34 31.48 30.64 31.28 31.38 31.30 31.45 31.60 31.51 30.95

27.65 28.04 27.30 28.09 27.20 28.90 30.96 30.65 31.40 32.15 30.83 32.13 31.36 31.37 29.25

0.24 0.57 0.68 0.70 0.43 2.56 0.52 0.01 0.12 0.77 0.47 0.68 0.24 0.14 1.70

31.96 32.25 33.15 32.14 32.46 33.14 37.29 36.98 37.05 37.56 37.66 37.07 37.12 37.32 39.55

31.83 33.64 32.69 33.68 32.19 33.55 36.71 36.79 37.05 37.72 36.35 38.16 37.14 37.44 39.46

0.13 1.39 0.46 1.54 0.27 0.41 0.58 0.19 0.00 0.16 1.31 1.09 0.02 0.12 0.09

27.27 28.22 28.96 28.30 27.72 21.21 34.45 37.07 34.51 34.72 34.87 30.47 35.26 35.05 29.54

27.26 28.24 28.53 28.20 27.73 25.59 33.28 38.49 34.59 35.32 34.63 30.76 35.64 33.78 26.06

0.01 0.02 0.43 0.10 0.01 4.38 1.17 1.42 0.08 0.60 0.24 0.29 0.38 1.27 3.48

1.29 1.29 1.25 1.29 1.29 2.00 1.33 1.44 1.33 1.36 1.36 1.37 1.33 1.34 2.00

1.36 1.34 1.32 1.27 1.18 1.79 1.35 1.40 1.32 1.49 1.41 1.37 1.31 1.35 2.10

0.07 0.06 0.07 0.02 0.11 0.21 0.02 0.04 0.01 0.12 0.05 0.00 0.02 0.01 0.10

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187

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N. C. Comelli et al.

tion of electronic effects of R1, O9, C8 and X10 and the polarization of bonds in O9=C8X10 are dependent upon the way R2 interacts with this region.

4 Conclusions In this work, we develop QSPR models for the structural and electronic properties of valproic acid and its derivatives in vacuum, using as structural descriptors the interchanged charges during donor/acceptor interactions between the valproyl, acyl, and the O9=C8X10 group. These relationships are validated with some test set compounds, and LeaveOne-Out Cross Validation is applied whenever it results possible. The QSPR models established reveal the important role of electronic effects of R1 and R2 on different properties of the polar region in Vpa and its derivatives, and allow affirming that the electronic effects of R1, O9, C8 and X10 and the polarization of bonds in O9=C8X10 are dependent upon the way R2 interacts with this region.

Acknowledgements We gratefully acknowledge the financial support provided by Consejo Nacional de Investigaciones Cientficas y Tcnicas (CONICET), Facultad de Ciencias Exactas, Universidad Nacional de La Plata and Facultad de Ciencias Agrarias, Universidad Nacional de Catamarca. R. M. L. acknowledges Universidad de la Cuenca del Plata for facilities provided during the course of this work.

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Received: August 18, 2011 Accepted: December 19, 2011 Published online: February 8, 2012

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