Quantitative structure–reactivity study on sulfonation of amines, alcohols and phenols

Abolghasem Beheshti; Hamid Mohammad Shiri; Hadi Farahani; Ali Mohajeri

doi:10.1016/j.arabjc.2013.10.009

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Original article

10 (

2_suppl

); S2659-S2667

doi:

10.1016/j.arabjc.2013.10.009

Quantitative structure–reactivity study on sulfonation of amines, alcohols and phenols

Abolghasem Beheshti^{^a}, Hamid Mohammad Shiri^{^b,⁎}, Hadi Farahani^{^c}, Ali Mohajeri^{^a}

a Solvent Management Laboratory, Gas Research Division, Research Institute of Petroleum Industry (RIPI), Tehran, Iran

b Department of Chemistry, Payamenoor University, Tehran, Iran

c Research Institute of Petroleum Industry (RIPI), Tehran, Iran

⁎Corresponding author. Tel.: +98 2161112788. hmohammadshiri@yahoo.com (Hamid Mohammad Shiri)

Received: 2012-10-29, Accepted: 2013-10-8, Published: 2013-05-01

Disclaimer:
This article was originally published by Elsevier and was migrated to Scientific Scholar after the change of Publisher.

Peer review under responsibility of King Saud University.

Abstract

Quantitative structure–reactivity relationship (QSRR) can be considered as a variant of quantitative structure property relationship (QSPR) studies, where the chemical reactivity of reactants in a specified chemical reaction is related to chemical structure. As follows, the sulfonation reaction yield of 24 amines, alcohols and phenols with sulfonyl chloride was studied by QSRR. Quantum chemical calculations (b3lyp/6-31+g (d)) were carried out to obtain the optimized geometry. The suitable set of molecular descriptors was calculated to represent the molecular structures of compounds, such as constitutional, topological, geometrical, electrostatic and quantum-chemical descriptors. The genetic algorithm (GA) was applied to select the variables that resulted in the best-fitted models. After the variable selection, multiple linear regression (MLR) was utilized to construct linear QSRR models. The maximum relative error in prediction (5.26) showed that the predictive ability of the model was satisfactory and it can be used for designing similar reactants with efficient sulfonation reaction.

Keywords

Quantitative structure–reactivity relationship

Sulfonation reaction

Quantum chemical calculations

Synthesis

Reaction yield

Show Related Articles from PubMed

1 Introduction

Sulfonamides are an important category of pharmaceutical compounds with a broad spectrum of biological activities. Sulfonamides drugs have broad applications in many areas of clinical medicine. Examples for recently approved drugs with a sulfonamide structure are the antihypertensive agent bosentan (Wu et al., 2001), the antiviral HIV protease inhibitor amprenavir (Clercq, 2001), and the phophodiesterase-5 inhibitor sildenafil (Rotella, 2002). In addition, numerous sulfonamide derivatives have been used in preclinical development. The sulfonamide partial structure appears to belong to the so-called “privileged structures” in medicinal chemistry (Evans et al., 1998), and it exhibits favorable pharmacokinetic properties including metabolic stability.

Furthermore, sulfonamides have been used as protecting groups of OH or NH functionalities for easy removal under mild conditions. Thus, there are significant demands by the pharmaceutical industry for cost, efficient and environmentally friendly procedures for the synthesis of these valuable compounds. The search for general, efficient synthesis of sulfonamides under mild conditions is of continuing interest for organic chemists. There are various synthetic methods for the preparation of sulfonamides (Gareau et al., 2003; Greenfield and Grosanu, 2008; Shaabani et al., 2007; Ozbek et al., 2007; Jafarpour et al., 2010; Meshram and Vishvanath, 2009 ), in which the most traditional method is usually performed by reacting an amine with a substituted sulfonyl chloride or anhydride often in the presence of a buffering base in an aprotic solvent. Although recently many efforts have been put into the development of novel sulfonamide synthesis, the conventional synthesis from amino compounds and sulfonyl chlorides is still the method of choice because of the reactivity and simplicity. The yields are variable, but can be improved by optimization. While satisfactory in a laboratory environment, most of the current protocols suffer on a larger scale when reaction efficiency is important or when applied in a parallel synthesis format when simplicity and generality are more valuable.

The use of computational methods for designing of molecules with desired activity, reactivity or property has been a growing area in chemistry and medicine. The efficient way to obtain a complete set of the data, without necessity of performing expensive laboratory experiments is the application of the quantitative structure–activity relationship (QSAR) techniques. In recent years, the concept of ‘benign by design’ has been stressed by the regulatory agencies which require chemical manufacturers to use environmentally safer chemicals. However, replacing chemicals already available on the market, with an equally useful, but “green” compound, is a daunting task. The goal is to design novel and benign compounds, with better chemical and physical properties, starting from the early stage of synthesis. New chemicals with better chemical and mechanical properties must also be tested for environmental pollution and animal toxicity. To achieve this goal, chemical, structural and toxicological information of the studied compounds can be referenced, while the toxicity of newer compounds, for which no data are available, can be predicted. Quantitative structure–activity relationships as emerging computational techniques in chemistry are mathematical equations relating chemical structure to a wide variety of physical, chemical, biological, and technological properties (Manish et al., in press; Nitendra et al., in press; Beheshti et al., 2012a,b; Riahi et al., 2009 ). The QSAR model, once established can be used to predict properties of compounds as yet unmeasured or even unknown. By the use of different chemometrics methods, a reasonable relationship between chemical property and structural parameters is discovered, by which chemists can obtain a deeper knowledge about the chemical system under study in one hand and predicting the chemical property of interest for new or even non-synthesized molecules on the other hand. This leads to the design of molecules with optimized property, activity or reactivity. Quantitative structure–reactivity relationship (QSRR) can be considered as a variant of QSPR studies, where the chemical reactivity of reactants or catalysts in a specified chemical reaction is related to chemical structure (Nigan and Klien, 1993; Wilcox and Carpenter, 1979; Korre and Klein, 1996; Tshuva et al., 2001; Hemmateenejad et al., 2009 ).

Design of sulfonation reaction with high efficiency is an important research in organic chemistry. In this way, a large number of reactants do not represent desirable yield in sulfonation reaction. Therefore resources and time are wasted during the discovery of efficient sulfonation reaction. Thus, computational methods are now becoming the expedite source of introducing a high yield sulfonation reaction. In this study for the first time, a continuation of our earlier studies (Beheshti et al., 2009, 2012a,b; Riahi et al., 2009 ), a series of amines, alcohols and phenols that reacted with sulfonyl chloride were subjected to structure–reactivity relationship, quantitatively.

2 Computational section

2.1

2.1 Quantum chemical calculations and data preparing

A large number of the alcohols, phenols, and the primary and secondary amines were sulfonylated in the presence of copper oxide in CH3CN solvent (Scheme 1). The QSRR study for the estimation of the sulfonation reaction yield is established. The data set was taken from the literature (Meshram and Vishvanath, 2009). The compounds are shown in Table 1. A common problem in QSRR modeling is choosing a proper description of the variance between the individual molecular structures within a set of compounds. The choice is very important for groups of structurally similar congeners (‘congeners’ are defined as compounds having the same carbon skeleton but differing substitution patterns). Because the compounds in these groups are highly similar, the relative differences between the descriptor values for the data set are so small. Since the descriptors must be determined as precisely as possible, quantum chemical calculation was chosen to calculate the descriptors. The chemical structures of the studied molecules were drawn with Hyperchem software (http://www.Hyper.com). All the calculations were carried out by Gaussian 98 (Frisch et al., 1998). Density functional theory (DFT) method B3LYP was selected to calculate gas-phase energies. The complete geometric optimizations and frequency calculations were performed at the level of B3LYP employing 6-31+g (d) basis set. The quantum chemical descriptors were calculated for each molecule is described in Table 2. The calculated descriptors can be classified into four different electronic categories including: local charges, dipoles, orbital energies and the quantum chemical indices of hardness (η), softness (S), electro-negativity (χ), and electrophylicity (ω), were calculated according to the previously introduced method (Thanikaivelan et al., 2000), which are the important electronic features used to describe stability, reactivity, chemical potential and other related properties of molecules (Hemmateenejad et al., 2009). Hardness has been used to understand chemical reactivity and stability of molecules (Parr and Pearson, 1983; Parr and Chattaraj, 1991). Electronegativity was introduced by Pauling as a power of an atom in a molecule to attract electron to it. Softness is a property of molecule that measures the extent of chemical reactivity. Electrophilicity was proposed (Parr et al., 1992) as a measure of energy lowering due to maximal electron flow between donor and acceptor. For more comprehensive investigation 6 different types of theoretical descriptors for each molecule were calculated utilizing CODESSA version 2.7.15 (http://www.codessa-pro.com). They included; constitutional, topological, geometrical, electrostatic, thermodynamic and quantum-chemicals descriptors (Table 2).

Table 1 Eexperimental and calculated sulfonation reaction yields of amines, alcohols and phenols with sulfonyl chloride.

No.	SY_Exp.	SY_Cal.	RE %
1	88	90.326	2.64
2	86	88.449	2.85
3	84	86.502	2.98
4	87	86.161	−0.96
5	88	88.608	0.69
6	85	83.09	−2.25
7	75	76.923	2.56
8	83	81.855	−1.38
9	92	91.722	−0.30
10	90	90.115	0.13
11	92	92.063	0.07
12	91	91.046	0.05
13	80	79.57	−0.54
14	87	88.347	1.55
15	90	89.149	−0.95
16	50	Excluded
17	92	87.157	−5.26
18	88	87.908	−0.10
19	87	85.761	−1.42
20	85	84.64	−0.42
21	70	70.609	0.87
22_Te	92	90.999	−1.09
23_Te	70	73.596	5.14
24_Te	83	80.393	−3.14
25_Te	82	79.518	−3.03
26_Te	86	86.09	0.10

Te; Test set.

Table 2 List of used descriptors for QSRR models.

No	Notation	Definition
List of descriptors were obtained from Gaussian output file
1	TDM	Total dipole moment
2	MNQ	Maximum of negative charges
3	SNQ	Sum of negative charges
4	ANQ	Average of negative charge
5	MPQ	Maximum of positive charges
6	SPQ	Sum of positive charges
7	APQ	Average of positive charge
8	RMSENQ	Root mean square error of negative charges
9	RMSEPQ	Root mean square error of positive charges
10	RMSETQ	Root mean square error of total charges
11	HOMO	Highest occupied molecular orbital
12	LUMO	Lowest unoccupied molecular orbital
13	η	Hardness
14	μ	Chemical potential
15	S	Softness
16	ω	Electrophilicity
17	χ	Electronegativity

Descriptor categories of CODESSA Pro software
18	Constitutional
19	Geometrical
20	Thermodynamical
21	Topological
22	Electrostatic
23	Quantum chemical

2.2

2.2 Descriptor selection

The calculated structural descriptors were collected in a (n × m) data matrix, where n and m represent the number of compounds and descriptors, respectively, and a column vector (y) of size m, whose elements were the yield of sulfonation reaction (Y).The calculated structural descriptors and the experimental sulfonation reaction yield values were analyzed with the aid of genetic algorithm multivariate linear regression (GA-MLR). Genetic algorithms (GAs) were introduced by Holland, and mimic nature’s evolutionary method of adapting to a changing environment (Holland, 1975). They are stochastic optimization methods and provide a powerful means to perform directed random searches in a large problem space as encountered in chemometrics and drug design. Each individual in a population is represented by a chromosome. After initialization of the first generation (step 1), the fitness of each individual is evaluated by an objective function (step 2). In the reproduction step (step 3), the genetic operators of parent selection, crossover and mutation are applied, thereby providing the first offspring generation. Iteration of steps 2 and 3 is performed until the objective function converges [21]. Multiple linear regression is one of the most used modeling methods in QSRR. According to Todeschini et al. (2004), the best fitness function, leave-one-out cross-validated correlation coefficient ( $Q_{LOO}^{2}$ ), was used as criteria for evaluating the credibility of each model. However, in MLR analysis the number of compounds in samples should be at least five times greater than the number of descriptors, and of course, the descriptors should be orthogonal (Tropsha et al., 2003). In order to minimize the information overlap in descriptors and to reduce the number of descriptors required in the regression equation, the concept of non-redundant descriptors was used in our study. The MLR method provided an equation linking the structural features to the yield values of the reaction:

(1)

Y = a_{0} + a_{1} x_{1} + \dots + a_{n} x_{n}

where the intercept (a₀) and the regression coefficients of the descriptors (a_i) are determined using the least-squares method. x_i has the common definition-variable or descriptor in this case. The elements of this vector are equivalent numerical values of the chemical descriptors. When the regression analysis is completed, the best models were chosen.

3 Results and discussion

3.1

3.1 QSRR model validation

Researchers (Meshram and Vishvanath, 2009) used a wide variety of compounds; aromatic amines, primary and secondary amines, alcohols and phenols to investigate the reaction with sulfonyl chloride in the presence of cupric oxide at room temperature. The yields of reactions are summarized in Table 1. As it is shown, the sulfonation reaction yields are varied between 50 and 92 by changing the substrates and their derivatives. It is important to note that the distribution of the reaction yield is not uniform. Compound O5 is isolated from other compounds in that it has a significant lower yield value in reaction with sulfonyl chloride (the yield values decrease uniformly from 92 until 70, but this value for O5 compound jumps to 50). Note that an isolated datum has a marked influence on the regression; the removal of such a chemical would completely change the model (Riahi et al., 2009). To investigate the effect of molecular structure on efficiency of sulfonation reaction, quantitative structure–reactivity relationship method was applied. Application of GA-MLR on the data comprising reaction yield as dependent variables and the calculated molecular descriptors as predictor variables resulted in the following equation:

(2)

Yield = 687.963 (\pm 72.056) - 0.869 (\pm 0.142) YZ Shadow + 0.101 (\pm 0.014) PPSA- 1 + 0.166 (\pm 0.015) WNSA- 2 - 620.304 (\pm 75.435) MSSbo

R_{Trian}^{2} = 0.908, R_{adj}^{2} = 0.884, Q_{LOO}^{2} = 0.859, Q_{LGO}^{2} = 0.809, {RMSE}_{Train} = 1.669, R_{Test}^{2} = 0.918, {RMSE}_{Test} = 2.319

The statistical quantities such as the square of the correlation coefficient (R²), square of the correlation coefficient of the leave one out cross validation (

Q_{LOO}^{2}

), square of the correlation coefficient of the leave group out cross validation (

Q_{LGO}^{2}

), adjusted R² (

R_{adj}^{2}

), root mean square error of train (RMSE_Train) and root mean square error of test (RMSE_Test), are presented to validate the proposed model. The constructed model used to predict reaction yield for the training and test sets. The predicted values are given in Table 1. The predicted values of reaction yield for the compounds in the training and test sets using Eq. (1) were plotted against the experimental values in Fig. 1. As can be seen from Table 1 and Fig. 1, the calculated values for the reaction yield are in good agreement with those of the experimental values. The maximum relative error (RE %) for the calculated sulfonation yield is 5.26% and the minimum value is 0.07%. These results show that GA selected descriptors in the model makes a good chemical sense.

Calculated vs. experimental sulfonation reaction yield.

In the QSRR studies a model may contain descriptors which are statistically well correlated to y but in reality there is no cause-effect relationship encoded in the respective correlations with y because they are not related to the mechanism of action. The Y-randomization test was applied in this contribution to test the later. The dependent variable vector (sulfonation yield) was randomly shuffled and the original descriptors matrix is kept fixed then a new QSRR model was developed. The models obtained under such conditions should be of poor quality and without real meaning. The new QSRR models (after several repetitions) were expected to have low R² and $Q_{LOO}^{2}$ values. If the R² and $Q_{LOO}^{2}$ values of these models were much lower than those of the original model, the model could be considered as reasonable, and had not been obtained by the chance. The results in Table 3 indicate that an acceptable model is obtained by GA-MLR method and the model developed is statistically significant and robust.

Table 3

R_{train}^{2}

and

Q_{LOO}^{2}

values after several Y-randomization tests.

Iteration	$R_{train}^{2}$	$Q_{LOO}^{2}$
1	0.301	0.054
2	0.023	0.423
3	0.210	0.004
4	0.602	0.259
5	0.403	0.031
6	0.194	0.017
7	0.430	0.044
8	0.097	0.060
9	0.081	0.322
10	0.112	0.090

The multi-collinearity between the above four descriptors were detected by calculating their variation inflation factors (VIF), which can be calculated as follows:

(3)

VIF = \frac{1}{1 - R^{2}}

where R² is the correlation coefficient of the multiple regression between the variables in the model. If VIF equals to 1, then no inter-correlation exists for each variable; if VIF falls into the range of 1–5, the related model is acceptable; and if VIF is larger than 10, the related model is unstable and recheck is necessary (Jaiswal et al., 2004; Shapiro and Guggenheim, 1998). The corresponding VIF values of the four descriptors are shown in Table 4. As can be seen from this table, all of the variables have VIF values of less than 5, indicating that the obtained model has statistical significance and the descriptors were found to be reasonably orthogonal.

Table 4 The brief descriptions of descriptors and their VIF values.

Descriptors	Definition	VIF^a
YZ shadow	YZ shadow	1.680
PPSA-1	PPSA-1 partial positive surface area [Zefirov’s PC]	3.321
WNSA-2	WNSA-2 Weighted PNSA (PNSA2^∗TMSA/1000) [Quantum-Chemical PC]	2.797
MSSbo	Max SIGMA–SIGMA bond order	1.936

^a Variation Inflation Factors (VIF).

The Williams plot, the plot of the standardized residuals versus the leverage (h_i), was exploited to visualize the applicability domain (OECD, 2007). A compound with leverage value more than warning leverage (h^∗) seriously influences the regression performance, but it does not appear to be an outlier because its standardized residual may be small, even though it has been excluded from the applicability domain. Moreover, a value of 3 for standardized residual is commonly used as a cut-off value for accepting predictions. The leverage and the standardized residual were combined for the characterization of the applicability domain. The Williams plot in Fig. 2 shows that the h_i values of all the compounds in the training and test sets are lower than the warning leverage (h^∗ = 0.75) and also the standardized residuals of these compounds were smaller than cut-off value.

Williams plot of MLR model. The training and test set samples are labeled differently. The dashed lines are the 3δ limit and the warning value of hat (h∗ = 0.75).

3.2

3.2 Interpretation of descriptors

By interpreting the descriptors contained in the QSRR model, it is possible to gain some insights into factors which are related to the reactivity of amines, alcohols and phenols with sulfonyl chloride. For this reason, an acceptable interpretation of the selected descriptors is provided below. The brief descriptions of descriptors are shown in Table 4.

The best fitted descriptors in the prediction model were among the Codessa descriptors. The YZ shadow, this geometrical descriptor, helps us to characterize the shape of the molecules. The shadow descriptors have been calculated by projecting the molecular surface on three mutually perpendicular planes, XY, YZ, and XZ (Rohrbaugh and Jurs, 1987). For the perspective along the X axis, the X coordinates would be disregarded and the molecule projected onto the Y/Z plane. A simple analogy, from which the name was derived, would be to obtain the shadow which results from directing parallel rays of light along the axis of perspective. The area of this projection will be used as an index of molecular shape. The shadow areas were calculated by applying 2D square grid on the molecular projection and by summation of the areas of the squares overlapped with a projection. The shadow areas for compound 24 are given in Fig. 3. These descriptors depend not only on conformation but also on the orientation of the molecule. The existence of the YZ shadow parameters in QSRR models indicates that sulfonation reaction yields depend on the shape, size and orientation of the pi-plane of the molecules. The negative sign in front of this descriptor indicates that an increase in the YZ shadow may decrease the sulfonation reaction yields of amines, alcohols and phenols with sulfonyl chloride. It can hence be said that increasing the YZ shadow, increases the steric hindrance, so the sulfonation reaction yields decrease consequently.

The two important descriptors in this equation show that electrostatic interactions are the effective factors controlling the sulfonation reaction. WNSA₂ is, the weighted PNSA (PNSA2^∗TMSA/1000) [Quantum-Chemical PC] descriptor. The contact surfaces where polar interactions can take place are characterized by a specific electronic distribution obtained by mapping atomic partial charges on the solvent-accessible surface where ${SA}_{a}^{+}$ and ${SA}_{a}^{-}$ are the surface area contributions of the ath positive and negative atoms, respectively. PPSA₁ is the sum of the solvent-accessible surface areas of all positively charged atoms: ${PPSA}_{1} = \sum {SA}_{a}^{+}$ WNSA₂ is the total charge weighted negative surface area (PNSA₂) multiplied by the total molecular solvent-accessible surface area (SASA) and divided by 1000:

(4)

{WNSA}_{2} = \frac{{PNSA}_{2} \cdot SASA}{1000}

(5)

{PNSA}_{2} = Q^{-} \sum {SA}_{a}^{-}

Q⁻ is the total negative charge.

PPSA₁ and WNSA₂ are two of the thirty different descriptors, which combine shape and electronic information to characterize molecules and therefore encode features responsible for polar interactions between molecules. The positive regression coefficient for these descriptors in Eq. (3) reflects the fact that the larger value of these descriptors leads to the higher sulfonation reaction yield values.

The most significant factor in this model is Max SIGMA–SIGMA bond order. This is valency-related descriptor in the type of quantum chemistry. This descriptor relates to the strength of intra-molecular bonding interactions and characterizes the stability of the molecules, their conformational flexibility and other valency-related properties follow (Long et al., 2009):

(6)

P_{AB} = \sum_{i = 1}^{occ} \sum_{μ \in A} \sum_{υ \in B} n_{i} c_{i μ} c_{j υ}

where the first summation is performed over all occupied molecular orbitals (n_i denotes the occupation number of the ith MO), and the two other summations over μ and υ, the atomic orbitals belonging to atoms A and B in the molecule, respectively. MO coefficients are denoted as c_iμ and c_jυ. The Max SIGMA–SIGMA bond order, the value of P_σ_–_σ (maximum σ–σ bond order) for a given pair of atomic species in the molecule, has a negative regression coefficient in the linear model as well. This indicates that keeping this index in the low level will promise better sulfonation reaction yield values when new compounds are designed.

4 Conclusion

This paper presents our current work to investigate the QSRR for designing efficient sulfonation reaction from aromatic amines, primary and secondary amines, alcohols and phenols with sulfonyl chloride. This work is the first attempt to develop QSRR model where the chemical reaction is related to chemical structure. The concluded QSRR model reflected high efficiency in predicting the sulfonation reaction yield. According to this model, the conformation and orientation of the molecule, electrostatic interactions and the stability of the molecules play a main role in the sulfonation reaction yield of compounds. Furthermore; we hope that the derived results will give some insights on chemical modifications that can be useful with the aim of designing new sulfonation reaction with improved yield values.

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Introduction

Computational section

Quantum chemical calculations and data preparing
Descriptor selection

Results and discussion

QSRR model validation
Interpretation of descriptors

Conclusion

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[1] Beheshti A., Riahi S., Ganjali M.R., . Electrochim. Acta. 2009;54:5368-5375.

[2] Beheshti A., Norouzi P., Ganjali M.R., . Int. J. Electrochem. Sci.. 2012;7:4811-4821.

[3] Beheshti A., Riahi S., Ganjali M.R., Norouzi P., . J. Comput. Chem.. 2012;33:732-747.

[4] Clercq E.D., . Curr. Med. Chem.. 2001;8:1543-1572.

[5] Evans B.E., Rittle K.E., Bock M.G., DiPardo R.M., Freidinger R.M., Whitter W.L., Lundell G.F., Veber D.F., Anderson P.S., Lotti V.J., Cerino D.J., Chen T.B., Kling P.J., Kunkerl K.A., Springer J.P., Hirshfield J., . J. Med. Chem.. 1998;31:2235-2246.

[6] http://www.gaussian.com/g_misc/g03/citation_g03.htm.

[7] Gareau Y., Pellicelli J., Laliberte P., Gauvreau D., . Tetrahedron Lett.. 2003;44:7821-7824.

[8] Greenfield A., Grosanu C., . Tetrahedron Lett.. 2008;49:6300-6303.

[9] Hemmateenejad B., Sanchooli M., Mehdipour A., . J. Phys. Org. Chem.. 2009;22:613-618.

[10] Holland J.H., . Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence. University of Michigan Press; 1975.

[11] Jafarpour M., Rezaeifard A., Aliabadi M., . Helv. Chim. Acta. 2010;93:405-413.

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Quantitative structure–reactivity study on sulfonation of amines, alcohols and phenols

Abstract

Keywords

Quantitative structure–reactivity relationship

Sulfonation reaction

Quantum chemical calculations

Synthesis

Reaction yield

1 Introduction

2 Computational section

2.1 Quantum chemical calculations and data preparing

2.2 Descriptor selection

3 Results and discussion

3.1 QSRR model validation

3.2 Interpretation of descriptors

4 Conclusion

References

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