A Robust Quantitative Structure-Property Relationship-Based Model for Estimation of Refractivity Indices of 101 Common Paraffin Derivatives Based on their Molecular Structures

Mehdi Nekoei


A robust linear quantitative structure-property relationship (QSPR) model has been constructed to model and predict the refractivity indices of 101 organic compounds as common halo-derivatives of normal paraffin by application of the structural descriptors combined with multiple linear regressions (MLR) method. In the main part of this study, theoretical molecular descriptors were adopted from the original pool through the stepwise feature selection method. A simple model with low standard errors and promising correlation coefficients was obtained. MLR method could model the relationship between refractivity and structural descriptors, perfectly. The accuracy of the proposed MLR model was illustrated using cross-validation, validation through an external test set, and Y-randomization techniques. The linear techniques such as MLR combined with a successful variable selection procedure are capable of generating an efficient QSPR model for predicting the refractivity indices of different compounds. The constructed model, with high statistical significance (R2train = 0.926; Ftrain = 240.675; R2test = 0.947; Ftest = 52.978; REP (%) = 1.219; Q2LOO = 0.914 and Q2LGO = 0.914), could be adequately used for the prediction and description of the affecting parameters on refractivity behavior of similar or even unknown compounds.


QSPR; Refractivity index; MLR; Molecular descriptors

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Dijksman J.A., Rietz F., Lorincz K.A., van Hecke M., Losert W., 2012. Invited Article: Refractive index matched scanning of dense granular materials. Rev Sci Instrum. 83(1), 011301.

Jorge P.A. S., Silva S.O., Gouveia C., Tafulo P., Coelho L., Caldas P., Viegas D., Rego G., Baptista J.M., Santos J.L., Frazao O., 2012. Fiber optic-based refractive index sensing at INESC Porto. Sensors. 12(6), 8371-8389.

Jaksic Z., Vukovic S., Matovic J., Tanaskovic D., 2011. Negative refractive index metasurfaces for enhanced biosensing. Materials. 4(1), 1-36.

Bandoz J., Le Liboux M., Nahoum R., Israel G., Raulin F., Torre J.P., 1992. A sensitive cryogenic refractometer. Application to the refractive index determination of pure or mixed liquid methane, ethane and nitrogen. Rev Sci Instrum. 63(5), 2967-2973.

Grange B.W., Stevenson W.H., Viskanta R., 1976. Refractive index of liquid solutions at low temperatures: an accurate measurement. Appl Opt. 15, 858-859.

Malitson I.H., 1965. Interspecimen comparison of the refractive index of fused silica. J Opt Soc Am. 55 (10), 1205-1208.

Moreels E., de Greef C., Finsy R., 1984. Laser light refractometer. Appl Opt. 23, 3010-3013.

Shenoy M., Sukhdev R., Thyagarajan K., 1990. Simple prism coupling technique to measure the refractive index of a liquid and its variation with temperature. Rev Sci Instrum. 61, 1010-1013.

Tilton L.W., Taylor J.K., 1938. Refractive index and dispersion of distilled water for visible radiation, and temperatures of 0 to 60°C. J Res Nat Bur Stand. 20, 419-477.

Wong L.Y., Anderson A., 1972. Refractive-index measurements of some low-temperature liquids. J Opt Soc Am. 62, 219-222.

Zaidi A.A., Makdisi Y., Bhatia K.S., Abutahun I., 1989. Accurate method for the determination of the refractive index of liquids using a laser. Rev Sci Instrum. 60, 803-805.

Nemoto S., 1992. Measurement of the refractive index of liquid using laser beam displacement. Appl Opt. 31, 6690-6694.

Abbate G., Attanasio A., Bernini U., Ragozzino E., Somma F., 1976. The direct determination of the temperature dependence of the refractive index of liquids and solids. J Phys D: Appl Phys. 9 1945-1951.

Andreasson S.D.H., Gustafsson S.E., Halling N.O., 1971. Measurment of the refractive index of transparent solids and fluids. J Opt Soc Am. 61(5), 595-599.

Appleby R., James D.W., Bowie C.A., 1984. An interference refractometer to measure the pressure and temperature dependence of the refractive index of liquids. Spectrochim Acta Mol Biomol Spectros. 40(8), 785-787.

Dobbins H.M., Peck E.R., 1973. Change of refractive index of water as a function of temperature. J Opt Soc Am. 63, 318-320.

Gagnon R.E., Gammon P.H., Kiefte H., Clouter J.M., 1979. Determination of the refractive index of liquid carbon monoxide. Appl Opt. 18, 1237-1239.

Kerl K., Jeschek M., 1982. Equipment for precise measurements of the complex refractive index of gases as a function of wavenumber, temperature and pressure. J Phys E. 15, 955-960.

Khashan M.A., 1979. Application of the Fabry-Perot interferometer as a refractometer. Opt Acta. 26, 881-888.

Schellekens P., Wilkening G., Reinboth F., Downs M.J., Birch K.P., Spronck J., 1986. Measurements of the refractive index of air using interference refractormeters. Metrologia. 22, 279-287.

Subramanian G., 1980. Refractive index by image-moire technique. J Phys E. 13, 111.

Kim H., Paulson S.E., 2013. Real refractive indices and volatility of secondary organic aerosol generated from photooxidation and ozonolysis of limonene, alpha-pinene and toluene. Atmos Chem Phys. 13(15), 7711-7723.

Odhner H., Jacobs D. T., 2012. Refractive index of liquid D2O for visible wavelengths. J Chem Eng Data. 57(1), 166-168.

Prabhakaran P., Jang K.K., Son Y., Yang D.Y., Lee K.S., 2013. Fabrication of microstructures containing high refractive index materials by two-photon lithography. Mol Cryst Liq Cryst. 578(1), 4-18.

Qu H., Skorobogatiy M., 2012. Resonant bio- and chemical sensors using low-refractive-index-contrast liquid-core Bragg fibers. Sensor Actuat B-Chem. 161(1), 261-268.

Wyngaard J.C., Seaman N., Kimmel S.J., Otte M., Di X., Gilbert K.E., 2001. Concepts, observations, and simulation of refractive index turbulence in the lower atmosphere. Radio Sci. 36 (4), 643-669.

Xie R.J., Hintzen H.T., 2013. Optical properties of (oxy)nitride materials: A review. J Am Ceram Soc. 96(3), 665-687.

Goudarzi N., Goodarzi M., Mohammadhosseini M.M., Nekooei M., 2009. QSPR models for prediction of half-wave potentials of some chlorinated organic compounds using SR-PLS and GA-PLS methods. Mol Phys. 107(17), 1739-1744.

Nekoei M., Salimi M., Dolatabadi M., Mohammadhosseini M., 2011. A quantitative structure-activity relationship study of tetrabutylphosphonium bromide analogs as muscarinic acetylcholine receptors agonists. J Serb Chem Soc. 76(8), 1117-1127.

Mohammadhosseini M., Deeb O., Alavi- Gharabagh A., Nekoei M., 2012. Exploring novel QSRRs for simulation of gas chromatographic retention indices of diverse sets of terpenoids in Pistacia lentiscus L. essential oil using stepwise and genetic algorithm multiple linear regressions. Anal Chem Lett. 2, 80-102.

Nekoei M., Mohammadhosseini M., 2014. Application of HS-SPME, SDME and cold-press coupled to GC/MS to analysis the essential oils of Citrus sinensis CV. Thomson Navel and QSRR study for prediction of retention indices by stepwise and genetic algorithm-multiple linear regression approaches. Anal Chem Lett. 4(2), 93-103.

Mohammadhosseini M., Zamani H.A., Akhlaghi H., Nekoei M., 2011. Hydrodistilled volatile oil constituents of the aerial parts of Prangos serpentinica (Rech.f., Aell. Esfand.) Hernnstadt and Heyn from Iran and quantitative structure-retention relationship simulation. J Essent Oil-Bear Plants. 14(5), 559-573.

Mohammadhosseini M., 2013. Novel PSO-MLR algorithm to predict the chromatographic retention behaviors of natural compounds. Anal Chem Lett. 3(4), 226-248.

Mohammadhosseini M., 2014. Prediction of the GC-MS retention indices for a diverse set of terpenes as constituent components of Camu-camu (Myrciaria dubia (HBK) McVaugh) volatile oil, using particle swarm optimization-multiple linear regression (PSO-MLR). Journal of Chemical Health Risks. 4(1), 75-95.

Mohammadhosseini M., 2012. Chemical profile and antibacterial activity in hydrodistilled oil from aerial parts of Prangos ferulacea (L.) Lindl. and prediction of gas chromatographic retention indices by using genetic algorithm multiple linear regressions. Asian J Chem. 24(9), 3814-3820.

Mohammadhosseini M., Nekoei M., 2013. Quantitative structure-electrochemistry relationship (QSER) study for prediction of half-wave reduction potentials of some chlorinated organic compounds by GA-MLR. Asian J Chem. 25, 349-352.

Nekoei M., Goudarzi N., Nekoei S., Mohammadhosseini M., 2014. QSAR study of arylsulfonylpiperazine inhibitors of 11β-HSD1 by GA-MLR, GA-PLS and GA-ANN. Anal Chem Lett. 4(1), 14-28.

Nekoei M., Mohammadhosseini M., Pourbasheer E., 2015. QSAR study of VEGFR-2 inhibitors by using genetic algorithm-multiple linear regressions (GA-MLR) and genetic algorithm-support vector machine (GA-SVM): A comparative approach. Med Chem Res. 24(7), 3037-3046.

Acevedo-Martinez J., Escalona-Arranz J. C., Villar-Rojas A., Tellez-Palmero F., Perez-Roses R., Gonzalez L., Carrasco-Velar R., 2006. Quantitative study of the structure-retention index relationship in the imine family. J Chromatogr A. 1102(1-2), 238-244.

Garkani-Nejad Z., Karlovits M., Demuth W., Stimpfl T., Vycudilik W., Jalali-Heravi M., Varmuza K., 2004. Prediction of gas chromatographic retention indices of a diverse set of toxicologically relevant compounds. J Chromatogr A. 1028(2), 287-295.

Héberger K., Kowalska T., 1999. Quantitative structure–retention relationships: VI. Thermodynamics of Kováts retention index–boiling point correlations for alkylbenzenes in gas chromatography Chemometr Intell Lab Syst. 47, 205-217.

Jalali-Heravi M., Fatemi M.H., 2001. Artificial neural network modeling of Kovats retention indices for noncyclic and monocyclic terpenes. J Chromatogr A. 915(1-2), 177-183.

Tulasamma P., Reddy K. S., 2006. Quantitative structure and retention relationships for gas chromatographic data: Application to alkyl pyridines on apolar and polar phases. J Mol Graphics Model. 25(4), 507-513.

Heberger K., Gorgeny M., 1999. Principal component analysis of Kovats indices for carbonyl compounds in capillary gas chromatography. J Chromatogr A. 845, 21-31.

Heberger K., Milczewska K., Voelkel A., 2005. Principal component analysis of polymer-solvent and filler-solvent interactions by inverse gas chromatography. Colloids and Surfaces A: Physicochem Eng Aspects. 260(1-3), 29-37.

Dean J. 1992. Lange’s Handbook of Chemistry. McGraw-Hill. 14th Edn, New York.

Todeschini R., Consonni V., 2000. Handbook of Molecular Descriptors. Wiley-VCH, Mannhold, R., Kubinyi, H., Timmerman, H. Weinheim, Germany.

Efron B., 1983. Estimating the error rate of a prediction rule: Improvement on cross-validation. J Amer Statist Assoc. 78, 316-331.

Tropsha A., Gramatica P., Gombar V. K., 2003. The importance of being earnest: Validation is the absolute essential for successful application and interpretation of QSPR models. QSAR Comb Sci. 22(1), 69-77.

Wold S., Eriksson L. 1995. Statistical Validation of QSAR Results. In Chemometrics Methods in Molecular Design. VCH Weinheim. Germany.


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