Comparison between Multi-Linear- and Radial-Basis-Function-Neural-Network-Based QSPR Models for The Prediction of The Critical Temperature, Critical Pressure and Acentric Factor of Organic Compounds
Abstract
1. Introduction
2. Results
3. Discussion
4. Methods
4.1. Database Selection
4.2. Molecular Modelling and Descriptor Generation
4.3. Multi-Linear Regression Correlations
4.4. Radial Basis Function Neural Networks
4.5. Model Validation
5. Conclusions
Supplementary Materials
Author Contributions
Funding
Conflicts of Interest
Abbreviations
absolute percent relative deviation | |
average absolute percent deviation | |
AM1 | Austin Model 1 |
ANN | artificial neural network |
GC | group contribution |
MLR | multi-linear regression |
NDDO | neglect of diatomic differential overlap |
QSPR | quantitative structure-property relationship |
RBFNN | radial basis function neural network |
root mean square error |
References
- Kontogeorgis, G.M.; Tassios, D.P. Critical constants and acentric factors for long-chain alkanes suitable for corresponding states applications. A critical review. Chem. Eng. J. 1997, 66, 35–49. [Google Scholar] [CrossRef]
- Joback, K.G.; Reid, R.C. Estimation of pure-component properties from group-contributions. Chem. Eng. Commun. 1987, 57, 233–243. [Google Scholar] [CrossRef]
- Han, B.; Peng, D.Y. A group-contribution correlation for predicting the acentric factors of organic compounds. Can. J. Chem. Eng. 1993, 71, 332–334. [Google Scholar] [CrossRef]
- Constantinou, L.; Gani, R.; O’Connell, J.P. Estimation of the acentric factor and the liquid molar volume at 298 K using a new group contribution method. Fluid Phase Equilib. 1995, 103, 11–22. [Google Scholar] [CrossRef]
- Marrero, J.; Gani, R. Group-contribution based estimation of pure component properties. Fluid Phase Equilib. 2001, 183–184, 183–208. [Google Scholar] [CrossRef]
- Hukkerikara, A.S.; Sarup, B.; Kate, A.T.; Abildskov, J.; Sin, G.; Gani, R. Group-contribution+ (GC+) based estimation of properties of pure components: Improved property estimation and uncertainty analysis. Fluid Phase Equilib. 2012, 321, 25–43. [Google Scholar] [CrossRef]
- Katritzky, A.R.; Kuanar, M.; Slavov, S.; Hall, C.D. Quantitative correlation of physical and chemical properties with chemical structure: Utility for prediction. Chem. Rev. 2010, 110, 5714–5789. [Google Scholar] [CrossRef] [PubMed]
- Dreyfus, G. Neural Networks: Methodology and Applications, 1st ed.; Springer: Berlin/Heidelberg, Germany, 2005; pp. 1–83. ISBN 978-3-540-22980-3. [Google Scholar]
- Chen, S.; Cowan, C.F.N.; Grant, P.M. Orthogonal least squares learning algorithm for radial basis function networks. IEEE Trans. Neural Netw. 1991, 2, 302–309. [Google Scholar] [CrossRef] [PubMed]
- Egolf, L.M.; Wessel, M.D.; Jurs, P.C. Prediction of boiling points and critical temperatures of industrially important organic compounds from molecular structure. J. Chem. Inf. Comput. Sci. 1994, 34, 947–956. [Google Scholar] [CrossRef]
- Katritzky, A.R.; Mu, L.; Karelson, M. Relationships of critical temperatures to calculated molecular properties. J. Chem. Inf. Comput. Sci. 1998, 38, 293–299. [Google Scholar] [CrossRef]
- Turner, B.E.; Costello, C.L.; Jurs, P.C. Prediction of critical temperatures and pressures of industrially important organic compounds from molecular structure. J. Chem. Inf. Comput. Sci. 1998, 38, 639–645. [Google Scholar] [CrossRef]
- Duchowicz, P.; Castro, E.A. Prediction of critical temperatures and critical pressures of some industrially relevant organic substances from rather simple topological descriptors. Russ. J. Gen. Chem. 2002, 72, 1867–1873. [Google Scholar] [CrossRef]
- Sola, D.; Ferri, A.; Banchero, M.; Manna, L.; Sicardi, S. QSPR prediction of N-boiling point and critical properties of organic compounds and comparison with a group-contribution method. Fluid Phase Equilib. 2008, 263, 33–42. [Google Scholar] [CrossRef]
- Sobati, M.A.; Abooali, D. Molecular based models for estimation of critical properties of pure refrigerants: Quantitative structure property relationship (QSPR) approach. Thermochim. Acta 2015, 602, 53–62. [Google Scholar] [CrossRef]
- Hall, L.H.; Story, C.T. Boiling point and critical temperature of a heterogeneous data set: QSAR with atom type electrotopological state indices using artificial neural networks. J. Chem. Inf. Comput. Sci. 1996, 36, 1004–1014. [Google Scholar] [CrossRef]
- Espinosa, G.; Yaffe, D.; Arenas, A.; Cohen, Y.; Giralt, F. A fuzzy ARTMAP-based quantitative structure-property relationship (QSPR) for predicting physical properties of organic compounds. Ind. Eng. Chem. Res. 2001, 40, 2757–2766. [Google Scholar] [CrossRef]
- Godavarthy, S.S.; Robinson, R.L., Jr.; Gasem, K.A.M. Improved structure–property relationship models for prediction of critical properties. Fluid Phase Equilib. 2008, 264, 122–136. [Google Scholar] [CrossRef]
- Gharagheizi, F.; Mehrpooya, M. Prediction of some important physical properties of sulfur compounds using quantitative structure–properties relationships. Mol. Divers. 2008, 12, 143–155. [Google Scholar] [CrossRef] [PubMed]
- Gharagheizi, F.; Eslamimanesh, A.; Mohammadi, A.H.; Richon, D. Determination of critical properties and acentric factors of pure compounds using the artificial neural network group contribution algorithm. J. Chem. Eng. Data 2011, 56, 2460–2476. [Google Scholar] [CrossRef]
- Yao, X.; Wang, Y.; Zhang, X.; Zhang, R.; Liu, M.; Hua, Z.; Fan, B. Radial basis function neural network-based QSPR for the prediction of critical temperature. Chem. Intell. Lab. Syst. 2002, 62, 217–225. [Google Scholar] [CrossRef]
- Yao, X.; Zhang, X.; Zhang, R.; Liu, M.; Hu, Z.; Fan, B. Radial basis function neural network based QSPR for the prediction of critical pressures of substituted benzenes. Comput. Chem. 2002, 26, 159–169. [Google Scholar] [CrossRef]
- Carande, W.H.; Kazakov, A.; Muzny, C.; Frenkel, M. Quantitative structure-property relationship predictions of critical properties and acentric factors for pure compounds. J. Chem. Eng. Data 2015, 60, 1377–1387. [Google Scholar] [CrossRef]
- Mokshina, E.G.; Kuz’min, V.E.; Nedostup, V.I. QSPR modeling of critical parameters of organic compounds belonging to different classes in terms of the simplex representation of molecular structure. Russ. J. Org. Chem. 2014, 50, 314–321. [Google Scholar] [CrossRef]
- Boozarjomehry, R.B.; Abdolahi, F.; Moosavian, M.A. Characterization of basic properties for pure substances and petroleum fractions by neural network. Fluid Phase Equilib. 2005, 221, 188–196. [Google Scholar] [CrossRef]
- Mohammadi, A.H.; Afzal, W.; Richon, D. Determination of critical properties and acentric factors of petroleum fractions using artificial neural networks. Ind. Eng. Chem. Res. 2008, 47, 3225–3232. [Google Scholar] [CrossRef]
- Hosseinifar, P.; Jamshidi, S. Development of a new generalized correlation to characterize physical properties of pure components and petroleum fractions. Fluid Phase Equilib. 2014, 363, 189–198. [Google Scholar] [CrossRef]
- The Database of the Project 801 of the Design Institute for Physical Property Data (DIPPR® 801), Electronic Version with Diadem® [CD-ROM], American Institute of Chemical Engineers (AIChE): New York, NY, USA, 2004.
- Todeschini, R.; Consonni, V. Molecular Descriptors for Chemoinformatics, 2nd ed.; Wiley-VCH: Weinheim, Germany, 2009; Volume I, pp. 109–117, 161, 598. ISBN 978-3-527-31852-0. [Google Scholar]
- Balaban, A.T.; Ivanciuc, O. Historical development of topological indices. In Topological Indices and Related Descriptors in QSAR and QSPR, 1st ed.; Devillers, J., Balaban, A.T., Eds.; Gordon and Breach Science Publishers: Amsterdam, The Netherlands, 1999; pp. 21–57. ISBN 90-5699-239-2. [Google Scholar]
- Basak, S.C. Information theoretic indices of neighborhood complexity and their applications. In Topological Indices and Related Descriptors in QSAR and QSPR, 1st ed.; Devillers, J., Balaban, A.T., Eds.; Gordon and Breach Science Publishers: Amsterdam, The Netherlands, 1999; pp. 563–593. ISBN 90-5699-239-2. [Google Scholar]
- Katritzky, A.R.; Petrukhin, R.; Jain, R.; Karelson, M. QSPR analysis of flash points. J. Chem. Inf. Comput. Sci. 2001, 41. [Google Scholar] [CrossRef]
- Zefirov, N.S.; Kirpichenok, M.A.; Izmailov, F.F.; Trofimov, M.I. Scheme for the calculation of the electronegativities of atoms in a molecule in the framework of Sanderson’s principle. Dokl. Akad. Nauk. SSSR 1987, 296, 883–887. [Google Scholar]
- AMPAC 8.15, Semichem, Inc.: Shawnee, KS, USA, 2004.
- Dewar, M.J.S.; Zoebisch, E.G.; Healy, E.F.; Stewart, J.J.P. AM1: A new general purpose quantum mechanical molecular model. J. Am. Chem. Soc. 1985, 107, 3902–3909. [Google Scholar] [CrossRef]
- Cramer, C.J. Essentials of Computational Chemistry: Theories and Models: Theories and Models, 2nd ed.; Wiley & Sons Ltd.: Chichester, UK, 2004; pp. 145–146. ISBN 978-0-470-09182-1. [Google Scholar]
- CODESSA 2.642, Semichem, Inc.: Shawnee, KS, USA, 1995.
- MATLAB 9.2.0, The MathWorks, Inc.: Natick, MA, USA, 2017.
MLR Model | RBFNN Model | ||||
---|---|---|---|---|---|
Training Set | Validation Set | Training Set | Validation Set | ||
Tc | total number of compounds | 215 | 91 | 215 | 91 |
compounds with AD% > 10% | 8 | 9 | - | 1 | |
compounds with AD% < 5% | 184 | 49 | 203 | 80 | |
AAD% | 3.2% | 6.2% | 0.92% | 1.7% | |
RMSE (K) | 22.0 | 37.4 | 7.2 | 11.9 | |
Pc | total number of compounds | 215 | 91 | 215 | 91 |
compounds with AD% > 10% | 40 | 25 | - | 3 | |
compounds with AD% < 5% | 124 | 45 | 171 | 60 | |
AAD% | 6.1% | 8.5% | 1.9% | 3.5% | |
RMSE (MPa) | 0.40 | 0.47 | 0.11 | 0.18 | |
ω | total number of compounds | 215 | 91 | 215 | 91 |
compounds with AD% > 10% | 65 | 45 | 1 | 7 | |
compounds with AD% < 5% | 98 | 25 | 168 | 39 | |
AAD% | 8.7% | 12.2% | 2.0% | 4.8% | |
RMSE (−) | 0.040 | 0.066 | 0.0086 | 0.023 |
Tc | Pc | ω | ||
---|---|---|---|---|
RMSE for MLR models | Egolf and coworkers [10] | 12 K | - | - |
Katritzky and coworkers [11] | 15 K | - | - | |
Turner and coworkers [12] | 7.7 K | 0.16 MPa | - | |
Sola and coworkers [14] | 12 K | 0.25 MPa | - | |
Sobati and Abooali [15] | 16.3 K | 0.27 MPa | - | |
this work (1) | 27.5 K | 0.42 MPa | 0.049 | |
RMSE for ANN models | Espinosa and coworkers [17] | 5.6 K | 0.08 MPa | - |
Gharagheizi and Mehrpooya [19] | 18 K | 0.17 MPa | 0.032 | |
Yao and coworkers [21] | 14 K | - | - | |
Yao and coworkers [22] | 0.15 MPa | - | ||
this work (1) | 8.8 K | 0.13 MPa | 0.015 |
Tc | Pc | ω | ||
---|---|---|---|---|
AAD% | MLR model (1) | 4.1% | 6.8% | 9.7% |
RBFNN model (1) | 1.2% | 2.3% | 2.8% | |
Gani’s GC method (2) | 2.7% | 8.5% | 14.1% | |
RMSE | MLR model (1) | 27.5 K | 0.42 MPa | 0.049 |
RBFNN model (1) | 8.8 K | 0.13 MPa | 0.015 | |
Gani’s GC method (2) | 31.1 K | 0.48 MPa | 0.099 |
Descriptor | Group | |
---|---|---|
Tc | Relative number of F atoms | Constitutional descriptor |
Number of aromatic bonds | Constitutional descriptor | |
Relative number of rings | Constitutional descriptor | |
Relative molecular weight | Constitutional descriptor | |
Moment of inertia B | Geometrical descriptor | |
HASA2/TMSA 1/2 | Electrostatic descriptor | |
HDCA2/TMSA | Electrostatic descriptor | |
Topographic electronic index (all pairs) | Electrostatic descriptor | |
Randic index (order 1) | Topological descriptor | |
Structural Information content (order 0) | Topological descriptor | |
Pc | Number of Cl atoms | Constitutional descriptor |
Relative number of rings | Constitutional descriptor | |
Molecular volume | Geometrical descriptor | |
Moment of inertia C | Geometrical descriptor | |
HASA1 | Electrostatic descriptor | |
HDSA1/TMSA | Electrostatic descriptor | |
FPSA3 | Electrostatic descriptor | |
Relative negative charged SA | Electrostatic descriptor | |
Relative positive charged SA | Electrostatic descriptor | |
count of H-donors sites | Electrostatic descriptor | |
ω | Relative number of double bonds | Constitutional descriptor |
Molecular surface area | Geometrical descriptor | |
Gravitation index (all bonds) | Geometrical descriptor | |
HDCA2 | Electrostatic descriptor | |
PNSA3 | Electrostatic descriptor | |
Polarity parameter (Qmax − Qmin) | Electrostatic descriptor | |
count of H-donors sites | Electrostatic descriptor | |
Topographic electronic index (all bonds) | Electrostatic descriptor | |
Structural Information content (order 0) | Topological descriptor | |
Kier & Hall index (order 2) | Topological descriptor |
© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
Share and Cite
Banchero, M.; Manna, L. Comparison between Multi-Linear- and Radial-Basis-Function-Neural-Network-Based QSPR Models for The Prediction of The Critical Temperature, Critical Pressure and Acentric Factor of Organic Compounds. Molecules 2018, 23, 1379. https://doi.org/10.3390/molecules23061379
Banchero M, Manna L. Comparison between Multi-Linear- and Radial-Basis-Function-Neural-Network-Based QSPR Models for The Prediction of The Critical Temperature, Critical Pressure and Acentric Factor of Organic Compounds. Molecules. 2018; 23(6):1379. https://doi.org/10.3390/molecules23061379
Chicago/Turabian StyleBanchero, Mauro, and Luigi Manna. 2018. "Comparison between Multi-Linear- and Radial-Basis-Function-Neural-Network-Based QSPR Models for The Prediction of The Critical Temperature, Critical Pressure and Acentric Factor of Organic Compounds" Molecules 23, no. 6: 1379. https://doi.org/10.3390/molecules23061379
APA StyleBanchero, M., & Manna, L. (2018). Comparison between Multi-Linear- and Radial-Basis-Function-Neural-Network-Based QSPR Models for The Prediction of The Critical Temperature, Critical Pressure and Acentric Factor of Organic Compounds. Molecules, 23(6), 1379. https://doi.org/10.3390/molecules23061379