Summary
The binding energy per nucleon of a system of 73 stable nuclei is was predicted by means of a multilinear regression using with nuclear structural descriptors as variables. Quantum similarity measures were chosen as these descriptors. Valuable results, q2=0.940 and r2=0.949, were achieved when using 3 parameters. The model is recalculated with only 60 nuclei as a training set, and then the binding energy per nucleon for the remaining nuclei was predicted. Finally, the randomisation test was used to validate the model and to confirm the real predictive power of the method.
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References
Kubinyi H., 3D QSAR in Drug Design (ESCOM, Leiden) 1993.
Carbó R., Arnau J. and Leyda L., Int. J. Quant. Chem., 17 (1980) 1185.
Carbó R. and Domingo L., Int. J. Quant. Chem., 23 (1987) 517.
Besalú E., Carbó R., Mestres J. and Solá M., Topics Curr. Chem., 173 (1995) 31.
Carbó R. and Besalú E., in Molecular Similarity and Reactivity: From Quantum Chemical to Phenomenological Approaches, edited by Carbó R. (Kluwer, Amsterdam) 1995.
Carbó-Dorca R., Besalú E., Amat L. and Fradera X., in Advances in Molecular Similarity, edited by Mezey P. G. and Carbó R., Vol. 1 (JAI Press, Greenwich) 1996.
Löwdin P. O., Phys. Rev., 97 (1955) 1474.
McWeeny R., Proc. R. Soc. London A, 253 (1959) 242.
Hohenberg P. and Kohn W., Phys. Rev. B, 136 (1964) 864.
Fradera X., Amat L., Besalú, E. and Carbó-Dorca R., Quant. Struct.-Act. Relat., 16 (1997) 25.
Lobato M., Amat L., Besalú E. and Carbó-Dorca R., Quant. Struct.-Act. Relat., 16 (1997) 465.
Amat L., Robert D., Besalú E. and Carbó-Dorca R., J. Chem. Inf. Comput. Sci., 39 (1998) 624.
Robert D. and Carbó-Dorca R., J. Chem. Inf. Comput. Sci., 39 (1998) 620.
Amat L., Carbó-Dorca R. and Ponec R., J. Comput. Chem., 19 (1998) 1575.
Robert D. and Carbó-Dorca R., J. Math. Chem., 23 (1998) 327.
Skyrme T. H. R., Nucl. Phys., 9 (1959) 615.
Vautherin D. and Brink D. M., Phys. Rev. C, 5 (1972) 626.
Bartel J., Quentin P., Brack M., Guet C. and Hakansson H.-B., Nucl. Phys. A, 235 (1977) 219.
Vautherin D., Phys. Rev. C, 7 (1973) 296.
Ring P. and Schuck P., The Nuclear Many Body Problem (Springer, Berlin) 1980.
Lawson R. D., Theory of the Nuclear Shell Model (Oxford University Press, New York) 1980.
Mardia K. V., Kent J. T. and Bibby J. M., Multivariate Analysis (Academic Press, London) 1979.
Eckart C. and Young G., Psychometrika, 1 (1936) 211.
Carbó R., Besalú E., Amat L. and Fradera X., J. Math. Chem., 18 (1995) 237.
Montgomery D. C. and Peck E. A., Introduction to Linear Regression Analysis (John Wiley, New York) 1992.
Allen D. M., Technometrics, 16 (1974) 125.
Audi G. and Wapstra A. H., Nucl. Phys. A, 595 (1995) 409. The experimental binding energy per nucleon can be downloaded from the Web Site: www.nndc.bnl.gov/nndscr/masses/MASS2EXP.MAS95.
Wold S. and Eriksson L., in Chemometric Methods in Molecular Design (VCH Pub. Inc., New York) 1995.
Fisher R., in The Design of Experiments (Hafner Pub., New York) 1966.
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Robert, D., Carbó-Dorca, R. Structure-property relationships in nuclei. Prediction of the binding energy per nucleon using a quantum similarity approach. Il Nuovo Cimento A (1971–1996) 111, 1311–1320 (1998). https://doi.org/10.1007/BF03545797
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DOI: https://doi.org/10.1007/BF03545797