Abstract
The notion of the chemical structure matrix (CSM) is introduced. The columns of the CSM represent the numbers of occurrences of different subgraphs in molecular graphs and are treated as vectors in a linear space. Any topological indices and physicochemical properties can also be treated as vectors in the same linear space. The QSPR problem is formally reduced to the search for linear correlations between vectors. A simple procedure for solving the problem is proposed. A novel method for establishing QSAR is outlined.
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E. A. Smolenskii, Dokl. Akad. Nauk, 1999, 365, 767 [Dokl. Chem., 1999 (Engl. Transl.)].
H. Wiener, J. Am. Chem. Soc., 1947, 69, 17.
H. Wiener, J. Am. Chem. Soc., 1947, 69, 2636.
H. Hosoya, Bull. Chem. Soc. Jpn, 1971, 44, 2332.
M. Randič, J. Am. Chem. Soc., 1975, 97, 6609.
E. A. Smolenskii, Zh. Vychisl. Mat. Mat. Fiz. [J. Comput. Math. Math. Phys.], 1962, 2, 371 (in Russian).
E. A. Smolenskii and A. L. Seifer, Zh. Fiz. Khim., 1963, 37, 2657 [J. Phys. Chem. USSR, 1963, n37 (Engl. Transl.)].
E. A. Smolenskii, Zh. Fiz. Khim., 1964, 38, 1288 [J. Phys. Chem. USSR, 1964, 38 (Engl. Transl.)].
E. A. Smolenskii and A. L. Seifer, Zh. Fiz. Khim., 1964, 38, 1548 [J. Phys. Chem. USSR, 1964, 38 (Engl. Transl.)].
D. E. Needham, I. C. Wei, and P. C. Seybold, J. Am. Chem. Soc., 1988, 110, 4186.
T. G. Schmalz, D. J. Klein, and D. L. Sandleback, J. Chem. Inf. Comput. Sci., 1992, 32, 54.
J. R. Platt, J. Phys. Chem., 1952, 56, 328.
V. M. Tatevsky and Yu. G. Papulov, Zh. Fiz. Khim., 1962, 36, 189 [J. Phys. Chem. USSR, 1962, 36 (Engl. Transl.)].
E. A. Smolenskii, Dokl. Akad. Nauk SSSR, 1976, 230, 373 [Dokl. Chem., 1976 (Engl. Transl.)].
W. J. Taylor, J. M. Pignocco, and F. D. Rossini, J. Res. Natl. Bur. St., 1945, 34, 413.
D. Bonchev, E. Marcel, and A. Dekmezian, J. Chem. Inf. Comput. Sci., 2001, 41, 1274.
D. H. Rouvray, in Chemical Applications of Topology and Graph Theory, Ed. R. B. King, Elsevier, Amsterdam, 1983, 159.
E. A. Smolenskii, J. Chem. Inf. Comput. Sci., 2004, 44, 522.
J. G. Topliss and R. P. Edwards, J. Med. Chem., 1979, 22, 1238.
E. A. Smolenskii, A. N. Ryzhov, A. L. Lapidus, and N. S. Zefirov, Dokl. Akad. Nauk, 2002, 387, 69 [Dokl. Chem., 2002 (Engl. Transl.)].
A. V. Kamernitskii, E. A. Smolenskii, G. M. Makeev, I. V. Vesela, N. M. Mirsalikhova, A. M. Turuta, and N. S. Zefirov, Bioorg. Khim., 2002, 28, 269 [Russ. J. Bioorg. Chem., 2002, 28 (Engl. Transl.)].
Z. Mihalić and N. Trinajstić, J. Mol. Struct. (THEOCHEM), 1991, 232, 65.
D. J. Klein, Int. J. Quantum Chem., 1986, 20, 153.
I. I. Baskin, M. I. Skvortsova, I. V. Stankevich, and N. S. Zefirov, J. Chem. Inf. Comput. Sci., 1995, 35, 527.
M. I. Skvortsova, I. I. Baskin, L. A. Skvortsov, V. A. Palyulin, N. S. Zefirov, and I. V. Stankevich, J. Mol. Struct. (THEOCHEM), 1999, 466, 211.
I. I. Baskin, Dokl. Akad. Nauk, 1994, 339, 346 [Dokl. Chem., 1994 (Engl. Transl.)].
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Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 9, pp. 1447–1453, September, 2006.
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Smolenskii, E.A. The chemical structure matrix and a new formalism for the QSPR problem. Russ Chem Bull 55, 1501–1507 (2006). https://doi.org/10.1007/s11172-006-0447-0
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DOI: https://doi.org/10.1007/s11172-006-0447-0