Six intermolecular potential energy functions incorporating mathematical functions such as the Golden ratio, Euler number and Pi, and three consecutive numbers in the Half Square, Lucas and Fibonacci sequences are proposed herein. It is shown that the Lucas potential function exhibits reasonable agreement with the Lennard-Jones(12-10) function, whilst the Golden ratio potential function describes the argon gas potential energy and the Lennard-Jones(14-7) function excellently. Both the Euler and Pi potential functions agree well with the Lennard-Jones(12-6) function, whilst the Fibonacci potential function exhibits very good correlation with the Lennard-Jones(9-6) function. The relatedness of the mathematical constants and sequences examined in this paper with application to intermolecular potential functions suggests their additional significance in the field of chemistry.
Similar content being viewed by others
References
Lim T.C. (2004). MATCH Commun. Math. Comput. Chem 50:185
Lim T.C. (2004). J. Math. Chem 36:261
Lim T.C. (2004). Z. Naturforsch A 59:116
Lim T.C. (2004). Czech. J. Phys 54:553
Lim T.C. (2004). Czech. J. Phys 54:947
Lim T.C. (2004). Chin. Phys. Lett 21:2167
Lim T.C. (2004). Phys. Scripta 70:347
Lim T.C. (2005). Chin. J. Phys 43:43
Lim T.C. (2005). Braz. J. Phys 35:641
Lim T.C. (2005). MATCH Commun. Math. Comput. Chem 54:29
Lim T.C. (2004). J. Math. Chem 36:139
Lim T.C. (2004). J. Math. Chem 36:147
Lim T.C. (2005). J. Math. Chem. 38:195
Lim T.C. (2005). J. Math. Chem 38:495
Lim T.C. (2005). Acta Chim. Slov 52:149
Lim T.C. (2005). Chem. Phys 320:54
Lennard-Jones J.E. (1924). Proc. Roy. Soc. Lond. A 106:463
Mecke R. (1927). Z. Phys 42:390
Sutherland G.B.B.M. (1938). Proc. Indian Acad. Sci 8:341
Morse P.M. (1929). Phys. Rev 34:57
Buckingham R.A. (1938). Proc. Roy. Soc. Lond. A 168:264
Wu C.K., and Yang C.T. (1944). J. Phys. Chem 48:295
Linnett J.W. (1940). Trans Faraday Soc 36:1123
Linnett J.W. (1942). Trans. Faraday Soc. 38:1
Damm W., Frontera A., Tirado-Rives J. and Jorgensen W.L. (1997). J. Comput. Chem 18:1955
Rappe A.K., Casewit C.J., Colwell K.S., Goddard W.A. III and Skiff W.M. (1992). J. Am. Chem. Soc 114:10024
Cornell W.D., Cieplak P., Bayly C.I., Gould I.R., Merz K.M. Jr, Ferguson G.M., Spellmeyer D.C., Fox T., Caldwell J.W., and Collman P.A. (1995). J. Am. Chem. Soc 117:5179
Nemethy G., Gibsen K.D., Palmer K.A., Yoon C.N., Paterlini G., Zagari A., Rumsey S., and Sheraga H.A. (1992). J. Phys. Chem 96:6472
Barlow S., Rohl A.A., Shi S., Freeman C.M., and O’Hare D. (1996). J. Am. Chem. Soc 118:7578
Hwang M.J., Stockfisch T.P., and Hagler A.T. (1994). J. Am. Chem. Soc. 116:2515
Halgren T.A. (1996). J. Comput. Chem 17:490
Mayo S.L., Olafson B.D., and Goddard W.A. III (1990). J. Phys. Chem 94:8897
Karasawa N., Dasgupta S., and Goddard W.A. III (1991). J. Phys. Chem 95:2260
Fan C.F., Cagin T., Chen Z.M., and Smith K.A. (1994). Macromolecules 27:2383
Lim T.C. (2006). Chin. J. Phys 44:19
Aziz R.A., and Chen H.H. (1977). J. Chem. Phys 67:5719
Maitland G.C., Rigby M., Smith E.B., and Wakeham W.A. (1981). Intermolecular Forces. Clarendon Press, Oxford, p. 581
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Lim, TC. On the Applicability of Mathematical Constants and Sequences in Intermolecular Potential Energy Functions. J Math Chem 41, 381–391 (2007). https://doi.org/10.1007/s10910-006-9084-y
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10910-006-9084-y
Keywords
- Euler constant
- Fibonacci sequence
- golden ratio
- intermolecular energy
- Lucas sequence
- Pi
- potential functions