Symbolic calculation in chemistry: Selected examples†
Michael P. Barnett,
Joseph F. Capitani,
Joachim von zur Gathen,
Jürgen Gerhard,
Corresponding Author
Michael P. Barnett
Department of Chemistry, Princeton University, Princeton, NJ 08544-1099
Department of Chemistry, Princeton University, Princeton, NJ 08544-1099Search for more papers by this authorJoseph F. Capitani
Joined Departments of Chemistry and Biochemistry, Manhattan College/The College of Mount Saint Vincent, Riverdale, NY 10471
Search for more papers by this authorJoachim von zur Gathen
Department of Computer Science, Electrical Engineering and Mathematics, University of Paderborn, Paderborn, Germany
Search for more papers by this authorMichael P. Barnett,
Joseph F. Capitani,
Joachim von zur Gathen,
Jürgen Gerhard,
Corresponding Author
Michael P. Barnett
Department of Chemistry, Princeton University, Princeton, NJ 08544-1099
Department of Chemistry, Princeton University, Princeton, NJ 08544-1099Search for more papers by this authorJoseph F. Capitani
Joined Departments of Chemistry and Biochemistry, Manhattan College/The College of Mount Saint Vincent, Riverdale, NY 10471
Search for more papers by this authorJoachim von zur Gathen
Department of Computer Science, Electrical Engineering and Mathematics, University of Paderborn, Paderborn, Germany
Search for more papers by this author†
Full titles of the journal articles that this paper cites are included in the Supplementary Material that is available from [email protected] on request or by clicking on http://www.interscience.wiley.com/jpages/0020-7608/suppmat.
Abstract
A selective classified bibliography of symbolic computation in some areas of chemistry is provided together with some examples of computer algebra algorithms and techniques to facilitate future joint work of chemists and computer scientists. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004
Supporting Information
| Filename | Description |
|---|---|
| suppmat_barnett.pdf400.4 KB | Supporting Information file suppmat_barnett.pdf |
Please note: The publisher is not responsible for the content or functionality of any supporting information supplied by the authors. Any queries (other than missing content) should be directed to the corresponding author for the article.
REFERENCES
- 1 Achim, C.; Bominaar, E.; Staples, R.; Munck, E.; Holm, R. Inorg Chem 2001, 40, 4389–4403.
- 2
Adams, B. G.
Algebraic Approach to Simple Quantum Systems;
Springer:
New York,
1994.
10.1007/978-3-642-57933-2 Google Scholar
- 3
Adams, B. G.;
Arteca, G. A.
Comput Phys
1994, 8,
343–341.
10.1063/1.168496 Google Scholar
- 4 Ageev, S. Z.; Isbister, D. J.; Sanctuary, B. C. Mol Phys 1994, 83, 193–210.
- 5 Ageev, S. Z.; Man, P. P.; Sanctuary, B. C. Mol Phys 1996, 88, 1277–1292.
- 6 Ageev, S. Z.; Sanctuary, B. C. Chem Phys Lett 1994, 225, 499–502.
- 7 Ageev, S. Z.; Sanctuary, B. C. Mol Phys 1995, 84, 835–844.
- 8 Ageev, S. Z.; Sanctuary, B. C. Chem Phys Lett 1996, 255, 71–78.
- 9 Ageev, S. Z.; Sanctuary, B. C. Mol Phys 1996, 87, 1423–1431.
- 10 Ajbar, A. Biotech Progr 2001, 17, 597–605.
- 11 Alberty, R. A. J Phys Chem B 2001, 105, 1109–1114.
- 12 Alberty, R. A. J Phys Chem B 2001, 105, 7865–7870.
- 13 Altermatt, U. D.; Brown, I. D. Acta Crystallogr A 1987, 43, 125–130.
- 14 Altmann, S. L.; Herzig, P. Point-Group Theory Tables; Clarendon Press: Oxford, UK, 1994.
- 15 Andenken, D.; Polansky, O. E.; Grund, R.; Kerber, A.; Laue, R. MATCH 1992, 27, 87–131.
- 16 Angelescu, D. E.; Bhatt, R. N. Phys Rev B, 2002, 65(7), art. no. 75211.
- 17 Anstis, G. Acta Crystallogr A 1999, 55, 197–203.
- 18 Arteca, G. A.; Mezey, P. G. J Comput Chem 1988, 9, 554–563.
- 19 Audoly, S.; Bellu, G.; D'Angiò, L.; Saccomani, M. P.; Cobelli, C. IEEE Trans Biomed Eng 2001, 48, 55–65.
- 20 Audoly, S.; D'Angiò, L.; Saccomani, M. P.; Cobelli, C. IEEE Trans Biomed Eng 1998, 45, 36–47.
- 21 Ayari, A.; Ayari, M. I.; Hussin, V. Comput Phys Comm 1998, 115, 416–427.
- 22 Bajer, J.; Lisonek, P. J Mod Opt 1991, 38, 719–729.
- 23 Bajer, J.; Perina, J. Opt Comm 1992, 92, 99–104.
- 24 Baldwin, D.; Göktas, Ü.; Hereman, W.; Hoong, L.; Martino, R. S.; Miller, J. C. ( in press).
- 25 Bancewicz, M. J Phys A 1998, 31, 3461–3467.
- 26 Bancewicz, T. Chem Phys Lett 1995, 244, 305–313.
- 27
Barnett, M. P.
SIGSAM Bull
2002, 36,
5–32.
10.1145/641239.641242 Google Scholar
- 28
Barnett, M. P.
In Proceedings of the 2003 International Symposium on Symbolic and Algebraic Computation;
J. R. Sendra, Ed.;
ACM Press:
New York,
2003, pp
1–2.
10.1145/860854.860856 Google Scholar
- 29 Barnett, M. P. Int J Quantum Chem 2003, 95, 791–805.
- 30 Barnett, M. P. Supplementary material.
- 31 Barnett, M. P.; Decker, T.; Krandick, W. J Chem Phys 2001, 114, 10265–10269.
- 32 Bartkowiak, M.; Henderson, J.; Oitmaa, J.; Debrito, P. Phys Rev B 1995, 51, 14077–14084.
- 33 Barvik, I.; Warns, C.; Reineker, P. Physica A 1998, 259, 65–80.
- 34 Bayram, M.; Bennett, J. P.; Dewar, M. C. Acta Biotheor 1993, 41, 53–62.
- 35 Bayram, M. Proc Ind Natl Sci Acad A 1997, 63, 241–249.
- 36 Bender, C. M.; Weniger, E. J. J Math Phys 2001, 42, 2167–2183.
- 37 Bennett, J. P.; Davenport, J. H.; Dewar, M. C.; Fisher, D. L.; Grinfeld, M.; Sauro, M. Lect Notes Cont Inf Sci 1991, 165, 23–30.
- 38 Bennett, J. P.; Grinfeld, M.; Hubble, J. J Symb Comput 1993, 15, 79–83.
- 39 Beskrovnyi, V. N. Comput Phys Comm 1998, 111, 76–86.
- 40 Bessis, N.; Bessis, G. Phys Rev A 1996, 53, 1330–1339.
- 41 Bishop, R. F.; Hale, R. G.; Xian, Y. Phys Rev Lett 1994, 73, 3157–3160.
- 42 Bittl, R. Chem Phys Lett 1993, 215, 279–284.
- 43 Bjerring, M.; Vosegaard, T.; Malmendal, A.; Nielsen, N. C. Concepts Magn Res A 2003, 18A, 111–129.
- 44 Blackett, A. J.; Stelbovics, A. T. Comput Phys Comm 1999, 116, 78–94.
- 45 Boens, N.; Szubiakowski, J.; Novikov, E.; Ameloot, M. J Chem Phys 2000, 112, 8260–8266.
- 46 Bouanich, J. P. Comput Phys Comm 1987, 47, 259–266.
- 47 Bouanich, J. P.; Ogilvie, J. F.; Tipping, R. H. Comput Phys Comm 1986, 39, 439–446.
- 48 Bouferguene, A.; Weatherford, C. A.; Jones, H. W. Phys Rev E 1999, 59, 2412–2423.
- 49 Boys, S. F.; Cook, G. B.; Reeves, C. M.; Shavitt, I. Nature 1956, 178, 1207–1209.
- 50 Bracken, P. Int J Quantum Chem 1996, 57, 235–243.
- 51 Bracken, P.; Bartlett, R. J. Int J Quantum Chem 1997, 62, 557–570.
- 52 Bracken, P.; C̆íz̆ek, J. J Math Phys 1997, 38, 5493–5504.
- 53 Bramley, M. J.; Green, W. H.; Handy, N. C. Mol Phys 1991, 73, 1183–1208.
- 54 Brown, H.; Bülow, R.; Neubüser, J.; Wondratschek, H.; Zassenhaus, H. Crystallographic Groups of Four-Dimensional Space; Wiley: New York, 1978.
- 55 Butcher, J.; Carminati, J.; Vu, K. T. Comput Phys Comm 2003, 155, 92–114.
- 56 Calucci, L.; Geppi, M. J Chem Info Comput Sci 2001, 41, 1006–1014.
- 57 CARAT . http://wwwb.math.rwth-aachen.de/carat/.
- 58 Cash, G. C. J Chem Info Comput Sci 1999, 39, 833–834.
- 59 Cash, G. C. J Chem Info Comput Sci 2000, 40, 1203–1206.
- 60 Chandrasekhar, P. Conducting Polymers, Fundamentals and Applications; Kluwer: Dordrecht, The Netherlands, 1999.
- 61 Chappell, M. J.; Godfrey, K. R.; Vajda, S. Math Biosci 1990, 102, 41–73.
- 62 Chen, J. Q.; Fan, P. D.; Paldus, J. Int J Quantum Chem 2000, 76, 585–599.
- 63 Chow, K. W. Phys Lett A 2001, 285, 319–326.
- 64 C̆íz̆ek, J.; Bracken, P. Phys Rev Lett 1996, 77, 211–214.
- 65 C̆íz̆ek, J.; Vinette, F.; Weniger, E. J. Int J Quantum Chem Quantum Chem Symp 1991, 25, 209–223.
- 66 C̆íz̆ek, J.; Vinette, F.; Weniger, E. J. (a) In de Groot, R. A.; Nadrchal, J., Eds.; (b) Int J Mod Phys C 1993, 4, 257–270.
- 67 C̆íz̆ek, J.; Weniger, E. J.; Bracken, P.; S̆pirko, V. Phys Rev E 1996, 53, 2925–2939.
- 68 Clarke, B. L. Adv Chem Phys 1980, 43, 1–217.
- 69 Coffey, M. Phys Rev B 1995, 52, R9851–R9854.
- 70 Collins, G. E.; Encarnacion, M. J.; Hong, H.; Johnson, J. R.; Krandick, W.; Mandache, A. M.; Neubacher, A.; Vielhaber, H. Saclib User's Guide. Technical Report 93-19; RISC-Linz, Johannes Kepler University: Linz, Austria, 1993.
- 71 Cox, D.; Little, J.; O'Shea, D. Ideals, Varieties and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra, 2nd ed.; Springer: New York, 1997.
- 72 Cox, H.; Smith, S. J.; Sutcliffe, B. T. Comput Phys Comm 1994, 84, 186–200.
- 73 Crawford, T. D. Ph.D. thesis, University of Georgia; 1996.
- 74 Crawford, T. D.; Lee, T. J.; Schaefer, H. F. J Chem Phys 1997, 107, 7943–7950.
- 75 Császár, A. G. J Phys Chem 1992, 96, 7898–7904.
- 76 Császár, A. G.; Handy, N. C. Mol Phys 1995, 86, 959–979.
- 77 Dannetun, P.; Lögdlund, M.; Fredriksson, C.; Lazzaroni, R.; Fauquet, C.; Stafström, S.; Spangler, C. W.; Bredás, J. L.; Salaneck, W. R. J Chem Phys 1994, 100, 6765–6771.
- 78
Davydov, A. S.
Solitons in Molecular Systems;
Kryachko, E. S., Trans.;
Kluwer:
Dordrecht, The Netherlands,
1985.
10.1007/978-94-017-3025-9 Google Scholar
- 79 de Lange, O. L.; Raab, R. E. Operator Methods in Quantum Mechanics; Clarendon Press: Oxford, UK, 1991.
- 80 Delhalle, J.; C̆íz̆ek, J. Int J Quantum Chem 1995, 56, 9–17.
- 81 Delhalle, J.; C̆íz̆ek, J.; Flamant, I.; Calais, J. L.; Fripiat, J. G. J Chem Phys 1994, 101, 10717–10729.
- 82 Dias, J. R.; Cash, G. C. J Chem Info Comput Sci 2001, 41, 129–133.
- 83 Dick, B. Chem Phys 1993, 171, 59–78.
- 84 Draeger, T. Comput Phys Comm 2001, 139, 246–262.
- 85 Dubey, R.; Khandelwal, G. S.; Pritchard, W. M. J Phys B 1991, 24, 57–63.
- 86 D'yachenko, G. G.; Petukhov, V. A. J Appl Spectrosc 2001, 68, 196–199.
- 87 Eick, B.; Gähler, F.; Nickel, W. Acta Crystallogr A 1997, 53, 467–474.
- 88 Eick, B.; Gähler, F.; Nickel, W. 2003, Cryst—Computing with Crystallographic Groups (a GAP package—see 110).
- 89 Emiris, I.; Mourrain, B. Algorithmica 1999, 25, 372–402.
- 90 Falcke, M.; Bär, M.; Engel, H.; Eiswirth, M. J Chem Phys 1992, 97, 4555–4563.
- 91 Falloon, P. E.; Wang, J. B. Comput Phys Comm 2001, 134, 167–182.
- 92 Fan, E. Phys Lett A 2001, 282, 18–22.
- 93 Farza, M.; Chéruy, A. Comput Appl Biosci 1994, 10, 477–488.
- 94 Feagin, J. M.; Kocbach, L.; Liska, R.; Nunez, A. www. fi.uib.no/AMOS/mathME; 1994.
- 95 Felsch, V.; Gähler, F. 2003, CrystCat—A Library of Crystallographic Groups, (a GAP package—see 110).
- 96 Fernández, F. M. J Phys A 1992, 25, 495–501.
- 97 Fernández, F. M. Private communication; 2003.
- 98 Fernández, F. M.; Castro, E. A. Algebraic Methods in Quantum Chemistry and Physics; CRC Press: Boca Raton, FL, 1996.
- 99 Fernandez, F. M.; Morales, J. A. Phys Lett A 1992, 165, 314–319.
- 100 Fernandez, F. M.; Morales, J. A. Phys Rev A 1992, 46, 318–326.
- 101 Finn, P. W.; Kavraki, L. E. Algorithmica 1999, 25, 347–371.
- 102 Folcia, C. L.; Ortega, J.; Extebarria, J. J Phys D 1999, 32, 2266–2277.
- 103 Fraser, S. J. J Chem Phys 1998, 109, 411–423.
- 104 Fripertinger, H. MATCH 1996, 33, 121–138.
- 105 Fritzsche, S.; Inghoff, T.; Bastug, T.; Tomaselli, M. Comput Phys Comm 2001, 139, 314–326.
- 106 Gähler, F. In Aperiodic '97, Proceedings of the International Conference on Aperiodic Crystals; de Boissieu, M.; Verger-Gaugry, J.-L.; Currat, R., Eds.; World Scientific: Singapore, 1998, pp 101–105.
- 107 Galceran, J.; Cecilia, J.; Companys, E.; Salvador, J.; Puy, J. J Phys Chem B 2000, 104, 7993–8000.
- 108 Gap, Y. T.; Tian, B. Int J Mod Phys C 2001, 12, 1383–1389.
- 109 Gao, Y. T.; Tian, B.; Wei, G. M. Int J Mod Phys C 2001, 12, 1417–1423.
- 110 The GAP group. GAP—Groups, Algorithms and Programming, 4th ed.; www.gap-system.org; 2000.
- 111 Gasparovic, C.; Cabanas, M.; Arus, C. J Magn Reson B 1995, 109, 146–152.
- 112 Gatermann, K.; Huber, B. J Symb Comput 2002, 33, 275–305.
- 113 von zur Gathen, J.; Gerhard, J. Modern Computer Algebra, 2nd ed.; Cambridge University Press: New York, 2003.
- 114 Gatti, F.; Iung, C.; Menou, M.; Justum, Y.; Nauts, A.; Chapuisat, X. J Chem Phys 1998, 108, 8804–8820.
- 115 Gatti, F.; Munoz, C.; Iung, C. J Chem Phys 2001, 114, 8275–8281.
- 116 Go, N.; Scheraga, H. A. Macromolecules 1973, 6, 273–281.
- 117 Golub, G. H.; Van Loan, C. F. Matrix Computations; Johns Hopkins University Press: Baltimore, 1996.
- 118 Gray, B. F.; Pritchard, H. O.; Sumner, F. H. J Chem Soc 1956, 2631–2635.
- 119 Greuel, G.-M.; Pfister, G.; Schönemann, H. Singular 2.0. A Computer Algebra System for Polynomial Computations; Centre for Computer Algebra, University of Kaiserslautern; www.singular.uni-kl.de; 2001.
- 120 Grinfeld, M.; Bennett, J.; Hubble, J. IAM J Math Appl Bus Ind 1997, 8, 157–166.
- 121 Grosse-Kunstleve, R. W. Acta Crystallogr A 1999, 55, 383–395.
- 122 Grotendorst, J.; Dornseiffer, J. Math Comput Sim 2000, 51, 451–471.
- 123 Grotendorst, J.; Jansen, P.; Schoberth, S. M. Maple Tech News 1994, 1, 55–62.
- 124 Grüner, T.; Kerber, A.; Laue, R.; Ruckdeschel, A. Molgen 4.0; www.mathe2.uni-bayreuth.de/molgen4/.
- 125 Guiasu, S. Int J Quantum Chem 1998, 68, 175–190.
- 126 Guiasu, S. Quantum Mechanics; Nova Science: Huntington, NY, 2001.
- 127 Hadinger, G.; Hadinger, G.; Bouty, O.; Aubert-Frecon, M. Phys Rev A 1994, 50, 1927–1930.
- 128 Hadinger, G.; Hadinger, G.; Magnier, S.; Aubert-Frecon, M. J Mol Spectrosc 1996, 175, 441–444.
- 129 Hadinger, G.; Tergiman, Y. S.; Hadinger, G. J Chem Phys 1988, 88, 4351–5356.
- 130 Handy, N. C. Mol Phys 1987, 61, 207–223.
- 131 Handy, N. C.; Carter, S.; Colwell, S. M. Mol Phys 1999, 96, 477–491.
- 132 Hardy, Y.; Steeb, W. Int J Mod Phys C 2001, 12, 235–245.
- 133 Harris, F. E. Phys Rev A 1997, 55, 1820–1831.
- 134 Harris, F. E. Int J Quantum Chem 1999, 75, 593–597.
- 135 Harris, F. E. Int J Quantum Chem 2002, 88, 701–734.
- 136 Head, A. K. Comput Phys Comm 1993, 77, 241–248.
- 137 Head, A. K. http://archives.math.utk.edu/software/ msdos/adv.diff.equations/lie/.html, 2003.
- 138 Head, A. K. Private communication; 2003.
- 139 Herbert, J. M.; Ermler, W. C. Comput Chem 1998, 22, 169–184.
- 140 Hereman, W. Euromath Bull 1994, 1, 45–79.
- 141 Hereman, W.; Zhuang, W. Acta Appl Math 1995, 39, 361–378.
- 142 Hergert, W.; Däne, M. Phys Status Solidi A 2003, 197, 620–634.
- 143 Holt, D.; Eick, B.; O'Brien, E. A. Handbook on Computational Group Theory (in preparation).
- 144 Hong, W. Z Naturforsch A 2000, 55, 397–400.
- 145 Hu, X.; Wang, D.; Tam, H.; Xue, W. Phys Lett A 1999, 262, 310–320.
- 146 Huson, D. H. www.mathematik.uni-bielefeld.de/∼huson/approach.html.
- 147
Hydon, P. E.
Symmetry Methods for Differential Equations;
Cambridge University Press:
New York,
2000.
10.1017/CBO9780511623967 Google Scholar
- 148 Hydon, P. E. Private communication; 2003.
- 149 N. H. Ibragimov, Ed. CRC Handbook of Lie Group Analysis of Differential Equations, vol. 1: Symmetries, Exact Solutions and Conservation Laws, vol. 2: Applications in Engineering and Physical Sciences; CRC Press: Boca Raton, FL, 1994–1995.
- 150 Ihn, T. Electronic Quantum Transport in Mesoscopic Semiconductor Structures; Tracts in Modern Physics 192; Springer: New York, 2003.
- 151 Isbister, D. J.; Krishnan, M. S.; Sanctuary, B. C. Mol Phys 1995, 86, 1517–1535.
- 152 Iung, C.; Gatti, F.; Viel, A.; Chapuisat, X. Phys Chem Chem Phys 1999, 1, 3377–3385.
- 153 Jang, E. K.; Han, O. H. J Kor Phys Soc 1997, 30, 115–122.
- 154 Janssen, M. H. M.; Parker, D. H.; Stolte, S. Chem Phys 1987, 113, 357–382.
- 155 Javanainen, J. Lecture Notes in Physics 420; Springer: New York, 1993, pp 119–132.
- 156 Javanainen, J.; Yoo, S. M. Phys Rev A 1993, 48, 3776–3785.
- 157 J̈emmer, P.; Knowles, P. J. Comput Phys Comm 1997, 100, 93–98.
- 158 J̈emmer, P.; Knowles, P. J. J Comput Chem 1998, 19, 300–307.
- 159 Jin, B.-Y.; Silbey, R. J Chem Phys 1995, 102, 4261–4268.
- 160 Johnston, H.; Sarkar, S. Phys Rev A 1995, 51, 4109–4115.
- 161 Johnston, H.; Sarkar, S. J Phys A 1995, 28, 3071–3091.
- 162 Jones, H. W. Int J Quantum Chem 1986, 29, 177–183.
- 163 Jones, H. W. Phys Rev A 1987, 35, 1923–1926.
- 164 Jones, H. W. J Comput Chem 1991, 12, 1217–1222.
- 165 Jones, H. W. Int J Quantum Chem 1992, 41, 749–754.
- 166 Jones, H. W. Int J Quantum Chem 1992, 42, 779–784.
- 167 Jones, H. W. Int J Quantum Chem 1993, 45, 21–30.
- 168 Jones, H. W. Int J Quantum Chem 1994, 51, 417–423.
- 169 Jones, H. W.; Jain, J. L. Int J Quantum Chem 2000, 80, 842–847.
- 170 Joosten, J. G. H. J Chem Phys 1985, 82, 2427–2432.
- 171 Joyce, G.; Pike, R.; Sarkar, S. J Phys A 1994, 27, 5265–5271.
- 172 Jumars, P. A. Am Naturalist 2000, 155, 528–543.
- 173 Kanters, R. P. F.; Char, B. W.; Addison, A. W. J Magn Reson A 1993, 101, 23–29.
- 174 Kemp-Harper, R.; Philp, D. J.; Kuchel, P. W. J Chem Phys 2001, 115, 2908–2916.
- 175
Kerber, A.
Applied Finite Group Actions, 2nd ed.;
Springer:
New York,
1999.
10.1007/978-3-662-11167-3 Google Scholar
- 176 Kerber, A.; Kohnert, A. MATCH 1998, 38, 163–172.
- 177 Kerber, A.; Laue, R.; Meringer, M. MATCH 2003, 47, 169–172.
- 178 Kim, Y. J.; Streitwieser, A.; Chow, A. A.; Fraenkel, G. Org Lett 1999, 1, 2069–2071.
- 179 Kirkwood, J. C.; Albrecht, A. C.; Ulness, D. J.; Stimson, M. J. J Chem Phys 1999, 111, 272–280.
- 180 Kivshar, Y. S.; Agrawal, G. Optical Solitons: From Fibers to Photonic Crystals; Academic Press: New York, 2003.
- 181 Korsch, H. J.; Glück, M. Eur J Phys 2002, 23, 413–426.
- 182 Kristoffersen, A.; Olaussen, K. J Phys C 1997, 9, 10801–10827.
- 183 Kuchel, P.; Durrant, C. J Magn Reson 1999, 139, 258–272.
- 184 Kuchel, P. W.; Durrant, C. J.; Chapman, B. E.; Jarrett, P. S.; Regan, D. G. J Magn Reson 2000, 145, 291–301.
- 185 Kuchel, P. W.; Fackerell, E. F. Bull Math Biol 1999, 61, 209–220.
- 186 Kuchel, P. W.; Lennon, A. L.; Durrant, C. J. J Magn Reson B 1996, 112, 1–17.
- 187 Kuchiev, M.; Ostrovsky, V. J Phys B 1998, 31, 2525–2538.
- 188 Ladik, J. J. Int J Quantum Chem 2000, 78, 450–458.
- 189 Lai, S. Int J Quantum Chem 1994, 52, 593–607.
- 190 Larsen, H.; Thorkildsen, G. Acta Crystallogr A 1998, 54, 511–512.
- 191 Laughlin, R. B. Science 1988, 242, 525–533.
- 192 Levelt, A. H. M. In Computer Algebra in Industry 2. Problem Solving in Practice; A. M. Cohen et al., Eds.; Wiley: New York, 1995, pp 227–238.
- 193 Levelt, A. H. M. www-math.sci.kun.nl/medewerkers/ahml/engels.pdf; 1998.
- 194 Levitt, M. H. Spin Dynamics: Basic Principles of NMR Spectroscopy; Wiley: New York, 2001.
- 195 Lewis, R. H.; Bridgett, S. (in preparation).
- 196 Li, J.; Pauncz, R. Int J Quantum Chem 1997, 62, 245–259.
- 197 Li, K. B.; Sanctuary, B. C. J Chem Info Comput Sci 1997, 37, 467–477.
- 198 Li, Z. B.; Liu, Y. P. Comput Phys Comm 2002, 148, 256–266.
- 199 Lipkin, H. Lie Groups for Pedestrians; North-Holland: Amsterdam, 1965.
- 200 Ljung, L.; Glad, T. Automatica 1994, 30, 265–276.
- 201 Loveall, D.; Hamley, M. B.; Miller, B. J.; Bartschat, K. Comput Phys Comm 2000, 124, 90–103.
- 202 Lustig, S.; Rastogi, S.; Wagner, N. J Comput Phys 1995, 122, 317–322.
- 203 Majumdar, A. J Magn Reson A 1996, 121, 121–126.
- 204 Man, P. P. J Magn Reson A 1995, 113, 40–46.
- 205 Manocha, D.; Zhu, Y. (a) Proceedings of the 2nd International Conference on Molecular Biology 1994, 285–294; (b) www.cs.unc.edu/dm/.
- 206 Manocha, D.; Zhu, Y.; Wright, W. (a) CABIOS. 11 1995, 71–86; (b) www.cs.unc.edu/dm/.
- 207 Mansfield, E. L.; Reid, G. J.; Clarkson, P. A. Comput Phys Comm 1998, 115, 460–488.
- 208 March, N. H.; Squire, R. H. Int J Quantum Chem 2003, 92, 261–275.
- 209 Margaria, G.; Riccomagno, E.; Chappell, M. C.; Wynn, H. P. Math Biosci 2001, 174, 1–26.
- 210 Martin, J.; François, J.; Gjebels, R. J Chem Phys 1992, 97, 3530–3536.
- 211 Martin, V.; Robledo, L. Comput Phys Comm 1996, 99, 113–127.
- 212 McCarthy, S. A.; Wang, J. B.; Abbott, P. C. Comput Phys Comm 2001, 141, 175–204.
- 213 McDowell, S. A. C. J Chem Phys 1996, 105, 4180–4184.
- 214 McDowell, S. A. C. Int J Quantum Chem 1997, 62, 343–351.
- 215 McDowell, S. A. C. J Chem Info Comput Sci 1998, 38, 1102–1104.
- 216 McDowell, H. K.; Clogston, A. M. J Chem Phys 1995, 102, 9026–9039.
- 217 McDowell, S. A. C.; Meath, W. Chem Phys 1997, 223, 23–32.
- 218 Meijer, P. H. E. J Chem Phys 1994, 101, 5140–5147.
- 219 Meissner, H.; Steinborn, E. O. Phys Rev A 1997, 56, 1189–1200.
- 220 Mercier, G. A. Magn Reson Imag 1998, 16, 811–828.
- 221 Mesquita, M. V.; Vasconcellos, Á. R.; Luzzi, R. Int J Quantum Chem 1996, 60, 689–697.
- 222 Metzler, R.; Compte, A. J Phys Chem B 2000, 104, 3858–3865.
- 223 Minimair, M.; Barnett, M. P. (to be published).
- 224 Mitani, M.; Aoki, Y.; Imamura, A. Int J Quantum Chem 1997, 64, 301–323.
- 225 Moritomo, Y.; Tokura, Y.; Oohashi, T.; Kojima, T.; Itsubo, A. J Chem Phys 1992, 96, 8507–8513.
- 226 Murray, R. M.; Li, Z.; Sastry, S. S. A Mathematical Introduction to Robotic Manipulation; CRC Press: Boca Raton, FL, 1994.
- 227 Nakao, T.; Tanaka, F.; Kohjiya, S. Macromolecules 2002, 35, 5649–5656.
- 228 Neubüser, J. In Computational Problems in Abstract Algebra, Proceedings of the 1967 Conference; Leech, J., Ed.;Pergamon: Oxford, UK, 1970, pp 1–19.
- 229 Ng, C. S.; Bhattacharjee, A. Nucl Instrum Meth Phys Res A 1999, 429, 88–93.
- 230 Nguyen, N.; Nguyen-Dang, T. T. Comput Phys Comm 1998, 115, 183–199.
- 231 Noble, C. J. Comput Phys Comm 1980, 19, 327–335.
- 232 Novak, I. J Chem Info Comput Sci 1999, 39, 579–581.
- 233
Olver, P.
Applications of Lie Groups to Differential Equations, 2nd ed.;
Springer:
New York,
1993.
10.1007/978-1-4612-4350-2 Google Scholar
- 234 Opgenorth, J.; Plesken, W.; Schulz, T. Acta Crystallogr A 1998, 54, 517–531.
- 235 Orlowski, A.; Wódkiewicz, K. Phys Rev A 1994, 50, 5355–5362.
- 236 Ouvrard, B. N.; Ouvrard, J. M.; Courtieu, J. Bull Soc Chim Fr 1994, 131, 227–241.
- 237 Ovsiannikov, L. V. Group Analysis of Differential Equations; Academic Press: New York, 1982.
- 238 Paldus, J. In Theoretical Chemistry: Advances and Perspectives, vol. 2; H. Eyring; D. Henderson, Eds.; Academic Press: New York, 1976, pp 131–290.
- 239 Panero, C.; Bini, R.; Schettino, V. J Chem Phys 1994, 100, 7938–7944.
- 240 Parkes, E. J.; Duffy, B. R. Comput Phys Comm 1996, 98, 288–300.
- 241 Perinova, V.; Luks, A.; Krepelka, J.; Sibilia, C.; Bertolotti, M. J Mod Opt 1996, 43, 13–38.
- 242 Piecuch, P. Int J Quantum Chem 1993, 47, 261–305.
- 243 Piecuch, P.; Paldus, J. J Math Chem 1997, 21, 51–70.
- 244 Piecuch, P.; Tobola, R.; Paldus, J. Phys Rev A 1996, 54, 1210–1241.
- 245 Pisanski, T.; Plavsic, D.; Randic, M. J Chem Info Comput Sci 2000, 40, 520–523.
- 246 Pokorny, A.; Herzig, P.; Altmann, S. L. Spectrochim Acta A 2001, 57, 1931–1939.
- 247
Pólya, G.;
Read, R. C.
Combinatorial Enumeration of Groups, Graphs, and Chemical Compounds;
Springer:
New York,
1987.
10.1007/978-1-4612-4664-0 Google Scholar
- 248 Pulov, V.; Uzunov, I.; Chacarov, E. Phys Rev E 1998, 57, 3468–3477.
- 249 Raksanyi, A.; Lecourtier, Y.; Walter, E.; Venot, A. Math Biosci 1985, 77, 245.
- 250 Ratkiewicz, A.; Truong, T. N. J Chem Info Comput Sci 2003, 43, 36–44.
- 251 Rempe, S. B.; Watts, R. O. J Chem Phys 1998, 108, 10084–10095.
- 252 Repetowicz, P.; Grimm, U.; Schreiber, M. Phys Rev B 1998, 58, 13482–13490.
- 253 Rerat, M.; Gelize, M.; Liotard, D. J Math Chem 1997, 22, 235–247.
- 254 Righi, A. F. M.; Kuhnen, C. A. Int J Mod Phys C 1997, 8, 1159–1168.
- 255 Rodriguez, I.; Ruiz-Cabello, J. Concepts Magn Reson 2001, 13, 143–147.
- 256 Rubenstein, B. Y.; Leshansky, A. M. Langmuir 2000, 16, 2049–2051.
- 257 Safouhi, H.; Pinchon, D.; Hoggan, P. Int J Quantum Chem 1998, 70, 181–188.
- 258 Sage, M. L. J Mol Struct 1990, 223, 407–413.
- 259 Salvador, J. M.; Hernandez, K.; Beltran, A.; Duran, R.; Mactutis, A. J Chem Info Sci 1998, 38, 1105–1110.
- 260 Samardzija, N.; Greller, L. D.; Wasserman, E. J Chem Phys 1989, 90, 2296–2304.
- 261 Sanchez, F.; Leflohic, M.; Besnard, P.; François, P.; Stephan, G. J Phys III 1995, 5, 281–295.
- 262
Sattinger, D. H.;
Weaver, O. L.
Lie Groups and Algebras with Applications to Physics, Geometry and Mechanics;
Wiley:
New York,
1986.
10.1007/978-1-4757-1910-9 Google Scholar
- 263 Schuermann, H. W.; Schmoldt, R. Z Phys B 1993, 92, 179–186.
- 264 Schulz, A. R.; Suedi, J. J Theor Biol 1996, 182, 397–403.
- 265 Schwegler, E.; Challacombe, M. J Chem Phys 1999, 111, 6223–6229.
- 266 Sedlák, M. J Chem Phys 1994, 101, 10140–10144.
- 267 Senthilvelan, M.; Poladian, L.; de Sterke, C. M. Phys Rev E 2002, 65, 66607, part 2.
- 268 Simonson, T.; Perahia, D. Comput Phys Comm 1995, 91, 291–303.
- 269 Skála, L.; C̆íz̆ek, J.; Dvorak, J.; S̆pirko, V. Phys Rev A 1996, 53, 2009–2020.
- 270 SMILES. http://www.daylight.com/dayhtml/smiles/.
- 271 Sobral, R. R.; Guimaraes, A. P.; da Silva, X. A. J Phys Condens Matter 1993, 5, L671–L676.
- 272 Sobral, R.; Guimaraes, A.; Da Silva, X. A. In Proceedings of the 9th International Symposium on Magnetic Anisotropy and Coercivity in Rare Earth Transition Metal Alloys; Missell, F. P., Ed.; World Scientific: Singapore, 1996, pp 175–184.
- 273 Souvignier, B. Acta Crystallogr A 2003, 59, 210–220.
- 274 Strange, R.; Manby, F. R.; Knowles, P. J. Comput Phys Comm 2001, 136, 310–318.
- 275 Straubinger, K.; Schick, F.; Lutz, O. Magn Reson Mater Phys Biol Med 1995, 3, 109–118.
- 276 Straubinger, K.; Schick, F.; Lutz, O. J Magn Reson B 1996, 110, 188–194.
- 277 Sugita, A.; Yamashita, M.; Kobayashi, T. J Chem Phys 2001, 114, 2369–2376.
- 278 Sushkin, N. V.; Phillies, G. D. J. J Chem Phys 1995, 103, 4600–4612.
- 279 Symbolic analysis focus group. www.ilovemaths.co.uk/sag/index.shtml.
- 280 Szöcs, V.; Banacky, P. Chem Phys 1994, 186, 161–173.
- 281 Szöcs, V.; Banacky, P.; Reineker, P. Chem Phys 1995, 199, 1–18.
- 282 Szöcs, V.; Kaufmann, H. J Chem Phys 1998, 109, 7431–7442.
- 283 Tadić, M.; Ikonić, Z.; Milanović, V. Phys Rev E 1996, 53, 6523–6529.
- 284 Takada, K. Comput Phys Comm 1992, 69, 142–154.
- 285 Tam, H.; Hu, X. Phys Lett A 2000, 272, 174–183.
- 286 Taneri, U.; Paldus, J. Int J Quantum Chem Quantum Chem Symp 1994, 28, 139–154.
- 287 Teboul, V.; Leduff, Y.; Bancewicz, T. J Chem Phys 1995, 103, 1384–1390.
- 288 Thiers, A. H. M.; Ephraim, M. J.; Janssen, T.; Janner, A. Comput Phys Comm 1993, 77, 167–189.
- 289 Thorkildsen, G.; Larsen, H. Acta Crystallogr A 1998, 54, 186–190.
- 290 Tian, B.; Gao, Y. T. Chaos Soliton Fract 1997, 8, 1651–1653.
- 291 Tian, B.; Gao, Y. T. Z Naturforsch A 2002, 57, 39–44.
- 292 Tian, B.; Gao, Y. T.; Xu, X. G. J Mod Opt Lett 2003, 50, 2185–2189.
- 293 Tian, B.; Li, W.; Gao, Y. T. Acta Mech 2003, 160, 235–239.
- 294 Tian, B.; Li, W.; Gao, Y. T. Int J Mod Phys C 2003, 14, 215–220.
- 295 Trinajstić, N. Chemical Graph Theory, 2nd ed.; CRC Press: Boca Raton, FL, 1992.
- 296 Ueta, T. J Phys Soc Jpn 1995, 64, 877–886.
- 297 Untidt, T. S.; Nielsen, N. C. Phys Rev E 2002, 65, 21108, 1–17.
- 298 van Almsick, M.; Dolhaine, H.; Honig, H. J Chem Info Comput Sci 2000, 40, 956–966.
- 299 van Almsick, M.; Dolhaine, H.; Honig, H. MATCH 2001, 43, 153–157.
- 300 van Eijck, B. P.; Kroon, J. J Phys Chem B 1997, 101, 1096–1100.
- 301 Vermaseren, J. A. M. In Computer Algebra in Science and Engineering; J. Fleischer; J. Grabmeier; F. W. Hehl; W. Küchlin, Eds.; World Scientific: Singapore, 1995, pp 67–76.
- 302 Vinette, F. Int J Quantum Chem 1992, 42, 1737–1746.
- 303 Vinette, F.; C̆íz̆ek, J. Comput Phys Comm 1988, 52, 34–41.
- 304 Wactlar, H. D.; Barnett, M. P. Comm ACM 1964, 7, 704.
- 305 Wang, D.; Kuppermann, A. J Chem Phys 2001, 115, 9184–9208.
- 306 Wang, J. B.; Midgley, S. Phys Rev B 1999, 60, 13668–13675.
- 307 Wang, J. B.; Williams, J. F. Comput Phys Comm 1993, 75, 275–282.
- 308 Wegener, M.; Schafer, W. Semiconductor optics and transport phenomena; Springer: New York, 2002.
- 309 Weniger, E. J. Ann Phys 1996, 246, 133–165.
- 310 Weniger, E. J. Phys Rev Lett 1996, 77, 2859–2862.
- 311 Weniger, E. J. Int J Quantum Chem 1966, 57, 265–280; erratum 58, 319–321.
- 312 Weniger, E. J. Comput Phys Comm 2001, 133, 202–228.
- 313 Weniger, E. J. Private communication; 2003.
- 314 Willetts, A.; Handy, N. C.; Green, W. H.; Jayatilaka, D. J Phys Chem 1990, 94, 5608–5616.
- 315 Williams, H.; Szalewicz, K.; Moszynski, R.; Jeziorski, B. J Chem Phys 1995, 103, 4586–4599.
- 316 Wittkopf, A. D. Introduction to the Rif Package; www. cecm.sfu.ca/wittkopf/Rif.html; 2003.
- 317 Wolf, T. Eur J Appl Math 2002, 13, 129–152.
- 318 Xantheas, S. S.; Sutcliffe, B. T. J Chem Phys 1995, 103, 8022–8030.
- 319 Xu, J.; Sanctuary, B. C. J Chem Info Comput Sci 1993, 33, 490–500.
- 320 Yildirim, N.; Bayram, M. Appl Math Comput 2000, 112, 41–48.
- 321 Yildirim, N. J Math Chem 2002, 32, 271–280.
- 322 Yoo, S. M.; Javanainen, J. Phys Rev A 1992, 45, 3071–3083.
- 323 Yu, L.; Huang, M.; Chen, M.; Chen, W.; Huang, W.; Zhu, Z. Opt Lett 1998, 23, 409–411.
- 324 Yura, H.; Hanson, S.; Lading, L. J Opt Soc Am A 1995, 12, 2040–2047.
- 325 Zhang, G.; Li, Z.; Duan, Y. Sci China Ser A 2001, 44, 396–401.
- 326 Zheng, Q. Math Biosci 1998, 151, 219–225.
- 327 Zielinski, T. J. Symbolic Mathematics Documents for Physical Chemistry. http://bluehawk.monmouth.edu/tzielins/mathcad/.
