Visualization and integration of quantum topological atoms by spatial discretization into finite elements
M. Rafat
Manchester Interdisciplinary Biocenter (MIB), The University of Manchester, 131 Princess Street, Manchester M1 7DN, Great Britain
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P. L. A. Popelier
Manchester Interdisciplinary Biocenter (MIB), The University of Manchester, 131 Princess Street, Manchester M1 7DN, Great Britain
Manchester Interdisciplinary Biocenter (MIB), The University of Manchester, 131 Princess Street, Manchester M1 7DN, Great BritainSearch for more papers by this authorM. Rafat
Manchester Interdisciplinary Biocenter (MIB), The University of Manchester, 131 Princess Street, Manchester M1 7DN, Great Britain
Search for more papers by this authorCorresponding Author
P. L. A. Popelier
Manchester Interdisciplinary Biocenter (MIB), The University of Manchester, 131 Princess Street, Manchester M1 7DN, Great Britain
Manchester Interdisciplinary Biocenter (MIB), The University of Manchester, 131 Princess Street, Manchester M1 7DN, Great BritainSearch for more papers by this authorAbstract
We present a novel algorithm to integrate property densities over the volume of a quantum topological atom. Atoms are grown outward, starting from a sphere centered on the nucleus, by means of a finite element meshing algorithm. Bond critical points and ring critical points require special treatment. The overall philosophy as well as intricate features of this meshing algorithm are given, followed by details of the quadrature over the finite elements. An effort has been made to design a streamlined and compact algorithm, focusing on the core of challenges arising in tracing the electron density's gradient vector field. The current algorithm also generates a new type of pictures that can be a Graphical User Interface. Excellent integration errors, L(Ω), are obtained, even for atoms with (narrow) tails or sharp corners. © 2007 Wiley Periodicals, Inc. J Comput Chem 2007
References
- 1
Bader, R. F. W.
Atoms in Molecules;
Clarendon Press:
Oxford,
1990.
10.1093/oso/9780198551683.001.0001 Google Scholar
- 2 Popelier, P. L. A. Atoms in Molecules. An Introduction; Pearson: London, Great Britain, 2000.
- 3
Popelier, P. L. A.;Smith, P. J. In
Chemical Modelling: Applications and Theory, Vol.
2,
Royal Society of Chemistry Specialist Periodical Report;
A. Hinchliffe, Ed.;
Royal Society of Chemistry:
Cambridge, UK,
2002; pp.
391–448,
Ch. 8.
10.1039/9781847553324-00391 Google Scholar
- 4 Popelier, P. L. A.;Aicken, F. M.;O'Brien, S. E. In Chemical Modelling: Applications and Theory, Vol. 1, Royal Society of Chemistry Specialist Periodical Report; A. Hinchliffe, Ed.; Royal Society of Chemistry: Cambridge, UK, 2000; pp. 143–198, Ch. 3.
- 5 Becke, A. D.;Edgecombe, K. E. J Chem Phys 1990, 92, 5397.
- 6 Silvi, B.;Savin, A. Nature (London) 1994, 371, 683.
- 7 Malcolm, N. O. J.;Popelier, P. L. A. J Comput Chem 2002, 24, 437.
- 8 Biegler-Koenig, F. W.;Nguyen-Dang, T. T.;Tal, Y.;Bader, R. F. W.;Duke, A. J. J Phys B 1981, 14, 2739.
- 9
Biegler-Koenig, F. W.;Bader, R. F. W.;Tang, T. H.
J Comput Chem
1981,
3,
317.
10.1002/jcc.540030306 Google Scholar
- 10 Breneman, C. M.;Rhem, M. Program FASTINT, Rensselaer Polytechnic, New York, USA, 1992.
- 11 Volkov, A.;Gatti, C.;Abramov, Y.;Coppens, P. Acta Crystallogr A 2000, 56, 252.
- 12 Bianchi, R.;Forni, A. J App Cryst 2005, 38, 232.
- 13 Stash, A.;Tsirelson, V. J Appl Cryst 2002, 35, 371.
- 14
Biegler-Koenig, F. W.;Schonbohm, J.;Bayles, D.
J Comput Chem
2001,
22,
545.
10.1002/1096-987X(20010415)22:5<545::AID-JCC1027>3.0.CO;2-Y Google Scholar
- 15 Biegler-Koenig, F. W.;Schonbohm, J. J Comput Chem 2002, 23, 1489.
- 16 Pendás, A. M.;Luaña, V. Program PROMOLDEN, University of Oviedo, 2002. Available at http://web.uniovi.es/qcg/d-DensEl/.
- 17
Popelier, P. L. A.
Comput Phys Commun
1998,
93,
212.
10.1016/0010-4655(95)00113-1 Google Scholar
- 18 Katan, C.;Rabiller, P.;Lecomte, C.;Guezo, M.;Oisona, V.;Souhassou, M. J Appl Cryst 2003, 36, 65.
- 19 Press, W. H.;Teukolsky, S. A.;Vetterling, W. T.;Flannery, B. P. Numerical Recipes; Cambridge University Press: Cambridge, UK, 1994.
- 20
Malcolm, N. O. J.;Popelier, P. L. A.
J Comput Chem
2002,
24,
1276.
10.1002/jcc.10250 Google Scholar
- 21 Noury, S.;Krokidis, X.;Fuster, F.;Silvi, B. Comput Chem 1999, 23, 597.
- 22 Savin, A.;Nesper, R.;Wengert, S.;Fassler, T. F. Angew Chem Int Ed Engl 1997, 36, 1808.
- 23 Popelier, P. L. A. Mol Phys 1996, 87, 1169.
- 24 Joe, B. Adv Eng Software 1991, 13, 325.
- 25 Rafat, M.;Devereux, M.;Popelier, P. L. A. J Mol Graph Model 2005, 24, 111.
- 26 Popelier, P. L. A. Comput Phys Commun 1998, 108, 180.
- 27 Clark, D. E.;Pickett, S. D. Drug Disc Today 2000, 5, 49.
- 28 Zienkiewicz, O. C. Finite Element Method; McGraw Hill; London, 1977.
- 29 Frisch, M. J.;Trucks, G. W.;Schlegel, H. B.;Scuseria, G. E.;Robb, M. A.;Cheeseman, J. R.;Zakrzewski, V. G.;Montgomery,JrJ. A.;Stratmann, R. E.;Burant, J. C.;Dapprich, S.;Millam, J. M.;Daniels, A. D.;Kudirn, K. N.;Strain, M. C.;Farkas, O.;Tomasi, J.;Barone, V.;Cossi, M.;Cammi, R.;Mennucci, B.;Pomelli, C.;Adamo, C.;Clifford, S.;Ochterski, J.;Petersson, G. A.;Ayala, P. Y.;Cui, Q.;Morokuma, K.;Malick, D. K.;Rabuck, A. D.;Raghavachari, K.;Foresman, J. B.;Cioslowski, J.;Ortiz, J. V.;Baboul, A. G.;Stefanov, B. B.;Liu, G.;Liashenko, A.;Piskorz, P.;Komaromi I.;Gomperts, R.;Martin, R. L.;Fox, D. J.;Keith, T.;Al-Laham, M. A.;Peng, C. Y.;Nanayakkara, A.;Gonzalez, C.;Challacombe, M.;Gill, P. M. W.;Johnson, B.;Chen, W.;Wong, M. W.;Andres, J. L.;Gonzalez, C.;Head-Gordon, M.;Replogle, E. S.;Pople, J. A. Gaussian 98, Revision A7. Gaussian, Inc, Pittsburgh PA, USA, 1998.
- 30 Popelier, P. L. A. Mol Phys 1996, 87, 1169.
- 31 Aicken, F. M.;Popelier, P. L. A. Can J Chem 2000, 78, 415.
- 32 Rafat, M.;Popelier, P. L. A. J Comp Chem 2007, 28, 292.
- 33 Stroud, A. H. Approximate Calculation of Multiple integrals; Prentice-Hall Englewood Cliffs, New Jersey, USA, 1971.
- 34 Gartling, D. K.;Hogan, R. E. COYOTE—A Finite Element Computer Program for Nonlinear Heat Conduction Problems, Part I: Theoretical Background; Sandia National Laboratories: Albuquerque, New Mexico, USA, 1994.
- 35
Biegler-Koenig, F. W.
J Comput Chem
2000,
21,
1040.
10.1002/1096-987X(200009)21:12<1040::AID-JCC2>3.0.CO;2-8 Google Scholar
