SYMBOLIC COMPUTATION IN CHEMISTRY AND RELATED NATURAL SCIENCES
Michael P. Barnett*
In quantum chemical calculations of the last few decades, Gaussian orbitals (GTOs) have displaced Slater orbitals (STOs)
almost entirely, because the molecular integrals that contain GTOs can be computed with much greater ease and speed. Interest
persists in STOs, however, and I am extending my early work on molecular integrals over STOs using the zeta-function expansion.
This current work is programmed largely in Mathematica, using my Mathscape package that supports mechanized derivations and
documentation in the style of traditional mathematical writing. Ongoing and recent work in related areas is listed below.
RECENT AND FORTHCOMING PUBLICATIONS
[1] M. P. Barnett, Chemical calculations and some chemicals that might calculate,
presented at Odyssey of Mathematics in Chemistry, University of Alberta, June 2-5, 2008, Int. J. Quant. Chem. 109 (8)1640-1657, 2009.
[2] M. P. Barnett, Reasoning in symbolic computation,
Communications in Computer Algebra, 42 (1) 1-17, 2008.
[3] M. P. Barnett and J. F. Capitani,
The MATHSCOUT Mathematica package to postprocess the output of other scientific programs,
Computer Physics Communications, 177, 944-950, 2007.
[4] M. P. Barnett, Mathscape and molecular integrals, Journal of Symbolic Computation, 42 (3) 265-289, 2007.
[5] M. P. Barnett, Symbolic calculation in the life sciences: trends and prospects,
Algebraic Biology 2005 - Computer Algebra in Biology, ed. H. Anai, K. Horimoto, Universal Academy Press, 1-18, Tokyo, 2006.
[6] M. P. Barnett and J. F. Capitani,
Modular chemical geometry and symbolic calculation,
in Mathematical Methods and Symbolic Calculation in Chemistry and Chemical Biology,
eds. M. P. Barnett and F. E. Harris, Int. J. Quant. Chem. 106 (1) 215-227, 2006.
[7] M. P. Barnett, Mathematical methods and symbolic calculation in chemistry and chemical biology --- the gathering momentum,
Int. J. Quant. Chem. Int J Quant Chem 106 (1) 351-354, 2006.
[8] M. Minimair and M. P. Barnett, Solving polynomial equations for chemical problems using Groebner bases,
Mol. Phys. 102 (23-24) 2521-2535, 2004.
[9] M. P. Barnett, J. F. Capitani, J. von zur Gathen and J. Gerhard,
Symbolic calculation in chemistry: selected examples,
Int. J. Quant. Chem. 100 (2) 80-104, 2004.
pdf
of version containing titles of cited papers.
[10] M. P. Barnett, Chemistry and computer algebra: past, present, future,
in J. R. Sendra, ed. Proceedings of the 2003 International Symposium on Symbolic and Algebraic Computation,
ACM Press: New York, 1-2, 2003.
[11] M. P. Barnett, Symbolic calculation of integrals by recurrence, SIGSAM Bulletin 37 {2} 49-63, 2003.
[12] M. P. Barnett, Molecular integrals and information processing,
Int. J. Quant. Chem. 95 (6) 791-805, 2003.
[13] M. P. Barnett, Transformation of harmonics for molecular calculations,
J. Chem. Inf. Comp. Sci. 43 (4) 1158-1165, 2003.
[14] M. P. Barnett, Computer algebra in the life sciences,
SIGSAM Bulletin, 36 (4) 5-32, 2002.
[15] M. P. Barnett, Digital erosion in the evaluation of molecular integrals,
Theor. Chem. Acc. 107 (4) 241-245, 2002.
[16] M. P. Barnett, T. Decker and W. Krandick,
Power series expansion of the roots of a secular equation containing symbolic elements:
Computer algebra and Moseley's law, J. Chem. Phys. 114 (23) 10265-10269, 2001.
[17] M. P. Barnett, Two-center nonexchange integrals over Slater orbitals,
J. Chem. Phys. 113 (21) 9419-9428, 2000.
[18] M. P. Barnett, Symbolic calculation of auxiliary functions for molecular integrals over Slater orbitals,
Int. J. Quantum Chem. 76 (3) 464-472, 2000.
[19] M. P. Barnett, Mathscape --- combining Mathematica and TeX, TUGBoat, 19 (2) 147-156, 1998.
[20] M. P. Barnett and K. R. Perry, Hierarchical addressing in symbolic computation,
Computers Math. Applic. 28 (8) 17-35, 1994.
[21] M. P. Barnett and K .R. Perry, Symbolic calculation for electronic publishing,
TUGBoat, 15 (3) 285-292, 1994.
[22] M. P.Barnett, Implicit rule formation in symbolic computation,
Computers Math. Applic. 26 (10) 35-50, 1993.
[23] M. P. Barnett, Algorithms,
in McGraw-Hill Encyclopedia of Science and Technology, 7th ed. 367-370, McGraw-Hill, New York, 1992.
[24] M. P. Barnett, Summing P[n][cos theta]/p[n] for certain polynomials p[n],
Computers Math. Applic. 21 (10) 79-86, 1991.
[25] M. P. Barnett, Some simple ways to construct and to use formulas mechanically,
ACM SIGSAM Bulletin, 25 (2) 21-29, 1991.
[26] M. P. Barnett, Molecular integrals over Slater orbitals, Chem. Phys. Letters, 166 (1) 65-70, 1990.
[27] M. P. Barnett and R. Xu, Infix to prefix conversion as a PST reduction, ACM SIGPLAN Notices 25 (5), 34-38, 1990.
[28] M. P. Barnett, Primitive string transformations as a reduction to normal form,
ACM SIGPLAN Notices 25 (5), 29-33, 1990.
[29] M. P. Barnett, Partial fraction formulas to sum slowly convergent series,
ACM SIGSAM Bulletin, 23 (3) 13-86, 1989.
[30] M. P. Barnett, Molecular systems to process analog and digital data associatively,
in Molecular Electronic Devices, ed. F. L. Carter, R. E. Siatkowski and H. Wohltjen, 229-244, North Holland, Amsterdam, 1988.
CURRENT INTERESTS
Links from catch phrases and citation numbers follow.
(1) overlap integrals, [4, 12, 15],
(2) Coulomb integrals, [17],
(3) other molecular integrals and related topics,
[11, 13, 18, 24, 26],
(4) nuclear magnetic resonance pulse sequences,
[1],
(5) two-electron atoms,
[16],
(6) small ring molecules [6],
(7) methods and applications of symbolic calculation /
computer algebra / functional programming, [1-22, 24],
(8) theory of biological information processing and
molecular electronics devices, [1, 27, 28, 30].
Inquiries should be addressed to
michaelb@princeton.edu.
Updated April 24, 2009.
* Visiting Research Collaborator, L. C. Allen group,
Department of Chemistry, Princeton University, Princeton, NJ 08544-1009 (1991-2002) and
Professor Emeritus of Computer and Information Science,
Brooklyn College of the City University of New York, Brooklyn, NY 11210-1229.