1887
Volume 2013, Issue 1
  •  E-ISSN:  Will be obtained soon 2223-506X

Abstract

This article is an introduction to a new approach to first principles electronic structure calculation. The starting point is the Hartree-Fock-Roothaan equation, in which molecular integrals are approximated by polynomials by way of Taylor expansion with respect to atomic coordinates and other variables. It leads to a set of polynomial equations whose solutions are eigenstate, which is designated as algebraic molecular orbital equation. Symbolic computation, especially, Gröbner bases theory, enables us to rewrite the polynomial equations into more trimmed and tractable forms with identical roots, from which we can unravel the relationship between physical parameters (wave function, atomic coordinates, and others) and numerically evaluate them one by one in order. Furthermore, this method is a unified way to solve the electronic structure calculation, the optimization of physical parameters, and the inverse problem as a forward problem.

Loading

Article metrics loading...

/content/journals/10.5339/connect.2013.14
2013-08-01
2020-04-01
Loading full text...

Full text loading...

/deliver/fulltext/connect/2013/1/connect.2013.14.html?itemId=/content/journals/10.5339/connect.2013.14&mimeType=html&fmt=ahah

References

  1. Bussei-Kenkyu, 2012;1(3):013103. In Japanese. Available at: http://bussei-kenkyu.jp/pdf/01/3/0030-013101.pdf
  2. Szabo A, Ostlund NS. Modern Quantum Chemistry: Introduction to Advanced Electronic Structure Theory. New York: Dover Publications 1996;
    [Google Scholar]
  3. Marx D, Hutter J. Ab Initio Molecular Dynamics: Theory and Implementation. Modern Methods and Algorithms of Quantum Chemistry, Vol. 1. 2nd ed 2000;:329477
    [Google Scholar]
  4. McLean AD, Yoshimine M. Tables of linear molecule wavefunctions. IBM J Res Dev. Supplement. 1967; 12::206
    [Google Scholar]
  5. Yasui J, Saika A. J Chem Phys. 1982; 76::468
    [Google Scholar]
  6. Yasui J, Bull Soc Discrete Variational Xα. In Japanese. 2009; 22:1,2:711
    [Google Scholar]
  7. Yasui J. Polynomial expressions of molecular integrals functionals over Slater-type-orbitals and its application to the extension of Hartree-Fock-Roothaan equation. Bull Soc Discrete Variational Xα. In Japanese. 2010; 23:1,2:5459
    [Google Scholar]
  8. Yasui J. Algebraic molecular orbital equation. Bull Soc Discrete Variational Xα. In Japanese. 2011; 23:1,2:4754
    [Google Scholar]
  9. Yasui J, to be published in Progress in Theoretical Chemistry and Physics, 2012, Springer
  10. Symbolic computation software Mathematica, http://www.wolfram.com
  11. Decker W, Greuel GM, Pfister G, Schoenemann H, Computer algebra system SINGULAR , http://www.singular.uni-kl.de/
  12. Möller HM. On decomposing systems of polynomial equations with finitely many solutions. Appl Algebra Engrg, Comm Comput. 1993; 4:4:217230
    [Google Scholar]
  13. Lazard D. Solving zero-dimensional algebraic systems. J Symbolic Comput. 1992; 13:2:117131. Available at: http://dx.doi.org/10.1016/S0747–7171(08)80086-7
    [Google Scholar]
  14. Sottile F, Eisenbud D, Grayson DR, Stillman M, Sturmfels B. Computations in algebraic geometry with Macaulay 2. Vol. 8. Berlin, Heidelberg, New York: Springer-Verlag 2001;:101130. Algorithms and Computations in Mathematics
    [Google Scholar]
  15. Cox DA, Little J, O'Shea D. Using Algebraic Geometry. 2nd ed. Berlin: Springer 2005;
    [Google Scholar]
  16. Barnett MP, Capitani JF, von zur Gathen J, Gerhard J. Symbolic calculation in chemistry: selected examples. Int J Quantum Chem. 2004; 100:2:80104
    [Google Scholar]
  17. Dewar MJS, Zoebisch EG, Healy EF, Stewart JJP. Development and use of quantum mechanical molecular models. 76. AM1: a new general purpose quantum mechanical molecular model. J Am Chem Soc. 1985; 107:13:39023909
    [Google Scholar]
  18. Stewart JJP. Optimization of parameters for semiempirical methods I. Method. J Comput Chem. 1989; 10:2:209220
    [Google Scholar]
  19. Brickenstein M. Reports on computer algebra. University of Keiserslautern, Center for Computational algebra, 2005(35). http://www.mathematik.uni-kl.de/∼zca/Reports_on_ca/35/paper_35_full.ps.gz
  20. Lichtblau D. Applications of Computer Algebra. Symbolic and Numeric Computation session. Linz, Austria, July 27–30;2008. http://downloads.hindawi.com/isrn/cm/aip/352806.pdf
  21. Arnold EA. Modular algorithms for computing Gröbner bases. J Symbolic Comput. 2003; 35:4:403419
    [Google Scholar]
  22. Yassen R, Algarni M. The three-center hybrid and four-center electron repulsion integrals over Slater type orbitals using Guseinov rotation-angular function. Int J Contemp Math Sci. 2012; 7:39:19031907
    [Google Scholar]
http://instance.metastore.ingenta.com/content/journals/10.5339/connect.2013.14
Loading
/content/journals/10.5339/connect.2013.14
Loading

Data & Media loading...

Supplements

Supplementary File 1

This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error