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Numerical evaluation of overlap integrals between atomic orbitals

Artykuł
Czasopismo : JOURNAL OF MOLECULAR STRUCTURE-THEOCHEM   Tom: 848, Zeszyt: 1-3, Strony: 34-39
Zbigniew Romanowski [1] , Stanisław Krukowski [1]
2008 angielski
Identyfikatory
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Słowa kluczowe
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Abstrakty ( angielski )
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The algorithm evaluating the overlap integrals for the numerical atomic orbitals is presented. The described algorithm is general and is based on the adaptive integration over the rectangular domain in cylindrical coordinate system. It is designed to apply for Kohn-Sham eigenproblem, which is solved by Linear Combination of Atomic Orbitals with the finite support. Double application of Wigner D-matrix relation, reduces the problem to specific case, where the overlap integral is transformed from R3 to R2. Assuming the finite support of the numerical atomic orbitals, the problem is reformulated in cylindrical coordinate system and simplified to the integration over the rectangular domain. In order to perform the numerical integration over the rectangular domain, the adaptive scheme is applied, based on the seven and five order quadratures. The exemplary results for selected atomic orbitals are presented.
Bibliografia
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  1. Parr, R.G.& Yang, W., "Density-Functional Theory of Atoms and Molecules", 1989
  2. Koch, W.& Holthausen, M.C., "A Chemist’s Guide to Density Functional Theory", 2000
  3. Jones, R.O.& Gunnarsson, O., "The density functional formalism, its applications and prospects", Rev. Mod. Phys., vol. 61, 1989, p.689
  4. Cramer, C.J., "Essentials of Computational Chemistry", 2004
  5. Boys, S.F., "Electronic wave functions I.A general meethod of calculation for the stationary states of any molecular system", Proc. Roy. Soc. A, vol. 200, 1950, p.542
  6. Mulliken, R.S.& Rieke, C.A.& Orloff, D.& Orloff, H., "Formulas and numerical tables for overlap integrals", J. Chem. Phys., vol. 17, 1949, p.1248
  7. Roothaan, C.C., "A study of two-center integrals useful in calculations on molecular structure. I", J. Chem. Phys., vol. 19, 1951, p.1445
  8. Stoer, J.& Bulirsch, R., "Introduction to Numerical Analysis", 2004
  9. Sorensen, D.C., "Numerical methods for large eigenvalue problems", Acta Numer., vol. 11, 2002, p.519-584
  10. Delley, B., "An all-electron numerical method for solving the local density functional for polyatomic molecules", J. Chem. Phys., vol. 92, 1990, p.508
  11. Soler, J.S.& Artacho, E.& Gale, J.D.& Garcia, A.& Junquera, J.& Ordejon, P.& Sanchez-Portal, D., "The SIESTA method for ab initio order-N material simulation", J. Phys.: Condens. Matter., vol. 14, 2002, p.2745
  12. Romanowski, Z., "Numerical solution of Kohn-Sham equation for atom", Acta Phys. Pol. B, vol. 38, 2007, p.1001
  13. Press, W.H.& Teukolsky, S.A.& Vetterling, W.T.& Flannery, B.P., "Numerical Recipes in C", 1990
  14. Becke, A.D., "A multicenter numerical integration scheme for polyatomic molecules", J. Chem. Phys., vol. 88, 1988, p.2547
  15. Lebedev, V.I.& Laikov, D., "A quadrature formula for the sphere of the 131st algebraic order of accuracy", Doklady Math., vol. 59, 3, 1999, p.477-481
  16. Lebedev, V.I., "A quadrature formula for the sphere of 59th algebraic order of accuracy", Russian Acad. Sci. Dokl. Math., vol. 50, 1995, p.283-286
  17. Bracewell, R.N., "The Fourier Transform and Its Applications", 2000
  18. Silverstone, H.J., "On the evaluation of two-center overlap and Coulomb integrals with noninteger-n Slater-Type Orbitals", J. Chem. Phys., vol. 45, 1966, p.4337
  19. Abramowitz, M.& Stegun, I.A., "Handbook of Mathematical Functions with Formulas, Graphs, and Methematical Tables", 1972, ninth ed.
  20. Arfken, G., "Mathematical Methods for Physists", 1970, second ed.
  21. Edmonds, M.E., "Angular Momentum in Quantum Mechanics", 1957
  22. Biedenharn, L.C.& Louck, J.D., "Angular Momentum in Quantum Physics", 1981
  23. Dooren, P.& Ridder, L., "An adaptive algorithm for numerical integration over an n-dimensional cube", J. Comput. Appl. Math., vol. 2, 1976, p.207-217
  24. Genz, A.C.& Malik, A.A., "An adaptive algorithm for numerical integration over an N-dimensional rectangular region", J. Comput. Appl. Math., vol. 6, 1980, p.295-302
  25. Stroud, A.H., "Approximate Calculation of Multiple Integrals", 1971
  26. Vosko, S.H.& Wilk, L.& Nusair, M., "Accurate spin dependent electron liquid correlation energies for local spin density calculations: A critical analysis", Can. J. Phys., vol. 58, 1980, p.1200
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