An all-electron numerical method for solving the local density functional for polyatomic molecules
J. Chem. Phys. 92, 508 (1990); doi:10.1063/1.458452
Issue Date: 1 January 1990
You are not logged in to this journal. Log in
A method for accurate and efficient local density functional calculations (LDF) on molecules is described and presented with results. The method, Dmol for short, uses fast convergent three-dimensional numerical integrations to calculate the matrix elements occurring in the Ritz variation method. The flexibility of the integration technique opens the way to use the most efficient variational basis sets. A practical choice of numerical basis sets is shown with a built-in capability to reach the LDF dissociation limit exactly. Dmol includes also an efficient, exact approach for calculating the electrostatic potential. Results on small molecules illustrate present accuracy and error properties of the method. Computational effort for this method grows to leading order with the cube of the molecule size. Except for the solution of an algebraic eigenvalue problem the method can be refined to quadratic growth for large molecules.
The Journal of Chemical Physics is copyrighted by The American Institute of Physics.
| History: | Received 26 June 1989; accepted 5 September 1989 |
| Permalink: |
http://link.aip.org/link/?JCPSA6/92/508/1 |
KEYWORDS and PACS
DENSITY FUNCTIONAL METHOD,
MATRIX ELEMENTS,
POLYATOMIC MOLECULES,
ELECTRONIC STRUCTURE,
NUMERICAL SOLUTION
- 31.20.Sy
Electronic structure of atoms and molecules: theory Specific calculations and results Density functional methods (local density approximation, local spin density approximation), X
methods
- YEAR: 1990
PUBLICATION DATA
0021-9606 (print)
1089-7690 (online)
REFERENCES (36)
For access to fully linked references, you need to log in.
For access to fully linked references, you need to Log in.
- C. C. J. Roothaan,
Rev. Mod. Phys. 23, 69 (1951 ). - G. G. Hall,
Proc. R. Soc. London Ser. A 205, 541 (1951 ). - P. Hohenberg and W. Kohn,
Phys. Rev. B 136, 864 (1964 ). - W. Kohn and L. J. Sham,
Phys. Rev. A 140, A1133 (1965 ). - L. Hedin and B. I. Lundqvist,
J. Phys. C 4, 2064 (1971 ). - U. v. Barth and L. Hedin,
J. Phys. C 5, 1629 (1972 ). - O. Gunnarsson and B. I. Lundqvist,
Phys. Rev. B 13, 4274 (1976 ). - E. Wimmer, A. J. Freeman, C.-L. Fu, P.-L. Cao, S.-H. Chou, and B. Delley, in Supercomputer Research in Chemistry and Chemical Engineering, ACS Symposium Series No. 353, edited by K. F. Jensen and D. G. Truhlar (American Chemical Society, Washington, D.C., 1987), p. 49ff.
- R. O. Jones and O. Gunnarsson, Rev. Mod. Phys. 61, 689 (1989).
- O. Gunnarsson, J. Harris, and R. O. Jones, Phys. Rev. B 29, 703 (1984).
- P. J. Braspenning, R. Zeller, A. Lodder, and P. H. Dederichs, Phys. Rev. B 29, 703 (1984).
- E. J. Baerends and P. Ros,
Int. J. Quant. Chem. Symp. 12, 169 (1978 ). - B. Delley, D. E. Ellis, and A. J. Freeman, Phys. Rev. Lett. 50, 488 (1983).
- S.-H. Chou, A. J. Freeman, S. Grigoras, T. M. Gentle, B. Delley, and E. Wimmer,
J. Am. Chem. Soc. 109, 1880 (1987 );
J. Chem. Phys. 89, 5177 (1988). - Ye Ling, A. J. Freeman, and B. Delley, Phys. Rev. B 39, 10144 (1989).
- B. Delley,
Chem. Phys. 110, 329 (1986 ). - P. Moeckly, D. Schwarzenbach, H.-B. Bürgi, J. Hauser, and B. Delley,
Acta Cryst. B 44, 636 (1988 ). - B. Delley (to be published).
- M. Levy, Proc. Natl. Acad. Sci. 76, 6062 (1979).
- J. C. Slater,
Phys. Rev. 81, 385 (1951 ); - L. Fritsche, Phys. Rev. B 33, 3976 (1986).
- U. v. Barth, in Many-Body Phenomena at Surfaces, edited by D. C. Langreth and H. Suhl (Academic, New York, 1984), p. 3ff.
- B. Delley and D. E. Ellis, J. Chem. Phys. 76, 1949 (1982).
- B. I. Dunlap, J. W. Connolly, and J. R. Sabin, J. Chem. Phys. 71, 3396 (1979).
- F. W. Averill and D. E. Ellis, J. Chem. Phys. 59, 6412 (1973).
- D. Heinemann, B. Fricke, and D. Kolb,
Chem. Phys. Lett. 145, 125 (1988 ). - L. Laaksonen, D. Sundholm, and P. Pyykkö,
Int. J. Quant. Chem. 27, 601 (1988 ). - F. L. Hirshfeld,
Theor. Chim. Acta B 44, 129 (1977 ). - A. D. Becke, J. Chem. Phys. 88, 2547 (1988).
- A. H. Stroud, Approximate Calculation of Multiple Integrals (Prentice-Hall, Englewood Cliffs, NJ, 1971).
- V. I. Lebedev,
Zh. Vychisl. Mat. Mat. Fiz. 15, 48 (1975 ). - V. I. Lebedev,
Zh. Vychisl. Mat. Mat. Fiz. 16, 293 (1977 ). - S. I. Konyaev, Mat. Zametki 25, 629 (1979).
- D. E. Ellis and G. S. Painter,
Phys. Rev. B 2, 2887 (1970 ). - This approach is similar to the method of A. D. Becke and R. M. Dickson, J. Chem. Phys. 89, 2993 (1988). The present method has been used to calculate the electrical field at the nucleus in Ref. 16 and is routinely being used in the selfconsistent calculations since 1987.
- P. M. Boerrigter, G. te Velde, and E. J. Baerends,
Int. J. Quant. Chem. 33, 87 (1988 ).








