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Relativistic parameterization of the SCC-DFTB method

Relativistic parameterization of the SCC-DFTB method. Henryk Witek Institute of Molecular Science & Department of Applied Chemistry National Chiao Tung University Hsinchu, Taiwan. Aims. Provide the DFTB community with a general and easy-to-use tool for developing Slater-Koster files

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Relativistic parameterization of the SCC-DFTB method

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  1. Relativistic parameterization of the SCC-DFTB method Henryk Witek Institute of Molecular Science & Department of Applied Chemistry National Chiao Tung University Hsinchu, Taiwan 232nd ACS meeting in SF, 12.09.2006

  2. Aims • Provide the DFTB community with a general and easy-to-use tool for developing Slater-Koster files • Develop a reliable set of SCC-DFTB parameters suitable for modeling chemical reactions

  3. Requirements • Important issues of the project • general character • relativistic framework • well-defined procedure • high automaticity • error control – test suite

  4. Theoretical framework • 4-component Dirac-Kohn-Sham equation • Modification of relativistic Dirac-Slater code of J.P. Desclaux • Comp. Phys. Comm. 1, 216 (1969) • Comp. Phys. Comm. 9, 31 (1975) • Density confinement • Spinor confinement

  5. Slater-Koster files • One-center quantities • orbital energies • orbital hardness • orbital spin-densities interaction parameters • Two-center quantities • Hamiltonian integrals • overlap integrals • repulsive potentials

  6. Input description • Atomic information • nuclear charge • number of electrons • shell occupations • Method information • exchange-correlation functional type • confinement radius • way to construct molecular XC potential • density superposition • potential superposition

  7. Output: spinors of carbon * atom electronic structure and final shell energies:     shell type      occupation       final energy  ========  ========  ==========     1 S1/2           2.00             -11.29598       2 S1/2           2.00              -0.44465       2 P1/2           1.00              -0.12665       2 P3/2           1.00              -0.12623   * radial overlap integrals for spinors     spinor 1        spinor 2            overlap integral    ======     ======         ===========      1 S1/2          2 S1/2             -0.000000000022

  8. Output: spinors of lead   * atom electronic structure and final shell energies:    shell type      occupation       final energy  =======   ========  =========      1 S1/2 2.00           -3256.80560      2 S1/2 2.00            -585.97772      2 P1/2 2.00            -564.09214      2 P3/2 4.00            -482.19388      3 S1/2 2.00            -141.89459 … … …       5 D3/2 4.00              -0.79336      5 D5/2 6.00              -0.68107      6 S1/2 2.00              -0.33752      6 P1/2 2.00              -0.09002      6 P3/2 0.00               -0.04704

  9. Output: spinors of lead    * radial overlap integrals for spinors    spinor 1        spinor 2            overlap integral   ======     ======          ===========     1 S1/2          2 S1/2              0.000000000068     1 S1/2          3 S1/2              0.000000000016     2 S1/2          3 S1/2              0.000000000186     2 P1/2          3 P1/2              0.000000000099     2 P3/2          3 P3/2              0.000000000094 … … …      2 P3/2          6 P3/2              0.000000000048     3 P3/2          6 P3/2             -0.000000000358     4 P3/2          6 P3/2             -0.000000001312     5 P3/2          6 P3/2              0.000000000096

  10. Output: atomic density  * error for the fitted atomic density at grid points    density           norm1              norm2             norm∞ ======      =======       ======      ======      dn             0.000010         0.000019         0.000104 * renormalization of fitted density       => density renormalized from 5.999981 to 6.000000 electrons C   * error for the fitted atomic density at grid points    density           norm1              norm2             norm∞ ======      =======       ======      ======       dn            0.030532         0.049705         0.147628 * renormalization of fitted density       => density renormalized from 82.000529 to 82.000000 electrons Pb

  11. radial density of lead

  12. Semi-relativistic orbitals • Scalar relativistic valence orbitals are obtained by: • neglecting small component • averaging spin-orbit components of every scalar orbital V.Heera, G. Seifert, P. Ziesche, J. Phys. B 17, 519 (1984)

  13. Large vs. small component

  14. Averaging spin-orbit split components of a spinor

  15. Output: orbitals of carbon  * info about scalar atomic orbitals     num    orbital     occupation       final energy       type    ====   =====  ========  =========    =====      1       1s           2.00 -11.29598         core      2       2s         2.00   -0.44465         valence      3       2p 2.00    -0.12637         valence * error for the fitted curve at grid points   orbital           norm1              norm2            norm∞  =====       ======        ======       ======      2s      0.000231        0.000721        0.005025      2p       0.000013       0.000025        0.000108 * renormalization after fit and neglecting small component      => orbital 2s renormalized from     0.999957   to     1.0d0      => orbital 2p renormalized from     0.999957   to     1.0d0

  16. Output: orbitals for lead  * info about scalar atomic orbitals     num     orbital     occupation       final energy         type    ====  ======  ========  ==========    =====      1       1s           2.00           -3256.80560         core      2       2s           2.00            -585.97772         core      3       2p           6.00            -509.49330         core      4       3s           2.00            -141.89459         core      5       3p           6.00            -119.52024         core      6       3d          10.00             -94.16394         core      7       4s           2.00             -32.79553         core      8       4p           6.00             -25.30912         core      9       4d          10.00             -15.92391         core      10       4f          14.00              -5.84011         core      11       5s           2.00              -5.53058        valence      12       5p           6.00              -3.33518        valence      13       5d        10.00            -0.72598        valence      14       6s           2.00               -0.33752        valence      15       6p           2.00               -0.06137        valence

  17. Output: orbitals for lead  * fitting valence orbitals with gaussians * error for the fitted curve at grid points   orbital           norm1              norm2             norm∞  =====       ======        ======       =======      5s        0.000048        0.000138        0.002025      5p        0.000047        0.000094        0.000988      5d        0.000143        0.000245        0.000807      6s        0.000108        0.000257        0.003610      6p        0.000026        0.000045        0.000371 * renormalization after fit and neglecting small component      => orbital 5s renormalized from     0.999235   to     1.0d0      => orbital 5p renormalized from     0.990674   to     1.0d0      => orbital 5d renormalized from     0.998799   to     1.0d0      => orbital 6s renormalized from     0.999913   to     1.0d0      => orbital 6p renormalized from     0.991615   to     1.0d0

  18. Relativistic vs. non-relativistic atomic orbitals: carbon atom

  19. Relativistic vs. non-relativistic atomic orbitals: carbon atom

  20. Relativistic vs. non-relativistic atomic orbitals: lead atom

  21. Relativistic vs. non-relativistic atomic orbitals: lead atom

  22. Confinement potential • Additional term Vconf in Dirac-Kohn-Sham effective potential • contraction of orbital’s exponential tail • relaxation of basis set • additional variational parameter in the formalism

  23. Effect of the confinement potentialradial density of Pb

  24. Repulsive potentials • Effective two-center, distance-dependent potentials accounting for • repulsion between atomic chemical cores • double counting terms in electronic part • Total DFTB energy is

  25. Constructing C-C repulsive potential M. Sternberg, Ph.D. Thesis

  26. repulsive C-C potential Malolepsza, Witek, and Morokuma, ChPL 412, 237 (2005)

  27. performance of new C-C potential Malolepsza, Witek, and Morokuma, ChPL 412, 237 (2005)

  28. Resultant repulsive potentials

  29. Derivatives of repulsive potentials

  30. Analytical form of potentials

  31. Analytical form of potentials • Atomization energies

  32. Analytical form of potentials • Equilibrium structures

  33. First derivatives of repulsive potential NO2 O3 NO2- H2O2 H2O H2O2 H3O+ NH3 O3 H2 O2

  34. First derivatives of repulsive potential NO2- HNO NO2, HNO NO NH3 HNO H2O2 H2O2 H3O+ H2O

  35. Conclusions • Convenient relativistic tool for automatic DFTB parameterization is suggested • New form of potential parameterization is proposed

  36. Acknowledgements • Christof Köhler • Keiji Morokuma • Marcus Elstner • Thomas Frauenheim

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