Relativistic parameterization of the scc dftb method
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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

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


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


Requirements
Requirements

  • Important issues of the project

    • general character

    • relativistic framework

    • well-defined procedure

    • high automaticity

    • error control – test suite


Theoretical framework
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


Slater koster files
Slater-Koster files

  • One-center quantities

    • orbital energies

    • orbital hardness

    • orbital spin-densities interaction parameters

  • Two-center quantities

    • Hamiltonian integrals

    • overlap integrals

    • repulsive potentials


Input description
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


Output spinors of carbon
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


Output spinors of lead
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


Output spinors of lead1
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


Output atomic density
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



Semi relativistic orbitals
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)




Output orbitals of carbon
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


Output orbitals for lead
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


Output orbitals for lead1
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






Confinement potential
Confinement potential atom

  • 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


Effect of the confinement potential radial density of pb
Effect of the confinement potential atomradial density of Pb


Repulsive potentials
Repulsive potentials atom

  • Effective two-center, distance-dependent potentials accounting for

    • repulsion between atomic chemical cores

    • double counting terms in electronic part

  • Total DFTB energy is


Constructing c c repulsive potential
Constructing C-C repulsive potential atom

M. Sternberg, Ph.D. Thesis


Repulsive c c potential
repulsive C-C potential atom

Malolepsza, Witek, and Morokuma, ChPL 412, 237 (2005)


Performance of new c c potential
performance of new C-C potential atom

Malolepsza, Witek, and Morokuma, ChPL 412, 237 (2005)





Analytical form of potentials1
Analytical form of potentials atom

  • Atomization energies


Analytical form of potentials2
Analytical form of potentials atom

  • Equilibrium structures


First derivatives of repulsive potential
First derivatives of repulsive potential atom

NO2

O3

NO2-

H2O2

H2O

H2O2

H3O+

NH3

O3

H2

O2


First derivatives of repulsive potential1
First derivatives of repulsive potential atom

NO2-

HNO

NO2, HNO

NO

NH3

HNO

H2O2

H2O2

H3O+

H2O


Conclusions
Conclusions atom

  • Convenient relativistic tool for automatic DFTB parameterization is suggested

  • New form of potential parameterization is proposed


Acknowledgements
Acknowledgements atom

  • Christof Köhler

  • Keiji Morokuma

  • Marcus Elstner

  • Thomas Frauenheim


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