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

2. 232 nd ACS meeting in SF, 13.09.2006 Aims Provide the DFTB community with a general and easy-to-use tool for developing Slater-Koster files 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 Develop a reliable set of SCC-DFTB parameters suitable for modeling chemical reactions

3. 232 nd ACS meeting in SF, 13.09.2006 Requirements Important issues of the project Important issues of the project general character general character relativistic framework relativistic framework well-defined procedure well-defined procedure high automaticity high automaticity error control – test suite error control – test suite

4. 232 nd ACS meeting in SF, 13.09.2006 Theoretical framework 4-component Dirac-Kohn-Sham equation 4-component Dirac-Kohn-Sham equation Modification of relativistic Dirac-Slater code of J.P. Desclaux Modification of relativistic Dirac-Slater code of J.P. Desclaux Comp. Phys. Comm. 1, 216 (1969) Comp. Phys. Comm. 1, 216 (1969) Comp. Phys. Comm. 9, 31 (1975) Comp. Phys. Comm. 9, 31 (1975) Density confinement Density confinement Spinor confinement Spinor confinement

5. 232 nd ACS meeting in SF, 13.09.2006 Slater-Koster files One-center quantities One-center quantities orbital energies orbital energies orbital hardness orbital hardness orbital spin-densities interaction parameters orbital spin-densities interaction parameters Two-center quantities Two-center quantities Hamiltonian integrals Hamiltonian integrals overlap integrals overlap integrals repulsive potentials repulsive potentials

6. 232 nd ACS meeting in SF, 13.09.2006 Input description Atomic information Atomic information nuclear charge nuclear charge number of electrons number of electrons shell occupations shell occupations Method information Method information exchange-correlation functional type exchange-correlation functional type confinement radius confinement radius way to construct molecular XC potential way to construct molecular XC potential density superposition density superposition potential superposition potential superposition

7. 232 nd ACS meeting in SF, 13.09.2006 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. 232 nd ACS meeting in SF, 13.09.2006 Output: spinors of lead * atom electronic structure and final shell energies: shell type occupation final energy ======= ======== ========= 1 S1/22.00 -3256.80560 2 S1/22.00 -585.97772 2 P1/22.00 -564.09214 2 P3/24.00 -482.19388 3 S1/22.00 -141.89459 … … … 5 D3/24.00 -0.79336 5 D5/26.00 -0.68107 6 S1/22.00 -0.33752 6 P1/22.00 -0.09002 6 P3/20.00 -0.04704

9. 232 nd ACS meeting in SF, 13.09.2006 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. 232 nd ACS meeting in SF, 13.09.2006 Output: atomic density * error for the fitted atomic density at grid points density norm 1 norm 2 norm ∞ ====== ======= ====== ====== dn 0.000010 0.000019 0.000104 * renormalization of fitted density => density renormalized from 5.999981 to 6.000000 electrons * error for the fitted atomic density at grid points density norm 1 norm 2 norm ∞ ====== ======= ====== ====== dn 0.030532 0.049705 0.147628 * renormalization of fitted density => density renormalized from 82.000529 to 82.000000 electrons C Pb

11. 232 nd ACS meeting in SF, 13.09.2006 radial density of lead

12. 232 nd ACS meeting in SF, 13.09.2006 Semi-relativistic orbitals Scalar relativistic valence orbitals are obtained by: Scalar relativistic valence orbitals are obtained by: neglecting small component neglecting small component averaging spin-orbit components of every scalar orbital averaging spin-orbit components of every scalar orbital V.Heera, G. Seifert, P. Ziesche, J. Phys. B 17, 519 (1984)

13. 232 nd ACS meeting in SF, 13.09.2006 Large vs. small component

14. 232 nd ACS meeting in SF, 13.09.2006 Averaging spin-orbit split components of a spinor

15. 232 nd ACS meeting in SF, 13.09.2006 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 norm 1 norm 2 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. 232 nd ACS meeting in SF, 13.09.2006 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. 232 nd ACS meeting in SF, 13.09.2006 Output: orbitals for lead * fitting valence orbitals with gaussians * error for the fitted curve at grid points orbital norm 1 norm 2 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. 232 nd ACS meeting in SF, 13.09.2006 Relativistic vs. non-relativistic atomic orbitals: carbon atom

19. 232 nd ACS meeting in SF, 13.09.2006 Relativistic vs. non-relativistic atomic orbitals: carbon atom

20. 232 nd ACS meeting in SF, 13.09.2006 Relativistic vs. non-relativistic atomic orbitals: lead atom

21. 232 nd ACS meeting in SF, 13.09.2006 Relativistic vs. non-relativistic atomic orbitals: lead atom

22. 232 nd ACS meeting in SF, 13.09.2006 Confinement potential Additional term V conf in Dirac-Kohn-Sham effective potential Additional term V conf in Dirac-Kohn-Sham effective potential contraction of orbital’s exponential tail contraction of orbital’s exponential tail relaxation of basis set relaxation of basis set additional variational parameter in the formalism additional variational parameter in the formalism

23. 232 nd ACS meeting in SF, 13.09.2006 Effect of the confinement potential radial density of Pb

24. 232 nd ACS meeting in SF, 13.09.2006 Repulsive potentials Effective two-center, distance-dependent potentials accounting for Effective two-center, distance-dependent potentials accounting for repulsion between atomic chemical cores repulsion between atomic chemical cores double counting terms in electronic part double counting terms in electronic part Total DFTB energy is Total DFTB energy is

25. 232 nd ACS meeting in SF, 13.09.2006 Constructing C-C repulsive potential M. Sternberg, Ph.D. Thesis

26. 232 nd ACS meeting in SF, 13.09.2006 repulsive C-C potential Malolepsza, Witek, and Morokuma, ChPL 412, 237 (2005)

27. 232 nd ACS meeting in SF, 13.09.2006 performance of new C-C potential Malolepsza, Witek, and Morokuma, ChPL 412, 237 (2005)

28. 232 nd ACS meeting in SF, 13.09.2006 Resultant repulsive potentials

29. 232 nd ACS meeting in SF, 13.09.2006 Derivatives of repulsive potentials

30. 232 nd ACS meeting in SF, 13.09.2006 Analytical form of potentials

31. 232 nd ACS meeting in SF, 13.09.2006 Analytical form of potentials Atomization energies Atomization energies

32. 232 nd ACS meeting in SF, 13.09.2006 Analytical form of potentials Equilibrium structures Equilibrium structures

33. 232 nd ACS meeting in SF, 13.09.2006 First derivatives of repulsive potential O2O2 O3O3 NO 2 O 3 NO 2 - H2H2 H2OH2O H 3 O + NH 3 H2O2H2O2 H2O2H2O2

34. 232 nd ACS meeting in SF, 13.09.2006 First derivatives of repulsive potential NO 2, HNO NO 2 - NO NH 3 HNO H2OH2O H3O+H3O+ H2O2H2O2 H2O2H2O2

35. 232 nd ACS meeting in SF, 13.09.2006 Conclusions Convenient relativistic tool for automatic DFTB parameterization is suggested Convenient relativistic tool for automatic DFTB parameterization is suggested New form of potential parameterization is proposed New form of potential parameterization is proposed

36. 232 nd ACS meeting in SF, 13.09.2006 Acknowledgements Christof Köhler Christof Köhler Keiji Morokuma Keiji Morokuma Marcus Elstner Marcus Elstner Thomas Frauenheim Thomas Frauenheim