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

232 nd ACS meeting in SF, 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

232 nd ACS meeting in SF, 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

232 nd ACS meeting in SF, 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

232 nd ACS meeting in SF, 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

232 nd ACS meeting in SF, 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

232 nd ACS meeting in SF, Output: spinors of carbon * atom electronic structure and final shell energies: shell type occupation final energy ======== ======== ========== 1 S1/ S1/ P1/ P3/ * radial overlap integrals for spinors spinor 1 spinor 2 overlap integral ====== ====== =========== 1 S1/2 2 S1/

232 nd ACS meeting in SF, Output: spinors of lead * atom electronic structure and final shell energies: shell type occupation final energy ======= ======== ========= 1 S1/ S1/ P1/ P3/ S1/ … … … 5 D3/ D5/ S1/ P1/ P3/

232 nd ACS meeting in SF, Output: spinors of lead * radial overlap integrals for spinors spinor 1 spinor 2 overlap integral ====== ====== =========== 1 S1/2 2 S1/ S1/2 3 S1/ S1/2 3 S1/ P1/2 3 P1/ P3/2 3 P3/ … … … 2 P3/2 6 P3/ P3/2 6 P3/ P3/2 6 P3/ P3/2 6 P3/

232 nd ACS meeting in SF, Output: atomic density * error for the fitted atomic density at grid points density norm 1 norm 2 norm ∞ ====== ======= ====== ====== dn * renormalization of fitted density => density renormalized from to electrons * error for the fitted atomic density at grid points density norm 1 norm 2 norm ∞ ====== ======= ====== ====== dn * renormalization of fitted density => density renormalized from to electrons C Pb

232 nd ACS meeting in SF, radial density of lead

232 nd ACS meeting in SF, 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)

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

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

232 nd ACS meeting in SF, Output: orbitals of carbon * info about scalar atomic orbitals num orbital occupation final energy type ==== ===== ======== ========= ===== 1 1s core 2 2s valence 3 2p valence * error for the fitted curve at grid points orbital norm 1 norm 2 norm ∞ ===== ====== ====== ====== 2s p * renormalization after fit and neglecting small component => orbital 2s renormalized from to 1.0d0 => orbital 2p renormalized from to 1.0d0

232 nd ACS meeting in SF, Output: orbitals for lead * info about scalar atomic orbitals num orbital occupation final energy type ==== ====== ======== ========== ===== 1 1s core 2 2s core 3 2p core 4 3s core 5 3p core 6 3d core 7 4s core 8 4p core 9 4d core 10 4f core 11 5s valence 12 5p valence 13 5d valence 14 6s valence 15 6p valence

232 nd ACS meeting in SF, Output: orbitals for lead * fitting valence orbitals with gaussians * error for the fitted curve at grid points orbital norm 1 norm 2 norm ∞ ===== ====== ====== ======= 5s p d s p * renormalization after fit and neglecting small component => orbital 5s renormalized from to 1.0d0 => orbital 5p renormalized from to 1.0d0 => orbital 5d renormalized from to 1.0d0 => orbital 6s renormalized from to 1.0d0 => orbital 6p renormalized from to 1.0d0

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

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

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

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

232 nd ACS meeting in SF, 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

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

232 nd ACS meeting in SF, 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

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

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

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

232 nd ACS meeting in SF, Resultant repulsive potentials

232 nd ACS meeting in SF, Derivatives of repulsive potentials

232 nd ACS meeting in SF, Analytical form of potentials

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

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

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

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

232 nd ACS meeting in SF, 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

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