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ADF2007.01 Applications (I) Prof. Mauro Stener (Trieste University) stener@univ.trieste.it

ADF2007.01 Applications (I) Prof. Mauro Stener (Trieste University) stener@univ.trieste.it. Outline. Relativistic effects TDDFT electronic excitations Valence electrons Core electrons Spin orbit coupling Exchange-correlation energy functionals E XC. Relativistic effects.

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ADF2007.01 Applications (I) Prof. Mauro Stener (Trieste University) stener@univ.trieste.it

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  1. ADF2007.01 Applications (I) Prof. Mauro Stener (Trieste University) stener@univ.trieste.it

  2. Outline • Relativistic effects • TDDFT electronic excitations • Valence electrons • Core electrons • Spin orbit coupling • Exchange-correlation energy functionals EXC ADF applications (I)http://www.scm.com

  3. Relativistic effects • Why? Inner shell electrons of “heavy” metals have relativistic velocities (transition elements of the 2nd and 3rd row of d-block) • General problem: The Dirac equation • (4 components) • Problems: variational collapse, large dimensions Large component Small component ADF applications (I)http://www.scm.com

  4. Relativistic effects: variational collapse • In quantum chemistry: finite basis set + Rayleigh-Ritz (RR) variational method • To employ the RR variational method the operator MUST be bounded from below: E E E = mc2 E = 0 E = 0 E = -mc2 ADF applications (I)http://www.scm.com

  5. Relativistic effects: transformation • In order to avoid the variational collapse and to keep only the “Large component” the Dirac hamiltonian can be properly transformed (approximation!) • Various recipes: Foldy-Wouthuysen, Douglass-Kroll, Pauli approximation… • in ADF: ZORA (Zero Order Regular Approximation) • WARNING! Special ZORA basis must be employed! ADF applications (I)http://www.scm.com

  6. Relativistic effects: AFD input • RELATIVISTIC Scalar ZORA • RELATIVISTIC SpinOrbit ZORA • Scalar: Spin-orbit terms are neglected • Conventional point group symmetry • geo opt, IR (analytical), TDDFT • Spin-orbit: • Double group symmetry • geo opt (ADF2007), IR (numerical), TDDFT(2007) ADF applications (I)http://www.scm.com

  7. 2p 2p3/2 2p 2p1/2 Spin-orbit interaction in atoms • If spin-orbit coupling is absent: orbital l and spin s are decoupled • 6 degenerate states • Spin-orbit coupling: • States are classified according to: ADF applications (I)http://www.scm.com

  8. Spin-orbit interaction in molecules • Similar to atoms: lower degeneracy • States classified according to Double Groups • Example: Ih ADF applications (I)http://www.scm.com

  9. WAu12: scalar relativistic electronic structure M. Stener, A. Nardelli, and G. Fronzoni J. Chem. Phys. 128, 134307 (2008) ADF applications (I)http://www.scm.com

  10. WAu12: spin-orbit electronic structure Exp: photodetachment of WAu12- ADF applications (I)http://www.scm.com

  11. TDDFT electronic excitations (valence) In general, the density (1)induced by an external TD perturbative field v(1) is: Where  is the dielectric susceptibility of the interacting system, not easily accessible ADF applications (I)http://www.scm.com

  12. TDDFT electronic excitations (valence) The actual TDDFT equation solved by ADF is: ADF applications (I)http://www.scm.com

  13. TDDFT electronic excitations (valence) i and j run over Nocc a and b run over Nvirt • Davidson iterative diagonalization • W matrix is not stored, efficient density fit! ADF applications (I)http://www.scm.com

  14. TDDFT electronic excitations (valence) • Input of ADF: • Warning: basis set and XC • Basis set: “diffuse” functions may be important • XC potential: correct asymptotic behavior is important: LB94, SAOP, GRAC Excitation Davidson & A2.u 150 SubEnd ONLYSING End ADF applications (I)http://www.scm.com

  15. TDDFT electronic excitations (valence) WAu12 SR ZORA TZ2P LB94 Excitation energy (eV) ADF applications (I)http://www.scm.com

  16. TDDFT electronic excitations (valence) Large systems up to Au1462+ • TDDFT SR • ZORA DZ LB94 • CINECA SP5 • 16 cpu 48h M. Stener, A. Nardelli, R. De Francesco and G. Fronzoni J. Phys. Chem. C 111, 11862 (2007) ADF applications (I)http://www.scm.com

  17. TDDFT electronic excitations (core) M. Stener, G. Fronzoni and M de Simone, CPL 373 (2003) 115. • The pairs ia e jb span the 1h-1p space • To limit the run of the indeces i and j to core orbitals • Core excitations become the lowest, are no more coupled with the valence, and  matrix is reduced: (j,b)  core orbitals   (i,a) Reduced  matrix ADF applications (I)http://www.scm.com

  18. TDDFT core excitations: Ti 2p TiCl4 G. Fronzoni, M. Stener, P. Decleva, F. Wang, T. Ziegler, E. van Lenthe, E.J. BaerendsChem. Phys. Lett. 416 56-63 (2005). • Inclusion of configuration mixing effects • Mandatory for degenerate core orbitals (2p) • ADF input: MODIFYEXCITATION USEOCCUPIED T2 2 SUBEND END ADF applications (I)http://www.scm.com

  19. TDDFT core excitations: Cr 2p CrO2Cl2 • Scalar relativistic AND spin orbit calculations • SR: negligible effect • SO: good description of both Cr2p1/2 and Cr2p3/2 features ADF applications (I)http://www.scm.com

  20. TDDFT core excitations: Cr 2p CrO2Cl2 XAS Cr 2p Exp.: Elettra Synchrotron Facility Gas Phase Beam Line (Trieste) unpublished ADF applications (I)http://www.scm.com

  21. TDDFT core excitations: TiO2 (110) Ti2p Ti19O32H’32H’’15 ADF applications (I)http://www.scm.com

  22. Exchange correlation functionals: EXC • LDA: VWN parametrization Geometry OK, NOT for binding energies! • GGA: many choices Good binding energies • Hybrid: many choices (B3LYP) employs HF exchange • Model: LB94, SAOP, GRACLB Correct asymptotic behavior: TDDFT electron excitation and dynamical polarizability • Meta – GGA: many choices ADF applications (I)http://www.scm.com

  23. Exchange correlation functionals: EXC • ADF input: XC {LDA {Apply} LDA {Stoll}} {GGA {Apply} GGA} {Model MODELPOT [IP]} {HARTREEFOCK} {HYBRID hybrid} end ADF applications (I)http://www.scm.com

  24. MO6 class of xc functionals Limitations of the Popular Functionals • Weak Interactions • Barrier Heights • Transition Metal Chemistry • Long-range Charge Transfer Y. Zhao, D. Truhlar, Univ. Minnesota Refs: http://comp.chem.umn.edu/info/DFT.htm ADF applications (I)http://www.scm.com

  25. Constraints and Parametrization UEG: uniform electron gas limit SCorF: self-correlation free HF: Hartree-Fock exchange TC: main-group thermochemistry BH: barrier heights NC: noncovalent interactions TM: transition metal chemistry ADF applications (I)http://www.scm.com

  26. ADF applications (I)http://www.scm.com

  27. Thank you for your attention! Questions now? Free 30-day trial available at www.scm.com Questions outside presentation to: info@scm.com ADF applications (I)http://www.scm.com

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