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

2. 16 April 2008 ADF workshop at CINECA ADF applications (I) http://www.scm.com Outline Relativistic effects TDDFT electronic excitations –Valence electrons –Core electrons –Spin orbit coupling Exchange-correlation energy functionals E XC

3. 16 April 2008 ADF workshop at CINECA ADF applications (I) http://www.scm.com Relativistic effects Why? Inner shell electrons of heavy metals have relativistic velocities (transition elements of the 2 nd and 3 rd row of d-block) General problem: The Dirac equation (4 components) –Problems: variational collapse, large dimensions Large component Small component

4. 16 April 2008 ADF workshop at CINECA ADF applications (I) http://www.scm.com 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 = 0 E E = mc 2 E = -mc 2

5. 16 April 2008 ADF workshop at CINECA ADF applications (I) http://www.scm.com 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!

6. 16 April 2008 ADF workshop at CINECA ADF applications (I) http://www.scm.com 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)

7. 16 April 2008 ADF workshop at CINECA ADF applications (I) http://www.scm.com 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: 2p 2p 1/2 2p 3/2

8. 16 April 2008 ADF workshop at CINECA ADF applications (I) http://www.scm.com Spin-orbit interaction in molecules Similar to atoms: lower degeneracy States classified according to Double Groups Example: I h I h Ih2Ih2 AgAg E 1g (1/2) T 1g E 1g (1/2) + G g (3/2) T 2g I g (5/2) GgGg E 2g (7/2) + I g (5/2) HgHg G g (3/2) + I g (5/2) AuAu E 1u (1/2) T 1u E 1u (1/2) + G u (3/2) T 2u I u (5/2) GuGu E 2u (7/2) + I u (5/2) HuHu G u (3/2) + I u (5/2)

9. 16 April 2008 ADF workshop at CINECA ADF applications (I) http://www.scm.com WAu 12 : scalar relativistic electronic structure M. Stener, A. Nardelli, and G. Fronzoni J. Chem. Phys. 128, 134307 (2008)

10. 16 April 2008 ADF workshop at CINECA ADF applications (I) http://www.scm.com WAu 12 : spin-orbit electronic structure Exp: photodetachment of WAu 12 -

11. 16 April 2008 ADF workshop at CINECA ADF applications (I) http://www.scm.com 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

12. 16 April 2008 ADF workshop at CINECA ADF applications (I) http://www.scm.com TDDFT electronic excitations (valence) The actual TDDFT equation solved by ADF is:

13. 16 April 2008 ADF workshop at CINECA ADF applications (I) http://www.scm.com Davidson iterative diagonalization matrix is not stored, efficient density fit! i and j run over N occ a and b run over N virt TDDFT electronic excitations (valence)

14. 16 April 2008 ADF workshop at CINECA ADF applications (I) http://www.scm.com 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

15. 16 April 2008 ADF workshop at CINECA ADF applications (I) http://www.scm.com TDDFT electronic excitations (valence) Excitation energy (eV) WAu 12 SR ZORA TZ2P LB94

16. 16 April 2008 ADF workshop at CINECA ADF applications (I) http://www.scm.com TDDFT electronic excitations (valence) Large systems up to Au 146 2+ M. Stener, A. Nardelli, R. De Francesco and G. Fronzoni J. Phys. Chem. C 111, 11862 (2007) TDDFT SR ZORA DZ LB94 CINECA SP5 16 cpu 48h

17. 16 April 2008 ADF workshop at CINECA ADF applications (I) http://www.scm.com TDDFT electronic excitations (core) 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: (i,a) (j,b) core orbitals Reduced matrix M. Stener, G. Fronzoni and M de Simone, CPL 373 (2003) 115.

18. 16 April 2008 ADF workshop at CINECA ADF applications (I) http://www.scm.com TDDFT core excitations: Ti 2p TiCl 4 Inclusion of configuration mixing effects Mandatory for degenerate core orbitals (2p) ADF input: MODIFYEXCITATION USEOCCUPIED T2 2 SUBEND END G. Fronzoni, M. Stener, P. Decleva, F. Wang, T. Ziegler, E. van Lenthe, E.J. Baerends Chem. Phys. Lett. 416 56-63 (2005).

19. 16 April 2008 ADF workshop at CINECA ADF applications (I) http://www.scm.com TDDFT core excitations: Cr 2p CrO 2 Cl 2 Scalar relativistic AND spin orbit calculations SR: negligible effect SO: good description of both Cr2p 1/2 and Cr2p 3/2 features

20. 16 April 2008 ADF workshop at CINECA ADF applications (I) http://www.scm.com TDDFT core excitations: Cr 2p CrO 2 Cl 2 XAS Cr 2p Exp.: Elettra Synchrotron Facility Gas Phase Beam Line (Trieste) unpublished

21. 16 April 2008 ADF workshop at CINECA ADF applications (I) http://www.scm.com TDDFT core excitations: TiO 2 (110) Ti2p Ti 19 O 32 H 32 H 15

22. 16 April 2008 ADF workshop at CINECA ADF applications (I) http://www.scm.com Exchange correlation functionals: E XC 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

23. 16 April 2008 ADF workshop at CINECA ADF applications (I) http://www.scm.com XC {LDA {Apply} LDA {Stoll}} {GGA {Apply} GGA} {Model MODELPOT [IP]} {HARTREEFOCK} {HYBRID hybrid} end Exchange correlation functionals: E XC ADF input:

24. 16 April 2008 ADF workshop at CINECA ADF applications (I) http://www.scm.com MO6 class of xc functionals Limitations of the Popular Functionals Weak InteractionsWeak Interactions Barrier HeightsBarrier Heights Transition Metal ChemistryTransition Metal Chemistry Long-range Charge TransferLong-range Charge Transfer Y. Zhao, D. Truhlar, Univ. Minnesota Refs: http://comp.chem.umn.edu/info/DFT.htm

25. 16 April 2008 ADF workshop at CINECA ADF applications (I) http://www.scm.com Constraints and Parametrization FunctionalConstraintsTraining Sets M06-LUEG, SCorF, no HFTC, BH, NC, TM M06UEG, SCorFTC, BH, NC, TM M06-2XUEG, SCorFTC, BH, NC M06-HFUEG, SCorF, full HFTC, BH, NC 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

26. 16 April 2008 ADF workshop at CINECA ADF applications (I) http://www.scm.com

27. 16 April 2008 ADF workshop at CINECA ADF applications (I) http://www.scm.com Thank you for your attention! Questions now? Free 30-day trial available at www.scm.comwww.scm.com Questions outside presentation to: info@scm.com