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ADF Applications (I) Prof. Mauro Stener (Trieste University)

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16 April 2008 ADF workshop at CINECA ADF applications (I) Outline Relativistic effects TDDFT electronic excitations –Valence electrons –Core electrons –Spin orbit coupling Exchange-correlation energy functionals E XC

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16 April 2008 ADF workshop at CINECA ADF applications (I) 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

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16 April 2008 ADF workshop at CINECA ADF applications (I) 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

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16 April 2008 ADF workshop at CINECA ADF applications (I) 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!

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16 April 2008 ADF workshop at CINECA ADF applications (I) 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)

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16 April 2008 ADF workshop at CINECA ADF applications (I) 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

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16 April 2008 ADF workshop at CINECA ADF applications (I) 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)

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

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16 April 2008 ADF workshop at CINECA ADF applications (I) WAu 12 : spin-orbit electronic structure Exp: photodetachment of WAu 12 -

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16 April 2008 ADF workshop at CINECA ADF applications (I) 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

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16 April 2008 ADF workshop at CINECA ADF applications (I) TDDFT electronic excitations (valence) The actual TDDFT equation solved by ADF is:

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16 April 2008 ADF workshop at CINECA ADF applications (I) 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)

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16 April 2008 ADF workshop at CINECA ADF applications (I) 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

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16 April 2008 ADF workshop at CINECA ADF applications (I) TDDFT electronic excitations (valence) Excitation energy (eV) WAu 12 SR ZORA TZ2P LB94

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

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16 April 2008 ADF workshop at CINECA ADF applications (I) 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.

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16 April 2008 ADF workshop at CINECA ADF applications (I) 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 (2005).

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16 April 2008 ADF workshop at CINECA ADF applications (I) 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

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

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16 April 2008 ADF workshop at CINECA ADF applications (I) TDDFT core excitations: TiO 2 (110) Ti2p Ti 19 O 32 H 32 H 15

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16 April 2008 ADF workshop at CINECA ADF applications (I) 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

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

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16 April 2008 ADF workshop at CINECA ADF applications (I) 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:

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16 April 2008 ADF workshop at CINECA ADF applications (I) 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

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16 April 2008 ADF workshop at CINECA ADF applications (I)

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16 April 2008 ADF workshop at CINECA ADF applications (I) Thank you for your attention! Questions now? Free 30-day trial available at Questions outside presentation to:

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