ADF 2007 01 Applications I Prof Mauro Stener

ADF 2007. 01 Applications (I) Prof. Mauro Stener (Trieste University) stener@univ. trieste. it ADF applications (I) http: //www. scm. com 16 April 2008 ADF workshop at CINECA

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 16 April 2008 ADF workshop at CINECA

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) Large • General problem: The Dirac equation (4 components) component Small – Problems: variational collapse, large dimensions ADF applications (I) http: //www. scm. component 16 April 2008 ADF workshop at CINECA

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

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 16 April 2008 ADF workshop at CINECA

Relativistic effects: AFD input RELATIVISTIC Scalar ZORA RELATIVISTIC Spin. Orbit ZORA • Scalar: Spin-orbit terms are neglected – Conventional point group symmetry – geo opt, IR (analytical), TDDFT • Spin-orbit: – Double group symmetry – geo opt (ADF 2007), IR (numerical), TDDFT(2007) ADF applications (I) http: //www. scm. com 16 April 2008 ADF workshop at CINECA

Spin-orbit interaction in atoms • If spin-orbit coupling is absent: orbital l and spin s are decoupled 2 p 6 degenerate states • Spin-orbit coupling: • States are classified according to: 2 p 2 p 3/2 2 p 1/2 ADF applications (I) http: //www. scm. com 16 April 2008 ADF workshop at CINECA

Spin-orbit interaction in molecules • Similar to atoms: lower degeneracy • States classified according to Double Groups I h 2 • Example: Ih Ag E 1 g(1/2) T 1 g E 1 g(1/2) + Gg(3/2) T 2 g Ig(5/2) Gg E 2 g(7/2) + Ig(5/2) Hg Gg(3/2) + Ig(5/2) Au E 1 u(1/2) T 1 u E 1 u(1/2) + Gu(3/2) T 2 u Iu(5/2) Gu E 2 u(7/2) + Iu(5/2) Hu Gu(3/2) + Iu(5/2) ADF applications (I) http: //www. scm. com 16 April 2008 ADF workshop at CINECA

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

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

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 16 April 2008 ADF workshop at CINECA

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

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

TDDFT electronic excitations (valence) • Input of ADF: Excitation Davidson & A 2. u 150 Sub. End ONLYSING End • Warning: basis set and XC – Basis set: “diffuse” functions may be important – XC potential: correct asymptotic behavior is important: LB 94, SAOP, GRAC ADF applications (I) http: //www. scm. com 16 April 2008 ADF workshop at CINECA

TDDFT electronic excitations (valence) WAu 12 SR ZORA TZ 2 P LB 94 Excitation energy (e. V) ADF applications (I) http: //www. scm. com 16 April 2008 ADF workshop at CINECA

TDDFT electronic excitations (valence) Large systems up to Au 1462+ TDDFT SR ZORA DZ LB 94 CINECA SP 5 16 cpu 48 h M. Stener, A. Nardelli, R. De Francesco and G. Fronzoni J. Phys. Chem. C 111, 11862 (2007) ADF applications (I) http: //www. scm. com 16 April 2008 ADF workshop at CINECA

TDDFT electronic excitations (core) M. Stener, G. Fronzoni and M de Simone, CPL 373 (2003) 115. ØThe pairs ia e jb span the 1 h-1 p space ØTo limit the run of the indeces i and j to core orbitals ØCore excitations become the lowest, are no more coupled with the valence, and matrix is reduced: (j, b) (i, a) core orbitals Reduced matrix ADF applications (I) http: //www. scm. com 16 April 2008 ADF workshop at CINECA

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

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

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

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

Exchange correlation functionals: EXC ØLDA: VWN parametrization Geometry OK, NOT for binding energies! ØGGA: many choices Good binding energies ØHybrid: many choices (B 3 LYP) employs HF exchange ØModel: LB 94, SAOP, GRACLB Correct asymptotic behavior: TDDFT electron excitation and dynamical polarizability ØMeta – GGA: many choices ADF applications (I) http: //www. scm. com 16 April 2008 ADF workshop at CINECA

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

MO 6 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 16 April 2008 ADF workshop at CINECA

Constraints and Parametrization Functional Constraints Training Sets UEG, SCor. F, no HF TC, BH, NC, TM M 06 UEG, SCor. F TC, BH, NC, TM M 06 -2 X UEG, SCor. F TC, BH, NC M 06 -HF UEG, SCor. F, full HF TC, BH, NC M 06 -L UEG: uniform electron gas limit SCor. F: 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 16 April 2008 ADF workshop at CINECA

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

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