Recent developments in ADF

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ADF2007.01 Applications (I) Prof. Mauro Stener
(Trieste University) stener_at_univ.trieste.it
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Outline

• Relativistic effects
• TDDFT electronic excitations
• Valence electrons
• Core electrons
• Spin orbit coupling
• Exchange-correlation energy functionals EXC

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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
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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
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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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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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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

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Spin-orbit interaction in molecules

• Similar to atoms lower degeneracy
• States classified according to Double Groups
• Example Ih

Ih Ih2
Ag E1g(1/2)
T1g E1g(1/2) Gg(3/2)
T2g Ig(5/2)
Gg E2g(7/2) Ig(5/2)
Hg Gg(3/2) Ig(5/2)
Au E1u(1/2)
T1u E1u(1/2) Gu(3/2)
T2u Iu(5/2)
Gu E2u(7/2) Iu(5/2)
Hu Gu(3/2) Iu(5/2)
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WAu12 scalar relativistic electronic structure
M. Stener, A. Nardelli, and G. Fronzoni J. Chem.
Phys. 128, 134307 (2008)
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WAu12 spin-orbit electronic structure
Exp photodetachment of WAu12-
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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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TDDFT electronic excitations (valence)
The actual TDDFT equation solved by ADF is
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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!

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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 En
d
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TDDFT electronic excitations (valence)
WAu12 SR ZORA TZ2P LB94
Excitation energy (eV)
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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)
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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
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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
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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

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TDDFT core excitations Cr 2p CrO2Cl2
XAS Cr 2p Exp. Elettra Synchrotron Facility Gas
Phase Beam Line (Trieste) unpublished
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TDDFT core excitations TiO2 (110) Ti2p
Ti19O32H32H15
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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

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Exchange correlation functionals EXC

• ADF input

XC LDA Apply LDA Stoll GGA Apply
GGA Model MODELPOT IP HARTREEFOCK HYBRID
hybrid end
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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
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Constraints and Parametrization
Functional Constraints Training Sets
M06-L UEG, SCorF, no HF TC, BH, NC, TM
M06 UEG, SCorF TC, BH, NC, TM
M06-2X UEG, SCorF TC, BH, NC
M06-HF UEG, SCorF, full HF TC, 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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