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 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 2nd
and 3rd row of d-block)
Large
• General problem: The Dirac equation
(4 components)
 mc 2  V

 c  p

component
c  p   
  

   E  
2

 mc  V   
  
– Problems: variational collapse, large dimensions
ADF applications (I)
http://www.scm.com
Small
component
16 April 2008
ADF workshop at CINECA
Relativistic effects: variational collapse
• In quantum chemistry: finite basis set + RayleighRitz (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
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 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
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
2p
6 degenerate states
• Spin-orbit coupling: s
ˆ  lˆ
ˆ
ˆ
j

l
 sˆ
• States are classified according to:
2p
2p3/2
2p1/2
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
Ih Ih2
• Example: Ih
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)
ADF applications (I)
http://www.scm.com
16 April 2008
ADF workshop at CINECA
WAu12: scalar relativistic electronic structure
M. Stener, A. Nardelli, and G. Fronzoni
J. Chem. Phys. 128, 134307 (2008)
0
W
WAu12
Au12
Au
[Xe]4f145d106s1
-2
-4
6p
6p
7t1u
8t1u
7hg(HOMO)
KS
-6
5ag
6ag
-8
5d
6s
5t2u
8hg(LUMO)
-10
7hg(HOMO)
6ag
5t2u
7hg
6s
7t1u
-12
5d
4ag
-14
5t1u
4hg
-16
5ag
4t1u
3ag
4ag
ADF applications (I)
http://www.scm.com
8hg(LUMO)
16 April 2008
ADF workshop at CINECA
WAu12: spin-orbit electronic structure
SR
SO
0
-2
Exp: photodetachment of WAu12X. Li, B. Kiran, J. Li, H.-J. Zhai and L.-S. Wang, Angew.
Chem. Int. Ed. 41, 4786 (2002)
-4
KS
-6
-8
6ag
5t2u
8hg
8e1g(1/2)
11iu(5/2)
LUMO
1.75 eV
-10
7hg
HOMO
9gg(3/2) + 12ig(5/2)
8gg(3/2) + 11ig(5/2)
1.09 eV
-12
-14
-16
5t1u
4hg
4ag
1.8 eV
6gu(3/2)+4e1u(1/2)
5ig(5/2) + 4gg(3/2)
0.9 eV
5e1g(1/2)
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:
 r,       , r, r 'v r ' ,  dr '
(1)
(1)
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:
FI 
2
EI FI
 ia , jb     ij ab  a   i   2 ( a   i ) K ia , jb ( b   j )
2
K ij ,kl
 1

ALDA
r  r  r'k r 'l r'
  dr  dr 'i r  j r 
 f xc
 r  r'

ADF applications (I)
http://www.scm.com
16 April 2008
ADF workshop at CINECA
TDDFT electronic excitations (valence)
FI 
ia , jb
2
EI FI
i and j run over Nocc
a and b run over Nvirt
Davidson iterative diagonalization
 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 &
A2.u 150
SubEnd
ONLYSING
End
• Warning: basis set and XC
– Basis set: “diffuse” functions may be important
– XC potential: correct asymptotic behavior is
important: LB94, SAOP, GRAC
ADF applications (I)
http://www.scm.com
16 April 2008
ADF workshop at CINECA
TDDFT electronic excitations (valence)
0
W
WAu12
-2
WAu12 SR
ZORA TZ2P
LB94
-4
6p
8t1u
KS
-6
6ag
-8
5d
6s
5t2u
8hg(LUMO)
-10
7hg(HOMO)
7t1u
-12
Excitation energy (eV)
-14
5t1u
4hg
-16
ADF applications (I)
http://www.scm.com
4ag
16 April 2008
ADF workshop at CINECA
5ag
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
16 April 2008
ADF workshop at CINECA
TDDFT electronic excitations (core)
M. Stener, G. Fronzoni and M de Simone, CPL 373 (2003) 115.
 ia , jb 
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)
  (i,a)
 core orbitals
Reduced  matrix
ADF applications (I)
http://www.scm.com
16 April 2008
ADF workshop at CINECA
TDDFT core excitations: Ti 2p TiCl4
G. Fronzoni, M. Stener, P. Decleva, F. Wang, T. Ziegler, E. van Lenthe, E.J. Baerends
Chem. 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
16 April 2008
ADF workshop at CINECA
TDDFT core excitations: Cr 2p CrO2Cl2
CrO2Cl2
30
2p (Cr) - RS
25
f x 100
20
2p
Scalar relativistic AND spin orbit
calculations
15
10
5
0
570
575
580
585
590
595
Excitation energy (eV)
14
2p (Cr) - RSO
12
10
2p3/2
2p1/2
f x 100
8
SR: negligible effect
SO: good description of both
Cr2p1/2 and Cr2p3/2 features
6
4
2
0
570
575
580
585
590
595
Excitation energy (eV)
ADF applications (I)
http://www.scm.com
16 April 2008
ADF workshop at CINECA
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
16 April 2008
ADF workshop at CINECA
TDDFT core excitations: TiO2 (110) Ti2p
30
Non Relativistic DZ
25
f · 10
2
20
15
10
5
0
Scalar Relativistic DZ
25
f · 10
2
20
15
10
Ti19O32H’32H’’15
5
0
Relativistic Spin-Orbit DZ
f · 10
2
10
5
0
452
454
456
458
460
462
464
466
468
calculated excitation energy (eV)
ADF applications (I)
http://www.scm.com
16 April 2008
ADF workshop at CINECA
470
472
Exchange correlation functionals: EXC
LDA
LDA
LDA: VWN parametrization E XC      XC   r dr
Geometry OK, NOT for binding energies!
GGA: many choices
GGA
    f  ,  dr
E XC
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


MGGA
    f  ,  ,  2  dr
E XC
ADF applications (I)
http://www.scm.com
16 April 2008
ADF workshop at CINECA
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
16 April 2008
ADF workshop at CINECA
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
16 April 2008
ADF workshop at CINECA
Constraints and Parametrization
Functional
Constraints
Training Sets
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
M06-L
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
16 April 2008
ADF workshop at CINECA
binding energy (kcal/mol)
20
hydrogen bonded (HB)
best estimate : 16.4 (HB)
Stacked (S)
12.2 (S)
15
10
5
-5
BLYP
B3LYP
PBE
B98
PBEh
TPSSh
BMK
M05-2X
M06-L
M06-HF
M06
M06-2X
0
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