adf2007.01 applications (i) prof. mauro stener (trieste university) [email protected]
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ADF2007.01 Applications (I) Prof. Mauro Stener (Trieste University) [email protected]. Outline. Relativistic effects TDDFT electronic excitations Valence electrons Core electrons Spin orbit coupling Exchange-correlation energy functionals E XC. Relativistic effects. - PowerPoint PPT PresentationTRANSCRIPT
ADF2007.01Applications (I)
Prof. Mauro Stener (Trieste University)[email protected]
16 April 2008ADF 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 EXC
16 April 2008ADF 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 2nd and 3rd row of d-block)
• General problem: The Dirac equation (4 components)
– Problems: variational collapse, large dimensions
EVmcpc
pcVmc2
2
Large
component
Small
component
16 April 2008ADF 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 = 0
E = mc2
E = -mc2
16 April 2008ADF 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!
16 April 2008ADF workshop at CINECA
ADF applications (I) http://www.scm.com
Relativistic effects: AFD input RELATIVISTIC Scalar ZORARELATIVISTIC 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)
16 April 2008ADF 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
ls ˆˆ slj ˆˆˆ
2p
2p1/2
2p3/2
16 April 2008ADF 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: 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)
16 April 2008ADF workshop at CINECA
ADF applications (I) http://www.scm.com
KS
-16
-14
-12
-10
-8
-6
-4
-2
0 W WAu12 Au12 Au
6s
6p
5d
6s
6p
5d
4t1u
4hg3ag
7hg(HOMO)
8hg(LUMO)
5t2u
6ag
4ag
5t1u
7hg
5t2u
7t1u8t1u
5ag
7t1u
5ag
[[XeXe]4f]4f14145d5d10106s6s11
6a6agg
8h8hgg(LUMO)(LUMO)
4a4agg
7h7hgg(HOMO)(HOMO)
WAu12: scalar relativistic electronic structureM. Stener, A. Nardelli, and G. FronzoniJ. Chem. Phys. 128, 134307 (2008)
16 April 2008ADF workshop at CINECA
ADF applications (I) http://www.scm.com
KS
-16
-14
-12
-10
-8
-6
-4
-2
0
5e1g(1/2)
4hg
7hg
8hg
5t2u
6ag
4ag
5t1u
5ig(5/2) + 4gg(3/2)6gu(3/2)+4e1u(1/2)
9gg(3/2) + 12ig(5/2)
8gg(3/2) + 11ig(5/2)
8e1g(1/2)11iu(5/2)
LUMO
HOMO
SR SO
1.75 eV1.75 eV
1.09 eV1.09 eV
WAu12: spin-orbit electronic structure
X. Li, B. Kiran, J. Li, H.-J. Zhai and L.-S. Wang, Angew. Chem. Int. Ed. 41, 4786 (2002)
X. Li, B. Kiran, J. Li, H.-J. Zhai and L.-S. Wang, Angew. Chem. Int. Ed. 41, 4786 (2002)
1.81.8eVeV0.90.9eVeV
Exp: photodetachment of WAu12-
16 April 2008ADF 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:
','',,, )1()1( rrrrr dv Where is the dielectric susceptibility of the interacting
system, not easily accessible
16 April 2008ADF workshop at CINECA
ADF applications (I) http://www.scm.com
III E FF 2
)()(2 ,2
, jbjbiaiaiaabijjbia K
''''
1', rrrrr
rrrrrr lk
ALDAxcjiklij fddK
TDDFT electronic excitations (valence)
The actual TDDFT equation solved by ADF is:
16 April 2008ADF workshop at CINECA
ADF applications (I) http://www.scm.com
III E FF 2
Davidson iterative diagonalization
matrix is not stored, efficient density fit!
jbia , i and j run over Nocc
a and b run over Nvirt
TDDFT electronic excitations (valence)
16 April 2008ADF 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
ExcitationDavidson &A2.u 150SubEndONLYSINGEnd
16 April 2008ADF workshop at CINECA
ADF applications (I) http://www.scm.com
KS
- 1 6
- 1 4
- 1 2
- 1 0
- 8
- 6
- 4
- 2
0 W W A u 1 2 A u 1 2 A u
6 s
6 p
5 d
6 s
6 p
5 d
4 t 1 u
4 h g3 a g
7 h g ( H O M O )
8 h g ( L U M O )
5 t 2 u
6 a g
4 a g
5 t 1 u
7 h g
5 t 2 u
7 t 1 u8 t 1 u
5 a g
7 t 1 u
5 a g
TDDFT electronic excitations (valence)
Excitation energy (eV)
WAu12 SR ZORA TZ2PLB94
16 April 2008ADF workshop at CINECA
ADF applications (I) http://www.scm.com
TDDFT electronic excitations (valence)Large systemsup to Au146
2+
M. Stener, A. Nardelli, R. De Francesco and G. FronzoniJ. Phys. Chem. C 111, 11862 (2007)
TDDFT SR ZORA DZ LB94 CINECA SP5 16 cpu 48h
16 April 2008ADF workshop at CINECA
ADF applications (I) http://www.scm.com
TDDFT electronic excitations (core)
jbia ,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.
16 April 2008ADF workshop at CINECA
ADF applications (I) http://www.scm.com
TDDFT core excitations: Ti 2p TiCl4
Inclusion of configuration mixing effects
Mandatory for degenerate core orbitals (2p)
ADF input:
MODIFYEXCITATIONUSEOCCUPIEDT2 2SUBENDEND
G. Fronzoni, M. Stener, P. Decleva, F. Wang, T. Ziegler, E. van Lenthe, E.J. BaerendsChem. Phys. Lett. 416 56-63 (2005).
16 April 2008ADF workshop at CINECA
ADF applications (I) http://www.scm.com
TDDFT core excitations: Cr 2p CrO2Cl2
Excitation energy (eV)
570 575 580 585 590 595
f x
100
0
5
10
15
20
25
30
570 575 580 585 590 595
0
2
4
6
8
10
12
14
f x
100
Excitation energy (eV)
2p (Cr) - RS
2p (Cr) - RSO
2p3/2 2p1/2
2p
CrO2Cl2
Scalar relativistic AND spin orbit calculations
SR: negligible effect
SO: good description of both Cr2p1/2 and Cr2p3/2 features
16 April 2008ADF workshop at CINECA
ADF applications (I) http://www.scm.com
TDDFT core excitations: Cr 2p CrO2Cl2
XAS Cr 2pExp.: Elettra Synchrotron FacilityGas Phase Beam Line (Trieste)unpublished
16 April 2008ADF workshop at CINECA
ADF applications (I) http://www.scm.com
Non Relativistic DZ
f ·
102
0
5
10
15
20
25
30
Scalar Relativistic DZ
f ·
102
0
5
10
15
20
25
Relativistic Spin-Orbit DZ
calculated excitation energy (eV)
452 454 456 458 460 462 464 466 468 470 472
f ·
102
0
5
10
TDDFT core excitations: TiO2 (110) Ti2p
Ti19O32H’32H’’15
16 April 2008ADF workshop at CINECA
ADF applications (I) http://www.scm.com
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
rr dE LDAXC
LDAXC
rdfEMGGAXC 2,,
rdfEGGAXC ,
16 April 2008ADF 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: EXC
ADF input:
16 April 2008ADF workshop at CINECA
ADF applications (I) http://www.scm.com
MO6 class of xc functionalsMO6 class of xc functionals
Limitations of the Popular FunctionalsLimitations 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. MinnesotaRefs: http://comp.chem.umn.edu/info/DFT.htm
16 April 2008ADF workshop at CINECA
ADF applications (I) http://www.scm.com
Constraints and Constraints and ParametrizationParametrizationFunctional 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 limitSCorF: self-correlation freeHF: Hartree-Fock exchange
TC: main-group thermochemistry TC: main-group thermochemistry BH: barrier heights BH: barrier heights NC: noncovalent interactions NC: noncovalent interactions TM: transition metal chemistryTM: transition metal chemistry
16 April 2008ADF workshop at CINECA
ADF applications (I) http://www.scm.com
16 April 2008ADF 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.comQuestions outside presentation to: [email protected]