ADF2007.01 Applications (I) Prof. Mauro Stener (Trieste University) [email protected]

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



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



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



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!



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)



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



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)



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)



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-



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



III E FF 2

)()(2 ,2

, jbjbiaiaiaabijjbia K

''''

1', rrrrr

rrrrrr lk

ALDAxcjiklij fddK


The actual TDDFT equation solved by ADF is:



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





• 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



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


Excitation energy (eV)

WAu12 SR ZORA TZ2PLB94



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



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.



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).



TDDFT core excitations: Cr 2p CrO2Cl2


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


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



TDDFT core excitations: Cr 2p CrO2Cl2

XAS Cr 2pExp.: Elettra Synchrotron FacilityGas Phase Beam Line (Trieste)unpublished



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



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 ,



XC

{LDA {Apply} LDA {Stoll}}

{GGA {Apply} GGA}

{Model MODELPOT [IP]}

{HARTREEFOCK}

{HYBRID hybrid}

end

Exchange correlation functionals: EXC

ADF input:



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



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





Thank you for your attention!

Questions now?

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Documents

ADF2007.01 Applications (I) Prof. Mauro Stener (Trieste University) [email protected]