A TDDFT study on the dichroism in the photoelectron angular distribution from a chiral transition...

A TDDFT study on the dichroism in the photoelectron angular distribution

from a chiral transition metal compound

M. Stener

Dipartimento di Scienze ChimicheUniversità degli Studi di Trieste

Via L. Giorgieri 1, 34127 TRIESTE - ITALY

Gordon Research Conference on Photoions, Photoionization & Photodetachment

January 31st - February 5th, 2010 Hotel Galvez Galveston, TX

GAS PHASE EXPERIMENT(RANDOMLY ORIENTED MOLECULES) PARTIAL

DIFFERENTIAL CROSS SECTION:

2)(2

2

0)(2 44, I

NI

I tTd

d kk

,

d

d I

In this work only Electric Dipole (E1) transition moments are considered:

M

e-

M+I

h

k

IN-1

coscos)(2

11

4

)(, 12 PDmP

d

dIrI

II

: Cross section: Asymmetry parameter

CHIRAL MOLECULES AND CIRCULARLY POLARIZED LIGHT

D: Dichroism

• emission angle: between photoelectron k and light propagation

• mr: +1 or -1 for left/right circular polarization

•D has opposite sign for enantiomeric pairs

• Dichroism D: Circular Dicroism in Angular Distribution (CDAD)

Theoretical Method

1. Esplicit treatment of photoelectron continuum

2. Multicentric B-spline basis set

3. Formalism: TDDFT

4. Parallel implemetation

5. Large matrices dim(H) 20000, 1 energy point: 1h with 256 cpu

What is new?

1. First TDDFT calculation of dichroic parameter D

2. First application on a chiral transition metal compound

3. First calculation of dichroism D over autoionization resonance (only TDDFT can do it!)

M. Stener, G. Fronzoni and P. Decleva, J. Chem. Phys., 122 234301(1-11) (2005).

M. Stener G. Fronzoni and P. DeclevaChem. Phys., 361, 49 - 60 (2009).

D

-0.1

0.0

0.1

12a (II)

D

-0.1

0.0

0.1

0.2

11a (II)

0 10 20 30 40-0.15

-0.10

-0.05

0.00

0.0516a (II)

-0.15

-0.10

-0.05

0.00

0.05

14a (II)

Photoelectron Energy (eV)

0 10 20 30 40

D

-0.10

-0.05

0.00

0.0513a (II)

-0.15

-0.10

-0.05

0.00

0.05

0.1015a (II)

S. Stranges, S. Turchini, M. Alagia, G. Alberti, G. Contini, P. Decleva, G. Fronzoni, M. Stener, N. Zema and T. Prosperi

J. Chem. Phys. 122 244303 (1-6) (2005).

Previous applications (Kohn-Sham) Circular Dichroism in Angular Distribution of Photoelectrons from Chiral

Molecules: S(-) methyl-oxirane

1. Good agreement KS Theory vs. Exp.

2. Dichroism decays to zero within few eVs above threshold

O

CH3H

HH

Chiral transition metal compound: -Co(acac)3

D3 point group symmetry

PES -Co(acac)3

KL B’

B’’C

M

KS

Eig

enva

lues

(eV

)

-12

-10

-8

acac (acac)3 CoCo(acac)3

LP+

LP-

Electronic structure: -Co(acac)3

3d

PES -Co(acac)3K

S E

igen

valu

es (

eV)

-12

-11

-10

-9

-8

L L: 18a1 + 15a2

B’

M

B’’

K: 30e

M: 29e + 14a2

B’: 28e

B”: 27e + 17a1

K

KS

Eig

enva

lues

(eV

)

-12

-11

-10

-9

-8


30e: Co 3d – 3 antibonding

KS

Eig

enva

lues

(eV

)

-12

-11

-10

-9

-8


18a1: Co 3d

KS

Eig

enva

lues

(eV

)

-12

-11

-10

-9

-8


15a2: 3

KS

Eig

enva

lues

(eV

)

-12

-11

-10

-9

-8


29e: Co 3d – 3 bonding

KS

Eig

enva

lues

(eV

)

-12

-11

-10

-9

-8


14a2: ligand LP-

KS

Eig

enva

lues

(eV

)

-12

-11

-10

-9

-8


28e: ligand LP-

KS

Eig

enva

lues

(eV

)

-12

-11

-10

-9

-8


17a1: ligand LP+

KS

Eig

enva

lues

(eV

)

-12

-11

-10

-9

-8


27e: Co 3d + ligand LP+

bonding

KS

Eig

enva

lues

(eV

)

-12

-11

-10

-9

-8


31e: Co 3d + ligand LP+

antibonding

E

E = 0

GS: Cr(3p)6 (…) (30e)6 (31e)0

Co(3p)-1 Co(31e)+1

(30e)-1

Co(acac)3: “Giant Autoionization”

Direct ionization

Autoionization

Excitation

M

M*

M+

“Giant” because the same principal Q.N.: Co 3p → Co 3d

Fig. 1

Photon Energy (eV)

0 20 40 60 80 100

Dic

hroi

sm (

D)

-0.2

-0.1

0.0

0.1

Asy

mm

etry

Pa

ram

ete

r (

)

-1

0

1

-Co(acac)3 30e

Cro

ss S

ectio

n (

Mb)

0

5

10

15

20

25

KSTDDFT

Fig. 2

Photon Energy (eV)

0 20 40 60 80 100

Dic

hroi

sm (

D)

-0.2

-0.1

0.0

0.1

Asy

mm

etry

Par

amet

er ( )

-1

0

1

-Co(acac)3 18a1

Cro

ss S

ectio

n (M

b)

0

5

10

15

20

KSTDDFT

Dichroism: -Co(acac)330e: Co 3d – 3 antibonding 18a1: Co 3d

Similar!

Different!

“Giant” autoionization: Co 3p → 3d

Fig. 6

Photon Energy (eV)

0 20 40 60 80 100

Dic

hroi

sm (

D)

-0.2

-0.1

0.0

0.1

Asy

mm

etry

Par

amet

er ( )

-1

0

1

-Co(acac)3 28e

Cro

ss S

ectio

n (M

b)

0

5

10

15

20

25

KSTDDFT

Dichroism: -Co(acac)3

28e: ligand LP-

Small Co 3d contribution:1. Very weak resonance in cross

section2. But … very strong ‘window’

resonance in dichroism!!!3. D is very sensitive!


Theory (TDDFT) vs experiment:

Preliminar experiment: D. Catone (private communication)

Elettra Sinchrotron (Trieste ITALY)





Complete disagreement!!!

-Co(acac)3 Band B" (27e + 28e)

Photon Energy (eV)

0 20 40 60 80 100

Dic

hroi

sm (

D)

-0.2

-0.1

0.0

0.1

-Co(acac)3 Band B' (17a1)

Dic

hro

ism

(D

)

-0.2

-0.1

0.0

0.1

0.2


Alternative assignment of B’ and B” bands: better agreement!!!

Theory (TDDFT) vs experiment: Preliminar experiment: D. Catone (private communication) at Elettra Sinchrotron (Trieste ITALY)

Cross section near the resonance: -Co(acac)3

-Co(acac)3

Photon Energy (eV)

58 60 62 64 66 68 70 72 74

Cro

ss S

ectio

n (M

b)

0

5

10

KLM

-Co(acac)3

Photon Energy (eV)

58 60 62 64 66 68 70 72 74

Cro

ss S

ectio

n (M

b)

0

5

10

B1B2C

Theory (TDDFT) vs experiment: Preliminar experiment: D. Catone (private communication) Elettra Sinchrotron (Trieste ITALY)

Conclusions

1. Method: Parallel multicenter B-spline TDDFT continuum.

2. Calculation of Dichroism (D) of -Co(acac)3.

3. Strong sensistivity of D parameter.

4. Comparison with preliminar experimental dichroism, possible revision of previous assignment.

5. Co 3p → 3d autoionization: Dichroism sensitive even for ligand orbitals.

6. Future perspectives: dichroism experiment on Co 3p → 3d autoionization.

Acknowledgments: Trieste University:

Prof. Piero Decleva

Prof. Giovanna Fronzoni

Dott. Daniele Toffoli

Dott. Devis Di Tommaso

Elettra Sinchrotron Trieste:

Dott. Daniele Catone

Dott. Tommaso Prosperi

Dott. Stefano Turchini

Thank you for your attention!

Additional slides

O

CH3H

HH

Density Functional Theory for Photoionization: the Kohn-Sham approach

)()()(2

1rVrVrVh XCCnuclKS

212

)2()1( dr

rVC

)]1([)1( XCXC VV

hKS : bound and continuum states can be extracted, and photoionization parameters calculated (, , D)

Well known limitation of the KS scheme:

• It is static: the response effects to the external time dependent electromagnetic field are neglected

),()(1 lmiilm YrBr

The main issue is proper basis set choice

EE C

B-splines: piecewise polynomials defined over an arbitrary grid-Polynomial order k-Knot sequence {t0 t1 … tn} over [t0, tn] = [0, Rmax]

Basis set approach

B-spline functions

One center expansion (OCE) { (r0) }All functions centered on a common origin 0

Multicenter expansion (LCAO) { (r0) } { 1(r1) } … { p(rp) }

OCE: very stable and robust, shows smooth but slow convergence with LMAX0

LCAO: converges much more quickly, but less stable, careful choice of numerical parameters. The basis becomes easily overcomplete

One Center Expansion: { }

Multicenter expansion: {p}

In the basis Hc = ESc

Bound states : standard diagonalization

Continuum states: Least Squares Approach

acAcAEH R 2||)(||min

A(E) = H – ES, N0 lowest eigenvalues ai 0Works fine, even with N0 a few hundred

Poisson equation VC = -4 is solved in the same basis. Gives the coulomb potential VC, avoiding the need of two electron integrals.

Linear response : general theory

),( rEXT External TD perturbation, with frequency (dipole)

),(,,, rrrrdrn EXT

,rn

Induced density by the external field

Dielectric susceptibility, not easy to calculate

TDDFT: general theory

),(,,, rrrrdrn SCFS

,

,),(),( rn

rdn

rndV

rr

rnrdrr

LDAXCEXTSCF

Coupled, but linear!

K(r,r’) (kernel)

TDDFT: instead of , use S of a model system of non-interacting electrons and a modified external potential: SCF

defines the kernel K

defines the susceptibility

VVV

Vn

nKV

extSCF

SCFS

extSCFS VVK )1(

The Response Equation becomes:

Exploit linearity of the problem:

To solve : represent the response equation in the B-spline basis set

M. Stener, G. Fronzoni and P. Decleva, J. Chem. Phys., 122 234301(1-11) (2005).

,rnzrd

Im4

c

ijSCF

jjii jrinn

c

22

,13

4

Dynamical polarizability:

Total cross section:

Partial cross section:

Well known limitation of the KS scheme:

• It is static: the response effects to the external time dependent electromagnetic field are neglected

The TDDFT includes such response effects:

• better agreement with experiment

• New effects can be modelled by theory: Autoionization

Cr(CO)6: Autoionization analysis

“Giant” autoionization:

Cr 3p → Cr 3d

Parallel implementation:M. Stener G. Fronzoni and P. Decleva

Chem. Phys., 361, 49 - 60 (2009).

Explicit expressions for , and D

Angular momentum transfer formalism, N. Chandra, J. Phys. B, 20 (1987) 3405.

Photoionization from chiral molecules

Linearly polarized light

)](cos1[4 2

0

Pd

d

)](cos2

1cos1[

4 20

PDmd

dr

Chiral molecule, Circularly polarized light

Forward-Backward asymmetry in the angular distribution

cos24

)()( 0 D

Or, switching the polarization of the light at the magic angle P2(cos)=0

3)()(

)()( D

II

II

KS

Eig

enva

lues

(eV

)

-12

-10

-8


LP+

LP-

acac ligand

A TDDFT study on the dichroism in the photoelectron angular distribution from a chiral transition...

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