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A TDDFT study on the dichroism in the photoelectron angular distribution from a chiral transition metal compound. M. Stener. Dipartimento di Scienze Chimiche Universit à degli Studi di Trieste Via L. Giorgieri 1, 34127 TRIESTE - ITALY. - PowerPoint PPT Presentation
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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
Electronic structure: -Co(acac)3
30e: Co 3d – 3 antibonding
KS
Eig
enva
lues
(eV
)
-12
-11
-10
-9
-8
Electronic structure: -Co(acac)3
18a1: Co 3d
KS
Eig
enva
lues
(eV
)
-12
-11
-10
-9
-8
Electronic structure: -Co(acac)3
15a2: 3
KS
Eig
enva
lues
(eV
)
-12
-11
-10
-9
-8
Electronic structure: -Co(acac)3
29e: Co 3d – 3 bonding
KS
Eig
enva
lues
(eV
)
-12
-11
-10
-9
-8
Electronic structure: -Co(acac)3
14a2: ligand LP-
KS
Eig
enva
lues
(eV
)
-12
-11
-10
-9
-8
Electronic structure: -Co(acac)3
28e: ligand LP-
KS
Eig
enva
lues
(eV
)
-12
-11
-10
-9
-8
Electronic structure: -Co(acac)3
17a1: ligand LP+
KS
Eig
enva
lues
(eV
)
-12
-11
-10
-9
-8
Electronic structure: -Co(acac)3
27e: Co 3d + ligand LP+
bonding
KS
Eig
enva
lues
(eV
)
-12
-11
-10
-9
-8
Electronic structure: -Co(acac)3
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!
Dichroism: -Co(acac)3
Theory (TDDFT) vs experiment:
Preliminar experiment: D. Catone (private communication)
Elettra Sinchrotron (Trieste ITALY)
Dichroism: -Co(acac)3
Theory (TDDFT) vs experiment:
Preliminar experiment: D. Catone (private communication)
Elettra Sinchrotron (Trieste ITALY)
Complete disagreement!!!
Dichroism: -Co(acac)3
Theory (TDDFT) vs experiment:
Preliminar experiment: D. Catone (private communication)
Elettra Sinchrotron (Trieste ITALY)
-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
Dichroism: -Co(acac)3
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.
Explicit expressions for , and D
Angular momentum transfer formalism, N. Chandra, J. Phys. B, 20 (1987) 3405.
Explicit expressions for , and D
Angular momentum transfer formalism, N. Chandra, J. Phys. B, 20 (1987) 3405.
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
Electronic structure: -Co(acac)3
LP+
LP-
acac ligand