CHELSEY CROSSE LEVINGER GROUP | COLORADO STATE UNIVERSITY LITERATURE SEMINAR | OCTOBER 23, 2013 P ROBING M OLECULAR E LECTRONIC S TRUCTURE U SING H IGH H ARMONIC G ENERATION T OMOGRAPHY
Jul 07, 2015
CHELSEY CROSSE
LEVINGER GROUP | COLORADO STATE UNIVERSITY
LITERATURE SEMINAR | OCTOBER 23, 2013
PROBING MOLECULAR
ELECTRONIC STRUCTURE
USING HIGH HARMONIC
GENERATION TOMOGRAPHY
MOLECULAR ELECTRONIC
STRUCTURE
1
Chang. Chemistry, 8th ed.; McGraw-Hill:New York, 2005.
Benzene Reactions, Tutorvista. chemistry.tutorvista.com/ (accessed 11 Oct. 2013).
Han, Choi, Kumar & Stanley. Nature Physics. 2010, 6, 633.
Bonding Geometry Phase Behavior
MOLECULAR ORBITALS
OF NITROGEN
2
Siriwardane. CHEM 281, LA Tech. www.chem.latech.edu (accessed 11 Oct. 2013).
N2 HOMO
Hydrogenic
Orbitals
Molecular
Orbitals
Highest
Occupied
Molecular
Orbital
EXPERIMENTAL METHODS OF
MEASURING MOLECULAR
STRUCTURE
3de Oteyza et al. Science. 2013, 340, 1434.
3Å
1. Observable
• High Harmonic
Generation (HHG)
radiation
2. Selective
• Tunneling probability
• Molecular alignment
4
MEASUREMENT REQUIREMENTS
FOR ORBITAL TOMOGRAPHY
5
OVERVIEW OF HIGH HARMONIC
GENERATION TOMOGRAPHY
Diveki et al. Chemical Physics, 2013, 414, 121.
”High Harmonic Generation” Wikipedia. en.wikipedia.org (accessed 18 Oct. 2013).
“A MOLECULE
BEING PROBED
BY ONE OF
ITS OWN
ELECTRONS”
New & Ward. Physical Review Letters. 1967, 19, 556.Hecht, J. “Photonic Frontiers: High Harmonic Generation,” LaserFocusWorld 2012.
6
HARMONIC GENERATION
IN A GAS JET
Nu
mb
er
of p
ho
ton
sHarmonic order (n)
• DIFFERENT PHYSICAL
MECHANISM
Low Intensity (I ≤1013 W/cm2)
• High Harmonic
Generation (HHG)
Harmonic order (n)
Nu
mb
er
of p
ho
ton
s
High Intensity ( I ≥1014 W/cm2)
• Plateau followed by linear
decrease
• Classical Harmonic
Generation:
• Odd order harmonics
• Linear trend
• Multi-photon Ionization
followed by electron
relaxation.
EXPERIMENTAL
SETUP
7Torres et. al. Physical Review Letters. 2007, 98, 203007.
Alignment: ~100 fs Ti:Sapph @ 808 nm,
I ≤ 1013 W/cm2
Probe: ~15 fs Ti:Sapph, I ~1014 W/cm2
Probe Alignment
SEMI-CLASSICAL
THREE STEP MODEL
Lewenstein et al. Physical Review A. 1994, 49, 2117.
Mahieu Seminar at UNG 2009. 8
0t ~ /2 0t ~ 3 /2 0t = 2
Elaser = 0
0t =
Elaser = 0
0t = 0
Elaser = 0 ElaserElaser
1. Tunneling (Quantum Mechanical)
2. Acceleration of Electron in Laser Field (Classical)
3. Recombination (Quantum Mechanical)
1.
1. Tunneling (Quantum Mechanical)
2. Acceleration of Electron in Laser Field (Classical)
3. Recombination (Quantum Mechanical)
1. Tunneling (Quantum Mechanical)
2. Acceleration of Electron in Laser Field (Classical)
3. Recombination (Quantum Mechanical)
2.
1. Tunneling (Quantum Mechanical)
2. Acceleration of Electron in Laser Field (Classical)
3. Recombination (Quantum Mechanical)
3.
9
e-
SEMI-CLASSICAL
THREE STEP MODEL
Ground state (SCHEMATIC)
0t = 0
Elaser = 0
EI
Ene
rgy
Distance from Molecular Center of Mass0
Mahieu Seminar at UNG 2009.
10
SEMI-CLASSICAL
THREE STEP MODEL
1. Tunneling (Quantum Mechanical)
e-
0t =
Elaser =0
Ene
rgy
Distance from Molecular Center of Mass0
0t ~ /2
Elaser
Mahieu Seminar at UNG 2009.
1. Observable
• HHG radiation
2. Selective
Tunneling probability
• Molecular alignment
11
MEASUREMENT REQUIREMENTS
FOR ORBITAL TOMOGRAPHY
e-
Energ
y
Distance from Molecular Center of Mass0
12
e-
SEMI-CLASSICAL
THREE STEP MODEL
2. Acceleration of Free Electron in Laser Field (Classical)
0t ~ 3 /2
Elaser
Ene
rgy
Distance from Molecular Center of Mass0
0t ~ /2
Elaser
Mahieu Seminar at UNG 2009.
13Distance from Molecular Center of Mass
0
Ene
rgy
e-
SEMI-CLASSICAL
THREE STEP MODEL
3. Recombination (Quantum Mechanical)
0t = 0
Elaser = 0
Mahieu Seminar at UNG 2009.
1. Observable
HHG radiation
2. Selective
Tunneling probability
• Molecular alignment
14
MEASUREMENT REQUIREMENTS
FOR ORBITAL TOMOGRAPHY
Energ
y
Distance from Molecular Center of Mass0
e-
THREE STEP MODEL
RELATES TO RADIATION
15
Diveki et al. Chemical Physics, 2013, 414, 121.
Itatani et. al. Nature. 2004, 432, 867.
IHHG µg(k, IL,q)a(
k, IL )
d f (
k,q)
1. Tunneling (Quantum Mechanical)
• Tunneling probability
2. Acceleration of Electron in Laser Field (Classical)
• Acceleration
3. Recombination (Quantum Mechanical)
• Transition dipole
matrix
d f (k,q) = <y0 (q ) | d̂ f | yc (
k)>
g(k, IL,q )
a(k, IL )
k
IL
q
CALIBRATION OF
MEASUREMENTS
• Function of laser characteristics
• Function of ionization potential
16
Diveki et al. Chemical Physics, 2013, 414, 121.
g(k, IL,q )
a(k, IL )
Given observation of a reference system:
<y0 (q ) | d̂ f | yc(k)> =
d f (
k,q )µ
1
R(q )
I(w, IL,q )
Iref (w, IL )
dreff (
k )
ANGULAR DEPENDENCE
IHHG µg(k, IL,q)a(
k, IL )
d f (
k,q)
17
TOMOGRAPHY INTERLUDE:
COMPUTED TOMOGRAPHY
Smith. The Scientist & Engineer's Guide to Digital Signal Processing. California Technical Publishing 1997. www.dspguide.com (accessed 16
Oct. 2013).
TOMOGRAPHY INTERLUDE:
COMPUTED TOMOGRAPHY
18
Smith. The Scientist & Engineer's Guide to Digital Signal Processing. California Technical Publishing 1997. www.dspguide.com (accessed 16
Oct. 2013).
19
MOLECULAR
TOMOGRAPHY
res et. al. Chemical Physics. 2013, 414, 121.
ab initio
HOMO
N2 HOMO
HHG Tomography
HOMO
20
MOLECULAR
ALIGNMENT
• Rotational Revival
• ~70% rotational
realignment
• Distinguishable within 5°
at 100K
• Molecular Sample
• T ~ 100 K
• Initial alignment:
• ~100 fs pulse
• I ~ 1013 W/cm2
• Induces rotational wave
packet
• NON-ADIABATIC
Lock et al. Physical Review Letters. 2012, 108, 133901.
1. Observable
HHG radiation
2. Selective
Tunneling probability
Molecular alignment
21
MEASUREMENT REQUIREMENTS
FOR ORBITAL TOMOGRAPHY
HHG TOMOGRAPHY
DATA: N2
22
Itatani et. al. Nature. 2004, 432, 867.
N2 HOMO
EX
PE
RIM
EN
TA
LT
HE
OR
ET
ICA
L
Assumptions:
• Born-Oppenheimer approximation
• Hartree-Fock approximation
• Koopman’s approximation
• Free electron is a plane wave
• Single active electron
• Neglect the Stark effect
• Neglect relativity
• Neglect Coulombic interaction
Assumptions:
Born-Oppenheimer approximation
Hartree-Fock approximation
Koopman’s approximation
• Free electron is a plane wave
• Single active electron
• Neglect the Stark effect
• Neglect relativity
• Neglect Coulombic interaction
Assumptions:
Born-Oppenheimer approximation
Hartree-Fock approximation
Koopman’s approximation
• Free electron is a plane wave
• Single active electron
• Neglect the Stark effect
• Neglect relativity
• Neglect Coulombic interaction
THE STRONG FIELD
APPROXIMATION
23Diveki et al. Chemical Physics, 2013, 414, 121.
Spanner, Patchkovskii. Chemical Physics 2013, 414 10.
CONTINUUM
WAVEFUNCTIONS
24
Spanner, Patchkovskii. Chemical Physics 2013, 414 10.
N2 HOMO
Modeled <yc |
yd
j = n < I j | N >
Dyson Orbital for
N2 Ionization:
CONTINUUM
WAVEFUNCTIONS
25
Spanner, Patchkovskii. Chemical Physics 2013, 414 10.
Dyson Orbital for
CO2 Ionization
Modeled <yc |
Assumptions:
Born-Oppenheimer approximation
Hartree-Fock approximation
Koopman’s approximation
o Free electron is a plane wave
• Single active electron
• Neglect the Stark effect
• Neglect relativity
• Neglect Coulombic interaction
Assumptions:
Born-Oppenheimer approximation
Hartree-Fock approximation
Koopman’s approximation
o Free electron is a plane wave
• Single active electron
• Neglect the Stark effect
• Neglect relativity
• Neglect Coulombic interaction
THE STRONG FIELD
APPROXIMATION
26Diveki et al. Chemical Physics, 2013, 414, 121.
Spanner, Patchkovskii. Chemical Physics 2013, 414 10.
MULTIPLE ACTIVE
ELECTRONS
Itatani et. al. Nature. 2004, 432, 867.
Patchkovskii, Zhao, Brabec, Villeneuve. Physical Review Letters. 2006, 97, 12003.
27
SINGLE ACTIVE
ELECTRON
MULTIPLE ACTIVE
ELECTRONS
THEORETICAL
Assumptions:
Born-Oppenheimer approximation
Hartree-Fock approximation
Koopman’s approximation
o Free electron is a plane wave
o Single active electron
• Neglect the Stark effect
• Neglect relativity
• Neglect Coulombic interaction
THE STRONG FIELD
APPROXIMATION
28Diveki et al. Chemical Physics, 2013, 414, 121.
Spanner, Patchkovskii. Chemical Physics 2013, 414 10.
REMAINING
DISTORTIONS
29
Patchkovskii, Zhao, Brabec, Villeneuve. Physical Review Letters. 2006, 97, 12003.
N2 HOMO
TH
EO
RE
TIC
AL
MU
LT
I A
CT
IVE
EL
EC
TR
ON
S
CHALLENGES:
• Closer energy
spacing
• Complex free
electron
wavefunctions
• Smaller molecular
dipoles
30
FUTURE GOAL:
POLYATOMIC MOLECULES
Siriwardane. CHEM 281, LA Tech. www.chem.latech.edu (accessed 11 Oct. 2013).
CHALLENGES:
• Closer energy
spacing
• Complex free
electron
wavefunctions
• Smaller molecular
dipoles
31
FUTURE GOAL:
POLYATOMIC MOLECULES
Dyson Orbital for
Corenene IonizationModeled
for Corenene
<yc |
Spanner, Patchkovskii. Chemical Physics 2013, 414 10.
CHALLENGES:
• Closer energy
spacing
• Complex free
electron
wavefunctions
• Possibility of smaller
torque
32
FUTURE GOAL:
POLYATOMIC MOLECULES
Allene
Acetylene
Torres et. al. Physical Review Letters. 2007, 98, 203007.
33
SUMMARY
• Physical mechanism
• Some agreement
• Revisions &
Remaining Distortions
• Polyatomic systems
Physical mechanism
• Some agreement
• Revisions &
Remaining Distortions
• Polyatomic systems
”High Harmonic Generation” Wikipedia. en.wikipedia.org (accessed 18 Oct. 2013).
Physical mechanism
Some agreement
• Revisions &
Remaining Distortions
• Polyatomic systems
EX
PE
RIM
EN
TA
LT
HE
OR
ET
ICA
L
Itatani et. al. Nature. 2004, 432, 867.
TH
EO
RE
TIC
AL
MU
LT
I A
CT
IVE
EL
EC
TR
ON
S
Patchkovskii, Zhao, Brabec, Villeneuve. Physical Review Letters. 2006, 97, 12003.
Physical mechanism
Some agreement
Revisions &
Remaining Distortions
• Polyatomic systems
Modeled
for Corenene
<yc |
Physical mechanism
Some agreement
Revisions &
Remaining Distortions
Polyatomic systems
Spanner, Patchkovskii. Chemical Physics 2013, 414 10.
Levinger Group:
• Dr. Nancy Levinger
• Ben Wiebenga-Sanford
Faculty:
• Dr. Elliot Bernstein
• Dr. Mario Marconi
• Dr. Carmen Menoni
• Dr. Amber Krummel
• Dr. Randy Bartels
Post-Doctorates & Staff Scientists:
• Dr. Brad Luther
• Dr. Christopher Rich
CSU Department of Chemistry
PEERS
Chemistry:
Laura Tvedte, Jenée Cyran,
Jake Nite, Kathryn Tracy
Electrical & Computer
Engineering:
Reed Hollinger, Clayton
Bargsten, Drew Schiltz
Communication:
Vicky Webber
Materials Science:
Katherine Sebeck
34
ACKNOWLEDGEMENTS
MULTIPLE ACTIVE
ELECTRONS
B-1
res et. al. Chemical Physics. 2013, 414, 121.
THEORETICAL – Hartree-Fock
N2 HOMO
HOMO HOMO-1
MULTIPLE ACTIVE
ELECTRONS
B-3
res et. al. Chemical Physics. 2013, 414, 121.
THEORETICAL EXPERIMENTAL
N2 HOMO
Harmonics 17-31H-F HOMO
MULTIPLE ACTIVE
ELECTRONS
B-3
res et. al. Chemical Physics. 2013, 414, 121.
THEORETICAL EXPERIMENTAL
N2 HOMO
Harmonics 17-31H-F HOMO-1
MULTI-ACTIVE
ELECTRONS
B-4
res et al Chemical Physics 414 (2013) 121–129
IL = 1.2x1014 W/cm2 IL = 1.0x1014 W/cm2
Inverse Fourier transform of the recombination dipole moment
yields:
RECONSTRUCTION
u = x ', z '
dur̂ (k ) =< y0 |u | k >=
1
R(q )
D(w, IL,q )
Dref (w, IL )
dreff (
k )
y0
u(x ', z ') =Ák ®
r '[du
r̂ (kx ',kz ' )]
u
res et al Chemical Physics 414 (2013) 121–129 C
Itatani et. al. Nature. 2004, 432, 867. D
HHG TOMOGRAPHY
DATA: N2
HHG Tomography
HOMO
0°
ELECTRON
TRAJECTORY
Time (TL)
Emission time (te)
x
0 1
Harmonicorder
15171921
Electron position
Long traj.Short traj. Chirp > 0 Chirp < 0
x(ti)=0v(ti)=0
0
Mairesse et al. Science 302, 1540 (2003) Kazamias and Balcou, PRA 69, 063416 (2004)
E