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